Abstract

Using the spin Hall effect of light, this work proposes a measurement technique of the magnetic properties of thin films. The beam shift of the spin Hall effect of light is used to replace the magneto-optical Kerr rotation angle as a parameter to characterize the magnetism of thin films. The technique can easily achieve an accuracy of 10−6 rad of the magneto-optical Kerr rotation angle which can, in theory, be further improved to 10−8 rad. We also proposed two methods to solve the problem of the exceeding linear response region of the measurement under high magnetic field intensity, making it more conducive to practical application. This technique has great potential for application in the magnetic measurement of ultra-thin films with particular emphasis on thicknesses within several atomic layers.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (4)

S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Precision measurement of the optical conductivity of atomically thin crystals via the photonic spin Hall effect,” Phys. Rev. Appl. 13(1), 014057 (2020).
[Crossref]

Q. Wang, T. Li, L. Luo, Y. He, X. Liu, Z. Li, Z. Zhang, and J. Du, “Measurement of hysteresis loop based on weak measurement,” Opt. Lett. 45(5), 1075–1078 (2020).
[Crossref]

K. Ogawa, H. Kobayashi, and A. Tomita, “Operational formulation of weak values without probe systems,” Phys. Rev. A 101(4), 042117 (2020).
[Crossref]

Z. Li, L. Xie, Q. Ti, P. Duan, Z. Zhang, and C. Ren, “Increasing the dynamic range of weak measurement with two pointers,” Phys. Rev. A 102(2), 023701 (2020).
[Crossref]

2019 (1)

X. Zhao, X. Zhang, H. Yang, W. Cai, Y. Zhao, Z. Wang, and W. Zhao, “Ultra-efficient spin-orbit torque induced magnetic switching in W/CoFeB/MgO structures,” Nanotechnology 30(33), 335707 (2019).
[Crossref]

2018 (6)

H. Riahi, M. Maaref, A. Lemaître, and K.-J. Jin, “Magneto-optical Kerr spectroscopy in ferromagnetic semiconductors: determination of the intrinsic complex magneto-optical voigt constant,” Semicond. Sci. Technol. 33(12), 125015 (2018).
[Crossref]

Z. Li, J. Qiu, L. Xie, L. Luo, X. Liu, Z. Zhang, C. Ren, and J. Du, “Retaining high precision and sensitivity for an extended range of phase estimation via modulated weak measurement,” Appl. Phys. Lett. 113(19), 191103 (2018).
[Crossref]

X. Zhou, L. Sheng, and X. Ling, “Photonic spin Hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref]

Y. Kim, Y.-S. Kim, S.-Y. Lee, S.-W. Han, S. Moon, Y.-H. Kim, and Y.-W. Cho, “Direct quantum process tomography via measuring sequential weak values of incompatible observables,” Nat. Commun. 9(1), 192 (2018).
[Crossref]

W.-L. Ma, P. Wang, W.-H. Leong, and R.-B. Liu, “Phase transitions in sequential weak measurements,” Phys. Rev. A 98(1), 012117 (2018).
[Crossref]

D. Li, T. Guan, F. Liu, A. Yang, Y. He, Q. He, Z. Shen, and M. Xin, “Optical rotation based chirality detection of enantiomers via weak measurement in frequency domain,” Appl. Phys. Lett. 112(21), 213701 (2018).
[Crossref]

2017 (3)

L. Xie, X. Qiu, L. Luo, X. Liu, Z. Li, Z. Zhang, J. Du, and D. Wang, “Quantitative detection of the respective concentrations of chiral compounds with weak measurements,” Appl. Phys. Lett. 111(19), 191106 (2017).
[Crossref]

I. V. Soldatov and R. Schäfer, “Advanced MOKE magnetometry in wide-field Kerr-microscopy,” J. Appl. Phys. 122(15), 153906 (2017).
[Crossref]

T. Tang, J. Li, L. Luo, P. Sun, and Y. Zhang, “Loss enhanced spin Hall effect of transmitted light through anisotropic epsilon- and mu- near-zero metamaterial slab,” Opt. Express 25(3), 2347 (2017).
[Crossref]

2016 (4)

T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6(1), 30762 (2016).
[Crossref]

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Zhang, and J. Du, “Estimation of optical rotation of chiral molecules with weak measurements,” Opt. Lett. 41(17), 4032–4035 (2016).
[Crossref]

S. Pang, J. R. G. Alonso, T. A. Brun, and A. N. Jordan, “Protecting weak measurements against systematic errors,” Phys. Rev. A 94(1), 012329 (2016).
[Crossref]

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, Ş. K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7(1), 13488 (2016).
[Crossref]

2015 (6)

L.-C. Wang, X.-D. Qiu, Z.-Y. Zhang, and R.-Y. Shi, “Photon spin splitting in magneto-optic Kerr effect,” Acta Phys. Sin. 64(17), 174202 (2015).
[Crossref]

O. Lee, L. You, J. Jang, V. Subramanian, and S. Salahuddin, “Flexible spin-orbit torque devices,” Appl. Phys. Lett. 107(25), 252401 (2015).
[Crossref]

L.-C. Wang, X.-D. Qiu, Z.-Y. Zhang, and R.-Y. Shi, “Photon spin splitting in magneto-optic Kerr effect,” Appl. Phys. Lett. 64, 174202 (2015).

