Abstract

Recent spectroscopic studies at terahertz frequencies for a variety of multiferroics endowed with both ferroelectric and magnetic orders have revealed the possible emergence of a new collective excitation, frequently referred to as electromagnon. It is magnetic in origin, but it becomes active in response to the electric field component of light. Here we give an overview of our recent advance in the terahertz time-domain spectroscopy of electromagnons, or electric-dipole active magnetic resonances, focused on perovskite manganites—RMnO3 (R denotes rare-earth ions). The respective electric and magnetic contributions to the observed magnetic resonance are firmly identified by the measurements of the light-polarization dependence using a complete set of the crystal orientations. We extract general optical features in a variety of the spin-ordered phases, including the A-type antiferromagnetic, collinear spin-ordered phase and the ferroelectric bc and ab spiral spin-ordered phases, which are realized by tuning the chemical composition of R, the temperature, and the external magnetic field. In addition to the antiferromagnetic resonances of Mn ions driven by the magnetic field component of light, we clarify that the electromagnon appears only for light that is polarized along the a axis, even in the collinear spin-ordered phase, and it grows in intensity with evolution of the spiral spin order but is independent of the direction of the spiral spin plane (bc or ab) or, equivalently, the direction of the ferroelectric polarization Ps (Psc or Psa). A possible origin of the observed magnetic resonances at terahertz frequencies is discussed by comparing the systematic experimental data presented here with theoretical considerations based on the Heisenberg model.

© 2009 Optical Society of America

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2009 (7)

N. Aliouane, K. Schmalzl, D. Senff, A. Maljuk, K. Prokeš, M. Braden, and D. N. Argyriou, “Flop of electric polarization driven by the flop of the Mn spin cycloid in multiferroic TbMnO3,” Phys. Rev. Lett. 102, 207205 (2009).
[CrossRef] [PubMed]

N. Kida, Y. Yamasaki, J. P. He, Y. Kaneko, Y. Ikebe, Y. Takahashi, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation at THz frequencies in bc and ab spiral spin phases of perovskite manganites,” J. Phys. Conf. Ser. 148, 012038 (2009); Proc. LXIII Yamada Conf. Photo-induced Phase Transition and Cooperative Phenomena.
[CrossRef]

R. Valdés Aguilar, M. Mostovoy, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Origin of electromagnon excitations in RMnO3,” Phys. Rev. Lett. 102, 047203 (2009).
[CrossRef] [PubMed]

A. Pimenov, A. Shuvaev, A. Loidl, F. Schrettle, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Magnetic and magnetoelectric excitations in TbMnO3,” Phys. Rev. Lett. 102, 107203 (2009).
[CrossRef] [PubMed]

J. S. Lee, N. Kida, S. Miyahara, Y. Yamasaki, Y. Takahashi, R. Shimano, N. Furukawa, and Y. Tokura, “Systematics of electromagnons in the spiral spin-ordered states of RMnO3,” Phys. Rev. B 79, 18043(R) (2009).

S. Pailhès, X. Fabrèges, L. P. Règnault, L. Pinsard-Godart, I. Mirebeau, F. Moussa, M. Hennion, and S. Petit, “Hybrid Goldstone modes in multiferroic YMnO3 studied by polarized inelastic neutron scattering,” Phys. Rev. B 79, 134409 (2009).
[CrossRef]

F. Kagawa, M. Mochizuki, Y. Onose, H. Murakawa, Y. Kaneko, N. Furukawa, and Y. Tokura, “Dynamics of multiferroic domain wall in spin-cycloidal ferroelectric DyMnO3,” Phys. Rev. Lett. 102, 057604 (2009).
[CrossRef] [PubMed]

2008 (12)

C. Fang and J. Hu, “An effective model of magnetoelectricity in multiferroic RMn2O5,” EPL 82, 57005 (2008).
[CrossRef]

M. Cazayous, Y. Gallais, A. Sacuto, R. de Sousa, D. Lebeugle, and D. Colson, “Possible observation of cycloidal electromagnons in BiFeO3,” Phys. Rev. Lett. 101, 037601 (2008).
[CrossRef] [PubMed]

M. K. Singh, R. S. Katiyar, and J. F. Scott, “New magnetic phase transitions in BiFeO3,” J. Phys.: Condens. Matter 20, 252203 (2008).
[CrossRef]

A. Pimenov, A. M. Shuvaev, A. A. Mukhin, and A. Loidl, “Electromagnons in multiferroic manganites,” J. Phys.: Condens. Matter 20, 434209 (2008).
[CrossRef]

D. Senff, N. Aliouane, D. N. Argyriou, A. Hiess, L. P. Regnault, P. Link, K. Hradil, Y. Sidis, and M. Braden, “Magnetic excitations in a cycloidal magnet: the magnon spectrum of multiferroic TbMnO3,” J. Phys.: Condens. Matter 20, 434212 (2008).
[CrossRef]

A. Pimenov, A. Loidl, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Terahertz spectroscopy of electromagnons in Eu1−xYxMnO3,” Phys. Rev. B 77, 014438 (2008).
[CrossRef]

N. Kida, Y. Ikebe, Y. Takahashi, J. P. He, Y. Kaneko, Y. Yamasaki, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation in the ferroelectric magnet DyMnO3,” Phys. Rev. B 78, 104414 (2008).
[CrossRef]

D. Senff, P. Link, N. Aliouane, D. N. Argyriou, and M. Braden, “Field dependence of magnetic correlations through the polarization flop transition in multiferroic TbMnO3: Evidence for a magnetic memory effect,” Phys. Rev. B 77, 174419 (2008).
[CrossRef]

Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, and Y. Tokura, “Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3,” Phys. Rev. Lett. 101, 187201 (2008).
[CrossRef] [PubMed]

N. Kida, Y. Yamasaki, R. Shimano, T. Arima, and Y. Tokura, “Electric-dipole active two-magnon excitation in ab spiral spin phase of a ferroelectric magnet Gd0.7Tb0.3MnO3,” J. Phys. Soc. Jpn. 77, 123704 (2008).
[CrossRef]

Y. Yamasaki, H. Sagayama, N. Abe, T. Arima, K. Sasai, M. Matsuura, K. Hirota, D. Okuyama, Y. Noda, and Y. Tokura, “Cycloidal spin order in the a axis polarized ferroelectric phase of orthorhombic perovskite manganite,” Phys. Rev. Lett. 101, 097204 (2008).
[CrossRef] [PubMed]

M. Mochizuki and N. Furukawa, “Mechanism of lattice-distortion-induced electric-polarization flop in the multiferroic perovskite manganites,” J. Phys. Soc. Jpn. 78, 053704 (2008).
[CrossRef]

2007 (10)

S.-W. Cheong and M. Mostovoy, “Multiferroics: a magnetic twist for ferroelectricity,” Nature Mater. 6, 13-20 (2007).
[CrossRef]

R. Ramesh and N. A. Spaldin, “Multiferroics: progress and prospects in thin films,” Nature Mater. 6, 21-29 (2007).
[CrossRef]

Y. Tokura, “Multiferroics-toward strong coupling between magnetism and polarization in a solid,” J. Magn. Magn. Mater. 310, 1145-1150 (2007).
[CrossRef]

H. Katsura, A. V. Balatsky, and N. Nagaosa, “Dynamical magnetoelectric coupling in helical magnet,” Phys. Rev. Lett. 98, 027203 (2007).
[CrossRef] [PubMed]

D. Senff, P. Link, K. Hradil, A. Hiess, L. P. Regnault, Y. Sidis, N. Aliouane, D. N. Argyriou, and M. Braden, “Magnetic excitations in TbMnO3: Evidence for a hybridized soft mode,” Phys. Rev. Lett. 98, 137206 (2007).
[CrossRef] [PubMed]

R. Valdés Aguilar, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Colossal magnon-phonon coupling in multiferroic Eu0.75Y0.25MnO3,” Phys. Rev. B 76, 060404(R) (2007).
[CrossRef]

Y. Yamasaki, H. Sagayama, T. Goto, M. Matsuura, K. Hirota, T. Arima, and Y. Tokura, “Electric control of spin helicity in a magnetic ferroelectric,” Phys. Rev. Lett. 98, 147204 (2007).
[CrossRef] [PubMed]

A. B. Sushkov, R. Valdés Aguilar, S. Park, S.-W. Cheong, and H. D. Drew, “Electromagnons in multiferroic YMn2O5 and TbMn2O5,” Phys. Rev. Lett. 98, 027202 (2007).
[CrossRef] [PubMed]

C. Jia, S. Onoda, N. Nagaosa, and J. H. Han, “Microscopic theory of spin-polarization coupling in multiferroics transition metal oxides,” Phys. Rev. B 76, 144424 (2007).
[CrossRef]

J. Strempfer, B. Bohnenbuck, M. Mostovoy, N. Aliouane, D. N. Argyriou, F. Schrettle, J. Hemberger, A. Krimmel, and M. v. Zimmermann, “Absence of commensurate ordering at the polarization flop transition in multiferroic DyMnO3,” Phys. Rev. B 75, 212402 (2007).
[CrossRef]

2006 (6)

A. Pimenov, A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. M. Balbashov, and A. Loidl, “Possible evidence for electromagnon in multiferroic manganites,” Nat. Phys. 2, 97-100 (2006).
[CrossRef]

A. Pimenov, T. Rudolf, F. Mayr, A. Loidl, A. A. Mukhin, and A. M. Balbashov, “Coupling of phonons and electromagnons in GdMnO3,” Phys. Rev. B 74, 100403(R) (2006).
[CrossRef]

Y. Tokura, “Multiferroics as quantum electromagnets,” Science 312, 1481-1482 (2006).
[CrossRef] [PubMed]

W. Eerenstein, N. D. Mathur, and J. F. Scott, “Multiferroic and magnetoelectric materials,” Nature (London) 442, 759-765 (2006).
[CrossRef]

M. Mostovoy, “Ferroelectricity in spiral magnets,” Phys. Rev. Lett. 96, 067601 (2006).
[CrossRef] [PubMed]

I. A. Sergienko and E. Datotto, “Role of the Dzyaloshinskii-Moriya interaction in multiferroic perovskites,” Phys. Rev. B 73, 094434 (2006).
[CrossRef]

2005 (6)

M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
[CrossRef] [PubMed]

H. Katsura, N. Nagaosa, and A. V. Balatsky, “Spin current and magnetoelectric effect in noncollinear magnets,” Phys. Rev. Lett. 95, 057205 (2005).
[CrossRef] [PubMed]

T. Kimura, G. Lawes, T. Goto, Y. Tokura, and A. P. Ramirez, “Magnetoelectric phase diagrams of orthorhombic RMnO3,” Phys. Rev. B 71, 224425 (2005).
[CrossRef]

T. Arima, T. Goto, Y. Yamasaki, S. Miyasaka, K. Ishii, M. Tsubota, T. Inami, Y. Murakami, and Y. Tokura, “Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric GdMnO3 and TbMnO3, compounds,” Phys. Rev. B 72, 100102(R) (2005).
[CrossRef]

