Tuning magnetic interactions with nonequilibrium optical phonon populations: a theoretical study

TL;DR

The paper develops a quantum framework for tuning magnetic exchange through nonequilibrium optical phonon pumping in insulating magnets, focusing on the diabatic regime where phonon frequencies exceed magnetic scales. Using a Lang-Firsov transformation, it derives an effective spin Hamiltonian with phonon-distribution dependent terms that generate additional exchanges $\delta J_1$, $J_2$, and chiral interactions under polarization, while enhancing magnetic anisotropy. Applying the method to 2D lattices (honeycomb, square, kagome, triangular) and spin models (Heisenberg, XYZ, Kitaev, Kitaev-Heisenberg), the authors demonstrate controllable frustration and potential access to spin-liquid regimes, and show that selective pumping can bolster Kitaev terms while suppressing Heisenberg terms. The results provide concrete, geometry-driven rules for mode and polarization selection to engineer magnetic states with currently achievable pump strengths and sub-gap frequencies, offering a pathway to optically realize exotic quantum phases with reduced electronic heating. Overall, this work highlights non-equilibrium phonon engineering as a versatile tool for magnetic interaction design and emergent quantum spin liquids in real materials.

Abstract

We theoretically explore how light-driven optical phonons can be used to drive magnetic exchange interactions into interesting physical regimes by developing a general theory of spin-phonon pumping in magnetic insulators with non-equilibrium optical phonon distributions, focusing on the diabatic regime where phonon frequencies are much larger than the magnetic interactions. We present several applications of spin-phonon pumping two-dimensional nearest-neighbor Heisenberg, XYZ and Kitaev models to examine what kind of further neighbor interactions and chiral fields can be generated, and how anisotropic couplings can be enhanced, showing that experimentally accessible non-equilibrium phonon distributions can generically drive significant frustration and realize a variety of spin liquid regimes. This effect is described for both direct and superexchange mechanisms, and we derive simple geometric rules for which phonon modes are ``spin-phonon'' active and for which magnetic interactions. Spin-phonon pumping provides an intriguing possibility for preferentially pumping specific magnetic interaction terms. In addition to generating further neighbor interactions, such pumping can lead to increased magnetic anisotropy for initially weakly anisotropic models, and selectively pumping the Kitaev-Heisenberg model can suppress undesirable Heisenberg terms while enhancing Kitaev interactions.

Figures (10)

• Figure 1: Optical phonons are pumped by IR light, inducing a non-equilibrium $q=0$ phonon distribution, $n_{ph}(\omega_0)$ that dynamically affects the interatomic distances (gray atoms) and induces phonon mediated changes to the magnetic interactions. The leading order quantum effects of this spin-phonon coupling both change the initial couplings, $\delta J_1$ and generate further neighbor couplings, $\delta J_2$. We also find that the magnetic exchange anisotropy is generically enhanced, and circularly polarized phonon modes can additionally generate chiral fields (not shown). Strong pumping without significant heating is possible for frequencies below the Mott gap, $\omega_0 \ll U$.
• Figure 2: Honeycomb phonons and exchange couplings. (a) The optical phonon mode, $E_g$ couples linearly to the spins. (b) Exchange couplings generated by $E_g$ phonon pumping for the nearest neighbour Heisenberg model. (c) $S=1/2$ exchange (left) and chiral (right) couplings arising from the center site ($i=0$) of Eq. (\ref{['eq:Aterm']}-\ref{['eq:Sterm']}). Exchange (chiral) interactions have units of $J_1^{(0)} \alpha^2 n_{ph} \frac{J_1^{(0)}}{\omega_0}$ ($\frac{\sqrt{3}}{2} J_1^{(0)} \alpha^2 n_{ph} \beta$). Using translational invariance leads to Eq. (\ref{['eq:Hccouplings']}).
• Figure 3: Spin-phonon pumping of the honeycomb Heisenberg model with $E_g$ phonon modes. Nearest, next-nearest neighbor, and chiral exchange couplings as a function of $\alpha^2 n_{ph}J_1^{(0)}/\omega_0$; note that $J_1$ vanishes for $\alpha^2 n_{ph}J_1^{(0)}/\omega_0 \approx .15$, leading to a divergence in $J_2/J_1$. A deconfined critical point or spin-liquid region is predicted for the $J_1-J_2$ honeycomb model at $J_2/J_1\sim .22$Clark2011Albuquerque2011Ganesh2013, here found with $\alpha^2 n_{ph}J_1^{(0)}/\omega_0 \sim .1$. Induced chiral fields ($J_\chi$) are plotted as a function of $\alpha^2 n_{ph}$ for $\omega_0/J_1^{(0)}=1/2$ and two opposite phonon polarizations, $\beta = 1$ (green, dashed) and $\beta=-1$ (red, dashed). A chiral spin liquid is predicted for $J_\chi/J_1 \sim .25$Hickey2016, here achieved for $\alpha^2 n_{ph} \sim .12$ and full polarization.
• Figure 4: Superexchange and linear spin-phonon coupling. (a) Superexchange paths typical of CuO$_2$ planes. The exchange interaction is mediated by electron hopping through the central anion resulting in $J_{1} \propto t_{pd}^4/\Delta_{pd}^3$. $J_1$ is sensitive to both the total length of the metal-anion bonds, as well as the angles involved. The phonon pumping has a linear effect on $J_{1}$ only if the right and left parts of the superexchange path add constructively, which leads to geometric constraints on the relevant phonon modes. (b) For a non-collinear superexchange path, linear spin-phonon coupling is present only for phonon displacements perpendicular to the bond, $u_3$. (c) For collinear superexchange paths, any orthogonal phonon displacement leads to a linear spin-phonon coupling.
• Figure 5: Edge-stuffed square lattice phonons and phonon pumped superexchange couplings. Three optical phonon modes have linear spin-phonon coupling: (a) $A_{2u}$, (b) $B_{2u}$ and (c) $E_u$. (d) The phonon pumping of these modes generates nearest and next-nearest neighbor interactions from initial $S=1/2$ nearest neighbor couplings. The polarization of the $E_u$ mode in the collinear case does not generate chiral couplings, but the non-collinear variation would allow polarization to generate a $C_4$ staggered chirality. (e) Nearest and next-nearest neighbor couplings as a function of $\alpha^2 n_{ph}J_1^{(0)}/\omega_0$. $A_{2u}$ and $B_{2u}$ are indistinguishable in the collinear case, while pumping $E_u$ gives a larger prefactor.