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348(6242), 1448–1451 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortu no, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

2014 (9)

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortu no, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
[Crossref]

J. Dressel, K. Y. Bliokh, and F. Nori, “Classical Field Approach to Quantum weak Measurements,” Phys. Rev. Lett. 112(11), 110407 (2014).
[Crossref]

X. Zhou, X. Li, H. Luo, and S. Wen, “Optimal preselection and postselection in weak measurements for observing photonic spin hall effect,” Appl. Phys. Lett. 104(5), 051130 (2014).
[Crossref]

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4(1), 011031 (2014).
[Crossref]

X. Zhou, X. Li, H. Luo, and S. Wen, “Optimal preselection and postselection in weak measurements for observing photonic spin Hall effect,” Appl. Phys. Lett. 104(5), 051130 (2014).
[Crossref]

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
[Crossref]

K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric Effects in Local Light-Matter Interactions,” Phys. Rev. Lett. 113(3), 033601 (2014).
[Crossref]

O. S. Maga na-Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112(20), 200401 (2014).
[Crossref]

2013 (4)

G. I. Viza, J. Martínez-Rincón, G. A. Howland, H. Frostig, I. Shomroni, B. Dayan, and J. C. Howell, “Weak-values technique for velocity measurements,” Opt. Lett. 38(16), 2949–2952 (2013).
[Crossref]

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, “Phase estimation with weak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref]

2012 (4)

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref]

K. Y. Bliokh and F. Nori, “Relativistic Hall effect,” Phys. Rev. Lett. 108(12), 120403 (2012).
[Crossref]

A. G. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre-and post-selected measurements,” Phys. Rep. 520(2), 43–133 (2012).
[Crossref]

P. Egan and J. A. Stone, “Weak-value thermostat with 0.2 mk precision,” Opt. Lett. 37(23), 4991–4993 (2012).
[Crossref]

2011 (4)

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
[Crossref]

N. Hermosa, A. M. Nugrowati, A. Aiello, and J. P. Woerdman, “Spin Hall effect of light in metallic reflection,” Opt. Lett. 36(16), 3200–3202 (2011).
[Crossref]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011).
[Crossref]

2010 (2)

J.-M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
[Crossref]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82(6), 063822 (2010).
[Crossref]

2009 (3)

2008 (3)

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[Crossref]

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

2007 (3)

M. Guillot, F. Zhang, Y. Xu, J. H. Yang, and X. Wei, “Is the first-order magneto-optical effect really proportional to the magnetization?” J. Appl. Phys. 101(9), 09C510 (2007).
[Crossref]

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref]

P. Gosselin, A. Bérard, and H. Mohrbach, “Spin Hall effect of photons in a static gravitational field,” Phys. Rev. D 75(8), 084035 (2007).
[Crossref]

2005 (1)

F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films,” Phys. Rev. Lett. 95(4), 047402 (2005).
[Crossref]

2004 (3)

K. Akahane, T. Kimura, and Y. Otani, “Development of high sensitive micro-Kerr magnetometer,” J. Magn. Soc. Jpn. 28(2), 122–127 (2004).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Topological spin transport of photons: the optical Magnus effect and Berry phase,” Phys. Lett. A 333(3-4), 181–186 (2004).
[Crossref]

M. Onoda, S. Murakami, and N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

2002 (1)

M. Evangelisti, J. Bartolomé, L. J. De Jongh, and G. Filoti, “Magnetic properties of α-iron (ii) phthalocyanine,” Phys. Rev. B 66(14), 144410 (2002).
[Crossref]

2000 (1)

Q. Qiu and Z S. D. Bader, “Surface magneto-optic Kerr effect,” Rev. Sci. Instrum. 71(3), 1243–1255 (2000).
[Crossref]

1998 (1)

C.-Y. You and S.-C. Shin, “Generalized analytic formulae for magneto-optical Kerr effects,” J. Appl. Phys. 84(1), 541–546 (1998).
[Crossref]

1993 (1)

Z. J. Yang and M. R. Scheinfein, “Combined three-axis surface magneto-optical Kerr effects in the study of surface and ultrathin-film magnetism,” J. Appl. Phys. 74(11), 6810–6823 (1993).
[Crossref]

