Band structure control in the altermagnetic candidate MnTe by temperature and strain

Abstract

The temperature and strain dependences of the optical conductivity spectrum of hexagonal manganese telluride (MnTe) were measured, revealing absorption in the terahertz (THz) region from spin-split bands to acceptor levels. The temperature dependence of the THz absorption peak is consistent with that of a ferromagnetic phase transition, even though MnTe exhibits no net magnetism. The temperature dependence was attributed to a change in the altermagnetic electronic structure. A Fano-like antisymmetric line shape in the optical phonon absorption was observed, which originates from the interaction between optical phonons and the spin-split bands. Additionally, under negative uniaxial pressure, the THz peak shifts away from the Fermi level (EF), suggesting that spin-splitting bands at energies away from EF, consistent with the theoretical prediction that the spin-splitting angle decreases. The observed behavior of the THz peak clearly shows that MnTe has the altermagnetic electronic structure.

Figures (7)

• Figure 1: (a) Temperature-dependent reflectivity [$R(\omega)$] spectra of the as-grown $(001)$ surfaces of MnTe in the photon energy $\hbar\omega$ range of $0.01-30$ eV after the reduction of the interference shown in the inset. The interference-reduction method is described in Sec. S2 in the supplementary material SM. A peak structure at around $\hbar\omega$$\sim0.02$ eV originates from optical phonons. (Inset) Raw $R(\omega)$ spectra at $T = 10$ and 370 K in the infrared region. Strong interference is observed in the photon energy above 0.1 eV due to the transparent character of the thin (thickness $\sim0.35$ mm) sample. (b) Temperature-dependent optical conductivity [$\sigma_1(\omega)$] spectra in the $\hbar\omega$ range below 2 eV obtained from the $R(\omega)$ spectra in (a). (Inset) Wide-range $\sigma_1(\omega)$ spectrum at $T = 370~{\rm K}$.
• Figure 2: (a) Temperature-dependent $R(\omega)$ spectra near the energy gap. Each spectrum is vertically shifted by 0.02 as the temperature increases. As shown in Fig. \ref{['fig:R']}(a), interferences are visible below the energy gap, and ends of the interference (marked by down arrows, evaluated as the crossing point of the envelop lines as shown at $T = 150~{\rm K}$) correspond to the onset of the energy gap ($E_g$). (b) Temperature-dependent $\sigma_1(\omega)$ spectra in the $\hbar\omega$ region below 300 meV. (c) $E_g$ (red solid circles) and the effective electron number ($N^{*}$, blue open squares) evaluated in the $\hbar\omega$ range of 20--200 meV as a function of temperature, accompanied by the square of magnetization [$M(T)^2$, thick dashed line] expected with the Mn$^{2+}~3d^5$ high-spin state ($J = 5/2$). $T_{\rm N}$ is shown by a vertical arrow.
• Figure 3: (a) $\sigma_1(\omega)$ spectra (circles) at temperatures of 10, 100, 200, and 370 K in the $\hbar\omega$ region below 150 meV and the fitting curves with three peaks at about 17, 20, and 60 meV at 10 K. (b) Fano asymmetric parameter ($1/q^2$, red solid circles) of the phonon peak and the peak intensity ($N^{*}$, blue open squares) of the 20-meV peak as a function of temperature. (c) Expected temperature-dependent electronic-structure change near $E_{\rm F}$ and the origins of the peaks in $\sigma_1(\omega)$ spectra.
• Figure 4: Negative strain dependence of the $\sigma_1(\omega)$ spectrum of MnTe at 10 K (solid lines) compared with the spectra at 10 and 200 K without applying strain (dashed lines). The value of the negative strain is described by the applied angle of the screw rotation, which is proportional to the negative strain strength with $\sim 0.8~\%$ at 360 degree without samples as shown in Fig. S2(c) in the supplementary material SM.
• Figure S1: (a) $\sigma_1(\omega)$ spectra (red circles) of all measured temperatures in the $\hbar\omega$ range below 150 meV and fitted by eq. \ref{['eq:fitting']}. The Fano function fitted to the phonon line, the Lorentz function fitted to the 20-meV peak, and the Lorentz function fitted to the in-gap peak are plotted as magenta dot-dashed, blue dotted, and green dashed lines, respectively, and their sum is shown as a black solid line. (Inset) Enlarged figure in the $\hbar\omega$ range of 12--22 meV. Peak energies (b), peak width (c), and effective electron number ($N^{*}$, d) of three peaks as a function of temperature. The phonon peak, the 20-meV peak, and the in-gap peak are plotted as red solid circles, blue open squares, and green solid triangles, respectively.