Methods of Calculation of the Magneto-Optical Characteristics of Ferromagnetic Materials
DOI:
https://doi.org/10.15407/ujpe65.4.310Keywords:
magneto-optical properties, optical conductivity tensor, off-diagonal components, Kerr effect, ferromagnetic materialsAbstract
We have calculated the optical and magneto-optical properties of ferromagnetics in a wide spectral range hv = 1.24–5.15 eV, by applying theoretical models which were reported earlier in the literature. This allowed us to find a connection between the conductivity and the measured values of the complex Kerr angle Θ in order to establish the most proper technique for processing the experimental data. The behavior of the dispersion curves of diagonal and non-diagonal components of the tensor of optical conductivity depends on the choice of signs of the imaginary parts of a complex Kerr angle and a refractive index, which should be taken into account in the data analysis. The differences between dispersion dependences are insignificant in the region of energies higher than 4.5 eV. In this paper, the classical theory of free electrons in metals has been applied to give more details about the magneto-optical Kerr effect in ferromagnetic samples.
References
John Kerr. On rotation of the plane of polarization by reflection from the pole of a magnet. Phil. Magaz. 3, 321 (1877). https://doi.org/10.1080/14786447708639245
A.D. Buckingham. Theoretical studies of the Kerr effect I: Deviations from a linear polarization law. Proc. Phys. Soc. A 68, 905 (1955). https://doi.org/10.1088/0370-1298/68/10/307
A.D. Buckingham. Theoretical studies of the Kerr effect II: The influence of pressure. Proc. Phys. Soc. A 68, 910 (1955). https://doi.org/10.1088/0370-1298/68/10/308
L. Uba, S. Uba, V.N. Antonov. Magneto-optical Kerr spectroscopy of noble metals. Phys. Rev. B 96, 235132 (2017). https://doi.org/10.1103/PhysRevB.96.235132
Xiang Gao, John A. Woollam, R.D. Kirby, D.J. Sellmyer, C.T. Tanaka, J. Nowak, J.S. Moodera. Dielectric tensor for magneto-optic NiMnSb. Phys. Rev. B 59, 9965 (1999). https://doi.org/10.1103/PhysRevB.59.9965
I.M. Boswarva, R.E. Howard, A.B. Lidiard, C.A. Coulson. Faraday effect in semiconductors. Proc. Royal Soc. London A 269, 125 (1962). https://doi.org/10.1098/rspa.1962.0166
W.H. Kleiner. Space-time symmetry of transport coefficients. Phys. Rev. 142, 318 (1966). https://doi.org/10.1103/PhysRev.142.318
V. Staschuk, V. Kravets, V. Lysiuk, O. Polyanska, V. Stukalenko, A. Yampolsky. Structure and optical properties of (Co41Fe39B20)x(SiO2)1−x nanocomposites. Ukr. J. Phys. 62 (8), 662 (2017). https://doi.org/10.15407/ujpe62.08.0666
D.H. Seib, W.E. Spicer. Photoemission and оptical studies of Cu-Ni аlloys. Phys. Rev. В 2, 1676 (1970). https://doi.org/10.1103/PhysRevB.2.1676
K.H.J. Buschow, P.G. van Engen, R. Jongebreur.Magneto-optical properties of metallic ferromagnetic materials. J. Magn. Magn. Mater. 38, 1 (1983). https://doi.org/10.1016/0304-8853(83)90097-5
S. Uba, A. Bonda, L. Uba, L. V. Bekenov, V.N. Antonov, A. Ernst. Electronic structure and magneto-optical Kerr effect spectra of ferromagnetic shape-memory Ni-Mn-Ga alloys: Experiment and density functional theory calculations. Phys. Rev. B 94, 054427 (2016) . https://doi.org/10.1103/PhysRevB.94.054427
P.N. Argyres. Theory of the Faraday and Kerr effects in ferromagnetics. Phys. Rev. 97, 2, 334 (1955). https://doi.org/10.1103/PhysRev.97.334
M. Born, E. Wolf. Principles of Optics (Pergamon Press, 1991).
S. Bord'acs, I. K'ezsm'arki, K. Ohgush, Y. Tokura. Experimental band structure of the nearly half-metallic CuCr2Se4: An optical and magneto-optical study. New J. Phys. 12, 053039 (2010). https://doi.org/10.1088/1367-2630/12/5/053039
P.M. Oppeneer, J. Sticht, T. Maurer, J. K¨obler. Ab initio investigation of microscopic enhancement factors in tuning the magneto-optical Kerr effect. Zeitschrift f¨ur Physik B Condensed Matter. 88, 309 (1992). https://doi.org/10.1007/BF01470918
Chun Yeol You, Sung Chul Shin. Determination of the off-diagonal element of the dielectric tensor without measuring the ellipticity. Appl. Phys. Lett. 68, 2882 (1996). https://doi.org/10.1063/1.116319
W. Reim, J. Schoenes. Magneto-optical spectroscopy of f-electron systems. In: Handbook of Ferromagnetic Materials, edited by K.H.J. Buschow, E.P. Wohlfarth (North-Holland, 1990), Ch. 2, pp. 133 -236. https://doi.org/10.1016/S1574-9304(05)80062-8
S. Patankar, J.P. Hinton, J. Griesmar, J. Orenstein, J.S. Dodge, Xufeng Kou, Lei Pan, Kang L. Wang, A.J. Bestwick, E.J. Fox, D. Goldhaber-Gordon, Jing Wang, and Shou-Cheng Zhang. Resonant magneto-optic Kerr effect in the magnetic topological insulator Cr:(Sbx,Bi1−x)2Te3. Phys. Rev. B 92, 214440 (2015). https://doi.org/10.1103/PhysRevB.92.214440
Frederic J. Kahn, P.S. Pershan, J.P. Remeika. Ultraviolet magneto-optical properties of single-crystal orthoferrites, garnets, and other ferric oxide compounds. Phys. Rev. 186 (3), 891 (1969). https://doi.org/10.1103/PhysRev.186.891
Sang Y. Kim, Sang J. Kim, Hun Seo, Myong R. Kim. Complex refractive indices of GeSbTe-alloy thin films: Effect of nitrogen doping and wavelength dependence. Jpn. J. Appl. Phys. 38, 1713 (1999). https://doi.org/10.1143/JJAP.38.1713
L.V. Poperenko, Yu.V. Kudrjavtsev, V.S. Stashchuk, Yang Pak Li. Optics of Metal Structures (Kyiv University, 2013) (in Ukrainian).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.