Abstract

An ultra-high vacuum compatible multipurpose chamber for magneto-optical reflection and transmission experiments with polarization analysis on magnetic systems is introduced. It is applicable in a broad photon energy range from the visible to the soft x-ray regime and for a wide angular range from grazing to normal incidence. It exploits a novel magnetization device based on rotating permanent magnets, which generates tuneable magnetic fields up to 570 mT in longitudinal, transverse and polar geometry. The unique combination of these features enables the feasibility of all typical magneto-optical spectroscopy techniques as T-MOKE, L-MOKE, P-MOKE, x-ray magneto optical linear dichroism, x-ray magnetic circular dichroism in reflection and Kerr polarization-spectroscopy, which is demonstrated for Co with focus on the Co 3p edges.

© 2013 Optical Society of America

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2012 (2)

D. Nolle, M. Weigand, P. Audehm, E. Goering, U. Wiesemann, C. Wolter, E. Nolle, and G. Schütz, “Note: unique characterization possibilities in the ultra high vacuum scanning transmission x-ray microscope (UHV-STXM) “MAXYMUS” using a rotatable permanent magnetic field up to 0.22 T,” Rev. Sci. Instrum. 83, 046112 (2012).
[CrossRef]

M. Gilbert, H.-Ch. Mertins, M. Tesch, O. Berges, H. Feilbach, and C. M. Schneider, “TetraMag: a compact magnetizing device based on eight rotating permanent magnets,” Rev. Sci. Instrum. 83, 025109 (2012).
[CrossRef]

2011 (1)

M. C. Biesinger, B. P. Payne, A. P. Grosvenor, L. W. M. Lau, A. R. Gerson, and R. St. C. Smart, “Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Cr, Mn, Fe, Co and Ni,” Appl. Surf. Sci. 257, 2717–2730 (2011).
[CrossRef]

2010 (3)

J. Yang, H. Liu, W. N. Martens, and R. L. Frost, “Synthesis and characterization of cobalt hydroxide, cobalt oxyhydroxide, and cobalt oxide nanodiscs,” J. Phys. Chem. C 114, 111–119 (2010).
[CrossRef]

R. Bjørk, C. R. H. Bahl, A. Smith, and N. Pryds, “Comparison of adjustable permanent magnetic field sources,” J. Magn. Magn. Mater. 322, 3664–3671 (2010).
[CrossRef]

S. Valencia, A. Kleibert, A. Gaupp, J. Rusz, D. Legut, J. Bansmann, W. Gudat, and P. M. Oppeneer, “Quadratic x-ray magneto-optical effect upon reflection in a near- normal-incidence configuration at the M edges of 3d-transition metals,” Phys. Rev. Lett. 104, 187401 (2010).
[CrossRef]

2009 (1)

2007 (2)

U. Berges, S. Döring, and C. Westphal, “TGM-Beamline at DELTA,” AIP Conf. Proc. 879, 583–586 (2007).
[CrossRef]

U. Berges, S. Döring, and C. Westphal, “PGM-Beamline at the Undulator U55 at DELTA,” AIP Conf. Proc. 879, 519–522 (2007).
[CrossRef]

2006 (1)

S. Valencia, A. Gaupp, W. Gudat, H.-Ch. Mertins, P. M. Oppeneer, D. Abramsohn, and C. M. Schneider, “Faraday rotation spectra at shallow core levels: 3p edges of Fe, Co, and Ni,” New J. Phys. 8, 254 (2006).
[CrossRef]

2005 (3)

M. Hecker, P. M. Oppeneer, S. Valencia, H.-Ch. Mertins, and C. M. Schneider, “Soft x-ray magnetic reflection spectroscopy at the 3p absorption edges of thin Fe films,” J. Electron Spectrosc. Relat. Phenom. 144, 881–884 (2005).
[CrossRef]

E. Arenholz and S. O. Prestemon, “Design and performance of an eight-pole resistive magnet for soft x-ray magnetic dichroism measurements,” Rev. Sci. Instrum. 76, 083908 (2005).
[CrossRef]

H.-Ch. Mertins, S. Valencia, A. Gaupp, W. Gudat, P. M. Oppeneer, and C. M. Schneider, “Magneto-optical polarization spectroscopy with soft x-rays,” Appl. Phys. A 80, 1011–1020 (2005).
[CrossRef]

2004 (3)

H.-Ch. Mertins, S. Valencia, D. Abramsohn, A. Gaupp, W. Gudat, and P. M. Oppeneer, “X-ray Kerr rotation and ellipticity spectra at the 2p edges of Fe, Co, and Ni,” Phys. Rev. B 69, 064407 (2004).
[CrossRef]

S. Valencia, H.-Ch. Mertins, D. Abramsohn, A. Gaupp, W. Gudat, and P. M. Oppeneer, “Interference effects in the x-ray Kerr rotation spectrum at the Fe 2p edge,” Physica B 345, 189–192 (2004).
[CrossRef]

N. Jaouen, J.-M. Tonnerre, G. Kapoujian, P. Taunier, J.-P. Roux, D. Raoux, and F. Sirotti, “An apparatus for temperature-dependent soft x-ray resonant magnetic scattering,” J. Synchrotron Radiat. 11, 353–357 (2004).
[CrossRef]

2003 (2)

P. M. Oppeneer, H.-Ch. Mertins, D. Abramsohn, A. Gaupp, W. Gudat, J. Kunes, and C. M. Schneider, “Buried antiferromagnetic films investigated by x-ray magneto-optical reflection spectroscopy,” Phys. Rev. B 67, 052401 (2003).
[CrossRef]

K. Godehusen, H.-Ch. Mertins, T. Richter, P. Zimmermann, and M. Martins, “Electron-correlation effects in the angular distribution of photoelectrons from Kr investigated by rotating the polarization axis of undulator radiation,” Phys. Rev. A 68, 012711 (2003).
[CrossRef]

2002 (4)

J. M. D. Coey, “Permanent magnet applications,” J. Magn. Magn. Mater. 248, 441–456 (2002).
[CrossRef]

H.-Ch. Mertins, D. Abramsohn, A. Gaupp, F. Schäfers, W. Gudat, O. Zaharko, H. Grimmer, and P. M. Oppeneer, “Resonant magnetic reflection coefficients at the Fe 2p edge obtained with linearly and circularly polarized soft X rays,” Phys. Rev. B 66, 184404 (2002).
[CrossRef]