1989 (1)

I. Duck, P. Stevenson, and E. Sudarshan, “The sense in which a “weak measurement” of a spin-1/2 particle’s spin component yields a value 100 phys,” Phys. Rev. D 40(6), 2112–2117 (1989).
[Crossref]

1988 (1)

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref]

1985 (1)

E. R. Moog and S. D. Bader, “Smoke signals from ferromagnetic monolayers: p (1× 1) Fe/Au (100),” Superlattices Microstruct. 1(6), 543–552 (1985).
[Crossref]

1877 (1)

J. Kerr, “On rotation of the plane of polarization by reflection from the pole of a magnet,” Philos. Mag. 3(19), 321–343 (1877).
[Crossref]

Aharonov, Y.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref]

Aiello, A.

N. Hermosa, A. M. Nugrowati, A. Aiello, and J. P. Woerdman, “Spin Hall effect of light in metallic reflection,” Opt. Lett. 36(16), 3200–3202 (2011).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref]

Akahane, K.

K. Akahane, T. Kimura, and Y. Otani, “Development of high sensitive micro-Kerr magnetometer,” J. Magn. Soc. Jpn. 28(2), 122–127 (2004).
[Crossref]

Albert, D. Z.

Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
[Crossref]

Alonso, J. R. G.

S. Pang, J. R. G. Alonso, T. A. Brun, and A. N. Jordan, “Protecting weak measurements against systematic errors,” Phys. Rev. A 94(1), 012329 (2016).
[Crossref]

Asano, M.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, Ş. K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7(1), 13488 (2016).
[Crossref]

Ashhab, S.

A. G. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre-and post-selected measurements,” Phys. Rep. 520(2), 43–133 (2012).
[Crossref]

Bader, S. D.

E. R. Moog and S. D. Bader, “Smoke signals from ferromagnetic monolayers: p (1× 1) Fe/Au (100),” Superlattices Microstruct. 1(6), 543–552 (1985).
[Crossref]

Bartolomé, J.

M. Evangelisti, J. Bartolomé, L. J. De Jongh, and G. Filoti, “Magnetic properties of α-iron (ii) phthalocyanine,” Phys. Rev. B 66(14), 144410 (2002).
[Crossref]

Belov, P. A.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortu no, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
[Crossref]

Bérard, A.

P. Gosselin, A. Bérard, and H. Mohrbach, “Spin Hall effect of photons in a static gravitational field,” Phys. Rev. D 75(8), 084035 (2007).
[Crossref]

Betz, M.

J.-M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
[Crossref]

J.-M. Ménard, A. E. Mattacchione, M. Betz, and H. M. van Driel, “Imaging the spin Hall effect of light inside semiconductors via absorption,” Opt. Lett. 34(15), 2312–2314 (2009).
[Crossref]

Bliokh, K. Y.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, Ş. K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7(1), 13488 (2016).
[Crossref]

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348(6242), 1448–1451 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortu no, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
[Crossref]

J. Dressel, K. Y. Bliokh, and F. Nori, “Classical Field Approach to Quantum weak Measurements,” Phys. Rev. Lett. 112(11), 110407 (2014).
[Crossref]

K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric Effects in Local Light-Matter Interactions,” Phys. Rev. Lett. 113(3), 033601 (2014).
[Crossref]

K. Y. Bliokh and F. Nori, “Relativistic Hall effect,” Phys. Rev. Lett. 108(12), 120403 (2012).
[Crossref]

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Topological spin transport of photons: the optical Magnus effect and Berry phase,” Phys. Lett. A 333(3-4), 181–186 (2004).
[Crossref]

Bliokh, Y. P.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, Ş. K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7(1), 13488 (2016).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Topological spin transport of photons: the optical Magnus effect and Berry phase,” Phys. Lett. A 333(3-4), 181–186 (2004).
[Crossref]

Boyd, R. W.

O. S. Maga na-Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112(20), 200401 (2014).
[Crossref]

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

Bretner, I.

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

Brun, T. A.

S. Pang, J. R. G. Alonso, T. A. Brun, and A. N. Jordan, “Protecting weak measurements against systematic errors,” Phys. Rev. A 94(1), 012329 (2016).
[Crossref]

Cabrera, G. G.

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011).
[Crossref]

Cai, W.

X. Zhao, X. Zhang, H. Yang, W. Cai, Y. Zhao, Z. Wang, and W. Zhao, “Ultra-efficient spin-orbit torque induced magnetic switching in W/CoFeB/MgO structures,” Nanotechnology 30(33), 335707 (2019).
[Crossref]

Chen, S.

