Loss of altermagnetic order and smooth restoration of Kramers' spin degeneracy with increasing temperature in CrSb and MnTe

Abstract

We describe how thermally induced spin fluctuations modify the electronic structures of two prototypical altermagnets, CrSb and MnTe, via application of the disordered local moment picture. For both materials, our self-consistent, ab initio calculations demonstrate that local magnetic moments persist on Cr and Mn atoms in their paramagnetic states, necessitating a spin-polarised description of the electronic structure even above the Néel temperature, $T_\mathrm{N}$. Moreover, Kramers' spin degeneracy, which is broken for both materials in their altermagnetic ground states, is shown to be smoothly restored - on the average - as the local moments thermally disorder. In metallic CrSb, this occurs at temperatures well below $T_\mathrm{N}$ and the signature effects of its altermagnetism are lost as the magnetic disorder induces heavy smearing of strongly dispersive electronic states around the Fermi energy. By contrast, in semiconducting MnTe, with its band gap largely unaffected by magnetic disorder, the spin degeneracy only returns at temperatures close to and above $T_\mathrm{N}$. We quantify the temperature dependence of the altermagnetic order parameter and the underlying electronic structures of both materials, with significant implications for their spin transport properties.

Figures (3)

• Figure 1: Comparison of the electronic structure of (a) CrSb and (b) MnTe in their altermagnetic ground states at $T=0$ K. We show both the band structure and total electronic density of states. For CrSb, which is metallic, we also show two slices of the Fermi surface. In both materials, the altermagnetic band splitting is visible along the $-M'$-$\Gamma'$-$M'$ path in reciprocal space.
• Figure 2: Comparison of the electronic structure of CrSb (a) and MnTe (b) in their paramagnetic states, as described within the DLM picture. We show both the BSF and total electronic density of states, both of which are heavily smeared at certain points by the magnetic disorder. For CrSb, which is metallic, we also show two slices of the Fermi surface. Because the Fermi surface is washed out by the magnetic disorder, we plot a contour of constant spectral weight, evidencing the six-fold degeneracy in both planes. In MnTe, which is semiconducting, the bandgap is largely unaffected by the magnetic disorder. Where band splitting was evidenced in Fig. \ref{['fig:altermagnetic_band_structure']}, we show the BSF in purple to indicate that it is now fully spin-degenerate.
• Figure 3: Evolving electronic structure of CrSb and MnTe as a function of temperature, $T$ and magnetic order, $m$. Panels (a) and (b) show the spin-resolved DOS of Cr and Mn in the limiting cases of $m=0$ and $m=1$. For $m=0$ this is a projection onto a single Cr/Mn atom embedded in the DLM-CPA effective medium. Panels (c) and (d) show calculated $m(T)$ for both materials. Finally, panels (e) and (f) show a spin-resolved, constant-$\mathbf{k}$ slice of the BSF for both materials as a function of magnetic order parameter around $E_\mathrm{F}$ at $\tilde{\mathbf{k}} = (\frac{2\pi\sqrt{3}}{3a}, 0, \frac{\pi}{2c})$, halfway between the points $\Gamma'$ and $M'$. Though local exchange-splitting around atoms persists even in the paramagnetic state, the altermagnetic band splitting rapidly diminishes with decreasing $m$.