Altermagnetism and Weak Magnetism in the Insulating Distorted Perovskite Antiferromagnet NaOsO$_3$

TL;DR

This study investigates altermagnetism in NaOsO$_3$, showing spin-split bands in a compensated AFM insulator and a very weak magnetism arising from Dzyaloshinskii-Moriya interactions within a distorted GdFeO$_3$-type perovskite. By combining GGA, SOC, and modest $U_{eff}$ with Wannier-based modeling, spin dynamics, and Berry-curvature analyses, it demonstrates altermagnetic spin splitting up to about $2\times10^{2}$ meV, chiral magnons in the THz range, and sizable anomalous Hall conductivity upon hole or electron doping. The results place NaOsO$_3$ in an unusual Slater–Mott crossover regime, highlighting how lattice distortions, SOC, and altermagnetic order yield a small-gap insulating state with weak magnetism and distinctive magnonic and transport properties that could enable spintronic applications.

Abstract

The GdFeO$_3$-type perovskite antiferromagnet NaOsO$_3$, calculated here to be altermagnetic for all three typical collinear antiferromagnetic orders, was suggested early on to be a Slater-type insulator, due in large part to its continuous metal-insulator transition and its small energy gap. Below the Néel temperature, the gap opens along with ``weak magnetism'', accompanied by a sharp change in the magnetic susceptibility and resistivity. Without explicit correlation in the band structure calculation, and neglecting spin-orbit coupling (SOC), already a gap opens. Inclusion of a modest on-site Coulomb repulsion ($U\sim$1 eV) is sufficient to eliminate a SOC-induced small band overlap, opening a gap similar to the experimentally observed gap of around 100 meV. Combined evidence supports the viewpoint that NaOsO$_3$ lies in an unusual crossover region between Slater and Mott insulator. The unreported altermagnetism in NaOsO$_3$ is demonstrated and its consequences are considered. The origin of the very weak magnetism has been investigated using a combination of {\it ab initio} calculations and symmetry analysis of the magnetic space group, confirming the origin lying in the Dzyaloshinskii-Moriya SOC buttressed by altermagnetic order. After determining the easy axis, our calculation leads to an Os spin canting angle of about 3$^{\circ}$, accounting for the observed weak magnetism and sharp change in the susceptibility. The altermagnetism spin-split bands (up to $\sim$100 meV) are accompanied by a chiral-split magnon spectrum in both acoustic and optical modes in the THz range, and lead to significant anomalous Hall conductivity upon hole doping.

Figures (15)

• Figure 1: Enlarged band structures of NaOsO$_3$ with (top) GGA, (middle) GGA+SOC, and (bottom) GGA+SOC+$U$ near $E_F$. Here, $U_{eff}$=0.5 eV and the Néel vector ${\bf N}\|\hat{z}$ were used. The spin characters are colored (red: spin-up, blue: spin-down), revealing the spin splittings along the $R-\Gamma$ line, indicating the altermagnetism character. Note that the splitting occurs only along the $R-\Gamma$ line (and inside the zone), but not along other symmetry directions. (For details, see Sec. IV \ref{['spin-splitting']}.) Band sticking is discussed in the text.
• Figure 2: Top: maximum splitting on the $k_x-k_y$ planes, for $k_z$ varying through the range of $0-\frac{\pi}{c}$. The variation in splittings is approximately quartic, as indicated from a fit to the data and shown by the red dashed lines (see text for more discussion). Bottom: sketch of the region showing spin-splitting in the orthorhombic BZ. In the red-shaded or lined regions, the Kramers spin-degenerate bands survive.
• Figure 3: Top: magnetic exchange parameters $J_{ij}$ versus the Os-Os distance $d_{ij}$, obtained for the GGA+SOC(${\bf N}||\hat{z}$)+$U$ at $U_{eff}=0.5$ eV. The Insets show (left) the two NN interactions separated by a tiny amount and (right) the four inequivalent NNN values. Note the difference in two ($J_2$ and $J'_2$) of the NNN values (filled circles by the red color) at $d_{ij}\approx5.358$ Å. Bottom: origin of the inequivalent $J_2$ and $J'_2$ depicted in the G-type AFM cell. In the cell, the large and small spheres indicate Os (red: spin-up, blue: spin-down) and O ions, respectively. The Na ions are not shown, for easier visualization.
• Figure 4: Magnon spectrum for the GGA+SOC(${\bf N}||\hat{z}$)+U at $U_{eff}=0.5$ eV. Here, the exchange integrals $J_{ij}$ are included up to the Os-Os distance $d_{ij}=6$ Å. The AM character reflects in the bifurcation in the acoustic and optic modes along the $R-\Gamma$ line. The (red) squares denote the experimental values adapted from Ref. calder2017. Inset: Blowup spectrum in the energy range above 130 meV along the $R(111)-\Gamma-R'(\bar{1}\bar{1}\bar{1})$ line where the bifurcations due to opposite chirality of the eigenvectors are clearly visible.
• Figure 5: Anomalous Hall conductivity $\sigma_{zx}$ for GGA+SOC(${\bf N}||\hat{z}$)+$U$ at $U_{eff}=0.5$ eV. For the case of ${\bf N}||\hat{z}$, $\sigma_{xy}=\sigma_{yz}=0$ by the magnetic space group symmetry (for details, see text). The (blue) dashed lines indicate doping levels of 0.29 holes, 0.11 holes, and 0.62 electrons (per f.u.), from left to right in order, estimated from the rigid band approximation. The zero value in the energy gap region shaded here indicates a topologically trivial insulating state.