S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Precision measurement of the optical conductivity of atomically thin crystals via the photonic spin Hall effect,” Phys. Rev. Appl. 13(1), 014057 (2020).
[Crossref]

Cho, Y.-W.

Y. Kim, Y.-S. Kim, S.-Y. Lee, S.-W. Han, S. Moon, Y.-H. Kim, and Y.-W. Cho, “Direct quantum process tomography via measuring sequential weak values of incompatible observables,” Nat. Commun. 9(1), 192 (2018).
[Crossref]

Dartora, C. A.

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011).
[Crossref]

Dayan, B.

de Campos, F. K. R.

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011).
[Crossref]

De Jongh, L. J.

M. Evangelisti, J. Bartolomé, L. J. De Jongh, and G. Filoti, “Magnetic properties of α-iron (ii) phthalocyanine,” Phys. Rev. B 66(14), 144410 (2002).
[Crossref]

Dixon, P. B.

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82(6), 063822 (2010).
[Crossref]

Dressel, J.

J. Dressel, K. Y. Bliokh, and F. Nori, “Classical Field Approach to Quantum weak Measurements,” Phys. Rev. Lett. 112(11), 110407 (2014).
[Crossref]

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
[Crossref]

Du, J.

Q. Wang, T. Li, L. Luo, Y. He, X. Liu, Z. Li, Z. Zhang, and J. Du, “Measurement of hysteresis loop based on weak measurement,” Opt. Lett. 45(5), 1075–1078 (2020).
[Crossref]

Z. Li, J. Qiu, L. Xie, L. Luo, X. Liu, Z. Zhang, C. Ren, and J. Du, “Retaining high precision and sensitivity for an extended range of phase estimation via modulated weak measurement,” Appl. Phys. Lett. 113(19), 191103 (2018).
[Crossref]

L. Xie, X. Qiu, L. Luo, X. Liu, Z. Li, Z. Zhang, J. Du, and D. Wang, “Quantitative detection of the respective concentrations of chiral compounds with weak measurements,” Appl. Phys. Lett. 111(19), 191106 (2017).
[Crossref]

X. Qiu, L. Xie, X. Liu, L. Luo, Z. Zhang, and J. Du, “Estimation of optical rotation of chiral molecules with weak measurements,” Opt. Lett. 41(17), 4032–4035 (2016).
[Crossref]

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
[Crossref]

Duan, P.

Z. Li, L. Xie, Q. Ti, P. Duan, Z. Zhang, and C. Ren, “Increasing the dynamic range of weak measurement with two pointers,” Phys. Rev. A 102(2), 023701 (2020).
[Crossref]

Duck, I.

I. Duck, P. Stevenson, and E. Sudarshan, “The sense in which a “weak measurement” of a spin-1/2 particle’s spin component yields a value 100 phys,” Phys. Rev. D 40(6), 2112–2117 (1989).
[Crossref]

Ebbesen, T. W.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref]

Egan, P.

Evangelisti, M.

M. Evangelisti, J. Bartolomé, L. J. De Jongh, and G. Filoti, “Magnetic properties of α-iron (ii) phthalocyanine,” Phys. Rev. B 66(14), 144410 (2002).
[Crossref]

Fan, D.

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
[Crossref]

Filho, H. T. S.

C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011).
[Crossref]

Filonov, D. S.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortu no, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
[Crossref]

Filoti, G.

M. Evangelisti, J. Bartolomé, L. J. De Jongh, and G. Filoti, “Magnetic properties of α-iron (ii) phthalocyanine,” Phys. Rev. B 66(14), 144410 (2002).
[Crossref]

Frostig, H.

Gao, F.

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
[Crossref]

Genet, C.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref]

Ginzburg, P.

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortu no, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
[Crossref]

Gong, Q.

Gorodetski, Y.

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[Crossref]

Gosselin, P.

P. Gosselin, A. Bérard, and H. Mohrbach, “Spin Hall effect of photons in a static gravitational field,” Phys. Rev. D 75(8), 084035 (2007).
[Crossref]

Guan, T.

D. Li, T. Guan, F. Liu, A. Yang, Y. He, Q. He, Z. Shen, and M. Xin, “Optical rotation based chirality detection of enantiomers via weak measurement in frequency domain,” Appl. Phys. Lett. 112(21), 213701 (2018).
[Crossref]

Guillot, M.

M. Guillot, F. Zhang, Y. Xu, J. H. Yang, and X. Wei, “Is the first-order magneto-optical effect really proportional to the magnetization?” J. Appl. Phys. 101(9), 09C510 (2007).
[Crossref]

Guo, G.-C.

