Abstract
Magnetoelectric coupling in multiferroic materials opens new routes to control the propagation of light. The new effects arise due to dynamic magnetoelectric susceptibility that cross-couples the electric and magnetic fields of light and modifies the solutions of Maxwell equations in media. In this paper, two major effects will be considered in detail: optical activity and asymmetric propagation. In case of optical activity the polarization plane of the input radiation rotates by an angle proportional to the magnetoelectric susceptibility. The asymmetric propagation is a counter-intuitive phenomenon and it represents different transmission coefficients for forward and backward directions. Both effects are especially strong close to resonance frequencies of electromagnons, i. e. excitations in multiferroic materials that reveal simultaneous electric and magnetic character.
Acknowledgements
This work was supported by the Russian Science Foundation (16-12-10531) and by the Austrian Science Funds (W 1243, I 2816-N27, I 1648-N27).
References
[1] Smolenskii GA, Chupis IE. Ferroelectromagnets. Sov Phys Usp. 1982;25:475.10.1070/PU1982v025n07ABEH004570Search in Google Scholar
[2] Krivoruchko VN, Yablonskii DA. Antiferroelectric resonance in noncentrosymmetric multi-sublattice magnets. Sov Phys JETP. 1988;67:1886.Search in Google Scholar
[3] Eremenko VV, Kharchenko NF, Litvinenko YG, Naumenko VM. Magneto-optics and spectroscopy of antiferromagnets. New York: Springer, 1992.10.1007/978-1-4612-2846-2Search in Google Scholar
[4] Turov EA. Purely antiferromagnetic oscillatory mode in a two-sublattice ferromagnetic phase. J Exp Theor Phys Lett. 2001;73:87–9.10.1134/1.1358426Search in Google Scholar
[5] Fiebig M. Revival of the magnetoelectric effect. J Phys D: Appl Phys. 2005;38:R123.10.1088/0022-3727/38/8/R01Search in Google Scholar
[6] Pimenov A, Mukhin AA, Ivanov VY, Travkin VD, Balbashov AM, Loidl A. Possible evidence for electromagnons in multiferroic manganites. Nat Phys. 2006;2:97.10.1038/nphys212Search in Google Scholar
[7] Sushkov AB, Valdes Aguilar R, Park S, Cheong S-W, Drew HD. Electromagnons in multiferroic YMn2O5 and TbMn2O5. Phys Rev Lett. 2007;98:027202.10.1103/PhysRevLett.98.027202Search in Google Scholar PubMed
[8] Takahashi Y, Kida N, Yamasaki Y, Fujioka J, Arima T, Shimano R, et al. Evidence for an electric-dipole active continuum band of spin excitations in multiferroic TbMnO3. Phys Rev Lett. 2008;101:187201.10.1103/PhysRevLett.101.187201Search in Google Scholar PubMed
[9] Kida N, Ikebe Y, Takahashi Y, He JP, Kaneko Y, Yamasaki Y, et al. Electrically driven spin excitation in the ferroelectric magnet DyMnO3. Phys Rev B. 2008;78:104414.10.1103/PhysRevB.78.104414Search in Google Scholar
[10] Pimenov A, Loidl A, Mukhin AA, Travkin VD, Ivanov VY, Balbashov AM. Terahertz spectroscopy of electromagnons in Eu1 – xYxMnO3. Phys Rev B. 2008;77:014438.10.1103/PhysRevB.77.014438Search in Google Scholar
[11] Valdes Aguilar R, Mostovoy M, Sushkov AB, Zhang CL, Choi YJ, Cheong S-W, et al. Origin of electromagnon excitations in multiferroic RMnO3. Phys Rev Lett. 2009;102:047203.10.1103/PhysRevLett.102.047203Search in Google Scholar PubMed
[12] Tokura Y, Seki Sh, Nagaosa N. Multiferroics of spin origin. Rep Prog Phys. 2014;77:076501.10.1088/0034-4885/77/7/076501Search in Google Scholar PubMed
[13] Dong Sh, Liu J-M, Cheong S-W, Ren Zh. Multiferroic materials and magnetoelectric physics: symmetry, entanglement, excitation, and topology. Adv Phys. 2015;64:519–626.10.1080/00018732.2015.1114338Search in Google Scholar