W. Kuch, X. Gao, and J. Kirschner, “Competition between in-plane and out-of-plane magnetization in exchange-coupled magnetic films,” Phys. Rev. B 65, 064406 (2002).
[CrossRef]

H. Höchst, D. Rioux, D. Zhao, and D. L. Huber, “Directional magnetization effects in magnetic circular dichroism spectra of Fe,” Phys. Rev. B 65, 064439 (2002).
[CrossRef]

2001 (8)

J. Geissler, E. Goering, M. Justen, F. Weigand, G. Schütz, J. Langer, D. Schmitz, H. Maletta, and R. Mattheis, “Pt magnetization profile in a Pt/Co bilayer studied by resonant magnetic x-ray reflectometry,” Phys. Rev. B 65, 020405(R) (2001).
[CrossRef]

S. S. Dhesi, G. van der Laan, E. Dudzik, and A. B. Shick, “Anisotropic spin–orbit coupling and magnetocrystalline anisotropy in vicinal co films,” Phys. Rev. Lett. 87, 067201 (2001).
[CrossRef]

S. A. Wolf, D. D. Awshalom, R. A. Buhrmann, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488–1495 (2001).
[CrossRef]

J. Kunes, P. M. Oppeneer, H.-Ch. Mertins, F. Schäfers, A. Gaupp, W. Gudat, and P. Novák, “X-ray Faraday effect at the L2,3 edges of Fe, Co, and Ni: theory and experiment,” Phys. Rev. B 64, 174417 (2001).
[CrossRef]

K. Starke, F. Heigl, A. Vollmer, M. Weiss, G. Reichardt, and G. Kaindl, “X-ray magneto-optics in lanthanides,” Phys. Rev. Lett. 86, 3415–3418 (2001).
[CrossRef]

H.-Ch. Mertins, P. M. Oppeneer, J. Kunes, A. Gaupp, D. Abramsohn, and F. Schäfers, “Observation of the x-ray magneto-optical Voigt effect,” Phys. Rev. Lett. 87, 047401 (2001).
[CrossRef]

M. R. Weiss, R. Follath, K. J. S. Sahwney, F. Senf, J. Bahrdt, W. Frentrup, A. Gaupp, S. Sasaki, M. Scheer, H.-Ch. Mertins, D. Abramsohn, F. Schäfers, W. Kuch, and W. Mahler, “The elliptically polarized undulator beamlines at BESSY II,” Nucl. Instrum. Methods Phys. Res. A 467–468, 449–452 (2001).
[CrossRef]

J. Bardt, W. Frentrup, A. Gaupp, M. Scheer, W. Gudat, G. Ingold, and S. Sasaki, “Elliptically polarizing insertion devices at BESSY II,” Nucl. Instrum. Methods Phys. Res. A 467–468, 21–29 (2001).
[CrossRef]

2000 (2)

H.-Ch. Mertins, F. Schäfers, X. Le Cann, A. Gaupp, and W. Gudat, “Faraday rotation at the 2p edges of Fe, Co, and Ni,” Phys. Rev. B 61, R874–R877 (2000).
[CrossRef]

F. Nolting, A. Scholl, J. Stöhr, J. W. Seo, J. Fompeyrine, H. Siegwart, J.-P. Locquet, S. Anders, J. Lüning, E. E. Fullerton, M. F. Toney, M. R. Scheinfein, and H. A. Padmore, “Direct observation of the alignment of ferromagnetic spins by antiferromagnetic spins,” Nature 405, 767–769 (2000).
[CrossRef]

1999 (6)

H. A. Dürr, E. Dudzik, S. S. Dhesi, J. B. Goedkoop, G. van der Laan, M. Belakhovsky, C. Moduta, A. Marty, and Y. Samson, “Chiral magnetic domain structures in ultrathin FePd films,” Science 284, 2166–2168 (1999).
[CrossRef]

P. Fischer, T. Eimüller, G. Schütz, G. Schmahl, P. Guttmann, and G. Bayreuther, “Magnetic domain imaging with a transmission x-ray microscope,” J. Magn. Magn. Mater. 198–199, 624–627 (1999).
[CrossRef]

J. B. Kortright, D. D. Awschalom, J. Stöhr, S. D. Bader, Y. U. Idzerda, S. S. P. Parkin, I. K. Schuller, and H.-C. Siegmann, “Research frontiers in magnetic materials at soft x-ray synchrotron radiation facilities,” J. Magn. Magn. Mater. 207, 7–44 (1999).
[CrossRef]

J. Nouges and I. K. Schuller, “Exchange bias,” J. Magn. Magn. Mater. 192, 203–232 (1999).
[CrossRef]

F. Schäfers, H.-Ch. Mertins, A. Gaupp, W. Gudat, M. Mertin, I. Packe, F. Schmolla, S. di Fonzo, G. Soullié, W. Jark, R. Walker, X. Le Cann, R. Nyholm, and M. Eriksson, “Soft-x-ray polarimeter with multilayer optics: complete analysis of the polarization state of light,” Appl. Opt. 38, 4074–4088 (1999).
[CrossRef]

M. A. Langell, M. D. Anderson, G. A. Carson, L. Peng, and S. Smith, “Valence-band electronic structure of Co3O4 epitaxy on CoO(100),” Phys. Rev. B 59, 4791–4798 (1999).
[CrossRef]

1998 (2)

G. A. Prinz, “Magnetoelectronics,” Science 282, 1660–1663 (1998).
[CrossRef]

M. Sacchi and A. Mirone, “Resonant reflectivity from a Ni(110) crystal: magnetic effects at the Ni 2p edges using linearly and circularly polarized photons,” Phys. Rev. B 57, 8408–8415 (1998).
[CrossRef]

1997 (2)

H. Höchst, D. Rioux, D. Zhao, and D. L. Huber, “Magnetic linear dichroism effects in reflection spectroscopy: a case study at the Fe M2,3 edge,” J. Appl. Phys. 81, 7584–7588 (1997).
[CrossRef]

S. Uba, L. Uba, A. Y. Perlov, A. N. Yaresko, V. N. Antonov, and R. Gontarz, “Experimental and ab initio theoretical study of optical and magneto-optical properties of Co/Cu multilayers,” J. Phys. 9, 447–460 (1997).

