Dynamical Generation of Higher-order Spin-Orbit Couplings, Topology and Persistent Spin Texture in Light-Irradiated Altermagnets

Abstract

Altermagnets have been identified as the third category of magnetic materials, exhibiting momentum-dependent spin splitting characterized by even powers of momentum. In this study, we show that when subjected to elliptically polarized light, these materials serve as an exemplary framework for the dynamic generation of topological bands featuring higher-order spin-orbit coupling (SOC). Notably, while the generated Zeeman field remains invariant to the particular altermagnetic ordering, the induced higher-order SOCs are related to the magnitude and symmetry of the altermagnetic order. Specifically, we show that an altermagnet exhibiting $k^n$-spin splitting can generate spin-orbit couplings up to $k^{n-1}$. In the limit of circularly polarized light, the only correction is $k^{n-1}$, with all lower-order contributions being nullified. Interestingly, light-induced SOCs significantly impact the low-energy band topology, where their Chern numbers change by $ΔC =\pm 1,2,3$ for $d,g,f$-wave altermagnets. Finally, we find a critical field in which a persistent spin texture is realized, a highly desirable state with predicted infinite spin lifetime. Our work showcases light as a powerful, controllable tool for engineering complex and exciting phenomena in altermagnets.

Figures (4)

• Figure 1: Summary of results. Light generates linear, cubic, quintic-k SOC in $d, g, i$-wave ALMs. The generated SOCs change Chern numbers of the low-energy bands by $\Delta C= \pm 1,2,3$ for $d, g, i$-wave ALMs. At a critical field an exact (nearly) PST emerges in $d$-wave ($g,i$-wave) ALMs.
• Figure 2: Fermi surface of irradiated planar altermagnets.The Fermi surface of altermagnets with (a) $d_{x^2-y^2}$-wave order for $\mu=0.5$, (b) $d_{x^2-y^2}$-wave order for $\mu=0.5$, (c) $g$-wave order for $\mu=0.35$, (d) $i$-wave order for $\mu=0.5$. (Black solid and dashed), (solid blue and red), (dashed blue and red) and (cyan and magenta) are representing spin up and down FSs for the case with (no), ($\eta=1,A_{x,y}=1.5$), ($\eta=-1,A_{x,y}=1.5$), ($\eta=1,A_x=1.8575, A_y=1$) lights. $t=1, \lambda=0.3, J=1, \omega=5$ is used for all plots.
• Figure 3: Persistent spin texture in altermagnets. Spin texture in (a) $d_{x^2-y^2}$-wave altermagnet without light (b) $d_{x^2-y^2}$-wave altermagnet at $\bar{A}^c_d$, (c) $g$-wave ALM at $\bar{A}^c_g$, (d) $i$-wave ALM at $\bar{A}^c_i$. Arrows show the in-plane spin-texture and cyan and magenta denote out of the plane spin polarization.
• Figure 4: Topology and Berry curvature. (a) Topological phase transition in $d_{x^2-y^2}$-wave ALM at $\bar{A}^c_d=\sqrt{\frac{\omega}{2\alpha \eta J}}$ with $\alpha=1$. (b) Chern number vs $\bar{A}$ with $\alpha=2$. Dashed line shows $\bar{A}^c_d$ with $\alpha=2$. $t=1, \lambda=0.3, J=1, \eta=1, \omega=5$ are used for all plots.