T. Goto, Y. Yamasaki, H. Watanabe, T. Kimura, and Y. Tokura, “Anticorrelation between ferromagnetism and ferroelectricity in perovskite manganites,” Phys. Rev. B 72, 220403(R) (2005).
[CrossRef]

R. Kajimoto, H. Mochizuki, H. Yoshizawa, H. Shintani, T. Kimura, and Y. Tokura, “R-dependence of spin exchange interactions in RMnO3 (R=rare-earth ions),” J. Phys. Soc. Jpn. 74, 2430-2433 (2005).
[CrossRef]

2004 (3)

T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J. Ihringer, and M. Fiebig, “Magnetic phase control by an electric field,” Nature (London) 430, 541-544 (2004).
[CrossRef]

T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and Y. Tokura, “Ferroelectricity and giant magnetocapacitance in perovskite rare-earth manganites,” Phys. Rev. Lett. 92, 257201 (2004).
[CrossRef] [PubMed]

E. Golovenchits and V. Sanina, “Magnetic and magnetoelectric dynamics in RMn2O5 (R=Gd and Eu),” J. Phys.: Condens. Matter 16, 4325-4334 (2004).
[CrossRef]

2003 (2)

T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, “Magnetic control of ferroelectric polarization,” Nature (London) 426, 55-58 (2003).
[CrossRef]

T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T. Takahashi, K. Ishizaka, and Y. Tokura, “Distorted perovskite with eg1 configuration as a frusrated spin system,” Phys. Rev. B 68, 060403(R) (2003).
[CrossRef]

2000 (1)

A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. Pimenov, A. Loidl, and A. M. Balbashov, “Antiferromagnetic resonance in the canted phase of La1−xSrxMnO3: Experimental evidence against electronic phase separation,” Europhys. Lett. 49, 514-520 (2000).
[CrossRef]

1999 (1)

I. S. Smirnova, “Normal modes of the LaMnO3 Pnma phase: comparison with La2CuO4 Cmna phase,” Physica B 262, 247-261 (1999).
[CrossRef]

1996 (1)

K. Hirota, N. Kaneko, A. Nishizawa, and Y. Endoh, “Two-dimensional planar ferromagnetic coupling in LaMnO3,” J. Phys. Soc. Jpn. 65, 3736-3739 (1996).
[CrossRef]

1995 (1)

T. Arima and Y. Tokura, “Optical study of electronic structure in perovskite-type RMO3 (R=La,Y; M=Sc,Ti,V,Cr,Mn,Fe,Co,Ni,Cu),” J. Phys. Soc. Jpn. 64, 2488-2501 (1995).
[CrossRef]

1993 (1)

T. Arima, Y. Tokura, and J. B. Torrance, “Variation of optical gap in perovskite-type 3d transition-metal oxides,” Phys. Rev. B 48, 17006-17009 (1993).
[CrossRef]

1982 (1)

G. A. Smolenski and I. E. Chupis, “Ferroelectromagnets,” Usp. Fiz. Nauk 137, 415-448 (1982) G. A. Smolenski and I. E. Chupis[Sov. Phys. Usp. 25, 475-493 (1982)].
[CrossRef]

G. A. Smolenski and I. E. Chupis, “Ferroelectromagnets,” Usp. Fiz. Nauk 137, 415-448 (1982) G. A. Smolenski and I. E. Chupis[Sov. Phys. Usp. 25, 475-493 (1982)].
[CrossRef]

1969 (1)

V. G. Bar'yakhtar and I. E. Chupis, “Quantum theory of oscillations in a ferroelectric ferromagnet,” Fiz. Tverd. Tela (Leningrad) 11, 3242-3247 (1969) V. G. Bar'yakhtar and I. E. Chupis[Sov. Phys. Solid State 11, 2628-2631 (1970)].

V. G. Bar'yakhtar and I. E. Chupis, “Quantum theory of oscillations in a ferroelectric ferromagnet,” Fiz. Tverd. Tela (Leningrad) 11, 3242-3247 (1969) V. G. Bar'yakhtar and I. E. Chupis[Sov. Phys. Solid State 11, 2628-2631 (1970)].

1966 (1)

T. Moriya, “Far infrared absorption by two magnon excitations in antiferromagnets,” J. Phys. Soc. Jpn. 21, 926-932 (1966).
[CrossRef]

1962 (1)

B. R. Cooper, R. J. Elliott, S. J. Nettel, and H. Suhl, “Theory of magnetic resonance in the heavy rare-earth metals,” Phys. Rev. 127, 57-68 (1962).
[CrossRef]

Abe, N.

Y. Yamasaki, H. Sagayama, N. Abe, T. Arima, K. Sasai, M. Matsuura, K. Hirota, D. Okuyama, Y. Noda, and Y. Tokura, “Cycloidal spin order in the a axis polarized ferroelectric phase of orthorhombic perovskite manganite,” Phys. Rev. Lett. 101, 097204 (2008).
[CrossRef] [PubMed]

Aliouane, N.

N. Aliouane, K. Schmalzl, D. Senff, A. Maljuk, K. Prokeš, M. Braden, and D. N. Argyriou, “Flop of electric polarization driven by the flop of the Mn spin cycloid in multiferroic TbMnO3,” Phys. Rev. Lett. 102, 207205 (2009).
[CrossRef] [PubMed]

D. Senff, P. Link, N. Aliouane, D. N. Argyriou, and M. Braden, “Field dependence of magnetic correlations through the polarization flop transition in multiferroic TbMnO3: Evidence for a magnetic memory effect,” Phys. Rev. B 77, 174419 (2008).
[CrossRef]

D. Senff, N. Aliouane, D. N. Argyriou, A. Hiess, L. P. Regnault, P. Link, K. Hradil, Y. Sidis, and M. Braden, “Magnetic excitations in a cycloidal magnet: the magnon spectrum of multiferroic TbMnO3,” J. Phys.: Condens. Matter 20, 434212 (2008).
[CrossRef]

J. Strempfer, B. Bohnenbuck, M. Mostovoy, N. Aliouane, D. N. Argyriou, F. Schrettle, J. Hemberger, A. Krimmel, and M. v. Zimmermann, “Absence of commensurate ordering at the polarization flop transition in multiferroic DyMnO3,” Phys. Rev. B 75, 212402 (2007).
[CrossRef]

D. Senff, P. Link, K. Hradil, A. Hiess, L. P. Regnault, Y. Sidis, N. Aliouane, D. N. Argyriou, and M. Braden, “Magnetic excitations in TbMnO3: Evidence for a hybridized soft mode,” Phys. Rev. Lett. 98, 137206 (2007).
[CrossRef] [PubMed]

Amann, U.

T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J. Ihringer, and M. Fiebig, “Magnetic phase control by an electric field,” Nature (London) 430, 541-544 (2004).
[CrossRef]

Argyriou, D. N.

N. Aliouane, K. Schmalzl, D. Senff, A. Maljuk, K. Prokeš, M. Braden, and D. N. Argyriou, “Flop of electric polarization driven by the flop of the Mn spin cycloid in multiferroic TbMnO3,” Phys. Rev. Lett. 102, 207205 (2009).
[CrossRef] [PubMed]

D. Senff, P. Link, N. Aliouane, D. N. Argyriou, and M. Braden, “Field dependence of magnetic correlations through the polarization flop transition in multiferroic TbMnO3: Evidence for a magnetic memory effect,” Phys. Rev. B 77, 174419 (2008).
[CrossRef]

D. Senff, N. Aliouane, D. N. Argyriou, A. Hiess, L. P. Regnault, P. Link, K. Hradil, Y. Sidis, and M. Braden, “Magnetic excitations in a cycloidal magnet: the magnon spectrum of multiferroic TbMnO3,” J. Phys.: Condens. Matter 20, 434212 (2008).
[CrossRef]

J. Strempfer, B. Bohnenbuck, M. Mostovoy, N. Aliouane, D. N. Argyriou, F. Schrettle, J. Hemberger, A. Krimmel, and M. v. Zimmermann, “Absence of commensurate ordering at the polarization flop transition in multiferroic DyMnO3,” Phys. Rev. B 75, 212402 (2007).
[CrossRef]

D. Senff, P. Link, K. Hradil, A. Hiess, L. P. Regnault, Y. Sidis, N. Aliouane, D. N. Argyriou, and M. Braden, “Magnetic excitations in TbMnO3: Evidence for a hybridized soft mode,” Phys. Rev. Lett. 98, 137206 (2007).
[CrossRef] [PubMed]

Arima, T.

N. Kida, Y. Yamasaki, J. P. He, Y. Kaneko, Y. Ikebe, Y. Takahashi, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation at THz frequencies in bc and ab spiral spin phases of perovskite manganites,” J. Phys. Conf. Ser. 148, 012038 (2009); Proc. LXIII Yamada Conf. Photo-induced Phase Transition and Cooperative Phenomena.
[CrossRef]

Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, and Y. Tokura, “Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3,” Phys. Rev. Lett. 101, 187201 (2008).
[CrossRef] [PubMed]

N. Kida, Y. Yamasaki, R. Shimano, T. Arima, and Y. Tokura, “Electric-dipole active two-magnon excitation in ab spiral spin phase of a ferroelectric magnet Gd0.7Tb0.3MnO3,” J. Phys. Soc. Jpn. 77, 123704 (2008).
[CrossRef]

N. Kida, Y. Ikebe, Y. Takahashi, J. P. He, Y. Kaneko, Y. Yamasaki, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation in the ferroelectric magnet DyMnO3,” Phys. Rev. B 78, 104414 (2008).
[CrossRef]

Y. Yamasaki, H. Sagayama, N. Abe, T. Arima, K. Sasai, M. Matsuura, K. Hirota, D. Okuyama, Y. Noda, and Y. Tokura, “Cycloidal spin order in the a axis polarized ferroelectric phase of orthorhombic perovskite manganite,” Phys. Rev. Lett. 101, 097204 (2008).
[CrossRef] [PubMed]

Y. Yamasaki, H. Sagayama, T. Goto, M. Matsuura, K. Hirota, T. Arima, and Y. Tokura, “Electric control of spin helicity in a magnetic ferroelectric,” Phys. Rev. Lett. 98, 147204 (2007).
[CrossRef] [PubMed]

T. Arima, T. Goto, Y. Yamasaki, S. Miyasaka, K. Ishii, M. Tsubota, T. Inami, Y. Murakami, and Y. Tokura, “Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric GdMnO3 and TbMnO3, compounds,” Phys. Rev. B 72, 100102(R) (2005).
[CrossRef]

T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T. Takahashi, K. Ishizaka, and Y. Tokura, “Distorted perovskite with eg1 configuration as a frusrated spin system,” Phys. Rev. B 68, 060403(R) (2003).
[CrossRef]

T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, “Magnetic control of ferroelectric polarization,” Nature (London) 426, 55-58 (2003).
[CrossRef]

T. Arima and Y. Tokura, “Optical study of electronic structure in perovskite-type RMO3 (R=La,Y; M=Sc,Ti,V,Cr,Mn,Fe,Co,Ni,Cu),” J. Phys. Soc. Jpn. 64, 2488-2501 (1995).
[CrossRef]

T. Arima, Y. Tokura, and J. B. Torrance, “Variation of optical gap in perovskite-type 3d transition-metal oxides,” Phys. Rev. B 48, 17006-17009 (1993).
[CrossRef]

Y. Takahashi, Y. Yamasaki, N. Kida, Y. Kaneko, T. Arima, R. Shimano, and Y. Tokura, “Comprehensive study on electromagnons and their coupling with optical phonons in Eu1−xYxMnO3 (x=0.1, 0.2, 0.3, 0.4, and 0.45),” submitted for publication (2009).