1996 (3)

M. Takahashi and J.-I. Igarashi, “Local approach to electronic excitations in MnO, FeO, CoO, and NiO,” Phys. Rev. B 54, 13566–13574 (1996).
[CrossRef]

H. Höchst, D. Zhao, and D. L. Huber, “Strong angular effects in reflection MCD measurements of M2,3 transitions utilizing a newly developed quadruple reflection polarizer,” J. Electron Spectrosc. Relat. Phenom. 80, 469–472 (1996).
[CrossRef]

P. Steiner, R. Zimmermann, F. Reinert, T. Engel, and S. Hüfner, “3s- and 3p-core level excitations in 3d-transition metal oxides from electron-energy-loss spectroscopy,” Z. Phys. B 99, 479–490 (1996).
[CrossRef]

1995 (2)

C. T. Chen, Y. U. Idzerda, H.-J. Lin, N. V. Smith, G. Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and F. Sette, “Experimental confirmation of the x-ray magnetic circular dichroism sum rules for iron and cobalt,” Phys. Rev. Lett. 75, 152–155 (1995).
[CrossRef]

J. B. Kortright, M. Rice, and R. Carr, “Soft-x-ray Faraday rotation at Fe L2,3 edges,” Phys. Rev. B 51, 10240–10243 (1995).
[CrossRef]

1994 (2)

O. Cugat, P. Hansson, and J. M. D. Coey, “Permanent magnet variable flux sources,” IEEE Trans. Magn. 30, 4602–4604 (1994).
[CrossRef]

S. Uba, L. Uba, and R. Gontarz, “Magnetooptical Kerr spectroscopy of Co/Pd layered structures,” IEEE Trans. Magn. 30, 806–808 (1994).
[CrossRef]

1993 (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54, 181–342 (1993), http://henke.lbl.gov/optical_constants/ .
[CrossRef]

1990 (1)

Z.-X. Shen, J. W. Allen, P. A. P. Lindberg, D. S. Dessau, B. O. Wells, A. Borg, W. Ellis, J. S. Kang, S.-J. Oh, I. Lindau, and W. E. Spicer, “Photoemission study of CoO,” Phys. Rev. B 42, 1817–1828 (1990).
[CrossRef]

1989 (2)

C. A. Strydom and H. J. Strydom, “X-ray photoelectron spectroscopy studies of some cobalt(II) nitrate complexes,” Inorganica Chimica Acta 159, 191–195 (1989).
[CrossRef]

A. Gaupp and M. Mast, “First experimental experience with a VUV polarimeter at BESSY,” Rev. Sci. Instrum. 60, 2213–2215 (1989).
[CrossRef]

1987 (2)

J. M. McKay, M. H. Mohamed, and V. E. Heinrich, “Localized 3p excitations in 3d transition- metal-series spectroscopy,” Phys. Rev. B 35, 4304–4309 (1987).
[CrossRef]

J. B. Kortright and A. Fischer-Colbrie, “Standing wave enhanced scattering in multilayer structures,” J. Appl. Phys. 61, 1130–1333 (1987).
[CrossRef]

1985 (1)

M. Fanfoni, S. Modesi, N. Motta, M. de Crescenzi, and R. Rosei, “Comparison between extended x-ray-absorption and extended electron energy-loss fine-structure results above the M2,3 edge of cobalt,” Phys. Rev. B 32, 7826–7829 (1985).
[CrossRef]

1969 (1)

B. Sonntag, R. Haensel, and C. Kunz, “Optical absorption measurements of the transition metals Ti, V, Cr, Mn, Fe, Co, Ni in the region of 3p electron transitions,” Solid State Commun. 7, 597–599 (1969).

1968 (1)

M. J. Freiser, “A survey of magnetooptic effects,” IEEE Trans. Magn. 4, 152–161 (1968).
[CrossRef]

1964 (2)

W. L. Roth, “The magnetic structure of Co3O4,” J. Phys. Chem. Solids 25, 1–10 (1964).
[CrossRef]

J. M. Ballantyne, “Kerr magneto-optic effect in thin cobalt films,” J. Opt. Soc. Am. 54, 1352 (1964).
[CrossRef]

1958 (1)

W. L. Roth, “Magnetic structures of MnO, FeO, CoO, and NiO,” Phys. Rev. 110, 1333–1341 (1958).
[CrossRef]

Abramsohn, D.

S. Valencia, A. Gaupp, W. Gudat, H.-Ch. Mertins, P. M. Oppeneer, D. Abramsohn, and C. M. Schneider, “Faraday rotation spectra at shallow core levels: 3p edges of Fe, Co, and Ni,” New J. Phys. 8, 254 (2006).
[CrossRef]

H.-Ch. Mertins, S. Valencia, D. Abramsohn, A. Gaupp, W. Gudat, and P. M. Oppeneer, “X-ray Kerr rotation and ellipticity spectra at the 2p edges of Fe, Co, and Ni,” Phys. Rev. B 69, 064407 (2004).
[CrossRef]

S. Valencia, H.-Ch. Mertins, D. Abramsohn, A. Gaupp, W. Gudat, and P. M. Oppeneer, “Interference effects in the x-ray Kerr rotation spectrum at the Fe 2p edge,” Physica B 345, 189–192 (2004).
[CrossRef]

P. M. Oppeneer, H.-Ch. Mertins, D. Abramsohn, A. Gaupp, W. Gudat, J. Kunes, and C. M. Schneider, “Buried antiferromagnetic films investigated by x-ray magneto-optical reflection spectroscopy,” Phys. Rev. B 67, 052401 (2003).
[CrossRef]

H.-Ch. Mertins, D. Abramsohn, A. Gaupp, F. Schäfers, W. Gudat, O. Zaharko, H. Grimmer, and P. M. Oppeneer, “Resonant magnetic reflection coefficients at the Fe 2p edge obtained with linearly and circularly polarized soft X rays,” Phys. Rev. B 66, 184404 (2002).
[CrossRef]

H.-Ch. Mertins, P. M. Oppeneer, J. Kunes, A. Gaupp, D. Abramsohn, and F. Schäfers, “Observation of the x-ray magneto-optical Voigt effect,” Phys. Rev. Lett. 87, 047401 (2001).
[CrossRef]

M. R. Weiss, R. Follath, K. J. S. Sahwney, F. Senf, J. Bahrdt, W. Frentrup, A. Gaupp, S. Sasaki, M. Scheer, H.-Ch. Mertins, D. Abramsohn, F. Schäfers, W. Kuch, and W. Mahler, “The elliptically polarized undulator beamlines at BESSY II,” Nucl. Instrum. Methods Phys. Res. A 467–468, 449–452 (2001).
[CrossRef]

Allen, J. W.

