Light-Induced Even-Parity Unidirectional Spin Splitting in Coplanar Antiferromagnets

TL;DR

This work shows that even-parity, unidirectional spin splitting can be realized in coplanar antiferromagnets by optical driving. Using Floquet engineering, a bilayer coplanar AFM under circularly polarized light develops an out-of-plane $d$-wave spin texture, with symmetry-protected nodal lines ensuring robustness to canting and a distinctive clover-like Drude spin conductivity. The approach complements known odd-parity unidirectional spin splittings in coplanar AFMs and parity-controlled phases in collinear AFMs, expanding the landscape of spin-split AFM phases. Possible experimental paths include symmetry-informed material screening or synthetic van der Waals bilayers, with verification via spin-resolved ARPES or spin-transport measurements.

Abstract

When a coplanar antiferromagnet (AFM) with $xy$-plane magnetic moments exhibits a spin-split band structure and unidirectional spin polarization along $z$, the spin polarization is forced to be an odd function of momentum by the fundamental symmetry $[\bar{C}_{2z}\|\mathcal{T}]$. Coplanar AFMs displaying such odd-parity unidirectional spin splittings are known as odd-parity magnets. In this work, we propose the realization of their missing even-parity counterparts. We begin by deriving the symmetry conditions required for an even-parity, out-of-plane spin splitting. We then show that irradiating a spin-degenerate coplanar AFM with circularly polarized light lifts the $[\bar{C}_{2z}|\mathcal{T}]$ constraint, dynamically generating this even-parity state. Specifically, the light-induced unidirectional spin splitting exhibits a $d$-wave texture in momentum space, akin to that of a $d$-wave altermagnet. We prove this texture's robustness against spin canting and show it yields a unique clover-like angular dependence in the Drude spin conductivity. Our work demonstrates that optical driving can generate novel spin-split phases in coplanar AFMs, thereby diversifying the landscape of materials exhibiting distinct spin splittings.

Figures (6)

• Figure 1: (a) Schematic of a bilayer coplanar AFM under CPL irradiation. The two layers are shifted relative to each other by $\bm{\tau}_x=a(1,0)$. Orange arrows on the lattice represent the magnetic order. Thin (thick) black solid lines denote the nearest-neighbor hoppings in the top (bottom) layer, and green dashed lines denote the interlayer hoppings. The inset illustrates the CPL-induced $d_{xy}$-wave out-of-plane spin splitting. (b) Top view of the bilayer system. The system can be regarded as a coplanar AFM model with all-out spin configuration ($M_x=M_y=M$). The inset shows the schematic of a unit cell, where sublattices and hoppings are labelled.
• Figure 2: (a) Energy bands of the static system (solid black lines, spin-degenerate) and of the system driven by CPL (dashed red and blue lines, spin-split). The left inset shows a detailed view of the spin-split band structure near the M point; the right inset shows the Brillouin zone with the high-symmetry paths used in the plot. (b) CPL-induced $d$-wave spin splitting on the Fermi surface at energy $E_F=-0.8$. The parameters are $t=0.4$, $t_s=0.7$, $t_a=0.3$, $M=0.5$, $A_0=0.6$, and $\omega=5$.
• Figure 3: Spin polarization on the Fermi surface at $E_F=-0.8$. The corresponding real-space canted magnetic moment configurations are shown in the insets. (a) Canting along the $y$ direction ($M_x=0.3$, $M_y=0.6$). (b) Canting along the $x$ direction ($M_x=0.6$, $M_y=0.3$). Other parameters are $t=0.4$, $t_s=0.7$, $t_a=0.3$, $A_0=0.6$, and $\omega=5$.
• Figure 4: (a) Angular dependence of the Drude spin conductivity at $E_F=-0.8$. The polar angle is defined between the applied electric field and the $x$-axis. Positive (negative) transverse (T) and longitudinal (L) spin conductivities are plotted with solid (dashed) green and orange lines, respectively. (b) Transverse spin conductivity as a function of the Fermi energy $E_F=\mu$. Parameters are $t=0.4$, $t_s=0.7$, $t_a=0.3$, $M_x=M_y=0.5$, $A_0=0.6$, and $\omega=10$.
• Figure S1: Illustration of the symmetry operations $[\bar{E}\|\mathcal{T}C_{2x}\mathcal{M}_{z}|\boldsymbol{\tau}_{x}]$, $[\bar{E}\|\mathcal{T}C_{2y}\mathcal{M}_{z}|\boldsymbol{\tau}_{y}]$ and $[C_{2(x-y)}\|C_{4z}|\boldsymbol{\tau}_{x}]$. The symbol $O$ in the top-row figures labels the unit cell at the origin (implicit in the middle and bottom rows). In (a)-(c), the dashed lines indicate the $C_{2x}$-, $C_{2y}$- and $C_{2(x-y)}$-rotation axes, respectively. In the left panel of (c), the symbol $\bigotimes$ indicates that the $C_{4z}$-rotation axis is perpendicular to the plane.