Electronic structure and exchange interactions in altermagnetic MnGeP$_2$ in the quasiparticle-self-consistent $GW$ approach

TL;DR

This work demonstrates that MnGeP2 in the I-4 2d chalcopyrite structure is an antiferromagnetic semiconductor with indirect and direct band gaps of about 1.87 eV and 2.44 eV, respectively, and exhibits altermagnetism with spin-splitting along select k-lines. Using the quasiparticle-self-consistent GW method with Bethe-Salpeter equation, the authors compute accurate electronic structures, optical response including excitons, and extract Heisenberg-like exchange interactions from transverse spin susceptibilities, finding a dominant antiferromagnetic Mn-Mn coupling within the primitive cell. The Néel temperature is estimated to be around 173 K (RPA) with a mean-field estimate near 401 K, and spin-wave dispersions reach about 58 meV, highlighting robust but finite-temperature spin dynamics. Carrier doping alone is insufficient to induce ferromagnetism, while MnGe antisite defects can create local ferromagnetic clusters and metallic defect bands; MnP-like phases may be needed to explain experimentally observed ferromagnetism, suggesting ferromagnetism in MnGeP2 is defect- or phase-driven rather than intrinsic to the perfect crystal.

Abstract

The QS$GW$ method is used to study the electronic band structure, optical dielectric function, and exchange interactions in chalcopyrite, $I\bar{4}2d$, structure MnGeP$_2$. The material is found to be an antiferromagnetic semiconductor with the lowest direct gap of 2.44 eV at the $Γ$ point and an indirect gap of 1.87 eV. The material is an altermagnet, with the two magnetic atoms of opposite spin related by a two-fold rotation operation perpendicular to the main 4-fold rotation inversion axis. The spin splittings along a low symmetry line like $PN$ are sizable, while at k-points on the diagonal mirror planes or on the twofold symmetry axes, the spin splitting is zero. The exchange interactions are calculated using a linear response approach. The antiferromagnetic exchange-interaction between nearest neighbors in the primitive unit cell is dominating and found to be slightly decreasing upon carrier doping. The transverse spin susceptibilities, which provide interatomic site exchange interactions after averaging over the muffin-tin spheres, are calculated from the $GW$ band structure and wave functions. From these exchange interactions, the spin wave spectra are obtained along the high symmetry lines and the Néel temperature is calculated using the mean-field and Tyablikov (RPA) estimations. The dielectric function and the optical absorption spectra are calculated, including excitonic effects, using the Bethe-Salpeter equation. The exchange interactions around Mn$_{\rm Ge}$ defect sites are also studied. While we find it can generate ferromagnetic interactions with neighboring spins, we did not find evidence of producing an overall ferromagnetic phase. If Mn antisites are introduced by exchanging Mn with a nearby Ge, the interactions stay largely antiferromagnetic. Adding Mn antisites leads to a metallic band structure.

Figures (9)

• Figure 1: Crystal structure of the conventional cell with the AFM spin arrangements on the Mn sites in pink, along with Ge sites in gray and P sites in green. Pink areas are the nearest neighbor tetrahedra surrounding each Mn. The image is generated using the VESTA 3 software Vesta.
• Figure 2: Band structure of MnGeP$_2$ obtained in the QS$GW^{BSE}$ approach, where the majority spin bands are shown in red and the minority spin bands are shown in blue. The Fermi energies are shifted to zero. (a) FM and (b) AFM.
• Figure 3: Total and partial densities of majority spin states (PDOS) in the QS$GW^{BSE}$ approach for AFM $I\bar{4}2d$ MnGeP$_2$. The partial contributions include the sum over all equivalent atoms of a given type but refer to partial wave contributions inside the spheres only, excluding those from the interstitial region and only showing the major contributions.
• Figure 4: (a) Conduction and valence bands obtained in the QS$GW^{BSE}$ level along the symmetry lines where major splittings occur: S=$(1/2-\eta,1/2-\eta,1/2)$; G=$(0,1/2-\zeta,1/2)$; N=$(1/4,1/4,1/4)$; P=$(0,1/2,1/4)$ in Cartesian coordinates with $\eta=\frac{1}{4}\left(1+\frac{a^2}{c^2}\right)$ and $\zeta=\frac{a^2}{2c^2}$. All $k_z$ values are scaled by $\frac{c}{a}$. The majority spin bands are shown in red and the minority spin bands are shown in blue. (b) Differences of majority minus the minority energies in successive bands. The labels marking the differences utilize the numbering in (a).
• Figure 5: $\epsilon_2 (\omega)$ obtained within the Bethe-Salpeter and independent particle approximation schemes applied in the $GW$ level. The vertical bars show the individual exciton (two-particle Hamiltonian) eigenvalues with height proportional their oscillator strengths in the low energy region up to +1 eV above the direct quasiparticle gap.