Z.-X. Shen, J. W. Allen, P. A. P. Lindberg, D. S. Dessau, B. O. Wells, A. Borg, W. Ellis, J. S. Kang, S.-J. Oh, I. Lindau, and W. E. Spicer, “Photoemission study of CoO,” Phys. Rev. B 42, 1817–1828 (1990).
[CrossRef]

Anders, S.

F. Nolting, A. Scholl, J. Stöhr, J. W. Seo, J. Fompeyrine, H. Siegwart, J.-P. Locquet, S. Anders, J. Lüning, E. E. Fullerton, M. F. Toney, M. R. Scheinfein, and H. A. Padmore, “Direct observation of the alignment of ferromagnetic spins by antiferromagnetic spins,” Nature 405, 767–769 (2000).
[CrossRef]

Anderson, M. D.

M. A. Langell, M. D. Anderson, G. A. Carson, L. Peng, and S. Smith, “Valence-band electronic structure of Co3O4 epitaxy on CoO(100),” Phys. Rev. B 59, 4791–4798 (1999).
[CrossRef]

Antonov, V. N.

S. Uba, L. Uba, A. Y. Perlov, A. N. Yaresko, V. N. Antonov, and R. Gontarz, “Experimental and ab initio theoretical study of optical and magneto-optical properties of Co/Cu multilayers,” J. Phys. 9, 447–460 (1997).

Arenholz, E.

E. Arenholz and S. O. Prestemon, “Design and performance of an eight-pole resistive magnet for soft x-ray magnetic dichroism measurements,” Rev. Sci. Instrum. 76, 083908 (2005).
[CrossRef]

Audehm, P.

D. Nolle, M. Weigand, P. Audehm, E. Goering, U. Wiesemann, C. Wolter, E. Nolle, and G. Schütz, “Note: unique characterization possibilities in the ultra high vacuum scanning transmission x-ray microscope (UHV-STXM) “MAXYMUS” using a rotatable permanent magnetic field up to 0.22 T,” Rev. Sci. Instrum. 83, 046112 (2012).
[CrossRef]

Awschalom, D. D.

J. B. Kortright, D. D. Awschalom, J. Stöhr, S. D. Bader, Y. U. Idzerda, S. S. P. Parkin, I. K. Schuller, and H.-C. Siegmann, “Research frontiers in magnetic materials at soft x-ray synchrotron radiation facilities,” J. Magn. Magn. Mater. 207, 7–44 (1999).
[CrossRef]

Awshalom, D. D.

S. A. Wolf, D. D. Awshalom, R. A. Buhrmann, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488–1495 (2001).
[CrossRef]

Bader, S. D.

J. B. Kortright, D. D. Awschalom, J. Stöhr, S. D. Bader, Y. U. Idzerda, S. S. P. Parkin, I. K. Schuller, and H.-C. Siegmann, “Research frontiers in magnetic materials at soft x-ray synchrotron radiation facilities,” J. Magn. Magn. Mater. 207, 7–44 (1999).
[CrossRef]

Bahl, C. R. H.

R. Bjørk, C. R. H. Bahl, A. Smith, and N. Pryds, “Comparison of adjustable permanent magnetic field sources,” J. Magn. Magn. Mater. 322, 3664–3671 (2010).
[CrossRef]

Bahrdt, J.

M. R. Weiss, R. Follath, K. J. S. Sahwney, F. Senf, J. Bahrdt, W. Frentrup, A. Gaupp, S. Sasaki, M. Scheer, H.-Ch. Mertins, D. Abramsohn, F. Schäfers, W. Kuch, and W. Mahler, “The elliptically polarized undulator beamlines at BESSY II,” Nucl. Instrum. Methods Phys. Res. A 467–468, 449–452 (2001).
[CrossRef]

Ballantyne, J. M.

Bansmann, J.

S. Valencia, A. Kleibert, A. Gaupp, J. Rusz, D. Legut, J. Bansmann, W. Gudat, and P. M. Oppeneer, “Quadratic x-ray magneto-optical effect upon reflection in a near- normal-incidence configuration at the M edges of 3d-transition metals,” Phys. Rev. Lett. 104, 187401 (2010).
[CrossRef]

Bardt, J.

J. Bardt, W. Frentrup, A. Gaupp, M. Scheer, W. Gudat, G. Ingold, and S. Sasaki, “Elliptically polarizing insertion devices at BESSY II,” Nucl. Instrum. Methods Phys. Res. A 467–468, 21–29 (2001).
[CrossRef]

Bayreuther, G.

P. Fischer, T. Eimüller, G. Schütz, G. Schmahl, P. Guttmann, and G. Bayreuther, “Magnetic domain imaging with a transmission x-ray microscope,” J. Magn. Magn. Mater. 198–199, 624–627 (1999).
[CrossRef]

Belakhovsky, M.

H. A. Dürr, E. Dudzik, S. S. Dhesi, J. B. Goedkoop, G. van der Laan, M. Belakhovsky, C. Moduta, A. Marty, and Y. Samson, “Chiral magnetic domain structures in ultrathin FePd films,” Science 284, 2166–2168 (1999).
[CrossRef]

Berges, O.

M. Gilbert, H.-Ch. Mertins, M. Tesch, O. Berges, H. Feilbach, and C. M. Schneider, “TetraMag: a compact magnetizing device based on eight rotating permanent magnets,” Rev. Sci. Instrum. 83, 025109 (2012).
[CrossRef]

Berges, U.

U. Berges, S. Döring, and C. Westphal, “TGM-Beamline at DELTA,” AIP Conf. Proc. 879, 583–586 (2007).
[CrossRef]

U. Berges, S. Döring, and C. Westphal, “PGM-Beamline at the Undulator U55 at DELTA,” AIP Conf. Proc. 879, 519–522 (2007).
[CrossRef]

Biesinger, M. C.

M. C. Biesinger, B. P. Payne, A. P. Grosvenor, L. W. M. Lau, A. R. Gerson, and R. St. C. Smart, “Resolving surface chemical states in XPS analysis of first row transition metals, oxides and hydroxides: Cr, Mn, Fe, Co and Ni,” Appl. Surf. Sci. 257, 2717–2730 (2011).
[CrossRef]

Bjørk, R.

R. Bjørk, C. R. H. Bahl, A. Smith, and N. Pryds, “Comparison of adjustable permanent magnetic field sources,” J. Magn. Magn. Mater. 322, 3664–3671 (2010).
[CrossRef]

Borg, A.

