Theory of bound magnetic polarons in cubic and uniaxial antiferromagnets

Abstract

Motivated by a recent debate about the origin of remanent magnetization and the corresponding anomalous Hall effect in antiferromagnets and altermagnets, a theory of bound magnetic polarons (BMPs) in anisotropic antiferromagnetic semiconductors is developed. The theory describes quantitatively the experimentally observed magnitude of excess magnetization and its dependence on the magnetic field in cubic antiferromagnetic EuTe. In contrast to the cubic case, our theory predicts the presence of magnetization hysteresis below Néel temperature in antiferromagnets with uniaxial anisotropy. We show, employing material parameters implied by experimental and ab initio results, that the magnitudes of remanent magnetization and the coercive field are in accord with recent experimental observations for altermagnetic hexagonal MnTe. While the altermagnets have an intrinsic contribution to the remanent magnetization and the anomalous Hall effect, our theory explains the origin of an extrinsic contribution. Our findings address, therefore, a question about the relative contribution to the remanent magnetization of bound magnetic polarons and weak ferromagnetism driven by the antisymmetric exchange interaction, the latter weakened by the formation of antiferromagnetic domains. Furthermore, we provide the theory of BMP spontaneous spin splitting, which can be probed optically.

Figures (3)

• Figure 1: Dependence of the magnetic moment per gram $M$ on the magnetic field calculated from Eq. \ref{['EuTe']} (dashed curves) compared to experimental results (solid curves) at (a) 4.2 K Oliveira:1972_PRB and (b),(c) 8 K Vitins:1975_PRB. The fitted BMP concentrations $n$ are display in the legend. The straight dotted lines show a linear asymptotic behavior and provide the magnitude of magnetic susceptibility $\chi$. An offset $16$ and $8\,$emu/g was added to (a),(b) respectively for readability - two arrows next to the vertical axis indicate the positions of $M=0$ for those two plots.
• Figure 2: Computed exchange energy $J_v$ for the valence band of MnTe in the non-relativistic case (green lines) and in the relativistic case with saturated magnetization along the $a$-axis (purple dots) and along the $c$-axis (orange triangles). The horizontal line is the experimental value of $J_v$ at the $\Gamma$ point of the valence band in (Cd,Mn)Te (see, Ref. Autieri:2021_PRB).
• Figure 3: (a) dependence of BMP free energy $F_p$ on the effective Bohr radii along the $c$-axis ($c^*$) and in the $c$-plane ($a^*$). The red point depicts a minimum found by the variational procedure. (b) dependence of the BMP free energy (minimized with respect to radii $a^*$ and $c^*$) on the magnetic field $H$ applied along the $c$-axis. The straight line is a linear asymptote corresponding to BMP's magnetic moment parallel to the magnetic field. Temperature $T=250\,$K for both plots.