Correlation of electronic structure and martensitic transition in epitaxial ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Ga}$ films

We investigate the martensitic transition of single crystalline ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Ga}\left(110\right)∕{\mathrm{Al}}_2{\mathrm{O}}_3\left(11\overline{2}0\right)$ and ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Ga}\left(100\right)∕\mathrm{Mg}\mathrm{O}\left(100\right)$ films using magnetometry, x-ray diffraction, x-ray absorption spectroscopy, and x-ray magnetic circular dichroism. The martensitic transition from the cubic austenite phase to the low symmetry martensite phase depends strongly on the chosen substrate. For (110) oriented films on ${\mathrm{Al}}_2{\mathrm{O}}_3$, the martensitic phase is significantly more stable than for the (100) oriented films on MgO. A remarkable change of the Ni x-ray absorption spectra occurs at the transition, indicating specific changes of the electronic structure. The observed changes are in agreement with theoretical predictions. The orbital to spin momentum ratio of the Ni moment increases significantly on entering the martensite state, thus explaining the macroscopic increase of magnetic anisotropy.

Figure 1

(Color online) 3D plot of ($h$00) scans of the (400) XRD reflection of the AS phase, indicating the MST with decreasing temperature. The individual scans were taken at constant temperature. The right inset shows the austenite phase. The left inset displays the twofold symmetry of the scattered intensity.

Figure 2

Maximum count rate of the austenite (220) and (400) reflections as function of temperature.

Figure 3

(Color online) Contour plot of $kl$ scans near the original, specular (400) XRD reflection of the AS phase. In the martensite phase, intensity is detected at the reciprocal lattice plane with coordinates $(h=3.85kl)$ (a) and $(h=4.20kl)$ (b), respectively.

Figure 4

(Color online) Magnetization vs temperature for a ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Ga}$ film on ${\mathrm{Al}}_2{\mathrm{O}}_3$ substrate. The high field data have been corrected with a constant diamagnetic contribution from the substrate. Inset: hysteresis loops for film parallel magnetic field at temperatures above and below the MST.

Figure 5

(Color online) (a) Absorption coefficient $k=(k^{+}+k^{-})∕2={\mu }_{\mathrm{Mn}}d=-\ln (I∕I_{\mathit{ref}})$ of x-ray light transmitted through a $d=83\mathrm{nm}$ thick ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Ga}$ (110) film on ${\mathrm{Al}}_2{\mathrm{O}}_3\left(11\overline{2}0\right)$ at the Mn $L_3$ edge for $T<T_{\mathrm{MST}}$ (dashed blue line) and $T>T_{\mathrm{MST}}$ (full red line). The green line is the difference curve $\Delta {\mu }_{\mathrm{Mn}}d$ multiplied by a factor of 5. (b) XMCD signal $({\mu }^{+}-{\mu }^{-})d$ for the respective temperatures.

Figure 6

(Color online) (a) Absorption coefficient $k=(k^{+}+k^{-})∕2={\mu }_{\mathrm{Mn}}d=-\ln (I∕I_{\mathrm{ref}})$ of x-ray light transmitted through a $d=83\mathrm{nm}$ thick ${\mathrm{Ni}}_2\mathrm{Mn}\mathrm{Ga}\left(110\right)$ film on ${\mathrm{Al}}_2{\mathrm{O}}_3\left(11\overline{2}0\right)$ at the Ni $L_3$ edge for $T<T_{\mathrm{MST}}$ (dashed blue line) and $T>T_{\mathrm{MST}}$ (full red line). The green line is the difference curve $\Delta {\mu }_{\mathrm{Ni}}d$ multiplied by a factor of 5. (b) XMCD signal $({\mu }^{+}-{\mu }^{-})d$ for the respective temperatures.

Figure 7

(Color online) (a) Absorption coefficient for $T<T_{\mathrm{MST}}$ (dashed blue line) and $T>T_{\mathrm{MST}}$ (full red line). Corresponding data from ab initio theory (Ref. 11) are shifted for comparison. (b) Difference between the data shown in (a) for $T>T_{\mathrm{MST}}$ and $T<T_{\mathrm{MST}}$. (c) Temperature dependence of the intensity of the XRD (400) reflection (full circles, red), $I\left(400\right)$, and of the intensity increase $\Delta I\left(\mathrm{A}\right)=I\left(T\right)-I\left(202\mathrm{K}\right)$ of feature A, as indicated in (a), in the Ni-XAS spectra (open circles), normalized to their respective room temperature values.

Figure 8

(Color online) (a) Orbital to spin momentum ratio for Mn (black triangles) and Ni (blue circles) of the sample shown in Fig. 7. (b) Effective spin moments per $d$ hole, $N_h$, for Mn (black triangles) and Ni (blue circles), excluding a $jj$-mixing correction factor $\left(c_{jj}\right)$ in the case of Mn. (c) Sum moment per f.u. calculated from spin and orbital moments of Ni and Mn assuming $N_h\left(\mathrm{Ni}\right)=1.3$, $N_h\left(\mathrm{Mn}\right)=4.3$, and $c_{jj}=1.5$ (circles). Error bars denote the statistical error, only, not considering systematic errors due $N_h$, $c_{jj}$, and finite polarization. The full red line indicates saturation magnetization data measured by magnetometry $\left(5\mathrm{T}\right)$. The vertical lines indicate $T_{\mathrm{MST}}$.