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

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 ${\mathrm{Ni}}_{60}{\mathrm{Mn}}_{13}{\mathrm{Ga}}_{27}$ composition were measured by means of the polarization modulation method over the photon energy range $0.8\le h\nu \le 5.8$ 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 first-principles 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 ${\mathrm{Ni}}_2\mathrm{MnGa}$ optical and magneto-optical response in terms of interband transitions. The band-by-band decomposition of the ${\mathrm{Ni}}_2\mathrm{MnGa}$ MOKE spectra is presented and the interband transitions responsible for the prominent structures in the spectra are identified.

Figure 1

Schematic representation of the crystal structure of ${\mathrm{Ni}}_2\mathrm{MnGa}$ alloy: (a) a high-temperature austenitic phase with a cubic lattice of $L{2}_1$ type (contains four primitive cells); (b) a body centered tetragonal $\left(bct\right)$ martensitic phase of $L{1}_0$ type; (c) the 3M premartensitic structure of $Pnmn$ orthorhombic type; (d) the martensitic 7M superstructure of $Immm$ orthorhombic type (e) modulated orthorhombic unite cell of ${\mathrm{Ni}}_2\mathrm{MnGa}$ martensite phase projected in the $a\text{−}c$ plane highlighting the atomic position modulation in its rational approximant 7M structure.

Figure 2

The symmetry separated GGA partial density of states [in states/(atom eV)] of ${\mathrm{Ni}}_2\mathrm{MnGa}$ for the high-temperature $Fm\overline{3}m$ structure.

Figure 3

The total [in states/(cell eV)] and partial [in states/(atom eV)] DOSs of ${\mathrm{Ni}}_2\mathrm{MnGa}$ for the 7M-like incommensurate modulated martensitic phase with the orthorhombic $Immm$ space group structure.

Figure 4

Upper panel: comparison between experimental diagonal optical conductivity ${\sigma }_{1xx}$ spectra (open magenta circles) of ${\mathrm{Ni}}_2\mathrm{MnGa}$ (Ref. [53]) and the spectra calculated for austenitic $Fm\overline{3}m$ cubic structure (full line) approximation. Lower panel: comparison of the experimental diagonal optical conductivity spectra for a low temperature stoichiometric ${\mathrm{Ni}}_2\mathrm{MnGa}$ alloy (open magenta) from Ref. [53] and our measurements in a Ni-rich ${\mathrm{Ni}}_{60}{\mathrm{Mn}}_{13}{\mathrm{Ga}}_{27}$ alloy (closed red circles) in the martensitic phase with the theoretically calculated spectra for stoichiometric (full blue curve), Ni-rich ${\mathrm{Ni}}_{56}{\mathrm{Mn}}_{19}{\mathrm{Ga}}_{25}$ (dashed black curve) and ${\mathrm{Ni}}_{62}{\mathrm{Mn}}_{13}{\mathrm{Ga}}_{25}$ (dotted magenta curve) alloys of the low-temperature $Immm$ orthorhombic type.

Figure 5

Upper panel: comparison between the experimental Kerr rotation spectrum [57] of ${\mathrm{Ni}}_{50.1}{\mathrm{Mn}}_{28.4}{\mathrm{Ga}}_{21.5}$ in the austenitic phase at 337 K (open magenta circles) and the calculated spectrum for the cubic $Fm\overline{3}m$ structure (full blue line) of ${\mathrm{Ni}}_{50}{\mathrm{Mn}}_{28}{\mathrm{Ga}}_{22}$ composition. Middle panel: experimental Kerr rotation spectra [Ref. [57] (open magenta circles) and Ref. [56] (open green circles)] of ${\mathrm{Ni}}_{50.1}{\mathrm{Mn}}_{28.4}{\mathrm{Ga}}_{21.5}$ in the martensitic phase in comparison with the calculated spectrum (full blue line) of ${\mathrm{Ni}}_{50}{\mathrm{Mn}}_{28}{\mathrm{Ga}}_{22}$ composition. Lower panel: the experimental Kerr rotation spectrum of ${\mathrm{Ni}}_{60}{\mathrm{Mn}}_{13}{\mathrm{Ga}}_{27}$ alloy in the martensitic phase (open magenta circles) in comparison with the calculated spectrum for the orthorhombic structure with ${\mathrm{Ni}}_2\mathrm{MnGa}$ and ${\mathrm{Ni}}_{56}{\mathrm{Mn}}_{19}{\mathrm{Ga}}_{25}$ compositions (dashed red line and full blue line, respectively).

Figure 6

Comparison between the experimental off-diagonal optical conductivity $\omega {\sigma }_{xy}$ spectra (blue open circles) of ${\mathrm{Ni}}_{60}{\mathrm{Mn}}_{13}{\mathrm{Ga}}_{27}$ alloy in the martensitic phase and the calculated spectra for the orthorhombic structure with ${\mathrm{Ni}}_{56}{\mathrm{Mn}}_{19}{\mathrm{Ga}}_{25}$ composition (full red lines).

Figure 7

Contributions of different interband transitions to the diagonal ${\sigma }_{1xx}$ and off-diagonal ${\sigma }_{2xy}$ spectra (thick solid lines) of ${\mathrm{Ni}}_2\mathrm{MnGa}$.

Figure 8

Fully relativistic spin-polarized GGA energy band structure of ${\mathrm{Ni}}_2\mathrm{MnGa}$ near the Fermi level.

Figure 9

Decomposition of the ${\sigma }_{1xx}$ and ${\sigma }_{2xy}n\to m$ interband transitions in ${\mathrm{Ni}}_2\mathrm{MnGa}$ alloy into transitions localized around different symmetry points and symmetry directions in the BZ.