Z.-X. Shen, J. W. Allen, P. A. P. Lindberg, D. S. Dessau, B. O. Wells, A. Borg, W. Ellis, J. S. Kang, S.-J. Oh, I. Lindau, and W. E. Spicer, “Photoemission study of CoO,” Phys. Rev. B 42, 1817–1828 (1990).
[CrossRef]

Born, M.

M. Born and E. Wolf, in Principles of Optics, (Pergamon, Oxford, 1980) pp. 1–139.

Buhrmann, R. A.

S. A. Wolf, D. D. Awshalom, R. A. Buhrmann, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488–1495 (2001).
[CrossRef]

Buschow, K. H. J.

K. H. J. Buschow, in Handbook of Magnetic Materials Vol. 19 (North-Holland, Amsterdam, 2011) pp. 1–283.

Carr, R.

J. B. Kortright, M. Rice, and R. Carr, “Soft-x-ray Faraday rotation at Fe L2,3 edges,” Phys. Rev. B 51, 10240–10243 (1995).
[CrossRef]

Carson, G. A.

M. A. Langell, M. D. Anderson, G. A. Carson, L. Peng, and S. Smith, “Valence-band electronic structure of Co3O4 epitaxy on CoO(100),” Phys. Rev. B 59, 4791–4798 (1999).
[CrossRef]

Chaban, E.

C. T. Chen, Y. U. Idzerda, H.-J. Lin, N. V. Smith, G. Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and F. Sette, “Experimental confirmation of the x-ray magnetic circular dichroism sum rules for iron and cobalt,” Phys. Rev. Lett. 75, 152–155 (1995).
[CrossRef]

Chen, C. T.

C. T. Chen, Y. U. Idzerda, H.-J. Lin, N. V. Smith, G. Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and F. Sette, “Experimental confirmation of the x-ray magnetic circular dichroism sum rules for iron and cobalt,” Phys. Rev. Lett. 75, 152–155 (1995).
[CrossRef]

Chtchelkanova, A. Y.

S. A. Wolf, D. D. Awshalom, R. A. Buhrmann, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488–1495 (2001).
[CrossRef]

Coey, J. M. D.

J. M. D. Coey, “Permanent magnet applications,” J. Magn. Magn. Mater. 248, 441–456 (2002).
[CrossRef]

O. Cugat, P. Hansson, and J. M. D. Coey, “Permanent magnet variable flux sources,” IEEE Trans. Magn. 30, 4602–4604 (1994).
[CrossRef]

Crist, B. V.

B. V. Crist, in Handbook of Monochromatic XPS Spectra, Vol. 2Commercially Pure Binary Oxides (XPS International Inc., 1999), p. 72.

Cugat, O.

O. Cugat, P. Hansson, and J. M. D. Coey, “Permanent magnet variable flux sources,” IEEE Trans. Magn. 30, 4602–4604 (1994).
[CrossRef]

Daughton, J. M.

S. A. Wolf, D. D. Awshalom, R. A. Buhrmann, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, “Spintronics: a spin-based electronics vision for the future,” Science 294, 1488–1495 (2001).
[CrossRef]

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54, 181–342 (1993), http://henke.lbl.gov/optical_constants/ .
[CrossRef]

de Crescenzi, M.

M. Fanfoni, S. Modesi, N. Motta, M. de Crescenzi, and R. Rosei, “Comparison between extended x-ray-absorption and extended electron energy-loss fine-structure results above the M2,3 edge of cobalt,” Phys. Rev. B 32, 7826–7829 (1985).
[CrossRef]

Dessau, D. S.

Z.-X. Shen, J. W. Allen, P. A. P. Lindberg, D. S. Dessau, B. O. Wells, A. Borg, W. Ellis, J. S. Kang, S.-J. Oh, I. Lindau, and W. E. Spicer, “Photoemission study of CoO,” Phys. Rev. B 42, 1817–1828 (1990).
[CrossRef]

Dhesi, S. S.

S. S. Dhesi, G. van der Laan, E. Dudzik, and A. B. Shick, “Anisotropic spin–orbit coupling and magnetocrystalline anisotropy in vicinal co films,” Phys. Rev. Lett. 87, 067201 (2001).
[CrossRef]

H. A. Dürr, E. Dudzik, S. S. Dhesi, J. B. Goedkoop, G. van der Laan, M. Belakhovsky, C. Moduta, A. Marty, and Y. Samson, “Chiral magnetic domain structures in ultrathin FePd films,” Science 284, 2166–2168 (1999).
[CrossRef]

di Fonzo, S.

Döring, S.

U. Berges, S. Döring, and C. Westphal, “PGM-Beamline at the Undulator U55 at DELTA,” AIP Conf. Proc. 879, 519–522 (2007).
[CrossRef]

U. Berges, S. Döring, and C. Westphal, “TGM-Beamline at DELTA,” AIP Conf. Proc. 879, 583–586 (2007).
[CrossRef]

Dudzik, E.

S. S. Dhesi, G. van der Laan, E. Dudzik, and A. B. Shick, “Anisotropic spin–orbit coupling and magnetocrystalline anisotropy in vicinal co films,” Phys. Rev. Lett. 87, 067201 (2001).
[CrossRef]

H. A. Dürr, E. Dudzik, S. S. Dhesi, J. B. Goedkoop, G. van der Laan, M. Belakhovsky, C. Moduta, A. Marty, and Y. Samson, “Chiral magnetic domain structures in ultrathin FePd films,” Science 284, 2166–2168 (1999).
[CrossRef]

Dürr, H. A.

H. A. Dürr, E. Dudzik, S. S. Dhesi, J. B. Goedkoop, G. van der Laan, M. Belakhovsky, C. Moduta, A. Marty, and Y. Samson, “Chiral magnetic domain structures in ultrathin FePd films,” Science 284, 2166–2168 (1999).
[CrossRef]

Eimüller, T.

P. Fischer, T. Eimüller, G. Schütz, G. Schmahl, P. Guttmann, and G. Bayreuther, “Magnetic domain imaging with a transmission x-ray microscope,” J. Magn. Magn. Mater. 198–199, 624–627 (1999).
[CrossRef]

Ellis, W.

Z.-X. Shen, J. W. Allen, P. A. P. Lindberg, D. S. Dessau, B. O. Wells, A. Borg, W. Ellis, J. S. Kang, S.-J. Oh, I. Lindau, and W. E. Spicer, “Photoemission study of CoO,” Phys. Rev. B 42, 1817–1828 (1990).
[CrossRef]

Engel, T.