X.-Y. Xu, Y. Kedem, K. Sun, L. Vaidman, C.-F. Li, and G.-C. Guo, “Phase estimation with weak measurement using a white light source,” Phys. Rev. Lett. 111(3), 033604 (2013).
[Crossref]

Han, S.-W.

Y. Kim, Y.-S. Kim, S.-Y. Lee, S.-W. Han, S. Moon, Y.-H. Kim, and Y.-W. Cho, “Direct quantum process tomography via measuring sequential weak values of incompatible observables,” Nat. Commun. 9(1), 192 (2018).
[Crossref]

Hansteen, F.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref]

F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecond photomagnetic switching of spins in ferrimagnetic garnet films,” Phys. Rev. Lett. 95(4), 047402 (2005).
[Crossref]

Hasman, E.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
[Crossref]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
[Crossref]

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref]

Hautmann, C.

J.-M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
[Crossref]

He, H.

He, Q.

D. Li, T. Guan, F. Liu, A. Yang, Y. He, Q. He, Z. Shen, and M. Xin, “Optical rotation based chirality detection of enantiomers via weak measurement in frequency domain,” Appl. Phys. Lett. 112(21), 213701 (2018).
[Crossref]

He, Y.

Q. Wang, T. Li, L. Luo, Y. He, X. Liu, Z. Li, Z. Zhang, and J. Du, “Measurement of hysteresis loop based on weak measurement,” Opt. Lett. 45(5), 1075–1078 (2020).
[Crossref]

D. Li, T. Guan, F. Liu, A. Yang, Y. He, Q. He, Z. Shen, and M. Xin, “Optical rotation based chirality detection of enantiomers via weak measurement in frequency domain,” Appl. Phys. Lett. 112(21), 213701 (2018).
[Crossref]

Hermosa, N.

Hosten, O.

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

Howell, J. C.

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4(1), 011031 (2014).
[Crossref]

G. I. Viza, J. Martínez-Rincón, G. A. Howland, H. Frostig, I. Shomroni, B. Dayan, and J. C. Howell, “Weak-values technique for velocity measurements,” Opt. Lett. 38(16), 2949–2952 (2013).
[Crossref]

D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82(6), 063822 (2010).
[Crossref]

Howland, G. A.

Hu, D.

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
[Crossref]

Ikuta, R.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, Ş. K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7(1), 13488 (2016).
[Crossref]

Imoto, N.

M. Asano, K. Y. Bliokh, Y. P. Bliokh, A. G. Kofman, R. Ikuta, T. Yamamoto, Y. S. Kivshar, L. Yang, N. Imoto, Ş. K. Özdemir, and F. Nori, “Anomalous time delays and quantum weak measurements in optical micro-resonators,” Nat. Commun. 7(1), 13488 (2016).
[Crossref]

Itoh, A.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99(4), 047601 (2007).
[Crossref]

Jang, J.

O. Lee, L. You, J. Jang, V. Subramanian, and S. Salahuddin, “Flexible spin-orbit torque devices,” Appl. Phys. Lett. 107(25), 252401 (2015).
[Crossref]

Jin, K.-J.

H. Riahi, M. Maaref, A. Lemaître, and K.-J. Jin, “Magneto-optical Kerr spectroscopy in ferromagnetic semiconductors: determination of the intrinsic complex magneto-optical voigt constant,” Semicond. Sci. Technol. 33(12), 125015 (2018).
[Crossref]

Jordan, A. N.

S. Pang, J. R. G. Alonso, T. A. Brun, and A. N. Jordan, “Protecting weak measurements against systematic errors,” Phys. Rev. A 94(1), 012329 (2016).
[Crossref]

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X. Zhou, X. Li, H. Luo, and S. Wen, “Optimal preselection and postselection in weak measurements for observing photonic spin hall effect,” Appl. Phys. Lett. 104(5), 051130 (2014).
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Acta Phys. Sin. (1)

L.-C. Wang, X.-D. Qiu, Z.-Y. Zhang, and R.-Y. Shi, “Photon spin splitting in magneto-optic Kerr effect,” Acta Phys. Sin. 64(17), 174202 (2015).
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Appl. Phys. Lett. (8)

X. Qiu, X. Zhou, D. Hu, J. Du, F. Gao, Z. Zhang, and H. Luo, “Determination of magneto-optical constant of Fe films with weak measurements,” Appl. Phys. Lett. 105(13), 131111 (2014).
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X. Zhou, X. Li, H. Luo, and S. Wen, “Optimal preselection and postselection in weak measurements for observing photonic spin Hall effect,” Appl. Phys. Lett. 104(5), 051130 (2014).
[Crossref]