[14] Kuzmenko AM, Shuvaev A, Dziom V, Pimenov A, Schiebl M, Mukhin AA, et al. Giant gigahertz optical activity in multiferroic ferroborate. Phys Rev B. 2014;89:174407.10.1103/PhysRevB.89.174407Search in Google Scholar
[15] Katsura H, Nagaosa N, Balatsky AV. Spin current and magnetoelectric effect in noncollinear magnets. Phys Rev Lett. 2005;95:057205.10.1103/PhysRevLett.95.057205Search in Google Scholar PubMed
[16] Mostovoy M. Ferroelectricity in spiral magnets. Phys Rev Lett. 2006;96:067601.10.1103/PhysRevLett.96.067601Search in Google Scholar PubMed
[17] Shuvaev A, Dziom V, Pimenov A, Schiebl M, Mukhin AA, Komarek AC, et al. Electric field control of terahertz polarization in a multiferroic manganite with electromagnons. Phys Rev Lett. 2013;111:227201.10.1103/PhysRevLett.111.227201Search in Google Scholar PubMed
[18] Miyahara S, Furukawa N. Theory of electric field induced one-magnon resonance in cycloidal spin magnets. ArXiv 0811.4082, 2008.Search in Google Scholar
[19] Mochizuki M, Furukawa N, Nagaosa N. Theory of electromagnons in the multiferroic Mn perovskites: the vital role of higher harmonic components of the spiral spin order. Phys Rev Lett. 2010;104:177206.10.1103/PhysRevLett.104.177206Search in Google Scholar PubMed
[20] Shuvaev AM, Travkin VD, Ivanov VY, Mukhin AA, Pimenov A. Evidence for electroactive excitation of the spin cycloid in TbMnO3. Phys Rev Lett. 2010;104:097202.10.1103/PhysRevLett.104.097202Search in Google Scholar PubMed
[21] Szaller D, Bordács S, Kocsis V, Rõõm T, Nagel U, Kézsmárki I. Effect of spin excitations with simultaneous magnetic- and electric-dipole character on the static magnetoelectric properties of multiferroic materials. Phys Rev B. 2014;89:184419.10.1103/PhysRevB.89.184419Search in Google Scholar
[22] Berreman DW. Optics in stratified and anisotropic media – 4x4-matrix formulation. J Opt Soc Am. 1972;62:502.10.1364/JOSA.62.000502Search in Google Scholar
[23] Shuvaev AM, Astakhov GV, Brüne C, Buhmann H, Molenkamp LW, Pimenov A. Terahertz magneto-optical spectroscopy in HgTe thin films. Semicond Sci Technol. 2012;27:124004.10.1088/0268-1242/27/12/124004Search in Google Scholar
[24] Stanislavchuk TN, Kang TD, Rogers PD, Standard EC, Basistyy R, Kotelyanskii AM, et al. Synchrotron radiation-based far-infrared spectroscopic ellipsometer with full Mueller-matrix capability. Rev Sci Instr. 2013;84:023901.10.1063/1.4789495Search in Google Scholar PubMed
[25] Kuzmenko AM, Dziom V, Shuvaev A, Pimenov A, Schiebl M, Mukhin AA, et al. Large directional optical anisotropy in multiferroic ferroborate. Phys Rev B. 2015;92:184409.10.1103/PhysRevB.92.184409Search in Google Scholar
[26] Mukhin AA. Unpublished data.Search in Google Scholar
[27] Vasiliev AN, Popova EA. Rare-earth ferroborates RFe3(BO3)4. Low Temp Phys. 2006;32:735–47.10.1063/1.2219496Search in Google Scholar
[28] Zvezdin AK, Krotov SS, Kadomtseva AM, Vorob’ev GP, Popov YF, Pyatakov AP, et al. Magnetoelectric effects in gadolinium iron borate GdFe3(BO3)4. JETP Lett. 2005;81:272–6.10.1134/1.1931014Search in Google Scholar
[29] Zvezdin AK, Vorob’ev GP, Kadomtseva AM, Popov YF, Pyatakov AP, Bezmaternykh LN, et al. Magnetoelectric and magnetoelastic interactions in NdFe3(BO3)4 multiferroics. JETP Lett. 2006;83:509–14.10.1134/S0021364006110099Search in Google Scholar
[30] Popov AI, Plokhov DI, Zvezdin AK. Quantum theory of magnetoelectricity in rare-earth multiferroics: Nd, Sm, and Eu ferroborates. Phys Rev B. 2013;87:024413.10.1103/PhysRevB.87.024413Search in Google Scholar