P. Steiner, R. Zimmermann, F. Reinert, T. Engel, and S. Hüfner, “3s- and 3p-core level excitations in 3d-transition metal oxides from electron-energy-loss spectroscopy,” Z. Phys. B 99, 479–490 (1996).
[CrossRef]

Eriksson, M.

Fanfoni, M.

M. Fanfoni, S. Modesi, N. Motta, M. de Crescenzi, and R. Rosei, “Comparison between extended x-ray-absorption and extended electron energy-loss fine-structure results above the M2,3 edge of cobalt,” Phys. Rev. B 32, 7826–7829 (1985).
[CrossRef]

Feilbach, H.

M. Gilbert, H.-Ch. Mertins, M. Tesch, O. Berges, H. Feilbach, and C. M. Schneider, “TetraMag: a compact magnetizing device based on eight rotating permanent magnets,” Rev. Sci. Instrum. 83, 025109 (2012).
[CrossRef]

Fischer, P.

P. Fischer, T. Eimüller, G. Schütz, G. Schmahl, P. Guttmann, and G. Bayreuther, “Magnetic domain imaging with a transmission x-ray microscope,” J. Magn. Magn. Mater. 198–199, 624–627 (1999).
[CrossRef]

Fischer-Colbrie, A.

J. B. Kortright and A. Fischer-Colbrie, “Standing wave enhanced scattering in multilayer structures,” J. Appl. Phys. 61, 1130–1333 (1987).
[CrossRef]

Follath, R.

M. R. Weiss, R. Follath, K. J. S. Sahwney, F. Senf, J. Bahrdt, W. Frentrup, A. Gaupp, S. Sasaki, M. Scheer, H.-Ch. Mertins, D. Abramsohn, F. Schäfers, W. Kuch, and W. Mahler, “The elliptically polarized undulator beamlines at BESSY II,” Nucl. Instrum. Methods Phys. Res. A 467–468, 449–452 (2001).
[CrossRef]

Fompeyrine, J.

F. Nolting, A. Scholl, J. Stöhr, J. W. Seo, J. Fompeyrine, H. Siegwart, J.-P. Locquet, S. Anders, J. Lüning, E. E. Fullerton, M. F. Toney, M. R. Scheinfein, and H. A. Padmore, “Direct observation of the alignment of ferromagnetic spins by antiferromagnetic spins,” Nature 405, 767–769 (2000).
[CrossRef]

Freiser, M. J.

M. J. Freiser, “A survey of magnetooptic effects,” IEEE Trans. Magn. 4, 152–161 (1968).
[CrossRef]

Frentrup, W.

J. Bardt, W. Frentrup, A. Gaupp, M. Scheer, W. Gudat, G. Ingold, and S. Sasaki, “Elliptically polarizing insertion devices at BESSY II,” Nucl. Instrum. Methods Phys. Res. A 467–468, 21–29 (2001).
[CrossRef]

M. R. Weiss, R. Follath, K. J. S. Sahwney, F. Senf, J. Bahrdt, W. Frentrup, A. Gaupp, S. Sasaki, M. Scheer, H.-Ch. Mertins, D. Abramsohn, F. Schäfers, W. Kuch, and W. Mahler, “The elliptically polarized undulator beamlines at BESSY II,” Nucl. Instrum. Methods Phys. Res. A 467–468, 449–452 (2001).
[CrossRef]

Frost, R. L.

J. Yang, H. Liu, W. N. Martens, and R. L. Frost, “Synthesis and characterization of cobalt hydroxide, cobalt oxyhydroxide, and cobalt oxide nanodiscs,” J. Phys. Chem. C 114, 111–119 (2010).
[CrossRef]

Fullerton, E. E.

F. Nolting, A. Scholl, J. Stöhr, J. W. Seo, J. Fompeyrine, H. Siegwart, J.-P. Locquet, S. Anders, J. Lüning, E. E. Fullerton, M. F. Toney, M. R. Scheinfein, and H. A. Padmore, “Direct observation of the alignment of ferromagnetic spins by antiferromagnetic spins,” Nature 405, 767–769 (2000).
[CrossRef]

Gao, X.

W. Kuch, X. Gao, and J. Kirschner, “Competition between in-plane and out-of-plane magnetization in exchange-coupled magnetic films,” Phys. Rev. B 65, 064406 (2002).
[CrossRef]

Gaupp, A.

S. Valencia, A. Kleibert, A. Gaupp, J. Rusz, D. Legut, J. Bansmann, W. Gudat, and P. M. Oppeneer, “Quadratic x-ray magneto-optical effect upon reflection in a near- normal-incidence configuration at the M edges of 3d-transition metals,” Phys. Rev. Lett. 104, 187401 (2010).
[CrossRef]

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J. B. Kortright, D. D. Awschalom, J. Stöhr, S. D. Bader, Y. U. Idzerda, S. S. P. Parkin, I. K. Schuller, and H.-C. Siegmann, “Research frontiers in magnetic materials at soft x-ray synchrotron radiation facilities,” J. Magn. Magn. Mater. 207, 7–44 (1999).
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J. Stöhr and H. C. Siegmann, in Magnetism, Springer Series in Solid State Sciences, (Berlin Heidelberg, 2006), pp. 351–468.

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N. Jaouen, J.-M. Tonnerre, G. Kapoujian, P. Taunier, J.-P. Roux, D. Raoux, and F. Sirotti, “An apparatus for temperature-dependent soft x-ray resonant magnetic scattering,” J. Synchrotron Radiat. 11, 353–357 (2004).
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S. Uba, L. Uba, A. Y. Perlov, A. N. Yaresko, V. N. Antonov, and R. Gontarz, “Experimental and ab initio theoretical study of optical and magneto-optical properties of Co/Cu multilayers,” J. Phys. 9, 447–460 (1997).

