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