Extremely strong spin-orbit coupling effect in light-element altermagnetic materials

TL;DR

This work tackles the challenge of achieving a strong spin-orbit coupling (SOC) in light-element altermagnetic materials. By combining symmetry analysis with first-principles density functional theory and dynamical mean-field theory, the authors predict an extremely strong effective SOC in NiF$_3$ and FeCO$_3$, attributes that arise from a cooperative interplay among crystal symmetry, electron occupancy, electronegativity, electron correlation, and intrinsic SOC, yielding $i$-wave altermagnetism. They formulate four design conditions under which such strong SOC can occur in light-element altermagnets and verify that FeCO$_3$ meets all four, while several analogous fluorides do not, explaining the observed SOC strengths. The results suggest a general route to discover light-element altermagnets with strong SOC and imply potential extensions to two-dimensional systems for high-temperature quantum anomalous Hall physics, as well as applicability to conventional antiferromagnets.

Abstract

Spin-orbit coupling is a key to realize many novel physical effects in condensed matter physics. Altermagnetic materials possess the duality of real-space antiferromagnetism and reciprocal-space ferromagnetism. It has not been explored that achieving strong spin-orbit coupling effect in light-element altermagnetic materials. In this work, based on symmetry analysis, the first-principles electronic structure calculations plus Dynamical Mean Field Theory, we demonstrate that there is strong spin-orbit coupling effect in light-element altermagnetic materials $\rm NiF_3$ and $\rm FeCO_3$, and then propose a mechanism for realizing such effective spin-orbit coupling. This mechanism reveals the cooperative effect of crystal symmetry, electron occupation, electronegativity, electron correlation, and intrinsic spin-orbit coupling. Our work provides an approach for searching light-element altermagnetic materials with an effective strong spin-orbit coupling.

Figures (9)

• Figure 1: The crystal structure and six collinear magnetic structures of $\rm NiF_3$. (a) and (b) are side and top views of the crystal structure, respectively. The cyan arrow represents the direction of easy magnetization axis. (c)-(h) are six different collinear magnetic structures including one ferromagnetic and five different collinear antiferromagnetic structures. The bond angle of Ni-F-Ni for the nearest neighbor Ni ions is 140 degrees. The primitive cell of $\rm NiF_3$ is shown in (d). The red and blue arrows represent spin-up and spin-down magnetic moments, respectively.
• Figure 2: The magnetic ground state of $\rm NiF_3$ and the corresponding properties. (a) Relative energies of six different magnetic states with the variation of correlation interaction $\rm U$. (b) and (c) are the corresponding Brillouin zone and the magnetic primitive cell of $\rm NiF_3$, respectively. The high-symmetry lines and points are marked in the BZ. The red and blue arrows represent spin-up and spin-down magnetic moments, respectively. (d) The anisotropic polarization charge densities. The red and blue represent spin-up and spin-down polarization charge density, respectively.
• Figure 3: Schematic diagram of the $\bm i$-wave magnetism and electronic band structures of altermagnetic $\rm NiF_3$. (a) Schematic diagram of the $\bm i$-wave magnetism. The red and blue parts represent spin up and down, respectively. (b) The electronic band structure without SOC along the high-symmetry directions. The red and blue lines represent spin-up and spin-down bands, respectively. (c) and (d) are the electronic band structures without and with SOC along the high-symmetry directions.
• Figure 4: The electronic properties of altermagnetic $\rm NiF_3$ under different correlation interaction $\rm U$. (a), (b) and (c) are the electronic band structures along the high-symmetry directions without SOC under correlation interaction $\rm U = 3,5,7 eV$, respectively. (d) The bandgap as a function of correlation interaction $\rm U$ under SOC.
• Figure 5: Magnetocrystalline anisotropy of $\rm NiF_3$ for the $x - y$ plane (a) and the $y - z$ plane (b). In (a), the $x$ and $y$ axes represent 0 degrees and 90 degrees, respectively. In (b), the $y$ and $z$ axes represent 0 degrees and 90 degrees, respectively. The red arrows represent the direction of easy magnetization axes.