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S. Valencia, A. Gaupp, W. Gudat, H.-Ch. Mertins, P. M. Oppeneer, D. Abramsohn, and C. M. Schneider, “Faraday rotation spectra at shallow core levels: 3p edges of Fe, Co, and Ni,” New J. Phys. 8, 254 (2006).
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H.-Ch. Mertins, S. Valencia, A. Gaupp, W. Gudat, P. M. Oppeneer, and C. M. Schneider, “Magneto-optical polarization spectroscopy with soft x-rays,” Appl. Phys. A 80, 1011–1020 (2005).
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J. Geissler, E. Goering, M. Justen, F. Weigand, G. Schütz, J. Langer, D. Schmitz, H. Maletta, and R. Mattheis, “Pt magnetization profile in a Pt/Co bilayer studied by resonant magnetic x-ray reflectometry,” Phys. Rev. B 65, 020405(R) (2001).
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K. Starke, F. Heigl, A. Vollmer, M. Weiss, G. Reichardt, and G. Kaindl, “X-ray magneto-optics in lanthanides,” Phys. Rev. Lett. 86, 3415–3418 (2001).
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M. R. Weiss, R. Follath, K. J. S. Sahwney, F. Senf, J. Bahrdt, W. Frentrup, A. Gaupp, S. Sasaki, M. Scheer, H.-Ch. Mertins, D. Abramsohn, F. Schäfers, W. Kuch, and W. Mahler, “The elliptically polarized undulator beamlines at BESSY II,” Nucl. Instrum. Methods Phys. Res. A 467–468, 449–452 (2001).
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D. Nolle, M. Weigand, P. Audehm, E. Goering, U. Wiesemann, C. Wolter, E. Nolle, and G. Schütz, “Note: unique characterization possibilities in the ultra high vacuum scanning transmission x-ray microscope (UHV-STXM) “MAXYMUS” using a rotatable permanent magnetic field up to 0.22 T,” Rev. Sci. Instrum. 83, 046112 (2012).
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H.-Ch. Mertins, D. Abramsohn, A. Gaupp, F. Schäfers, W. Gudat, O. Zaharko, H. Grimmer, and P. M. Oppeneer, “Resonant magnetic reflection coefficients at the Fe 2p edge obtained with linearly and circularly polarized soft X rays,” Phys. Rev. B 66, 184404 (2002).
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M. Hecker, P. M. Oppeneer, S. Valencia, H.-Ch. Mertins, and C. M. Schneider, “Soft x-ray magnetic reflection spectroscopy at the 3p absorption edges of thin Fe films,” J. Electron Spectrosc. Relat. Phenom. 144, 881–884 (2005).
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J. Yang, H. Liu, W. N. Martens, and R. L. Frost, “Synthesis and characterization of cobalt hydroxide, cobalt oxyhydroxide, and cobalt oxide nanodiscs,” J. Phys. Chem. C 114, 111–119 (2010).
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Phys. Rev. B (15)

H.-Ch. Mertins, D. Abramsohn, A. Gaupp, F. Schäfers, W. Gudat, O. Zaharko, H. Grimmer, and P. M. Oppeneer, “Resonant magnetic reflection coefficients at the Fe 2p edge obtained with linearly and circularly polarized soft X rays,” Phys. Rev. B 66, 184404 (2002).
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P. M. Oppeneer, H.-Ch. Mertins, D. Abramsohn, A. Gaupp, W. Gudat, J. Kunes, and C. M. Schneider, “Buried antiferromagnetic films investigated by x-ray magneto-optical reflection spectroscopy,” Phys. Rev. B 67, 052401 (2003).
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J. Kunes, P. M. Oppeneer, H.-Ch. Mertins, F. Schäfers, A. Gaupp, W. Gudat, and P. Novák, “X-ray Faraday effect at the L2,3 edges of Fe, Co, and Ni: theory and experiment,” Phys. Rev. B 64, 174417 (2001).
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[CrossRef]

H.-Ch. Mertins, S. Valencia, D. Abramsohn, A. Gaupp, W. Gudat, and P. M. Oppeneer, “X-ray Kerr rotation and ellipticity spectra at the 2p edges of Fe, Co, and Ni,” Phys. Rev. B 69, 064407 (2004).
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Phys. Rev. Lett. (5)

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[CrossRef]

S. S. Dhesi, G. van der Laan, E. Dudzik, and A. B. Shick, “Anisotropic spin–orbit coupling and magnetocrystalline anisotropy in vicinal co films,” Phys. Rev. Lett. 87, 067201 (2001).
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[CrossRef]

H.-Ch. Mertins, P. M. Oppeneer, J. Kunes, A. Gaupp, D. Abramsohn, and F. Schäfers, “Observation of the x-ray magneto-optical Voigt effect,” Phys. Rev. Lett. 87, 047401 (2001).
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Physica B (1)

S. Valencia, H.-Ch. Mertins, D. Abramsohn, A. Gaupp, W. Gudat, and P. M. Oppeneer, “Interference effects in the x-ray Kerr rotation spectrum at the Fe 2p edge,” Physica B 345, 189–192 (2004).
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[CrossRef]

Science (3)

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Solid State Commun. (1)

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Figures (20)

Fig. 1.
Fig. 1.

Experimental geometries: (a) L-MOKE: rotation and change of ellipticity of linearly polarized light appears upon reflection on a longitudinally magnetized sample. This is detected by a polarization analysis (not shown). Circularly polarized light changes its intensity, depending on parallel/antiparallel orientation of helicity and magnetization direction. This is detected by XMCD reflectivity measurements. (b) P-MOKE: rotation of the polarization plane and change of the ellipticity of linearly polarized light appears upon reflection of polar magnetized samples. This is detected by a polarization analysis (not shown). A plain intensity measurement of circularly polarized light is called XMCD in reflection similar to situation (a). (c) T-MOKE: linearly p-polarized light impinges a transversally magnetized sample and shows a change in the reflected intensity only. A detailed description is found in Section 2.2.

Fig. 2.
Fig. 2.

Principle of detecting the XMLD. The reflectance R, R of the sample differs for the two magnetization directions M, M parallel and perpendicular to the electric field component E of the incident linear polarized light.

Fig. 3.
Fig. 3.

Top view of the XMAPS chamber. The incident light (a) passes a set of pinholes, filters and monitoring devices (b) and is reflected (transmitted) by the sample in the middle of the magnetization device TetraMag (c) placed on a two circle goniometer. (d) The reflected (transmitted) light can be detected with photodiodes or photomultipliers, respectively. (e) The polarization state of light can be analyzed by a Rabinovich detector or (g) a Wollaston prism based detector. (f) The in situ sample transfer takes place via a transfer chamber mounted at position.

Fig. 4.
Fig. 4.

Magnetization device TetraMag placed in the center of the two-circle goniometer. The light interacts with the sample in the center of the TetraMag. Four strong (north and south poles colored in green and red, respectively) and four weak (not shown) permanent magnets create a homogeneous field in the sample area that is tunable by rotating the magnets (black arrows).

Fig. 5.
Fig. 5.

Polarization detector based on a Wollaston prism. The incident light (a) is split by a Wollaston prism (b) in its s- and p-polarized components. These are detected separately by two photomultipliers (c). Rotation of the whole detector about γ allows for a full polarization analysis.

