Efficient two-color Floquet control of the RKKY interaction in altermagnets

Abstract

Magnetic impurities in real materials can mask the intrinsic spin-dependent properties of hosts. They interact indirectly through the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism, which limits the use of isolated impurity spins in applications such as qubits and spintronics. Suppressing the RKKY interaction would therefore enable access to the host's unperturbed behavior while simultaneously isolating impurity spins for functional use. Although single-color laser driving can suppress the RKKY interaction, it typically requires strong fields that may be impractical or destabilizing. To overcome these limitations, we show that two-color laser driving provides efficient and tunable control over all components of the RKKY interaction using two weak laser fields. Focusing on two-dimensional Rashba altermagnets, we show that interference between one- and two-photon processes produces altermagnet-specific Floquet corrections. These include additional AC Stark shifts, magnetizations, spin-orbit renormalization, and emergent in-plane Zeeman fields that are absent under single-color driving and in non-altermagnetic systems. Notably, two-color driving induces a finite $z$-component of the Dzyaloshinskii-Moriya (DM) interaction, stabilizing in-plane chiral magnetism and related textures in Rashba altermagnets. These effects enable tunable, near-complete on-off switching of the Heisenberg, Ising, and DM interactions through a Lifshitz-like modulation of the Fermi surface. We also show that the tuning process is highly sensitive to the chirality of both beams. We further map phase diagrams for ferromagnetic and antiferromagnetic impurity alignment with clockwise and counterclockwise canting as functions of Rashba coupling and altermagnetic order. Finally, we discuss candidate material platforms and experimental feasibility.

Figures (8)

• Figure 1: Schematic illustration of two-color Floquet engineering of the RKKY interaction in a 2D Rashba altermagnet. Two coherent laser beams irradiate the system, with frequencies $\omega_1$ and $\omega_2$, amplitudes $A_0$ and $\mathcal{S}A_0$ (where $\mathcal{S}$ denotes the relative strength of the second-harmonic component), phases $\phi_1$ and $\phi_2$, and chiralities $\eta_1$ and $\eta_2$. Two localized magnetic moments, $\mathbf{S}_1$ and $\mathbf{S}_2$, interact indirectly via the laser-modified itinerant electrons, yielding a tunable RKKY exchange. The relative amplitude ratio and chirality of the beams control the strength, anisotropy, and components of the RKKY coupling.
• Figure 2: Angular dependence of the RKKY interaction in a 2D Rashba altermagnet for fixed impurity separation $R=35$ Å, Rashba coupling $\lambda_{\rm R}=0.3~\mathrm{eV\cdot}$Å, altermagnetic strength $M_{\rm d}=0.7$, and orientation $\theta_M^{\rm d}=0$. (a) representative pristine Heisenberg ($J_{\rm H}$) and Ising ($J_{\rm I}$) components as functions of the relative impurity angle $\varphi_R$ in the absence of driving, illustrating the $2\pi$ periodicity and the intrinsic anisotropy of the altermagnetic band structure. (b) Dependence of the same components on the relative angle $\phi$ between the two circularly polarized driving fields, showing an essentially isotropic response.
• Figure 3: Distance dependence of the Heisenberg ($J_{\rm H}$), Ising ($J_{\rm I}$), and DM ($D_\alpha$) components of the RKKY interaction under single- and two-color driving for fixed Rashba coupling $\lambda_{\rm R}=0.3~\mathrm{eV\cdot}$Å, altermagnetic strength $M_{\rm d}=0.7$, and orientation $\theta_M^{\rm d}=0$. While single-color driving [(a)--(e)] suppresses all exchange channels only at large amplitudes, two-color driving achieves comparable suppression at substantially reduced peak fields [(f)--(j)] with a 54% reduction in the primary beam amplitude and the addition of a secondary beam whose amplitude is also reduced by 10%, demonstrating a markedly more efficient control protocol.
• Figure 4: Out-of-plane DM interaction $D_z$ as a function of the drive parameter (a) $\mathcal{A}$ and (b) $\mathcal{S}$ under single- and two-color driving, respectively, at fixed impurity separation $R = 35$ Å, Rashba coupling $\lambda_{\rm R}=0.3~\mathrm{eV\cdot}$Å, altermagnetic strength $M_{\rm d}=0.7$, and altermagnetic orientation $\theta_M^{\rm d}=0$. While $D_z$ is strictly forbidden under monochromatic circular driving, bichromatic excitation induces a sizable and oscillatory $D_z$ due to Floquet-engineered in-plane Zeeman-like fields $\Omega_x$ and $\Omega_y$ in Eq. \ref{['eq_8']}.
• Figure 5: Evolution of the lower Floquet quasienergy band $E_-(\mathbf{k})$ in a 2D Rashba altermagnet under monochromatic and bichromatic driving for $d_{x^2-y^2}$- and $d_{xy}$-wave altermagnets. Starting from a (a) parabolic dispersion above the Fermi level ($\mu=0$) in the absence of RSOC, altermagnetism, and driving, successive tuning of (b) $\lambda_{\rm R}$, (c) $M_{\rm d}$, and (d)--(l) the laser parameters reshapes the low-energy electronic structure. Red lines on the $\mu=0$ plane indicate the corresponding Fermi surfaces. (d) Single-color driving ($\mathcal{A}=0.15$, $\mathcal{S}=0$) in the $d_{x^2-y^2}$-wave altermagnet modifies the band extrema via virtual photon processes, partially tuning states at the Fermi level. In contrast, (e)--(h) bichromatic driving systematically shifts the global minimum of $E_-(\mathbf{k})$ upward with increasing $\mathcal{S}$, inducing a controlled Lifshitz-like disappearance of the Fermi surface. (i)--(l) The same behavior is observed for the $d_{xy}$-wave altermagnet, demonstrating that the Floquet-engineered Lifshitz transition is robust across different altermagnetic symmetries. Parameters are $\lambda_{\rm R}=0.3~\mathrm{eV\cdot}$Å, $M_{\rm d}=0.7$, $\eta_{1,2}=+1$, and $\theta_M^{\rm d}=0~(\pi/4)$ for the $d_{x^2-y^2}$- ($d_{xy}$-) wave case.