Parity and time-reversal invariant Ising spin ordering

Abstract

The interplay of antiferromagnetic order, momentum-dependent Bloch spin-splitting, time-reversal (T), and parity (P) symmetries in non-relativistic systems has emerged as a central theme for spintronics. Two well-known examples are P-preserving and T-violating altermagnets and P-violating and T-preserving odd-parity magnets. These both exhibit an Ising, or uniaxial, Bloch spin-splitting. Here we introduce a new class of coplanar AFMs that generate a P and T symmetric, translation-invariant Ising spin order in real space. Naively, such AFMs are not expected to exhibit unusual phenomena. Here we show that the spin-rotational symmetry breaking generated by these AFMs allows: pure non-relativistic longitudinal (or transverse) spin-conductivities, the generation of non-relativistic altermagnetic spin-splittings through circularly polarized light, and the generation of non-relativistic odd-parity spin-splittings through parity symmetry breaking, by, for example, applied electric fields. We identify 16 candidate materials in the Magndata database for which our theory applies and provide effective microscopic models and DFT-based results that highlight the large emergent responses.

Figures (7)

• Figure 1: The four classes of translationally-invariant spin orders under $(P,T)$ symmetries. This paper covers the yellow dotted region.
• Figure 2: Spin configuration of the coplanar AFM state, denoted by red solid arrows. Its inversion pair is illustrated by blue dashed arrows. The inversion center is at the X mark. Black solid lines denote the nonmagnetic unit cell. For $(P,T)=(-,+)$ state, inversion symmetry acts non-trivially on the AFMyu2025, while for $(P,T)=(+,+)$ state inversion is trivial.
• Figure 3: Spin conductivities for SG127(2c) with wavevector $A=(\pi,\pi,\pi)$. Here ${\bf S}_1\times{\bf S}_2$ has $A_{1g}$ spatial symmetry, giving a longitudinal spin conductivities with $\sigma_{xx}^l=\sigma_{yy}^l$. Hopping parameters $t_{x0}=1$eV, $t_{z0}=0.5t_{x0}$, $t_1=0.8t_{x0}$, $t_2=0$, and $\mu=0.3t_{x0}$ are used. The lattice constant is 6Å. The nonrelativistic spin conductivity is significant for moderately strong spin ordering.
• Figure 4: Nonrelativistic spin Berry curvature of U$_2$Ni$_2$In summed over the occupied bands in the $k_z = 0$ plane. The solid lines indicate the intersections of the Fermi surface with this plane. The color scale is shown on a logarithmic scale.
• Figure 5: Phase diagram for $\beta_4=0$ is shown as thick black dashed line. When $\beta_4\neq0$, the two collinear phases mix up, and the phase boundary between collinear and coplanar phases is at the blue dotted line.