Fig. 6.
Fig. 6.

Top: principles of the Rabinovich detector: s- and p-polarized light is separated exploiting the different reflectivity at the Brewster angle. Bottom: the incident light (a) is detected by a GaAs:P-photodiode (b) after reflection from the analyzer mirror (c) set to the Brewster angle. For a polarization analysis mirror and detector are rotated about the light axis (γ–scan) via a commercial goniometer (d). The mirror and the diode can be adjusted by a small noncommercial two-circle goniometer (e). A two axial bearing (f) provides easy alignment of the complete device with respect to the light axis.

Fig. 7.
Fig. 7.

Experimental data of (a) the magnetic flux density at the sample position depending on the angle of the magnets and (b) the magnetic flux density in x direction along the x axis in the sample plane for different field strengths.

Fig. 8.
Fig. 8.

Energy dependent reflectivity (top) at 50° incidence for transverse magnetic fields. The T-MOKE asymmetry (bottom) is deduced from the reflectance curves via Eq. (13).

Fig. 9.
Fig. 9.

Angular dependent reflectivity (top) at 60.5 eV for transversal fields. The corresponding T-MOKE asymmetry (bottom) is deduced from the reflectivity according to Eq. (13).

Fig. 10.
Fig. 10.

Reflected intensity of Co as a function of the applied transversal magnetic field at 40° incidence. Maximum asymmetry appears at the 3p resonance near 60.5 eV (left inset). Right inset: details of the hysteresis loop.

Fig. 11.
Fig. 11.

Energy dependent reflectivity of Co across the 2p edges (top) at 15° grazing incidence for transversal magnetization. The 2p3/2 edge around 787 eV shows a multifold structure that is assigned to oxidation states. The corresponding T-MOKE asymmetry shows maximum values at the 2p3/2 edge near 788 eV and expands toward the 2p1/2 edge at ca. 803 eV.

Fig. 12.
Fig. 12.

Energy dependent reflectivity (top) of Co at 50° incidence for longitudinal magnetization. The longitudinal XMCD reflectivity asymmetry (bottom) is deduced from the reflectance according to Eq. (9). Symbols: experimental data; line: calculation based on magnetic Co in the volume and nonmagnetic CoO near the surface. For details see text.

Fig. 13.
Fig. 13.

Reflectance spectra for different angles of incidence for longitudinal magnetization (filled, open black circles). Structures (a) and (b) are assigned to metallic Co, structures (c) and (d) are assigned to oxidized Co in the near-surface region. The relative intensity of structures (c) and (d) increase from near-normal incidence (θ=80°) toward grazing incidence (θ=30°). Red filled diamonds: modeled spectra composed of pure metallic Co (blue open circles [54]) and Co3O4 (open green circles [57]). For details see text.

Fig. 14.
Fig. 14.

Top: angular dependent reflectivity of Co at 59.7 eV in longitudinal geometry. The XMCD reflectivity asymmetry (bottom, points) is deduced from the reflectivity according to Eq. (9). The line shows the expected angular dependence (details see text).

Fig. 15.
Fig. 15.

Top: reflectivity spectrum of Co at 75° for polar magnetization. Middle: P-MOKE asymmetry calculated from the two reflectivity curves. Bottom: polar Kerr rotation deduced from polarization analysis at 30° grazing incidence.

Fig. 16.
Fig. 16.

Reflectivity (top) at the Co 3p edge at 50° incidence for two orientations between magnetization and polarization of the incident light: perpendicular (R) and parallel (R). The XMLD asymmetry is deduced from the two reflectivity spectra according to Eq. (15).

Fig. 17.
Fig. 17.

Reflectivity (top) at the Co 2p edge at 15° grazing incidence for two orientations between magnetization and polarization of the incident light: perpendicular (R) and parallel (R). The XMLD asymmetry is deduced from the two reflectivity spectra via Eq. (15).

Fig. 18.
Fig. 18.

Polarization analyzer spectrum. After reflection or transmission the signal (red) is phase shifted and of lower amplitude compared to the incoming signal (black). The phase shift contains information about the rotation θK of the polarization plane and the stroke contains information about the ellipticity ε.

Fig. 19.
Fig. 19.

Bottom: L-MOKE rotation and ellipticity spectra at 30° incidence (filled symbols) and T-MOKE and longitudinal XMCD reflectivity asymmetry (open symbols). Top: reflectivity spectra for transversal field at 30° incidence, from which the T-MOKE asymmetry AT (bottom) was deduced.

Fig. 20.
Fig. 20.

L-MOKE rotation of Co in the visible region for s-polarized light at θ=33°. The reflectivity of Co is shown in the inset.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

Rs,p=rs,prs,p*,rs,p=|rs,p|eiδs,pTs,p=ts,pts,p*,ts,p=|ts,p|eiδs,pΔ=δsδp.
S0=[(Ep)2+(Es)2]S1=[(Ep)2(Es)2]/S0S2=2EpEscos(δpδs)/S0=(EsEp*+Es*Ep)/S0S3=2EpEssin(δpδs)/S0=(EsEp*Es*Ep)/S0.
sin2ε=S3
tan2θ=S2/S1.
f(e·e)F0i((e×e)·M)F1+(e·M)(e·M)F2.
n±=1(δ0±Δδ)+i(β0±Δβ).
θKp+iεKp=rps/rppin0nQ(n2n02)cosϕitanϕtcos(ϕi+ϕt).
rL=(rss±ΔspΔsprpp).
AL=RL+RLRL++RL=2Im{Δsp(rss+rpp)}/(|rss|2+|rpp|2+2|Δsp|2).
AL=(aLS3)/(1pp(1S32)1/2)withaL=2Im{Δsp(rss+rpp)}/(|rss|2+|rpp|2+2|Δsp|2)andpp=(|rss|2|rpp|2)/(|rss|2+|rpp|2+2|Δsp|2).
θKs+iεKsi(n+n)n0n+nn02cosϕicos(ϕiϕt)
θKp+iεKpi(n+n)n0n+nn02cosϕicos(ϕi+ϕt)
rT=(rss00rpp±Δpp).
AT=R+RR++R.
A=aT(1+S1)/(1pTS1)withaT=2Re{Δpprpp}/[|rss|2+|rpp|2+|Δpp|2]andpT=(|rss|2|rpp|2|Δpp|2)/(|rss|2+|rpp|2+|Δpp|2).
ALD=RRR+R=Re{(εε)cosϕicosϕtn¯(n¯2fp1)(tan2ϕt+1)}.

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