Electronic structure and magneto-optical Kerr effect spectra of ferromagnetic shape-memory Ni-Mn-Ga alloys: Experiment and density functional theory calculations

Abstract

In this joint experimental and ab initio study, we focused on the influence of the chemical composition and martensite phase transition on the electronic, magnetic, optical, and magneto-optical properties of the ferromagnetic shape-memory Ni-Mn-Ga alloys. The polar magneto-optical Kerr effect (MOKE) spectra for the polycrystalline sample of the Ni-Mn-Ga alloy of Ni 60 Mn 13 Ga 27 composition were measured by means of the polarization modulation method over the photon energy range 0.8 hν 5.8 eV in magnetic field up to 1.5 T. The optical properties (refractive index n and extinction coefficient k) were measured directly by spectroscopic ellipsometry using the rotating analyzer method. To complement experiments, extensive firstprinciples calculations were made with two different first-principles approaches combining the advantages of a multiple scattering Green function method and a spin-polarized fully relativistic linear-muffin-tin-orbital method. The electronic, magnetic, and MO properties of Ni-Mn-Ga Heusler alloys were investigated for the cubic austenitic and modulated 7M-like incommensurate martensitic phases in the stoichiometric and off-stoichiometric compositions. The optical and MOKE properties of Ni-Mn-Ga systems are very sensitive to the deviation from the stoichiometry. It was shown that the ab initio calculations reproduce well experimental spectra and allow us to explain the microscopic origin of the Ni 2 MnGa optical and magneto-optical response in terms of interband transitions. The band-by-band decomposition of the Ni 2 MnGa MOKE spectra is presented and the interband transitions responsible for the prominent structures in the spectra are identified.

Methods of Calculation of the Magneto-Optical Characteristics of Ferromagnetic Materials

“…In some cases, different expressions for˜are used:˜= − [10,17] and˜= + [11,13]. The similar situation is with the expression for the complex Kerr angle [11,[14][15][16][17]. We have found that such differences are noteworthy and may result in different dispersion curves for non-diagonal components of the optical conductivity tensor˜m opt (ℎ ).…”

“…Pairs of curves calculated applying different signs in expressions (A-D) and which almost overlap are marked by two numbers each. Some curves are identical [in the case of positive numbers for 2 (1,2) and (11,12), respectively, A, B versions of expression (14) and C, D versions of expression (16)]; the others have the same values, but opposite signs [absolute values (7,8) and (11,12) of C, D, versions of expressions (15) and (16) respectively].…”

“…However, the authors introduced diverse expressions which link the refractive index˜and the Kerr angleΘ:˜(ℎ ) = = (ℎ ) ± (ℎ ),Θ(ℎ ) = (ℎ ± (ℎ ). In some cases, different expressions for˜are used:˜= − [10,17] and˜= + [11,13]. The similar situation is with the expression for the complex Kerr angle [11,[14][15][16][17].…”

“…Magneto-optical properties of the amorphous ferromagnetic material, Co 41 Fe 39 B 20 , which can be used further as a part of (Co 41 Fe 39 B 20 ) (SiO 2 ) 100− nanocomposites as a more reliable substance for recording information, were studied in [11]. Various models from the literature connect its optical and magneto-optical properties by describing the relationship between the optical conductivity and the measured values of the real (ℎ ) (polarization plane rotation) and complex parts (ℎ ) (ellipticity) of the complex Kerr angleΘ(ℎ ).…”

“…In order to determine the optical conductivity tensor components, a method based on measurements of the complex Kerr angleΘ(ℎ ) was applied [12][13][14][15][16][17][18][19][20]. The relations connecting the component of the optical conductivity tensor˜(or dielectric permit-tivity˜) with the complex Kerr rotation angle are presented, for example, in [11,[14][15][16][17][18][19]. However, the authors introduced diverse expressions which link the refractive index˜and the Kerr angleΘ:˜(ℎ ) = = (ℎ ) ± (ℎ ),Θ(ℎ ) = (ℎ ± (ℎ ).…”