D. Li, T. Guan, F. Liu, A. Yang, Y. He, Q. He, Z. Shen, and M. Xin, “Optical rotation based chirality detection of enantiomers via weak measurement in frequency domain,” Appl. Phys. Lett. 112(21), 213701 (2018).
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L. Xie, X. Qiu, L. Luo, X. Liu, Z. Li, Z. Zhang, J. Du, and D. Wang, “Quantitative detection of the respective concentrations of chiral compounds with weak measurements,” Appl. Phys. Lett. 111(19), 191106 (2017).
[Crossref]

X. Zhou, X. Li, H. Luo, and S. Wen, “Optimal preselection and postselection in weak measurements for observing photonic spin hall effect,” Appl. Phys. Lett. 104(5), 051130 (2014).
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Z. Li, J. Qiu, L. Xie, L. Luo, X. Liu, Z. Zhang, C. Ren, and J. Du, “Retaining high precision and sensitivity for an extended range of phase estimation via modulated weak measurement,” Appl. Phys. Lett. 113(19), 191103 (2018).
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[Crossref]

L.-C. Wang, X.-D. Qiu, Z.-Y. Zhang, and R.-Y. Shi, “Photon spin splitting in magneto-optic Kerr effect,” Appl. Phys. Lett. 64, 174202 (2015).

J. Appl. Phys. (4)

M. Guillot, F. Zhang, Y. Xu, J. H. Yang, and X. Wei, “Is the first-order magneto-optical effect really proportional to the magnetization?” J. Appl. Phys. 101(9), 09C510 (2007).
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[Crossref]

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[Crossref]

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Nano Lett. (1)

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
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Nanotechnology (1)

X. Zhao, X. Zhang, H. Yang, W. Cai, Y. Zhao, Z. Wang, and W. Zhao, “Ultra-efficient spin-orbit torque induced magnetic switching in W/CoFeB/MgO structures,” Nanotechnology 30(33), 335707 (2019).
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Nat. Commun. (3)

P. V. Kapitanova, P. Ginzburg, F. J. Rodríguez-Fortu no, D. S. Filonov, P. M. Voroshilov, P. A. Belov, A. N. Poddubny, Y. S. Kivshar, G. A. Wurtz, and A. V. Zayats, “Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes,” Nat. Commun. 5(1), 3226 (2014).
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Nat. Photonics (1)

K. Y. Bliokh, F. J. Rodríguez-Fortu no, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
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Opt. Express (1)

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Philos. Mag. (1)

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Phys. Lett. A (1)

K. Y. Bliokh and Y. P. Bliokh, “Topological spin transport of photons: the optical Magnus effect and Berry phase,” Phys. Lett. A 333(3-4), 181–186 (2004).
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Phys. Rep. (2)

K. Y. Bliokh and F. Nori, “Transverse and longitudinal angular momenta of light,” Phys. Rep. 592, 1–38 (2015).
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A. G. Kofman, S. Ashhab, and F. Nori, “Nonperturbative theory of weak pre-and post-selected measurements,” Phys. Rep. 520(2), 43–133 (2012).
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Phys. Rev. A (7)

Z. Li, L. Xie, Q. Ti, P. Duan, Z. Zhang, and C. Ren, “Increasing the dynamic range of weak measurement with two pointers,” Phys. Rev. A 102(2), 023701 (2020).
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K. Ogawa, H. Kobayashi, and A. Tomita, “Operational formulation of weak values without probe systems,” Phys. Rev. A 101(4), 042117 (2020).
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S. Pang, J. R. G. Alonso, T. A. Brun, and A. N. Jordan, “Protecting weak measurements against systematic errors,” Phys. Rev. A 94(1), 012329 (2016).
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W.-L. Ma, P. Wang, W.-H. Leong, and R.-B. Liu, “Phase transitions in sequential weak measurements,” Phys. Rev. A 98(1), 012117 (2018).
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D. J. Starling, P. B. Dixon, A. N. Jordan, and J. C. Howell, “Precision frequency measurements with interferometric weak values,” Phys. Rev. A 82(6), 063822 (2010).
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H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin Hall effect of light near the Brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
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C. A. Dartora, G. G. Cabrera, K. Z. Nobrega, V. F. Montagner, M. H. K. Matielli, F. K. R. de Campos, and H. T. S. Filho, “Lagrangian-Hamiltonian formulation of paraxial optics and applications: Study of gauge symmetries and the optical spin Hall effect,” Phys. Rev. A 83(1), 012110 (2011).
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Phys. Rev. Appl. (1)

S. Chen, X. Ling, W. Shu, H. Luo, and S. Wen, “Precision measurement of the optical conductivity of atomically thin crystals via the photonic spin Hall effect,” Phys. Rev. Appl. 13(1), 014057 (2020).
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Phys. Rev. B (2)