Balatsky, A. V.

H. Katsura, A. V. Balatsky, and N. Nagaosa, “Dynamical magnetoelectric coupling in helical magnet,” Phys. Rev. Lett. 98, 027203 (2007).
[CrossRef] [PubMed]

H. Katsura, N. Nagaosa, and A. V. Balatsky, “Spin current and magnetoelectric effect in noncollinear magnets,” Phys. Rev. Lett. 95, 057205 (2005).
[CrossRef] [PubMed]

Balbashov, A. M.

A. Pimenov, A. Shuvaev, A. Loidl, F. Schrettle, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Magnetic and magnetoelectric excitations in TbMnO3,” Phys. Rev. Lett. 102, 107203 (2009).
[CrossRef] [PubMed]

A. Pimenov, A. Loidl, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Terahertz spectroscopy of electromagnons in Eu1−xYxMnO3,” Phys. Rev. B 77, 014438 (2008).
[CrossRef]

A. Pimenov, T. Rudolf, F. Mayr, A. Loidl, A. A. Mukhin, and A. M. Balbashov, “Coupling of phonons and electromagnons in GdMnO3,” Phys. Rev. B 74, 100403(R) (2006).
[CrossRef]

A. Pimenov, A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. M. Balbashov, and A. Loidl, “Possible evidence for electromagnon in multiferroic manganites,” Nat. Phys. 2, 97-100 (2006).
[CrossRef]

A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. Pimenov, A. Loidl, and A. M. Balbashov, “Antiferromagnetic resonance in the canted phase of La1−xSrxMnO3: Experimental evidence against electronic phase separation,” Europhys. Lett. 49, 514-520 (2000).
[CrossRef]

A. M. Balbashov, G. V. Kozlov, A. A. Mukhin, and A. S. Prokhorov, “Submillimeter Spectroscopy of Antiferromagnetic Dielectrics. Rare-earth Orthoferrites,” in High Frequency Processes in Magnetic Materials, (eds. G.Srinivasan and A.N.Slavin) pp 56-98 (World Scientific, Singapore, 1995).

Bar'yakhtar, V. G.

V. G. Bar'yakhtar and I. E. Chupis, “Quantum theory of oscillations in a ferroelectric ferromagnet,” Fiz. Tverd. Tela (Leningrad) 11, 3242-3247 (1969) V. G. Bar'yakhtar and I. E. Chupis[Sov. Phys. Solid State 11, 2628-2631 (1970)].

V. G. Bar'yakhtar and I. E. Chupis, “Quantum theory of oscillations in a ferroelectric ferromagnet,” Fiz. Tverd. Tela (Leningrad) 11, 3242-3247 (1969) V. G. Bar'yakhtar and I. E. Chupis[Sov. Phys. Solid State 11, 2628-2631 (1970)].

Bohnenbuck, B.

J. Strempfer, B. Bohnenbuck, M. Mostovoy, N. Aliouane, D. N. Argyriou, F. Schrettle, J. Hemberger, A. Krimmel, and M. v. Zimmermann, “Absence of commensurate ordering at the polarization flop transition in multiferroic DyMnO3,” Phys. Rev. B 75, 212402 (2007).
[CrossRef]

Braden, M.

N. Aliouane, K. Schmalzl, D. Senff, A. Maljuk, K. Prokeš, M. Braden, and D. N. Argyriou, “Flop of electric polarization driven by the flop of the Mn spin cycloid in multiferroic TbMnO3,” Phys. Rev. Lett. 102, 207205 (2009).
[CrossRef] [PubMed]

D. Senff, P. Link, N. Aliouane, D. N. Argyriou, and M. Braden, “Field dependence of magnetic correlations through the polarization flop transition in multiferroic TbMnO3: Evidence for a magnetic memory effect,” Phys. Rev. B 77, 174419 (2008).
[CrossRef]

D. Senff, N. Aliouane, D. N. Argyriou, A. Hiess, L. P. Regnault, P. Link, K. Hradil, Y. Sidis, and M. Braden, “Magnetic excitations in a cycloidal magnet: the magnon spectrum of multiferroic TbMnO3,” J. Phys.: Condens. Matter 20, 434212 (2008).
[CrossRef]

D. Senff, P. Link, K. Hradil, A. Hiess, L. P. Regnault, Y. Sidis, N. Aliouane, D. N. Argyriou, and M. Braden, “Magnetic excitations in TbMnO3: Evidence for a hybridized soft mode,” Phys. Rev. Lett. 98, 137206 (2007).
[CrossRef] [PubMed]

Broholm, C.

M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
[CrossRef] [PubMed]

Cazayous, M.

M. Cazayous, Y. Gallais, A. Sacuto, R. de Sousa, D. Lebeugle, and D. Colson, “Possible observation of cycloidal electromagnons in BiFeO3,” Phys. Rev. Lett. 101, 037601 (2008).
[CrossRef] [PubMed]

Cheong, S.-W.

R. Valdés Aguilar, M. Mostovoy, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Origin of electromagnon excitations in RMnO3,” Phys. Rev. Lett. 102, 047203 (2009).
[CrossRef] [PubMed]

A. B. Sushkov, R. Valdés Aguilar, S. Park, S.-W. Cheong, and H. D. Drew, “Electromagnons in multiferroic YMn2O5 and TbMn2O5,” Phys. Rev. Lett. 98, 027202 (2007).
[CrossRef] [PubMed]

S.-W. Cheong and M. Mostovoy, “Multiferroics: a magnetic twist for ferroelectricity,” Nature Mater. 6, 13-20 (2007).
[CrossRef]

R. Valdés Aguilar, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Colossal magnon-phonon coupling in multiferroic Eu0.75Y0.25MnO3,” Phys. Rev. B 76, 060404(R) (2007).
[CrossRef]

M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
[CrossRef] [PubMed]

Choi, Y. J.

R. Valdés Aguilar, M. Mostovoy, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Origin of electromagnon excitations in RMnO3,” Phys. Rev. Lett. 102, 047203 (2009).
[CrossRef] [PubMed]

R. Valdés Aguilar, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Colossal magnon-phonon coupling in multiferroic Eu0.75Y0.25MnO3,” Phys. Rev. B 76, 060404(R) (2007).
[CrossRef]

Chupis, I. E.

G. A. Smolenski and I. E. Chupis, “Ferroelectromagnets,” Usp. Fiz. Nauk 137, 415-448 (1982) G. A. Smolenski and I. E. Chupis[Sov. Phys. Usp. 25, 475-493 (1982)].
[CrossRef]

G. A. Smolenski and I. E. Chupis, “Ferroelectromagnets,” Usp. Fiz. Nauk 137, 415-448 (1982) G. A. Smolenski and I. E. Chupis[Sov. Phys. Usp. 25, 475-493 (1982)].
[CrossRef]

V. G. Bar'yakhtar and I. E. Chupis, “Quantum theory of oscillations in a ferroelectric ferromagnet,” Fiz. Tverd. Tela (Leningrad) 11, 3242-3247 (1969) V. G. Bar'yakhtar and I. E. Chupis[Sov. Phys. Solid State 11, 2628-2631 (1970)].

V. G. Bar'yakhtar and I. E. Chupis, “Quantum theory of oscillations in a ferroelectric ferromagnet,” Fiz. Tverd. Tela (Leningrad) 11, 3242-3247 (1969) V. G. Bar'yakhtar and I. E. Chupis[Sov. Phys. Solid State 11, 2628-2631 (1970)].

Colson, D.

M. Cazayous, Y. Gallais, A. Sacuto, R. de Sousa, D. Lebeugle, and D. Colson, “Possible observation of cycloidal electromagnons in BiFeO3,” Phys. Rev. Lett. 101, 037601 (2008).
[CrossRef] [PubMed]

Cooper, B. R.

B. R. Cooper, R. J. Elliott, S. J. Nettel, and H. Suhl, “Theory of magnetic resonance in the heavy rare-earth metals,” Phys. Rev. 127, 57-68 (1962).
[CrossRef]

Datotto, E.

I. A. Sergienko and E. Datotto, “Role of the Dzyaloshinskii-Moriya interaction in multiferroic perovskites,” Phys. Rev. B 73, 094434 (2006).
[CrossRef]

de Sousa, R.

M. Cazayous, Y. Gallais, A. Sacuto, R. de Sousa, D. Lebeugle, and D. Colson, “Possible observation of cycloidal electromagnons in BiFeO3,” Phys. Rev. Lett. 101, 037601 (2008).
[CrossRef] [PubMed]

Drew, H. D.

R. Valdés Aguilar, M. Mostovoy, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Origin of electromagnon excitations in RMnO3,” Phys. Rev. Lett. 102, 047203 (2009).
[CrossRef] [PubMed]

A. B. Sushkov, R. Valdés Aguilar, S. Park, S.-W. Cheong, and H. D. Drew, “Electromagnons in multiferroic YMn2O5 and TbMn2O5,” Phys. Rev. Lett. 98, 027202 (2007).
[CrossRef] [PubMed]

R. Valdés Aguilar, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Colossal magnon-phonon coupling in multiferroic Eu0.75Y0.25MnO3,” Phys. Rev. B 76, 060404(R) (2007).
[CrossRef]

Eerenstein, W.

W. Eerenstein, N. D. Mathur, and J. F. Scott, “Multiferroic and magnetoelectric materials,” Nature (London) 442, 759-765 (2006).
[CrossRef]

Elliott, R. J.

B. R. Cooper, R. J. Elliott, S. J. Nettel, and H. Suhl, “Theory of magnetic resonance in the heavy rare-earth metals,” Phys. Rev. 127, 57-68 (1962).
[CrossRef]

Endoh, Y.

K. Hirota, N. Kaneko, A. Nishizawa, and Y. Endoh, “Two-dimensional planar ferromagnetic coupling in LaMnO3,” J. Phys. Soc. Jpn. 65, 3736-3739 (1996).
[CrossRef]

Fabrèges, X.

S. Pailhès, X. Fabrèges, L. P. Règnault, L. Pinsard-Godart, I. Mirebeau, F. Moussa, M. Hennion, and S. Petit, “Hybrid Goldstone modes in multiferroic YMnO3 studied by polarized inelastic neutron scattering,” Phys. Rev. B 79, 134409 (2009).
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Fang, C.

C. Fang and J. Hu, “An effective model of magnetoelectricity in multiferroic RMn2O5,” EPL 82, 57005 (2008).
[CrossRef]

Fiebig, M.

T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J. Ihringer, and M. Fiebig, “Magnetic phase control by an electric field,” Nature (London) 430, 541-544 (2004).
[CrossRef]

Fujioka, J.

Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, and Y. Tokura, “Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3,” Phys. Rev. Lett. 101, 187201 (2008).
[CrossRef] [PubMed]

Furukawa, N.

J. S. Lee, N. Kida, S. Miyahara, Y. Yamasaki, Y. Takahashi, R. Shimano, N. Furukawa, and Y. Tokura, “Systematics of electromagnons in the spiral spin-ordered states of RMnO3,” Phys. Rev. B 79, 18043(R) (2009).

F. Kagawa, M. Mochizuki, Y. Onose, H. Murakawa, Y. Kaneko, N. Furukawa, and Y. Tokura, “Dynamics of multiferroic domain wall in spin-cycloidal ferroelectric DyMnO3,” Phys. Rev. Lett. 102, 057604 (2009).
[CrossRef] [PubMed]

Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, and Y. Tokura, “Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3,” Phys. Rev. Lett. 101, 187201 (2008).
[CrossRef] [PubMed]

M. Mochizuki and N. Furukawa, “Mechanism of lattice-distortion-induced electric-polarization flop in the multiferroic perovskite manganites,” J. Phys. Soc. Jpn. 78, 053704 (2008).
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S. Miyahara and N. Furukawa, “Theory of electric field induced one-magnon resonance in cycloidal spin magnets,” Preprint at http://arxiv.org/cond-mat/0811.4082 (2008).

Gallais, Y.

M. Cazayous, Y. Gallais, A. Sacuto, R. de Sousa, D. Lebeugle, and D. Colson, “Possible observation of cycloidal electromagnons in BiFeO3,” Phys. Rev. Lett. 101, 037601 (2008).
[CrossRef] [PubMed]

Golovenchits, E.

E. Golovenchits and V. Sanina, “Magnetic and magnetoelectric dynamics in RMn2O5 (R=Gd and Eu),” J. Phys.: Condens. Matter 16, 4325-4334 (2004).
[CrossRef]

Goto, T.

Y. Yamasaki, H. Sagayama, T. Goto, M. Matsuura, K. Hirota, T. Arima, and Y. Tokura, “Electric control of spin helicity in a magnetic ferroelectric,” Phys. Rev. Lett. 98, 147204 (2007).
[CrossRef] [PubMed]

T. Kimura, G. Lawes, T. Goto, Y. Tokura, and A. P. Ramirez, “Magnetoelectric phase diagrams of orthorhombic RMnO3,” Phys. Rev. B 71, 224425 (2005).
[CrossRef]

T. Arima, T. Goto, Y. Yamasaki, S. Miyasaka, K. Ishii, M. Tsubota, T. Inami, Y. Murakami, and Y. Tokura, “Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric GdMnO3 and TbMnO3, compounds,” Phys. Rev. B 72, 100102(R) (2005).
[CrossRef]

T. Goto, Y. Yamasaki, H. Watanabe, T. Kimura, and Y. Tokura, “Anticorrelation between ferromagnetism and ferroelectricity in perovskite manganites,” Phys. Rev. B 72, 220403(R) (2005).
[CrossRef]

T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and Y. Tokura, “Ferroelectricity and giant magnetocapacitance in perovskite rare-earth manganites,” Phys. Rev. Lett. 92, 257201 (2004).
[CrossRef] [PubMed]

T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, “Magnetic control of ferroelectric polarization,” Nature (London) 426, 55-58 (2003).
[CrossRef]

Han, J. H.

C. Jia, S. Onoda, N. Nagaosa, and J. H. Han, “Microscopic theory of spin-polarization coupling in multiferroics transition metal oxides,” Phys. Rev. B 76, 144424 (2007).
[CrossRef]

Harris, A. B.

M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
[CrossRef] [PubMed]

He, J. P.

N. Kida, Y. Yamasaki, J. P. He, Y. Kaneko, Y. Ikebe, Y. Takahashi, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation at THz frequencies in bc and ab spiral spin phases of perovskite manganites,” J. Phys. Conf. Ser. 148, 012038 (2009); Proc. LXIII Yamada Conf. Photo-induced Phase Transition and Cooperative Phenomena.
[CrossRef]

N. Kida, Y. Ikebe, Y. Takahashi, J. P. He, Y. Kaneko, Y. Yamasaki, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation in the ferroelectric magnet DyMnO3,” Phys. Rev. B 78, 104414 (2008).
[CrossRef]

Hemberger, J.

J. Strempfer, B. Bohnenbuck, M. Mostovoy, N. Aliouane, D. N. Argyriou, F. Schrettle, J. Hemberger, A. Krimmel, and M. v. Zimmermann, “Absence of commensurate ordering at the polarization flop transition in multiferroic DyMnO3,” Phys. Rev. B 75, 212402 (2007).
[CrossRef]

Hennion, M.

S. Pailhès, X. Fabrèges, L. P. Règnault, L. Pinsard-Godart, I. Mirebeau, F. Moussa, M. Hennion, and S. Petit, “Hybrid Goldstone modes in multiferroic YMnO3 studied by polarized inelastic neutron scattering,” Phys. Rev. B 79, 134409 (2009).
[CrossRef]

Hiess, A.

D. Senff, N. Aliouane, D. N. Argyriou, A. Hiess, L. P. Regnault, P. Link, K. Hradil, Y. Sidis, and M. Braden, “Magnetic excitations in a cycloidal magnet: the magnon spectrum of multiferroic TbMnO3,” J. Phys.: Condens. Matter 20, 434212 (2008).
[CrossRef]

D. Senff, P. Link, K. Hradil, A. Hiess, L. P. Regnault, Y. Sidis, N. Aliouane, D. N. Argyriou, and M. Braden, “Magnetic excitations in TbMnO3: Evidence for a hybridized soft mode,” Phys. Rev. Lett. 98, 137206 (2007).
[CrossRef] [PubMed]

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Y. Yamasaki, H. Sagayama, N. Abe, T. Arima, K. Sasai, M. Matsuura, K. Hirota, D. Okuyama, Y. Noda, and Y. Tokura, “Cycloidal spin order in the a axis polarized ferroelectric phase of orthorhombic perovskite manganite,” Phys. Rev. Lett. 101, 097204 (2008).
[CrossRef] [PubMed]

Y. Yamasaki, H. Sagayama, T. Goto, M. Matsuura, K. Hirota, T. Arima, and Y. Tokura, “Electric control of spin helicity in a magnetic ferroelectric,” Phys. Rev. Lett. 98, 147204 (2007).
[CrossRef] [PubMed]

K. Hirota, N. Kaneko, A. Nishizawa, and Y. Endoh, “Two-dimensional planar ferromagnetic coupling in LaMnO3,” J. Phys. Soc. Jpn. 65, 3736-3739 (1996).
[CrossRef]

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T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J. Ihringer, and M. Fiebig, “Magnetic phase control by an electric field,” Nature (London) 430, 541-544 (2004).
[CrossRef]

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D. Senff, N. Aliouane, D. N. Argyriou, A. Hiess, L. P. Regnault, P. Link, K. Hradil, Y. Sidis, and M. Braden, “Magnetic excitations in a cycloidal magnet: the magnon spectrum of multiferroic TbMnO3,” J. Phys.: Condens. Matter 20, 434212 (2008).
[CrossRef]

D. Senff, P. Link, K. Hradil, A. Hiess, L. P. Regnault, Y. Sidis, N. Aliouane, D. N. Argyriou, and M. Braden, “Magnetic excitations in TbMnO3: Evidence for a hybridized soft mode,” Phys. Rev. Lett. 98, 137206 (2007).
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C. Fang and J. Hu, “An effective model of magnetoelectricity in multiferroic RMn2O5,” EPL 82, 57005 (2008).
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T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J. Ihringer, and M. Fiebig, “Magnetic phase control by an electric field,” Nature (London) 430, 541-544 (2004).
[CrossRef]

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N. Kida, Y. Yamasaki, J. P. He, Y. Kaneko, Y. Ikebe, Y. Takahashi, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation at THz frequencies in bc and ab spiral spin phases of perovskite manganites,” J. Phys. Conf. Ser. 148, 012038 (2009); Proc. LXIII Yamada Conf. Photo-induced Phase Transition and Cooperative Phenomena.
[CrossRef]

N. Kida, Y. Ikebe, Y. Takahashi, J. P. He, Y. Kaneko, Y. Yamasaki, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation in the ferroelectric magnet DyMnO3,” Phys. Rev. B 78, 104414 (2008).
[CrossRef]

Inami, T.

T. Arima, T. Goto, Y. Yamasaki, S. Miyasaka, K. Ishii, M. Tsubota, T. Inami, Y. Murakami, and Y. Tokura, “Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric GdMnO3 and TbMnO3, compounds,” Phys. Rev. B 72, 100102(R) (2005).
[CrossRef]

Ishihara, S.

T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T. Takahashi, K. Ishizaka, and Y. Tokura, “Distorted perovskite with eg1 configuration as a frusrated spin system,” Phys. Rev. B 68, 060403(R) (2003).
[CrossRef]

Ishii, K.

T. Arima, T. Goto, Y. Yamasaki, S. Miyasaka, K. Ishii, M. Tsubota, T. Inami, Y. Murakami, and Y. Tokura, “Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric GdMnO3 and TbMnO3, compounds,” Phys. Rev. B 72, 100102(R) (2005).
[CrossRef]

Ishizaka, K.

T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T. Takahashi, K. Ishizaka, and Y. Tokura, “Distorted perovskite with eg1 configuration as a frusrated spin system,” Phys. Rev. B 68, 060403(R) (2003).
[CrossRef]

T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, “Magnetic control of ferroelectric polarization,” Nature (London) 426, 55-58 (2003).
[CrossRef]

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A. Pimenov, A. Shuvaev, A. Loidl, F. Schrettle, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Magnetic and magnetoelectric excitations in TbMnO3,” Phys. Rev. Lett. 102, 107203 (2009).
[CrossRef] [PubMed]

A. Pimenov, A. Loidl, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Terahertz spectroscopy of electromagnons in Eu1−xYxMnO3,” Phys. Rev. B 77, 014438 (2008).
[CrossRef]

A. Pimenov, A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. M. Balbashov, and A. Loidl, “Possible evidence for electromagnon in multiferroic manganites,” Nat. Phys. 2, 97-100 (2006).
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A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. Pimenov, A. Loidl, and A. M. Balbashov, “Antiferromagnetic resonance in the canted phase of La1−xSrxMnO3: Experimental evidence against electronic phase separation,” Europhys. Lett. 49, 514-520 (2000).
[CrossRef]

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C. Jia, S. Onoda, N. Nagaosa, and J. H. Han, “Microscopic theory of spin-polarization coupling in multiferroics transition metal oxides,” Phys. Rev. B 76, 144424 (2007).
[CrossRef]

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M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
[CrossRef] [PubMed]

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F. Kagawa, M. Mochizuki, Y. Onose, H. Murakawa, Y. Kaneko, N. Furukawa, and Y. Tokura, “Dynamics of multiferroic domain wall in spin-cycloidal ferroelectric DyMnO3,” Phys. Rev. Lett. 102, 057604 (2009).
[CrossRef] [PubMed]

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R. Kajimoto, H. Mochizuki, H. Yoshizawa, H. Shintani, T. Kimura, and Y. Tokura, “R-dependence of spin exchange interactions in RMnO3 (R=rare-earth ions),” J. Phys. Soc. Jpn. 74, 2430-2433 (2005).
[CrossRef]

Kaneko, N.

