Spin polarization engineering in $d$-wave altermagnets

TL;DR

This work addresses controlling spin polarization in two-dimensional $d$-wave altermagnets with zero net magnetization by introducing a multi-field platform that combines gating-induced Rashba SOC, circularly polarized light (CPL) Floquet engineering, and in-plane electric fields to realize tunable spin polarizations along $x$, $y$, and $z$ directions. The approach uses a dressed (Floquet) Hamiltonian to capture CPL effects and leverages the Edelstein effect to generate in-plane polarizations, while CPL supplies an out-of-plane $\langle S^z \rangle$. The results reveal anisotropic, switchable in-plane polarizations controlled by light helicity and doping, and identify a critical light potential $\Delta_c \approx \pm \frac{m\,\lambda^2}{\hbar^2\,\mathcal{D}}$ at which the in-plane components vanish and reverse. Additionally, spin-selective doping induces chiral optical activity, a feature unique to altermagnets, offering a route to chiral photonics and spintronics. The framework predicts experimentally accessible polarizations for realistic gating, optical intensities, and in-plane fields, suggesting a practical path to full spin control in altermagnets.

Abstract

Altermagnets host unconventional spin-polarized bands despite zero net magnetization, but controlling their spin structure remains challenging. We propose a multi-field approach to engineer spin polarization in $d$-wave altermagnets using gating, optical driving, and in-plane electric fields, which enable tunable and switchable polarizations along multiple directions. Optical driving induces out-of-plane ($z$) polarization, while gating and in-plane fields generate $x$- and $y$-polarizations via the Edelstein effect, all of which are experimentally detectable. We further find that spin- and band-selective doping induces chiral optical activity, a feature unique to altermagnets. Our approach provides a versatile route for full control of spin polarization in altermagnets.

Figures (4)

• Figure 1: (a) Schematic of a two-dimensional $d$-wave altermagnet gated by $\pm V$ electrodes and illuminated by circularly polarized light (CPL, gold colored spiral). (b) Spin-resolved Fermi contours for pristine spin-up (red) and spin-down (blue) states. (c) Gating induces Rashba spin-orbit coupling, reshaping the Fermi surface while maintaining spin balance. (d) CPL breaks this balance, generating anisotropic spin textures. CPL engineers out-of-plane polarization $\langle \hat{S}^z \rangle$ via Floquet drives, while gating and in-plane fields $(E^x,E^y)$ allow tunable and switchable control of in-plane $\langle \hat{S}^x \rangle$ and $\langle \hat{S}^y \rangle$ via the Edelstein effect. The spin polarizations are noncollinear.
• Figure 2: Calculated spin (‘s’) and orbital (‘o’) Edelstein susceptibilities $\chi_{ij}/\chi_0$ ($\chi_0 = e/4\pi^2$) versus light potential $\Delta$ under CPL for an ideal altermagnet with $\mathcal{D}=1$ and weak RSOC $\lambda=0.2$ eV$\cdot$Å. Panels (a,b): chemical potentials $\mu = \varepsilon_\mp$ (band edges at $\vec{k}=0$). Panels (c,d) separate intra- and interband contributions. Without light ($\Delta=0$), in-plane fields yield $\chi_{xy}$ and $\chi_{yx}$ of opposite sign. With CPL ($\Delta \neq 0$), anisotropic susceptibilities, large tunable spin polarizations, and chiral optical activity emerge, demonstrating directional control. At $\Delta_{\rm c}\!\approx \!\pm 5.7$ meV (insets), in-plane spin polarizations vanish and subsequently reverse as the spin susceptibilities change sign. This highlights the synergy of Edelstein and Floquet mechanisms in achieving highly tunable spin responses in Rashba altermagnets. Note that all $\chi_{z j}$ components in (a,b) coincide at zero, causing the dashed lines to lie directly on top of the solid lines.
• Figure 3: Calculated transverse spin susceptibilities $\chi_{xy}/\chi_0$ (blue) and $\chi_{yx}/\chi_0$ (red) versus RSOC $\lambda$ in an ideal altermagnet ($\mathcal{D}=1$) for various light potentials: $\Delta = 0$ (solid), $+3.2$ meV (dashed), and $-3.2$ meV (dotted). Panel (a): $\mu = \varepsilon_-$ at $\vec{k} = 0$ for the spin-down band; panel (b): $\mu = \varepsilon_+$ at $\vec{k} = 0$ for the spin-up band. Chiral optical activity from combined light and in-plane fields is independent of finite RSOC.
• Figure 4: Calculated spin susceptibilities $\chi_{xy}$ (a) and $\chi_{yx}$ (b) for doping into the spin-up band ($\mu = \varepsilon_+$) with weak RSOC $\lambda = 0.2$ eV$\cdot$Å. For spin-down doping ($\mu = \varepsilon_-$), the behaviors reverse. Both components are plotted versus light potential $\Delta$ and altermagnetism $\mathcal{D}$, illustrating highly tunable CPL-induced spin polarizations and the critical phase boundary where polarizations switch.