J.-M. Ménard, A. E. Mattacchione, H. M. van Driel, C. Hautmann, and M. Betz, “Ultrafast optical imaging of the spin Hall effect of light in semiconductors,” Phys. Rev. B 82(4), 045303 (2010).
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M. Evangelisti, J. Bartolomé, L. J. De Jongh, and G. Filoti, “Magnetic properties of α-iron (ii) phthalocyanine,” Phys. Rev. B 66(14), 144410 (2002).
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Phys. Rev. D (2)

I. Duck, P. Stevenson, and E. Sudarshan, “The sense in which a “weak measurement” of a spin-1/2 particle’s spin component yields a value 100 phys,” Phys. Rev. D 40(6), 2112–2117 (1989).
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P. Gosselin, A. Bérard, and H. Mohrbach, “Spin Hall effect of photons in a static gravitational field,” Phys. Rev. D 75(8), 084035 (2007).
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Phys. Rev. Lett. (13)

K. Y. Bliokh, Y. Gorodetski, V. Kleiner, and E. Hasman, “Coriolis effect in optics: unified geometric phase and spin-Hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
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Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101(4), 043903 (2008).
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A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin Hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
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Y. Gorodetski, K. Y. Bliokh, B. Stein, C. Genet, N. Shitrit, V. Kleiner, E. Hasman, and T. W. Ebbesen, “Weak measurements of light chirality with a plasmonic slit,” Phys. Rev. Lett. 109(1), 013901 (2012).
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K. Y. Bliokh and F. Nori, “Relativistic Hall effect,” Phys. Rev. Lett. 108(12), 120403 (2012).
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Y. Aharonov, D. Z. Albert, and L. Vaidman, “How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100,” Phys. Rev. Lett. 60(14), 1351–1354 (1988).
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J. Dressel, K. Y. Bliokh, and F. Nori, “Classical Field Approach to Quantum weak Measurements,” Phys. Rev. Lett. 112(11), 110407 (2014).
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O. S. Maga na-Loaiza, M. Mirhosseini, B. Rodenburg, and R. W. Boyd, “Amplification of angular rotations using weak measurements,” Phys. Rev. Lett. 112(20), 200401 (2014).
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K. Y. Bliokh, Y. S. Kivshar, and F. Nori, “Magnetoelectric Effects in Local Light-Matter Interactions,” Phys. Rev. Lett. 113(3), 033601 (2014).
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Phys. Rev. X (1)

A. N. Jordan, J. Martínez-Rincón, and J. C. Howell, “Technical advantages for weak-value amplification: when less is more,” Phys. Rev. X 4(1), 011031 (2014).
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Rev. Mod. Phys. (1)

J. Dressel, M. Malik, F. M. Miatto, A. N. Jordan, and R. W. Boyd, “Colloquium: Understanding quantum weak values: Basics and applications,” Rev. Mod. Phys. 86(1), 307–316 (2014).
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Rev. Sci. Instrum. (1)

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Sci. Rep. (2)

X. Zhou, L. Sheng, and X. Ling, “Photonic spin Hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
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T. Tang, C. Li, and L. Luo, “Enhanced spin Hall effect of tunneling light in hyperbolic metamaterial waveguide,” Sci. Rep. 6(1), 30762 (2016).
[Crossref]

Science (4)

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
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X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
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K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348(6242), 1448–1451 (2015).
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Semicond. Sci. Technol. (1)

H. Riahi, M. Maaref, A. Lemaître, and K.-J. Jin, “Magneto-optical Kerr spectroscopy in ferromagnetic semiconductors: determination of the intrinsic complex magneto-optical voigt constant,” Semicond. Sci. Technol. 33(12), 125015 (2018).
[Crossref]