K. Hirota, N. Kaneko, A. Nishizawa, and Y. Endoh, “Two-dimensional planar ferromagnetic coupling in LaMnO3,” J. Phys. Soc. Jpn. 65, 3736-3739 (1996).
[CrossRef]

Kaneko, Y.

F. Kagawa, M. Mochizuki, Y. Onose, H. Murakawa, Y. Kaneko, N. Furukawa, and Y. Tokura, “Dynamics of multiferroic domain wall in spin-cycloidal ferroelectric DyMnO3,” Phys. Rev. Lett. 102, 057604 (2009).
[CrossRef] [PubMed]

N. Kida, Y. Yamasaki, J. P. He, Y. Kaneko, Y. Ikebe, Y. Takahashi, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation at THz frequencies in bc and ab spiral spin phases of perovskite manganites,” J. Phys. Conf. Ser. 148, 012038 (2009); Proc. LXIII Yamada Conf. Photo-induced Phase Transition and Cooperative Phenomena.
[CrossRef]

N. Kida, Y. Ikebe, Y. Takahashi, J. P. He, Y. Kaneko, Y. Yamasaki, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation in the ferroelectric magnet DyMnO3,” Phys. Rev. B 78, 104414 (2008).
[CrossRef]

Y. Takahashi, Y. Yamasaki, N. Kida, Y. Kaneko, T. Arima, R. Shimano, and Y. Tokura, “Comprehensive study on electromagnons and their coupling with optical phonons in Eu1−xYxMnO3 (x=0.1, 0.2, 0.3, 0.4, and 0.45),” submitted for publication (2009).

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M. K. Singh, R. S. Katiyar, and J. F. Scott, “New magnetic phase transitions in BiFeO3,” J. Phys.: Condens. Matter 20, 252203 (2008).
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H. Katsura, A. V. Balatsky, and N. Nagaosa, “Dynamical magnetoelectric coupling in helical magnet,” Phys. Rev. Lett. 98, 027203 (2007).
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H. Katsura, N. Nagaosa, and A. V. Balatsky, “Spin current and magnetoelectric effect in noncollinear magnets,” Phys. Rev. Lett. 95, 057205 (2005).
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M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
[CrossRef] [PubMed]

Kida, N.

J. S. Lee, N. Kida, S. Miyahara, Y. Yamasaki, Y. Takahashi, R. Shimano, N. Furukawa, and Y. Tokura, “Systematics of electromagnons in the spiral spin-ordered states of RMnO3,” Phys. Rev. B 79, 18043(R) (2009).

N. Kida, Y. Yamasaki, J. P. He, Y. Kaneko, Y. Ikebe, Y. Takahashi, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation at THz frequencies in bc and ab spiral spin phases of perovskite manganites,” J. Phys. Conf. Ser. 148, 012038 (2009); Proc. LXIII Yamada Conf. Photo-induced Phase Transition and Cooperative Phenomena.
[CrossRef]

N. Kida, Y. Yamasaki, R. Shimano, T. Arima, and Y. Tokura, “Electric-dipole active two-magnon excitation in ab spiral spin phase of a ferroelectric magnet Gd0.7Tb0.3MnO3,” J. Phys. Soc. Jpn. 77, 123704 (2008).
[CrossRef]

Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, and Y. Tokura, “Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3,” Phys. Rev. Lett. 101, 187201 (2008).
[CrossRef] [PubMed]

N. Kida, Y. Ikebe, Y. Takahashi, J. P. He, Y. Kaneko, Y. Yamasaki, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation in the ferroelectric magnet DyMnO3,” Phys. Rev. B 78, 104414 (2008).
[CrossRef]

Y. Takahashi, Y. Yamasaki, N. Kida, Y. Kaneko, T. Arima, R. Shimano, and Y. Tokura, “Comprehensive study on electromagnons and their coupling with optical phonons in Eu1−xYxMnO3 (x=0.1, 0.2, 0.3, 0.4, and 0.45),” submitted for publication (2009).

J. S. Lee, N. Kida, Y. Yamasaki, M. Mochizuki, R. Shimano, and Y. Tokura, “Lattice dynamics of multiferroic perovskite manganites,” manuscript in preparation.

Kim, S. B.

M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
[CrossRef] [PubMed]

Kimura, T.

T. Kimura, G. Lawes, T. Goto, Y. Tokura, and A. P. Ramirez, “Magnetoelectric phase diagrams of orthorhombic RMnO3,” Phys. Rev. B 71, 224425 (2005).
[CrossRef]

R. Kajimoto, H. Mochizuki, H. Yoshizawa, H. Shintani, T. Kimura, and Y. Tokura, “R-dependence of spin exchange interactions in RMnO3 (R=rare-earth ions),” J. Phys. Soc. Jpn. 74, 2430-2433 (2005).
[CrossRef]

T. Goto, Y. Yamasaki, H. Watanabe, T. Kimura, and Y. Tokura, “Anticorrelation between ferromagnetism and ferroelectricity in perovskite manganites,” Phys. Rev. B 72, 220403(R) (2005).
[CrossRef]

T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and Y. Tokura, “Ferroelectricity and giant magnetocapacitance in perovskite rare-earth manganites,” Phys. Rev. Lett. 92, 257201 (2004).
[CrossRef] [PubMed]

T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, “Magnetic control of ferroelectric polarization,” Nature (London) 426, 55-58 (2003).
[CrossRef]

T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T. Takahashi, K. Ishizaka, and Y. Tokura, “Distorted perovskite with eg1 configuration as a frusrated spin system,” Phys. Rev. B 68, 060403(R) (2003).
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A. M. Balbashov, G. V. Kozlov, A. A. Mukhin, and A. S. Prokhorov, “Submillimeter Spectroscopy of Antiferromagnetic Dielectrics. Rare-earth Orthoferrites,” in High Frequency Processes in Magnetic Materials, (eds. G.Srinivasan and A.N.Slavin) pp 56-98 (World Scientific, Singapore, 1995).

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J. Strempfer, B. Bohnenbuck, M. Mostovoy, N. Aliouane, D. N. Argyriou, F. Schrettle, J. Hemberger, A. Krimmel, and M. v. Zimmermann, “Absence of commensurate ordering at the polarization flop transition in multiferroic DyMnO3,” Phys. Rev. B 75, 212402 (2007).
[CrossRef]

Lawes, G.

T. Kimura, G. Lawes, T. Goto, Y. Tokura, and A. P. Ramirez, “Magnetoelectric phase diagrams of orthorhombic RMnO3,” Phys. Rev. B 71, 224425 (2005).
[CrossRef]

T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and Y. Tokura, “Ferroelectricity and giant magnetocapacitance in perovskite rare-earth manganites,” Phys. Rev. Lett. 92, 257201 (2004).
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M. Cazayous, Y. Gallais, A. Sacuto, R. de Sousa, D. Lebeugle, and D. Colson, “Possible observation of cycloidal electromagnons in BiFeO3,” Phys. Rev. Lett. 101, 037601 (2008).
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J. S. Lee, N. Kida, S. Miyahara, Y. Yamasaki, Y. Takahashi, R. Shimano, N. Furukawa, and Y. Tokura, “Systematics of electromagnons in the spiral spin-ordered states of RMnO3,” Phys. Rev. B 79, 18043(R) (2009).

J. S. Lee, N. Kida, Y. Yamasaki, M. Mochizuki, R. Shimano, and Y. Tokura, “Lattice dynamics of multiferroic perovskite manganites,” manuscript in preparation.

Link, P.

D. Senff, N. Aliouane, D. N. Argyriou, A. Hiess, L. P. Regnault, P. Link, K. Hradil, Y. Sidis, and M. Braden, “Magnetic excitations in a cycloidal magnet: the magnon spectrum of multiferroic TbMnO3,” J. Phys.: Condens. Matter 20, 434212 (2008).
[CrossRef]

D. Senff, P. Link, N. Aliouane, D. N. Argyriou, and M. Braden, “Field dependence of magnetic correlations through the polarization flop transition in multiferroic TbMnO3: Evidence for a magnetic memory effect,” Phys. Rev. B 77, 174419 (2008).
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D. Senff, P. Link, K. Hradil, A. Hiess, L. P. Regnault, Y. Sidis, N. Aliouane, D. N. Argyriou, and M. Braden, “Magnetic excitations in TbMnO3: Evidence for a hybridized soft mode,” Phys. Rev. Lett. 98, 137206 (2007).
[CrossRef] [PubMed]

Loidl, A.

A. Pimenov, A. Shuvaev, A. Loidl, F. Schrettle, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Magnetic and magnetoelectric excitations in TbMnO3,” Phys. Rev. Lett. 102, 107203 (2009).
[CrossRef] [PubMed]

A. Pimenov, A. M. Shuvaev, A. A. Mukhin, and A. Loidl, “Electromagnons in multiferroic manganites,” J. Phys.: Condens. Matter 20, 434209 (2008).
[CrossRef]

A. Pimenov, A. Loidl, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Terahertz spectroscopy of electromagnons in Eu1−xYxMnO3,” Phys. Rev. B 77, 014438 (2008).
[CrossRef]

A. Pimenov, T. Rudolf, F. Mayr, A. Loidl, A. A. Mukhin, and A. M. Balbashov, “Coupling of phonons and electromagnons in GdMnO3,” Phys. Rev. B 74, 100403(R) (2006).
[CrossRef]

A. Pimenov, A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. M. Balbashov, and A. Loidl, “Possible evidence for electromagnon in multiferroic manganites,” Nat. Phys. 2, 97-100 (2006).
[CrossRef]

A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. Pimenov, A. Loidl, and A. M. Balbashov, “Antiferromagnetic resonance in the canted phase of La1−xSrxMnO3: Experimental evidence against electronic phase separation,” Europhys. Lett. 49, 514-520 (2000).
[CrossRef]

Lonkai, T.

T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J. Ihringer, and M. Fiebig, “Magnetic phase control by an electric field,” Nature (London) 430, 541-544 (2004).
[CrossRef]

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T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J. Ihringer, and M. Fiebig, “Magnetic phase control by an electric field,” Nature (London) 430, 541-544 (2004).
[CrossRef]

Lynn, J. W.

M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
[CrossRef] [PubMed]

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N. Aliouane, K. Schmalzl, D. Senff, A. Maljuk, K. Prokeš, M. Braden, and D. N. Argyriou, “Flop of electric polarization driven by the flop of the Mn spin cycloid in multiferroic TbMnO3,” Phys. Rev. Lett. 102, 207205 (2009).
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W. Eerenstein, N. D. Mathur, and J. F. Scott, “Multiferroic and magnetoelectric materials,” Nature (London) 442, 759-765 (2006).
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Y. Yamasaki, H. Sagayama, N. Abe, T. Arima, K. Sasai, M. Matsuura, K. Hirota, D. Okuyama, Y. Noda, and Y. Tokura, “Cycloidal spin order in the a axis polarized ferroelectric phase of orthorhombic perovskite manganite,” Phys. Rev. Lett. 101, 097204 (2008).
[CrossRef] [PubMed]

Y. Yamasaki, H. Sagayama, T. Goto, M. Matsuura, K. Hirota, T. Arima, and Y. Tokura, “Electric control of spin helicity in a magnetic ferroelectric,” Phys. Rev. Lett. 98, 147204 (2007).
[CrossRef] [PubMed]

Mayr, F.