[31] Kuz’menko AM, Mukhin AA, Ivanov VY, Kadomtseva AM, Bezmaternykh LN. Effects of the interaction between R and Fe modes of the magnetic resonance in RFe3(BO3)4 rare-earth iron borates. JETP Lett. 2011;94:294–300.10.1134/S0021364011160119Search in Google Scholar
[32] Zheludev A, Sato T, Masuda T, Uchinokura K, Shirane G, Roessli B. Spin waves and the origin of commensurate magnetism in Ba2CoGe2O7. Phys Rev B. 2003;68:024428.10.1103/PhysRevB.68.024428Search in Google Scholar
[33] Hutanu V, Sazonov A, Murakawa H, Tokura Y, Náfrádi B, Chernyshov D. Symmetry and structure of multiferroic Ba2CoGe2O7. Phys. Rev. B 2011;84:212101.10.1103/PhysRevB.84.212101Search in Google Scholar
[34] Murakawa H, Onose Y, Miyahara S, Furukawa N, Tokura Y. Ferroelectricity induced by spin-dependent metal-ligand hybridization in Ba2CoGe2O7. Phys Rev Lett. 2010;105:137202.10.1103/PhysRevLett.105.137202Search in Google Scholar PubMed
[35] Murakawa H, Onose Y, Miyahara S, Furukawa N, Tokura Y. Comprehensive study of the ferroelectricity induced by the spin-dependent d-p hybridization mechanism in Ba2XGe2O7 (X = Mn Co and Cu). Phys Rev B. 2012;85:174106.10.1103/PhysRevB.85.174106Search in Google Scholar
[36] Yi HT, Choi YJ, Lee S, Cheong S-W. Multiferroicity in the square-lattice antiferromagnet of Ba2CoGe2O7. Appl Phys Lett. 2008;92:212904.10.1063/1.2937110Search in Google Scholar
[37] Yamauchi K, Barone P, Picozzi S. Theoretical investigation of magnetoelectric effects in Ba2CoGe2O7. Phys Rev B. 2011;84:165137.10.1103/PhysRevB.84.165137Search in Google Scholar
[38] Perez-Mato JM, Ribeiro JL. On the symmetry and the signature of atomic mechanisms in multiferroics: the example of Ba2CoGe2O7. Acta Crystallogr Sect A. 2011;67:264–8.10.1107/S0108767311010282Search in Google Scholar PubMed
[39] Toledano P, Khalyavin DD, Chapon LC. Spontaneous toroidal moment and field-induced magnetotoroidic effects in Ba2CoGe2O7. Phys Rev B. 2011;84:094421.10.1103/PhysRevB.84.094421Search in Google Scholar
[40] Arima T. Ferroelectricity induced by proper-screw type magnetic order. J Phys Soc Jpn. 2007;76:073702.10.1143/JPSJ.76.073702Search in Google Scholar
[41] Bordacs S, Kezsmarki I, Szaller D, Demko L, Kida N, Murakawa H, et al. Chirality of matter shows up via spin excitations. Nat Phys. 2012;8:734–8.10.1038/nphys2387Search in Google Scholar
[42] Penc K, Romhányi J, Rõõm T, Nagel U, Antal Á, Fehér T, et al. Spin-stretching modes in anisotropic magnets: spin-wave excitations in the multiferroic Ba2CoGe2O7. Phys Rev Lett. 2012;108:257203.10.1103/PhysRevLett.108.257203Search in Google Scholar PubMed
[43] Stokes GG. On the perfect Blackness of the Central Spot in Newton’s Rings, and on the Verification of Fresnel’s Formula for the intensities of Reflected and Reflacted Rays. In: Cambridge Library Collection – Mathematics vol. 2. Cambridge: Cambridge University Press, 2009:89–103.10.1017/CBO9780511702259.008Search in Google Scholar
[44] von Helmholtz H. Handbuch der physiologischen Optik, vol. 1, 1st ed. Leipzig: Leopold Voss, 1856.Search in Google Scholar
[45] Born M, Wolf E. Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. Cambridge: Cambridge University Press, 2000.10.1063/1.1325200Search in Google Scholar
[46] Kuzmenko AM, Dziom V, Shuvaev A, Pimenov A, Szaller D, Mukhin AA, et al. Sign change of polarization rotation under time or space inversion in magnetoelectric YbAl3(BO3)4. Phys Rev B. 2019;99:224417.10.1103/PhysRevB.99.224417Search in Google Scholar
[47] Kézsmárki I, Szaller D, Bordács S, Kocsis V, Tokunaga Y, Taguchi Y, et al. One-way transparency of four-coloured spin-wave excitations in multiferroic materials. Nat Commun. 2014;5:3203.10.1038/ncomms4203Search in Google Scholar PubMed
