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

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.

💡 Research Summary

This paper presents a comprehensive theoretical framework for dynamically tuning magnetic exchange interactions in insulating materials using light-driven, non-equilibrium optical phonons. The core idea is that by selectively exciting specific optical phonon modes with infrared light, one can create a non-thermal phonon population that acts as a dynamical lattice distortion, thereby modifying the effective spin Hamiltonian.

The authors develop a general theory based on the linear spin-phonon coupling model. They employ a Lang-Firsov unitary transformation to decouple spin and phonon degrees of freedom in the diabatic regime, where phonon frequencies are much larger than magnetic exchange energies. Averaging over the phonon degrees of freedom yields an effective spin Hamiltonian whose terms depend on the non-equilibrium phonon occupation number, n_ph. This effective Hamiltonian contains two key types of phonon-pumping-dependent terms: 1) a symmetric term (H_S) that generates new symmetric exchange interactions (e.g., second-neighbor couplings) and modifies existing ones, scaling linearly with n_ph, and 2) an antisymmetric term (H_A) that can generate three-spin chiral interactions (S_i · (S_j × S_k)), but only if circularly polarized phonons are selectively pumped within a degenerate phonon doublet.

The paper applies this general formalism to various two-dimensional lattice geometries (square, triangular, honeycomb) and spin models (Heisenberg, XYZ, Kitaev). A major outcome is the derivation of simple, intuitive “geometric rules” that predict which phonon modes are effective in tuning which magnetic interactions, depending on the exchange mechanism (direct or superexchange). For instance, to affect a particular bond, one should pump a phonon mode that induces atomic displacements along that bond’s direction.

Key demonstrated applications include:

• Enhancing Frustration: In a nearest-neighbor Heisenberg model, phonon pumping can generate significant second-neighbor interactions, introducing or enhancing magnetic frustration.
• Tuning Anisotropy: For the XYZ model, pumping can selectively enhance specific anisotropic exchange couplings.
• Engineering Kitaev Interactions: A highly significant result is the application to the Kitaev-Heisenberg model. The theory shows that by carefully choosing the pumped phonon mode, one can suppress the undesirable isotropic Heisenberg term while simultaneously enhancing the highly anisotropic Kitaev interaction. This provides a potential pathway to stabilize the Kitaev quantum spin liquid phase, a long-sought exotic state of matter.

The authors also discuss experimental feasibility, estimating that with realistic material parameters and currently achievable pumped phonon occupancies (n_ph ~ 0.1-1), the induced changes to exchange interactions can be on the order of a few percent to tens of percent—sufficient to drive qualitative phase changes in highly sensitive frustrated magnets.

In conclusion, this work establishes “spin-phonon pumping” as a novel and powerful theoretical concept for the non-equilibrium control of magnetism. It provides a blueprint for using phonons as a precise tool to selectively tailor complex spin Hamiltonians, offering a promising route to realize and manipulate exotic quantum states like spin liquids in real materials.