A. Pimenov, T. Rudolf, F. Mayr, A. Loidl, A. A. Mukhin, and A. M. Balbashov, “Coupling of phonons and electromagnons in GdMnO3,” Phys. Rev. B 74, 100403(R) (2006).
[CrossRef]

Mirebeau, I.

S. Pailhès, X. Fabrèges, L. P. Règnault, L. Pinsard-Godart, I. Mirebeau, F. Moussa, M. Hennion, and S. Petit, “Hybrid Goldstone modes in multiferroic YMnO3 studied by polarized inelastic neutron scattering,” Phys. Rev. B 79, 134409 (2009).
[CrossRef]

Miyahara, S.

J. S. Lee, N. Kida, S. Miyahara, Y. Yamasaki, Y. Takahashi, R. Shimano, N. Furukawa, and Y. Tokura, “Systematics of electromagnons in the spiral spin-ordered states of RMnO3,” Phys. Rev. B 79, 18043(R) (2009).

Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, and Y. Tokura, “Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3,” Phys. Rev. Lett. 101, 187201 (2008).
[CrossRef] [PubMed]

S. Miyahara and N. Furukawa, “Theory of electric field induced one-magnon resonance in cycloidal spin magnets,” Preprint at http://arxiv.org/cond-mat/0811.4082 (2008).

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T. Arima, T. Goto, Y. Yamasaki, S. Miyasaka, K. Ishii, M. Tsubota, T. Inami, Y. Murakami, and Y. Tokura, “Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric GdMnO3 and TbMnO3, compounds,” Phys. Rev. B 72, 100102(R) (2005).
[CrossRef]

Mochizuki, H.

R. Kajimoto, H. Mochizuki, H. Yoshizawa, H. Shintani, T. Kimura, and Y. Tokura, “R-dependence of spin exchange interactions in RMnO3 (R=rare-earth ions),” J. Phys. Soc. Jpn. 74, 2430-2433 (2005).
[CrossRef]

Mochizuki, M.

F. Kagawa, M. Mochizuki, Y. Onose, H. Murakawa, Y. Kaneko, N. Furukawa, and Y. Tokura, “Dynamics of multiferroic domain wall in spin-cycloidal ferroelectric DyMnO3,” Phys. Rev. Lett. 102, 057604 (2009).
[CrossRef] [PubMed]

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Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, and Y. Tokura, “Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3,” Phys. Rev. Lett. 101, 187201 (2008).
[CrossRef] [PubMed]

Y. Takahashi, Y. Yamasaki, N. Kida, Y. Kaneko, T. Arima, R. Shimano, and Y. Tokura, “Comprehensive study on electromagnons and their coupling with optical phonons in Eu1−xYxMnO3 (x=0.1, 0.2, 0.3, 0.4, and 0.45),” submitted for publication (2009).

Tokura, Y.

J. S. Lee, N. Kida, S. Miyahara, Y. Yamasaki, Y. Takahashi, R. Shimano, N. Furukawa, and Y. Tokura, “Systematics of electromagnons in the spiral spin-ordered states of RMnO3,” Phys. Rev. B 79, 18043(R) (2009).

N. Kida, Y. Yamasaki, J. P. He, Y. Kaneko, Y. Ikebe, Y. Takahashi, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation at THz frequencies in bc and ab spiral spin phases of perovskite manganites,” J. Phys. Conf. Ser. 148, 012038 (2009); Proc. LXIII Yamada Conf. Photo-induced Phase Transition and Cooperative Phenomena.
[CrossRef]

F. Kagawa, M. Mochizuki, Y. Onose, H. Murakawa, Y. Kaneko, N. Furukawa, and Y. Tokura, “Dynamics of multiferroic domain wall in spin-cycloidal ferroelectric DyMnO3,” Phys. Rev. Lett. 102, 057604 (2009).
[CrossRef] [PubMed]

N. Kida, Y. Yamasaki, R. Shimano, T. Arima, and Y. Tokura, “Electric-dipole active two-magnon excitation in ab spiral spin phase of a ferroelectric magnet Gd0.7Tb0.3MnO3,” J. Phys. Soc. Jpn. 77, 123704 (2008).
[CrossRef]

Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, and Y. Tokura, “Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3,” Phys. Rev. Lett. 101, 187201 (2008).
[CrossRef] [PubMed]

N. Kida, Y. Ikebe, Y. Takahashi, J. P. He, Y. Kaneko, Y. Yamasaki, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation in the ferroelectric magnet DyMnO3,” Phys. Rev. B 78, 104414 (2008).
[CrossRef]

Y. Yamasaki, H. Sagayama, N. Abe, T. Arima, K. Sasai, M. Matsuura, K. Hirota, D. Okuyama, Y. Noda, and Y. Tokura, “Cycloidal spin order in the a axis polarized ferroelectric phase of orthorhombic perovskite manganite,” Phys. Rev. Lett. 101, 097204 (2008).
[CrossRef] [PubMed]

Y. Yamasaki, H. Sagayama, T. Goto, M. Matsuura, K. Hirota, T. Arima, and Y. Tokura, “Electric control of spin helicity in a magnetic ferroelectric,” Phys. Rev. Lett. 98, 147204 (2007).
[CrossRef] [PubMed]

Y. Tokura, “Multiferroics-toward strong coupling between magnetism and polarization in a solid,” J. Magn. Magn. Mater. 310, 1145-1150 (2007).
[CrossRef]

Y. Tokura, “Multiferroics as quantum electromagnets,” Science 312, 1481-1482 (2006).
[CrossRef] [PubMed]

T. Kimura, G. Lawes, T. Goto, Y. Tokura, and A. P. Ramirez, “Magnetoelectric phase diagrams of orthorhombic RMnO3,” Phys. Rev. B 71, 224425 (2005).
[CrossRef]

R. Kajimoto, H. Mochizuki, H. Yoshizawa, H. Shintani, T. Kimura, and Y. Tokura, “R-dependence of spin exchange interactions in RMnO3 (R=rare-earth ions),” J. Phys. Soc. Jpn. 74, 2430-2433 (2005).
[CrossRef]

T. Arima, T. Goto, Y. Yamasaki, S. Miyasaka, K. Ishii, M. Tsubota, T. Inami, Y. Murakami, and Y. Tokura, “Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric GdMnO3 and TbMnO3, compounds,” Phys. Rev. B 72, 100102(R) (2005).
[CrossRef]

T. Goto, Y. Yamasaki, H. Watanabe, T. Kimura, and Y. Tokura, “Anticorrelation between ferromagnetism and ferroelectricity in perovskite manganites,” Phys. Rev. B 72, 220403(R) (2005).
[CrossRef]

T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and Y. Tokura, “Ferroelectricity and giant magnetocapacitance in perovskite rare-earth manganites,” Phys. Rev. Lett. 92, 257201 (2004).
[CrossRef] [PubMed]

T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, “Magnetic control of ferroelectric polarization,” Nature (London) 426, 55-58 (2003).
[CrossRef]

T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T. Takahashi, K. Ishizaka, and Y. Tokura, “Distorted perovskite with eg1 configuration as a frusrated spin system,” Phys. Rev. B 68, 060403(R) (2003).
[CrossRef]

T. Arima and Y. Tokura, “Optical study of electronic structure in perovskite-type RMO3 (R=La,Y; M=Sc,Ti,V,Cr,Mn,Fe,Co,Ni,Cu),” J. Phys. Soc. Jpn. 64, 2488-2501 (1995).
[CrossRef]

T. Arima, Y. Tokura, and J. B. Torrance, “Variation of optical gap in perovskite-type 3d transition-metal oxides,” Phys. Rev. B 48, 17006-17009 (1993).
[CrossRef]

Y. Takahashi, Y. Yamasaki, N. Kida, Y. Kaneko, T. Arima, R. Shimano, and Y. Tokura, “Comprehensive study on electromagnons and their coupling with optical phonons in Eu1−xYxMnO3 (x=0.1, 0.2, 0.3, 0.4, and 0.45),” submitted for publication (2009).

J. S. Lee, N. Kida, Y. Yamasaki, M. Mochizuki, R. Shimano, and Y. Tokura, “Lattice dynamics of multiferroic perovskite manganites,” manuscript in preparation.

Torrance, J. B.

T. Arima, Y. Tokura, and J. B. Torrance, “Variation of optical gap in perovskite-type 3d transition-metal oxides,” Phys. Rev. B 48, 17006-17009 (1993).
[CrossRef]

Travkin, V. D.

A. Pimenov, A. Shuvaev, A. Loidl, F. Schrettle, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Magnetic and magnetoelectric excitations in TbMnO3,” Phys. Rev. Lett. 102, 107203 (2009).
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A. Pimenov, A. Loidl, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Terahertz spectroscopy of electromagnons in Eu1−xYxMnO3,” Phys. Rev. B 77, 014438 (2008).
[CrossRef]

A. Pimenov, A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. M. Balbashov, and A. Loidl, “Possible evidence for electromagnon in multiferroic manganites,” Nat. Phys. 2, 97-100 (2006).
[CrossRef]

A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. Pimenov, A. Loidl, and A. M. Balbashov, “Antiferromagnetic resonance in the canted phase of La1−xSrxMnO3: Experimental evidence against electronic phase separation,” Europhys. Lett. 49, 514-520 (2000).
[CrossRef]

Tsubota, M.

T. Arima, T. Goto, Y. Yamasaki, S. Miyasaka, K. Ishii, M. Tsubota, T. Inami, Y. Murakami, and Y. Tokura, “Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric GdMnO3 and TbMnO3, compounds,” Phys. Rev. B 72, 100102(R) (2005).
[CrossRef]

Vajk, O. P.

M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
[CrossRef] [PubMed]

Valdés Aguilar, R.

R. Valdés Aguilar, M. Mostovoy, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Origin of electromagnon excitations in RMnO3,” Phys. Rev. Lett. 102, 047203 (2009).
[CrossRef] [PubMed]

A. B. Sushkov, R. Valdés Aguilar, S. Park, S.-W. Cheong, and H. D. Drew, “Electromagnons in multiferroic YMn2O5 and TbMn2O5,” Phys. Rev. Lett. 98, 027202 (2007).
[CrossRef] [PubMed]

R. Valdés Aguilar, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Colossal magnon-phonon coupling in multiferroic Eu0.75Y0.25MnO3,” Phys. Rev. B 76, 060404(R) (2007).
[CrossRef]

Watanabe, H.

T. Goto, Y. Yamasaki, H. Watanabe, T. Kimura, and Y. Tokura, “Anticorrelation between ferromagnetism and ferroelectricity in perovskite manganites,” Phys. Rev. B 72, 220403(R) (2005).
[CrossRef]

Yamasaki, Y.

