Exchange interactions, spin wave spectra, and critical (Néel) temperature calculations in altermagnetic MnGeP₂

We show that antiferromagnetic (AFM) chalcopyrite, I-42d, structure MnGeP₂ should be an altermagnet, where the two magnetic 3d-Mn atoms (with magnetic moments ~ +/-5 μ_B) of opposite spin are related by a two-fold rotation operation perpendicular to the main four-fold rotation inversion axis. Notably, the electronic band structure exhibits a sizable spin splitting (~0.4 eV) along low-symmetry lines, such as NP and SG, but zero splitting along various high-symmetry lines, in accordance with a group theoretical analysis.

We employ the quasiparticle-self-consistent GW method to calculate the electronic band structure, Heisenberg exchange interactions, and the magnon spectrum of MnGeP₂. The exchange interactions are obtained from the transverse spin-spin magnetic susceptibility, χ^+-(r,r',t-t'), calculated from the band structure eigenvalues and Bloch states. The antiferromagnetic exchange-interaction between the two Mn atoms in the primitive unit cell is dominating (-1.02 mRy), and at least an order of magnitude larger in absolute value than any longer-range exchange interaction. The spin wave dispersion relation is calculated using a linear response approach to the Heisenberg model and agrees well with an analytical expression obtained by only keeping the dominant interaction. The poles of the dynamic χ^+-(r,r',t-t') are in excellent agreement with the spin wave dispersion calculated from the static Heisenberg Hamiltonian. The Néel temperature is calculated within the mean-field (630 K) and random phase- Tyablikov (242 K) approximations, adjusted by quantum corrections. Unfortunately, until now, the underlying AFM structure of MnGeP₂ has been masked by the presence of a ferromagnetic MnP secondary phase in experimental studies.