[48] Kronig RL. On the theory of dispersion of X-rays. J Opt Soc Am. 1926;12:547–57.10.1364/JOSA.12.000547Search in Google Scholar
[49] Kramers HA. Diffusion of light by atoms. Atti Congr Int Fisici. 1927;2:545–57.Search in Google Scholar
[50] Arima T. Magneto-electric optics in non-centrosymmetric ferromagnets. J Phys: Condens Matter. 2008;20:434211.10.1088/0953-8984/20/43/434211Search in Google Scholar
[51] Bordács S, Kocsis V, Tokunaga Y, Nagel U, Rõõm T, Takahashi Y, et al. Unidirectional terahertz light absorption in the pyroelectric ferrimagnet CaBaCo4O7. Phys Rev B. 2015;92:214441.10.1103/PhysRevB.92.214441Search in Google Scholar
[52] Rikken GL, Raupach E. Observation of magneto-chiral dichroism. Nature. 1997;390:493.10.1038/37323Search in Google Scholar
[53] Szaller D, Bordács S, Kézsmárki I. Symmetry conditions for nonreciprocal light propagation in magnetic crystals. Phys Rev B. 2013;87:014421.10.1103/PhysRevB.87.014421Search in Google Scholar
[54] Kocsis V, Penc K, Rõõm T, Nagel U, Vít J, Romhányi J, et al. Identification of antiferromagnetic domains via the optical magnetoelectric effect. Phys Rev Lett. 2018;121:057601.10.1103/PhysRevLett.121.057601Search in Google Scholar PubMed
[55] Kuzmenko AM, Szaller D, Kain T, Dziom V, Weymann L, Shuvaev A, et al. Switching of magnons by electric and magnetic fields in multiferroic borates. Phys Rev Lett. 2018;120:027203.10.1103/PhysRevLett.120.027203Search in Google Scholar PubMed
[56] Tokura Y. Multiferroics – toward strong coupling between magnetization and polarization in a solid. J Magn Magn Mater. 2007;310:1145–50.10.1016/j.jmmm.2006.11.198Search in Google Scholar
[57] Kézsmárki I, Kida N, Murakawa H, Bordács S, Onose Y, Tokura Y. Enhanced directional dichroism of terahertz light in resonance with magnetic excitations of the multiferroic Ba2CoGe2O7 oxide compound. Phys Rev Lett. 2011;106:057403.10.1103/PhysRevLett.106.057403Search in Google Scholar PubMed
[58] Viirok J, Nagel U, Rõõm T, Farkas DG, Balla P, Szaller D, et al. Directional dichroism in the paramagnetic state of multiferroics: A case study of infrared light absorption in Sr2CoSi2O7 at high temperatures. Phys Rev B. 2019;99:014410.10.1103/PhysRevB.99.014410Search in Google Scholar
[59] Kézsmárki I, Nagel U, Bordács S, Fishman RS, Lee JH, Yi HT, et al. Optical diode effect at spin-wave excitations of the room-temperature multiferroic BiFeO3. Phys Rev Lett. 2015;115:127203.10.1103/PhysRevLett.115.127203Search in Google Scholar PubMed
© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Controlling of light with electromagnons
- Sample preparation for Raman microspectroscopy
- Spiral spin structures and skyrmionsin multiferroics
- Determining wildland fire markers in residential structures using thermal desorption gas chromatography mass spectrometry
- Optics/instrumentation
- Green routes to silicon-based materials and their environmental implications
- Dynamical magnetoelectric phenomena of skyrmions in multiferroics
Articles in the same Issue
- Controlling of light with electromagnons
- Sample preparation for Raman microspectroscopy
- Spiral spin structures and skyrmionsin multiferroics
- Determining wildland fire markers in residential structures using thermal desorption gas chromatography mass spectrometry
- Optics/instrumentation
- Green routes to silicon-based materials and their environmental implications
- Dynamical magnetoelectric phenomena of skyrmions in multiferroics