N. Kida, Y. Yamasaki, J. P. He, Y. Kaneko, Y. Ikebe, Y. Takahashi, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation at THz frequencies in bc and ab spiral spin phases of perovskite manganites,” J. Phys. Conf. Ser. 148, 012038 (2009); Proc. LXIII Yamada Conf. Photo-induced Phase Transition and Cooperative Phenomena.
[CrossRef]

J. S. Lee, N. Kida, S. Miyahara, Y. Yamasaki, Y. Takahashi, R. Shimano, N. Furukawa, and Y. Tokura, “Systematics of electromagnons in the spiral spin-ordered states of RMnO3,” Phys. Rev. B 79, 18043(R) (2009).

N. Kida, Y. Yamasaki, R. Shimano, T. Arima, and Y. Tokura, “Electric-dipole active two-magnon excitation in ab spiral spin phase of a ferroelectric magnet Gd0.7Tb0.3MnO3,” J. Phys. Soc. Jpn. 77, 123704 (2008).
[CrossRef]

N. Kida, Y. Ikebe, Y. Takahashi, J. P. He, Y. Kaneko, Y. Yamasaki, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation in the ferroelectric magnet DyMnO3,” Phys. Rev. B 78, 104414 (2008).
[CrossRef]

Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, and Y. Tokura, “Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3,” Phys. Rev. Lett. 101, 187201 (2008).
[CrossRef] [PubMed]

Y. Yamasaki, H. Sagayama, N. Abe, T. Arima, K. Sasai, M. Matsuura, K. Hirota, D. Okuyama, Y. Noda, and Y. Tokura, “Cycloidal spin order in the a axis polarized ferroelectric phase of orthorhombic perovskite manganite,” Phys. Rev. Lett. 101, 097204 (2008).
[CrossRef] [PubMed]

Y. Yamasaki, H. Sagayama, T. Goto, M. Matsuura, K. Hirota, T. Arima, and Y. Tokura, “Electric control of spin helicity in a magnetic ferroelectric,” Phys. Rev. Lett. 98, 147204 (2007).
[CrossRef] [PubMed]

T. Goto, Y. Yamasaki, H. Watanabe, T. Kimura, and Y. Tokura, “Anticorrelation between ferromagnetism and ferroelectricity in perovskite manganites,” Phys. Rev. B 72, 220403(R) (2005).
[CrossRef]

T. Arima, T. Goto, Y. Yamasaki, S. Miyasaka, K. Ishii, M. Tsubota, T. Inami, Y. Murakami, and Y. Tokura, “Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric GdMnO3 and TbMnO3, compounds,” Phys. Rev. B 72, 100102(R) (2005).
[CrossRef]

Y. Takahashi, Y. Yamasaki, N. Kida, Y. Kaneko, T. Arima, R. Shimano, and Y. Tokura, “Comprehensive study on electromagnons and their coupling with optical phonons in Eu1−xYxMnO3 (x=0.1, 0.2, 0.3, 0.4, and 0.45),” submitted for publication (2009).

J. S. Lee, N. Kida, Y. Yamasaki, M. Mochizuki, R. Shimano, and Y. Tokura, “Lattice dynamics of multiferroic perovskite manganites,” manuscript in preparation.

Yoshizawa, H.

R. Kajimoto, H. Mochizuki, H. Yoshizawa, H. Shintani, T. Kimura, and Y. Tokura, “R-dependence of spin exchange interactions in RMnO3 (R=rare-earth ions),” J. Phys. Soc. Jpn. 74, 2430-2433 (2005).
[CrossRef]

Zhang, C. L.

R. Valdés Aguilar, M. Mostovoy, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Origin of electromagnon excitations in RMnO3,” Phys. Rev. Lett. 102, 047203 (2009).
[CrossRef] [PubMed]

R. Valdés Aguilar, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Colossal magnon-phonon coupling in multiferroic Eu0.75Y0.25MnO3,” Phys. Rev. B 76, 060404(R) (2007).
[CrossRef]

M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
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J. Strempfer, B. Bohnenbuck, M. Mostovoy, N. Aliouane, D. N. Argyriou, F. Schrettle, J. Hemberger, A. Krimmel, and M. v. Zimmermann, “Absence of commensurate ordering at the polarization flop transition in multiferroic DyMnO3,” Phys. Rev. B 75, 212402 (2007).
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N. Kida, Y. Yamasaki, J. P. He, Y. Kaneko, Y. Ikebe, Y. Takahashi, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation at THz frequencies in bc and ab spiral spin phases of perovskite manganites,” J. Phys. Conf. Ser. 148, 012038 (2009); Proc. LXIII Yamada Conf. Photo-induced Phase Transition and Cooperative Phenomena.
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N. Kida, Y. Yamasaki, R. Shimano, T. Arima, and Y. Tokura, “Electric-dipole active two-magnon excitation in ab spiral spin phase of a ferroelectric magnet Gd0.7Tb0.3MnO3,” J. Phys. Soc. Jpn. 77, 123704 (2008).
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R. Kajimoto, H. Mochizuki, H. Yoshizawa, H. Shintani, T. Kimura, and Y. Tokura, “R-dependence of spin exchange interactions in RMnO3 (R=rare-earth ions),” J. Phys. Soc. Jpn. 74, 2430-2433 (2005).
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Nat. Phys. (1)

A. Pimenov, A. A. Mukhin, V. Yu. Ivanov, V. D. Travkin, A. M. Balbashov, and A. Loidl, “Possible evidence for electromagnon in multiferroic manganites,” Nat. Phys. 2, 97-100 (2006).
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Nature (London) (3)

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Phys. Rev. B (15)

C. Jia, S. Onoda, N. Nagaosa, and J. H. Han, “Microscopic theory of spin-polarization coupling in multiferroics transition metal oxides,” Phys. Rev. B 76, 144424 (2007).
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T. Arima, Y. Tokura, and J. B. Torrance, “Variation of optical gap in perovskite-type 3d transition-metal oxides,” Phys. Rev. B 48, 17006-17009 (1993).
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T. Kimura, S. Ishihara, H. Shintani, T. Arima, K. T. Takahashi, K. Ishizaka, and Y. Tokura, “Distorted perovskite with eg1 configuration as a frusrated spin system,” Phys. Rev. B 68, 060403(R) (2003).
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T. Goto, Y. Yamasaki, H. Watanabe, T. Kimura, and Y. Tokura, “Anticorrelation between ferromagnetism and ferroelectricity in perovskite manganites,” Phys. Rev. B 72, 220403(R) (2005).
[CrossRef]

J. Strempfer, B. Bohnenbuck, M. Mostovoy, N. Aliouane, D. N. Argyriou, F. Schrettle, J. Hemberger, A. Krimmel, and M. v. Zimmermann, “Absence of commensurate ordering at the polarization flop transition in multiferroic DyMnO3,” Phys. Rev. B 75, 212402 (2007).
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T. Arima, T. Goto, Y. Yamasaki, S. Miyasaka, K. Ishii, M. Tsubota, T. Inami, Y. Murakami, and Y. Tokura, “Magnetic-field-induced transition in the lattice modulation of colossal magnetoelectric GdMnO3 and TbMnO3, compounds,” Phys. Rev. B 72, 100102(R) (2005).
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T. Kimura, G. Lawes, T. Goto, Y. Tokura, and A. P. Ramirez, “Magnetoelectric phase diagrams of orthorhombic RMnO3,” Phys. Rev. B 71, 224425 (2005).
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A. Pimenov, T. Rudolf, F. Mayr, A. Loidl, A. A. Mukhin, and A. M. Balbashov, “Coupling of phonons and electromagnons in GdMnO3,” Phys. Rev. B 74, 100403(R) (2006).
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R. Valdés Aguilar, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Colossal magnon-phonon coupling in multiferroic Eu0.75Y0.25MnO3,” Phys. Rev. B 76, 060404(R) (2007).
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A. Pimenov, A. Loidl, A. A. Mukhin, V. D. Travkin, V. Yu. Ivanov, and A. M. Balbashov, “Terahertz spectroscopy of electromagnons in Eu1−xYxMnO3,” Phys. Rev. B 77, 014438 (2008).
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N. Kida, Y. Ikebe, Y. Takahashi, J. P. He, Y. Kaneko, Y. Yamasaki, R. Shimano, T. Arima, N. Nagaosa, and Y. Tokura, “Electrically driven spin excitation in the ferroelectric magnet DyMnO3,” Phys. Rev. B 78, 104414 (2008).
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Phys. Rev. Lett. (15)

R. Valdés Aguilar, M. Mostovoy, A. B. Sushkov, C. L. Zhang, Y. J. Choi, S.-W. Cheong, and H. D. Drew, “Origin of electromagnon excitations in RMnO3,” Phys. Rev. Lett. 102, 047203 (2009).
[CrossRef] [PubMed]

Y. Takahashi, N. Kida, Y. Yamasaki, J. Fujioka, T. Arima, R. Shimano, S. Miyahara, M. Mochizuki, N. Furukawa, and Y. Tokura, “Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3,” Phys. Rev. Lett. 101, 187201 (2008).
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T. Goto, T. Kimura, G. Lawes, A. P. Ramirez, and Y. Tokura, “Ferroelectricity and giant magnetocapacitance in perovskite rare-earth manganites,” Phys. Rev. Lett. 92, 257201 (2004).
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M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, “Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3,” Phys. Rev. Lett. 95, 087206 (2005).
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Y. Yamasaki, H. Sagayama, T. Goto, M. Matsuura, K. Hirota, T. Arima, and Y. Tokura, “Electric control of spin helicity in a magnetic ferroelectric,” Phys. Rev. Lett. 98, 147204 (2007).
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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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Figures (15)

Fig. 1
Fig. 1

Temperature dependence of (a) dielectric constant ε at 10 kHz and (b) ferroelectric polarization P s of Tb Mn O 3 with each crystallographic axis in zero magnetic field [8].

Fig. 2
Fig. 2

(a) Magnetoelectric phase diagrams of R Mn O 3 with change of the Mn–O–Mn bond angle, as reproduced from [52, 53] (R represents rare-earth ions). The solid curves are merely the guide to the eyes. (b) Magnified view of (a), showing the emergence of the ferroelectric phases for R = Gd , Tb, and Dy. By changing the Mn–O–Mn bond angle, R Mn O 3 shows the large variations of the spin structures with temperature, including the A-type (layer-type) antiferromagnetic (AFM), collinear spin-ordered, b c and a b spiral spin-ordered, and E-type AFM phases. The schematic illustrations of these phases are shown in (c)–(g); Mn ions and their spins are highlighted by circles and arrows, respectively. e i j is the unit vector connecting adjacent spins, S i and S j . According to the spin-current mechanism, as formulated by Eq. (1), the ferroelectric polarization P s appears along the c and a axes in the b c and a b spiral spin-ordered phases, respectively.

