Principal spectra describing magnetooptic permittivity tensor in cubic crystals

Abstract

We provide unified phenomenological description of magnetooptic effects being linear and quadratic in magnetization. The description is based on few principal spectra, describing elements of permittivity tensor up to the second order in magnetization. Each permittivity tensor element for any magnetization direction and any sample surface orientation is simply determined by weighted summation of the principal spectra, where weights are given by crystallographic and magnetization orientations. The number of principal spectra depends on the symmetry of the crystal. In cubic crystals owning point symmetry we need only four principal spectra. Here, the principal spectra are expressed by ab-initio calculations for bcc Fe, fcc Co and fcc Ni in optical range as well as in hard and soft x-ray energy range, i.e. at the 2p-and 3p-edges. We also express principal spectra analytically using modified Kubo formula. PACS numbers: 42.50.Ct, 78.20.Ls, 78.70.Dm, 78.40.Kc There is a vast number of physical phenomena proportional to quadratic form of magnetization. In case of dc transport phenomena, the most well-known examples are anisotropy magnetoresistance (AMR) [1,2] or longitudinal Hall effect [3]. Within the magnetooptic community, the field of magnetooptic effects quadratic in magnetization is complicated by incredible number of nomenclature, being called Cotton-Mouton effect, Voigt effect, quadratic magnetooptic Kerr effect (QMOKE) [4], magnetic linear birefringence, X-ray magnetic linear dichroism (XMLD) [5,6], magnetic double refraction, magnetooptic orientation effect, magnetooptic anisotropy, Hubert-Schäfer effect or magnetorefractive effect [7,8]. The nomenclature is not strictly defined, however it refers either to type of samples (liquid, gas, solid state) or it refers to experimental configurations of the setup (namely detecting change of light intensity or detecting change of polarization state upon variation of magnetization direction). Although those effects are usually not considered as single phenomena, they originate from equal parts of permittivity tensors (i.e. from equal symmetry breaking). Notice, that recently new types of quadratic-in-magnetization effects arose, for example anisotropic magneto-thermopower [9, 10] in spin-caloritronics. Within some generalization, one can expect that any magneto-transport linear in magnetization will have its quadratic-in-magnetization counterpart.The first observation of magnetooptic effects quadratic in magnetization dates back more than century ago in works of Kerr [11], Majorana [12] and Cotton and Moutton [13], where magnetic birefringence was observed in liquids and colloids. Later, those quadratic magnetooptic response was observed in gases, solid state materials and obviously also in ferromagnetic materials. See large reviews of Smolenskii et al [14] and Ferré, Gehring [15] from 80's. The anisotropy of magnetooptic effects (i.e. dependence of QMOKE on crystal and field orientations) was investigated for various systems. However, the investigation were mostly d...

Dynamics of optical excitations in a Fe/MgO(001) heterostructure from time-dependent density functional theory

“…3. The bulk results agree well with the results of previous calculations [79][80][81][82] obtained within the same level of approximation. For metallic Fe, including the microscopic contributions from the exchange correlation kernel does not notably alter the results, even with long-range corrections.…”

Quadratic magneto-optic Kerr effect spectroscopy of Fe epitaxial films on MgO(001) substrates

“…We discuss possibilities of how to handle the Drude contribution in Appendix D. By broadening the spectra and applying Kramers-Kronig relations, we obtain a full permittivity tensor ε for each direction of M . The spectra for K, G s and 2G 44 are obtained directly from the permittivity tensors ε [72].…”

Cubic magneto-optic Kerr effect in Ni(111) thin films with and without twinning

“…QMOKE showed to be sensitive to the structural ordering of Heusler compounds [17,18] and to spin-orbit torque effects [19]. Vectorial magnetometry including QMOKE [20][21][22][23][24], QMOKE spectroscopy [18,[25][26][27][28], as well as QMOKE microscopy [29,30] have been realized. However, any higher-order MOKE, such as cubic-inmagnetization MOKE (CMOKE), being proportional to M 3 , has only been mentioned very rarely so far [31][32][33] and has not yet been systematically investigated.…”