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E. R. Moog and S. D. Bader, “Smoke signals from ferromagnetic monolayers: p (1× 1) Fe/Au (100),” Superlattices Microstruct. 1(6), 543–552 (1985).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. SHEL on the surface of a magnetic thin film, $z$ axis is the normal of the film surface, $x$ axis is parallel to the incident plane and $y$ axis is perpendicular to the incident plane. The coordinate system of the beam is ${(x}_{i, r}, y_{i,r},z_{i,r})$, where $i$, $r$ represents incident and reflected beam respectively, and $\delta \pm$ represents the transverse shift of the beam.
Fig. 2.
Fig. 2. The magnetic properties measurement system, The light source is a He-Ne laser (wavelength=632.8 nm), HWP is for adjusting the light intensity, the focal lengths of the lenses L$_1$ and L$_2$ are 50 mm and 250 mm respectively, P$_1$ and P$_2$ are Glan laser polarizers, CCD is a charge-coupled device, the applied magnetic field $\boldsymbol {H}$ is perpendicular to the sample surface.
Fig. 3.
Fig. 3. The hysteresis loop of 20 nm NiFe film measured by SHEL under room temperature, the substrate is glass. Curve 1 is from the initial state to the maximum positive applied magnetic field intensity, cure 2 is from the maximum positive applied magnetic field intensity to the maximum negative applied magnetic field intensity, curve 3 is from the maximum negative applied magnetic field intensity back to the positive applied magnetic field intensity, curve 1, 2, and 3 form a hysteresis loop.
Fig. 4.
Fig. 4. (a) Dependent relationship of beam shift with film thickness under normal conditions, 1, 2, 3 refer to the three stages when the film is very thin, the film is in the middle thickness and the film is very thick, respectively (b) Amplified shift dependence with FePc film thickness under room temperature. The applied magnetic field intensity is $\boldsymbol {H} = 0.05$ T (black curve), 0.3 T (red curve), 0.5 T (blue curve), respectively.
Fig. 5.
Fig. 5. (a) The hysteresis loop of 30 nm Co film measured by SHEL under room temperature, the substrate is glass (b) The dependence relationship of the amplified shift $\delta$ of SHEL and post-selection angle $\theta$ (c) The hysteresis loop modified by 20.

Equations (20)

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ε ~ = ε ( 1 i Q z i Q y i Q z 1 i Q z i Q y i Q x 1 )
| H ( k i , r ) = | p ( k i , r ) cot θ i , r k y i , r | s ( k i , r ) ,
| V ( k i , r ) = | s ( k i , r ) + cot θ i , r k y i , r | p ( k i , r ) ,
[ | p ( k r ) | s ( k r ) ] = [ r p p r p s r s p r s s ] [ | p ( k i ) | s ( k i ) ] .
[ | H ( k r ) | V ( k r ) ] = [ r p p k r y ( r p s r s p ) cot θ i k 0 r p s + k r y ( r p p + r s s ) cot θ i k 0 r s p k r y ( r p p + r s s ) cot θ i k 0 r s s k r y ( r p s r s p ) cot θ i k 0 ] [ | H ( k i ) | V ( k i ) ] ,
r p p = n 1 cos θ i n 0 cos θ t n 1 cos θ i + n 0 cos θ t 2 i n 0 n 1 cos θ i sin θ t Q x n 1 cos θ i + n 0 cos θ t ,
r s s = n 0 cos θ i n 1 cos θ t n 0 cos θ i + n 1 cos θ t ,
r p s = i n 0 n 1 cos θ i ( cos θ t Q z sin θ t Q y ) ( n 1 cos θ i + n 0 cos θ t ) ( n 0 cos θ i + n 1 cos θ t ) cos θ t , a l i g n
r s p = i n 0 n 1 cos θ i ( cos θ t Q z + sin θ t Q y ) ( n 1 cos θ i + n 0 cos θ t ) ( n 0 cos θ i + n 1 cos θ t ) cos θ t ,
r p p = n 2 cos θ 0 n 0 cos θ 2 n 2 cos θ 0 + n 0 cos θ 2 + 4 π i n 0 d cos θ 0 ( n 2 2 cos 2 θ 1 n 1 2 cos 2 θ 2 ) λ ( n 0 cos θ 2 + n 2 cos θ 0 ) 2 ,
r s s = n 0 cos θ 0 n 2 cos θ 2 n 0 cos θ 0 + n 2 cos θ 2 + 4 π i n 0 d cos θ 0 ( n 1 2 cos 2 θ 1 n 2 2 cos 2 θ 2 ) λ ( n 0 cos θ 0 + n 2 cos θ 2 ) 2 ,
r p s = 4 π n 0 n 1 d cos θ 0 ( Q z n 1 cos θ 2 Q y n 2 sin θ 1 ) λ ( n 0 cos θ 0 + n 2 cos θ 2 ) ( n 0 cos θ 2 + n 2 cos θ 0 ) ,
r s p = 4 π n 0 n 1 d cos θ 0 ( Q z n 1 cos θ 2 + Q y n 2 sin θ 1 ) λ ( n 0 cos θ 0 + n 2 cos θ 2 ) ( n 0 cos θ 2 + n 2 cos θ 0 ) .
| Ψ p o s t H = sin γ | H + cos γ | V ,
| Ψ p o s t V = sin γ | V + cos γ | H ,
| Φ p o s t = w 2 π d k x d k y exp [ ( R + i z ) ( k x 2 + k y 2 ) 2 k 0 ] | k x | k y | Ψ p o s t Ψ p o s t Ψ r ,
δ = Φ p o s t | i k y | Φ p o s t Φ p o s t Φ p o s t .
θ H = r s p / r p p ,
θ V = r p s / r s s .
δ modified = { δ a , θ θ c 2 δ max δ b , θ > θ c .