Fig. 3
Fig. 3

Overall optical spectrum of Tb Mn O 3 , ranging from 2 meV to 10 eV , in the ferroelectric b c spiral spin-ordered phase, measured around 10 K . E ω was set parallel to the a axis. (a) Real Re [ ε μ ] and (b) imaginary Im [ ε μ ] parts of the ε μ spectrum up to 90 meV . The low-energy part of the Im [ ε μ ] spectrum below 21 meV is multiplied by 10. Inset shows the Im [ ε μ ] spectrum up to 10 eV , measured at 10 K . Below 10 meV , both Re [ ε μ ] and Im [ ε μ ] spectra were obtained by terahertz time-domain spectroscopy. Above 10 meV , we used the Fourier transform spectrometer ( 0.01 0.8 eV ) and the grating spectrometer ( 0.3 36 eV ) .

Fig. 4
Fig. 4

Low-energy electrodynamics of the spin excitation of (a) Gd Mn O 3 at 12 K , (b) Tb Mn O 3 at 12 K , and (c) Dy Mn O 3 at 9 K , for E ω a and H ω c . Upper and lower panels show the real Re [ ε μ ] and imaginary Im [ ε μ ] parts of the ε μ spectra, respectively. Around 10 K , the b c spiral spin-ordered phase is realized for Tb Mn O 3 and Dy Mn O 3 , while the A-type antiferromagnetic phase for Gd Mn O 3 .

Fig. 5
Fig. 5

Temperature dependence of (a) dielectric constant ε at 10 kHz and (b) ferroelectric polarization P s of Dy Mn O 3 with each crystallographic axis in zero magnetic field [7, 8]. The magnetic field ( b ) dependence of (c) dielectric constant along the a axis at 10 kHz and (d) P s ( P s c and P s a ).

Fig. 6
Fig. 6

Light-polarization dependence of the spin excitations in the b c spiral spin-ordered phase of Dy Mn O 3 , measured around 10 K , using a complete set of the crystal faces ( a c , a b , and b c ). The crystal orientations with respect to E ω and H ω are indicated in the figures. Upper and lower panels show the real Re [ ε μ ] and imaginary Im [ ε μ ] parts of the ε μ spectra (symbols), respectively. Im [ ε μ ] spectra shown in (d) are vertically offset for clarify. Note that the scales of the vertical axes in (a) and (b) are different in (c) and (d), respectively. The solid curves shown in (a) and (b) are results of a least-square fit to reproduce lower- and higher-lying peak structures by assuming two Lorentz oscillators for ε. On the other hand, the ε μ spectra shown in (c) and (d) can be reproduced by two Lorentz oscillators for ε and μ.

Fig. 7
Fig. 7

Temperature dependence of (a) real Re [ ε μ ] and (b) imaginary Im [ ε μ ] parts of the selected ε μ spectra of Dy Mn O 3 for E ω a and H ω c . The solid curves are results of a least-square fit to reproduce lower- and higher-lying peak structures in the b c spiral spin-ordered phase below 19 K by assuming two Lorentz oscillators for ε. The selected ε μ spectra of Dy Mn O 3 in the magnetic field applied along the b axis, measured at 7 K , are also included. Above 19 K , the data can be fitted by the single Lorentz oscillator.

Fig. 8
Fig. 8

Integrated spectral weight per Mn-site ( N eff ), as defined by Eq. (2) in the text, of the a c surface crystal plate of Dy Mn O 3 as a function of (a) temperature in zero magnetic field and (b) magnetic field at 7 K . N eff for E ω a and H ω a are represented by circles and squares, respectively. The solid curves are merely the guide to the eyes. Inset of (a) shows the magnified view below 45 K . For comparison, N eff for H ω a are multiplied by 40. The horizontal dashed line in the inset of (a), also multiplied by 40, represents the estimated contribution of the background absorption for E ω c to N eff for H ω a . The vertical solid lines in (a) and the inset of (a) indicate the ferroelectric transition temperature of 19 K and the Néel transition temperature of 42 K . In (b), the magnetic field of 20 kOe , at which the direction of the ferroelectric polarization is flopped from the c axis to the a axis or the spiral spin plane changes from b c to a b , is indicated by the vertical solid line.

Fig. 9
Fig. 9

(a) Thermally induced ferroelectricity in the a b spiral spin-ordered phase of Gd 0.7 Tb 0.3 Mn O 3 [53]. The ferroelectric polarization P s emerges along the a axis between 16 K and 24 K , accompanied by the change of the dielectric constant ε along the a axis at 10 kHz . The critical temperatures for A-type antiferromagnetic (AFM) order with the weak ferromagnetism along the c axis, a b spiral spin order, and collinear spin order, are 16 K , 24 K , and 42 K , respectively, as indicated by vertical lines. (b) Temperature dependence of the integrated spectral weight per Mn-site ( N eff ), as defined by Eq. (2) in the text, of the a c surface crystal plate of Gd 0.7 Tb 0.3 Mn O 3 . N eff for E ω a and H ω a are represented by circles and squares, respectively. For comparison, N eff for H ω a are multiplied by 10. The solid curves in (b) are merely the guide to the eyes.

Fig. 10
Fig. 10

Magnetoelectric phase diagrams of (a) Tb Mn O 3 and (b) Gd 0.7 Tb 0.3 Mn O 3 . Data indicated by closed circles are taken from [2, 8, 53] and the solid curves with shaded area are merely to guide the eyes. The b c spiral spin plane of Tb Mn O 3 , acting as a source of the ferroelectric polarization P s along the c axis, can be flopped to the a b spiral spin plane ( P s a ) by an application of the magnetic field H along the b axis. This magnetically induced a b spiral spin-ordered phase smoothly connects with the thermally induced a b spiral spin-ordered phase of Gd 0.7 Tb 0.3 Mn O 3 . The terahertz measurements in the paraelectric collinear spin-ordered phase, a b spiral spin-ordered phase, and A-type antiferromagnetic (AFM) phase of Gd 0.7 Tb 0.3 Mn O 3 were performed in zero H, as indicated by the right-side vertical arrow in (b).

Fig. 11
Fig. 11

Light-polarization dependence of the spin excitations in the a b spiral spin-ordered phase of Gd 0.7 Tb 0.3 Mn O 3 , measured around 17 K , using a complete set of the crystal faces ( a c , a b , and b c ). The crystal orientations with respect to E ω and H ω are indicated in the figures. Upper and lower panels show the real Re [ ε μ ] and imaginary Im [ ε μ ] parts of the ε μ spectra (symbols), respectively. Im [ ε μ ] spectra shown in (d) are vertically offset for clarify. Note that the scales of the vertical axes in (a) and (b) are different in (c) and (d), respectively. The solid curves shown in (a) and (b) are results of a least-square fit to reproduce lower- and higher-lying peak structures by assuming two Lorentz oscillators for ε. On the other hand, the ε μ spectra shown in (c) and (d) can be reproduced by two Lorentz oscillators for ε and μ.

Fig. 12
Fig. 12

Temperature dependence of the real Re [ ε μ ] (upper panels) and imaginary Im [ ε μ ] (lower panels) parts of the selected ε μ spectra of Gd 0.7 Tb 0.3 Mn O 3 for (a) E ω a and H ω c , (b) E ω c and H ω a , and (c) E ω b and H ω c . Im [ ε μ ] spectra shown in (b) and (c) are vertically offset for clarity. Note that the scale of the vertical axis in the upper panel of (a) is different from that of (b) and (c). The solid curves shown in (a) are results of a least-square fit to reproduce lower- and higher-lying peak structures by assuming two Lorentz oscillators for ε. The ε μ spectra shown in (b) and (c) can be reproduced by two Lorentz oscillators for ε and μ.

Fig. 13
Fig. 13

Heisenberg model for R Mn O 3 with nearest-neighbor ferromagnetic interactions J 1 ( < 0 ) , antiferromagnetic interactions for next-nearest-neighbor along the b axis J 2 ( > 0 ) , and interlayer interactions J c ( > 0 ) . The unit cell is written by dot-dashed lines, where four inequivalent spin sites exist due to the orthorhombic lattice distortions. Thin (blue) arrows describe the ground-state spin configuration for the b c cycloidal state.

Fig. 14
Fig. 14

Magnon dispersions along the b axis for Dy Mn O 3 , Tb Mn O 3 , and Gd 0.7 Tb 0.3 Mn O 3 . See Table 1 for the parameter values. q c represents the wavenumber along the c axis.

Fig. 15
Fig. 15

(a) Cycloidal spin structures, orbital ordering pattern on Mn sites, distortions of O sites, and direction of symmetric spin-dependent polarizations P e . The directions of P e , which are defined by an angle φ, are shown by thick (brown) arrows. Thin (blue) arrows describe the ground-state spin configuration for the a b cycloidal state. (b) For the case of E ω a polarization, the magnitudes of P e are modified, as shown on each bond due to spin structure modifications. Thin bold arrows are spin structures modulated by the electric fields, and dotted arrows are spin structures without electric fields. Thus oscillating electric field can induce the effective transverse staggered fields shown by shorter thin (red) arrows, which can act as a source of the electric-dipole active one-magnon resonance at zone boundary. (c) For the case of E ω b polarization, the phase of E ω P e is staggered, whereas spins along the a axis are uniform. In this case, the effective fields cancel out, and no one-magnon resonance occurs.

Tables (2)

Tables Icon

Table 1 Nearest-Neighbor Ferromagnetic Interaction J 1 , Next-Nearest-Neighbor Antiferromagnetic Interaction J 2 , and Interlayer Antiferromagnetic Interaction J c for Dy Mn O 3 , Tb Mn O 3 , and Gd 0.7 Tb 0.3 Mn O 3 [35, 37, 41]

Tables Icon

Table 2 Comparison of Observed Peak Positions (in a Unit of meV) for Electromagnons and AFMRs with Theoretical Estimations Based on the Heisenberg Model for Dy Mn O 3 , Tb Mn O 3 , and Gd 0.7 Tb 0.3 Mn O 3

Equations (13)

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P s e i j × ( S i × S j ) ,
N eff = 2 m 0 V π e 2 ω 1 ω 2 ω Im [ ε ( ω ) μ ( ω ) ] d ω ,
Im [ ε μ ] = Re [ ε ] Im [ μ ] + Im [ ε ] Re [ μ ] ,
H 0 = J 1 n . n . S i S j + J 2 n . n . n . S i S j + J c i . l . S i S j + D α i ( S i α ) 2 ,
S i + 1 2 S a i , S i 1 2 S a i , S i z S a i a i .
H 0 = q ω q α q α q + const .
ω q = 2 S A q 2 B q 2 ,
A q = 2 J 1 cos θ 2 J 1 cos 2 θ 2 cos π q a a cos π q b b J 2 cos 2 θ + J 2 cos 2 θ cos 2 π q b b + J c + D 4 ,
B q = 2 J 1 sin 2 θ 2 cos π q a a cos π q b b + J 2 sin 2 θ cos 2 π q b b + J c cos π q c c + D 4 ,
α q = c q a q + s q a q ,
α q = c q a q + s q a q ,
P e Π ( q z b ) ( α q z b α q z b ) ,
Im χ α α ( ω ) = N S 3 Π 2 cos 2 ϕ sin 2 θ × ( c q z b s q z b ) 2 δ ( ω ω z b ) δ α , a .

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