Interfacial Spin-Lattice Coupling

• Interfacial spin-lattice coupling is the dynamic interaction between spin degrees of freedom and lattice vibrations at material boundaries, leading to hybrid magnon-phonon modes.
• The mechanism involves Rashba-induced interactions and strain effects, as evidenced by Raman and infrared spectroscopy in topological and oxide heterostructures.
• This coupling underpins device innovations by enabling nonreciprocal phonon propagation and tunable spintronic functionalities through precise interface engineering.

Interfacial spin-lattice coupling refers to the physical phenomenon whereby spin degrees of freedom and lattice vibrations (phonons) become dynamically coupled at the interface between different materials, particularly in systems with strong spin-orbit coupling, broken inversion symmetry, or engineered heterostructures. This coupling yields intricate modifications of magnon, phonon, and mixed magnon–phonon excitations, enabling novel magnetic, transport, and nonreciprocal acoustic responses at interfaces such as those between topological insulators and magnetic materials, or between ferromagnets and heavy metals.

1. Microscopic Mechanisms of Interfacial Spin-Lattice Coupling

At structurally and electronically noncentrosymmetric interfaces, such as those encountered between a ferromagnetic film and a substrate, interfacial spin-lattice coupling may manifest via spin-orbit interactions with Rashba symmetry. The Rashba Hamiltonian for conduction electrons is given by

$$H_R^0 = \frac{\alpha_R}{\hbar} (\boldsymbol\sigma \times \mathbf{p}) \cdot \hat{z},$$

where $\alpha_R$ is the Rashba coefficient, $\boldsymbol\sigma$ are Pauli matrices, and $\mathbf{p}$ is the crystal momentum (Go et al., 19 Jan 2026). When ions are displaced, electrons perceive a velocity-dependent correction, resulting in an interfacial energy density

$$\mathcal{H}_{SL} = \lambda_{SL}\, \mathbf{m}\cdot\left(\hat{z} \times \dot{\mathbf{u}}\right),$$

with $\lambda_{SL}$ reflecting microscopic Rashba and exchange parameters. No gradient of displacement is required owing to the purely interfacial nature of this "Rashba-like" coupling.

In hybrid heterostructures, such as Bi$_2$Te$_3$/FePS$_3$, proximity-induced spin-phonon coupling arises where phonons in a non-magnetic topological insulator (TI) hybridize with the phononic/magnonic excitations of an adjacent antiferromagnet (AFM) (Maity et al., 2022). DFT calculations and Raman spectroscopy establish that interfacial strain, bond-angle modifications, and exchange interactions strongly mediate this coupling, evidenced by shifts in phonon frequencies and softening of magnon modes.

In 3$d$/5$d$ oxide hybrids (e.g., Sr$_3$NiIrO$_6$), interfacial spin-lattice coupling is rooted in the strong sensitivity of the Ir–O network to magnetic and vibrational perturbations. Specific infrared-active phonons modulate magnetic exchange pathways both within and between chains (O'Neal et al., 2019). Here, phonon eigenvectors induce coordinated atomic displacements across chains, enabling inter-chain magnetic communication.

2. Theoretical Frameworks and Modeling

To quantitatively model interfacial spin-lattice coupling, Ginzburg–Landau (GL) theory is employed for coupled phonon-magnon fields at interfaces. The free energy functional for two coupled order parameters (TI and AFM phonon/magnon fields) is

$$F[\Psi_{TI}, \Psi_{AF}] = \frac{1}{2}\alpha_{TI}(T)|\Psi_{TI}|^2 + \frac{1}{4}\beta_{TI}|\Psi_{TI}|^4 + \frac{1}{2}\alpha_{AF}(T)|\Psi_{AF}|^2 + \frac{1}{4}\beta_{AF}|\Psi_{AF}|^4 - \lambda (\Psi_{TI}\Psi_{AF}^* + c.c.),$$

with $\lambda$ quantifying the spin-phonon coupling strength (Maity et al., 2022). Hybridization leads to anticrossing of magnon and phonon branches; the frequency shifts $\Delta\omega$ track the square of the AFM order parameter $m(T)$.

In the Rashba-induced context, integrating out magnon fields yields a phonon Lagrangian with a "kineo-elastic" term,

$$\mathcal{L}_{ke} = \int d^2 r\, \eta\, u_{xy}\, \dot{u}_x,$$

where $\eta$ depends on the microscopic spin-lattice coupling and the magnetoelastic constant. This term induces an odd-in-momentum ($k$) and odd-in-frequency ($\omega$) nonreciprocity in phonon propagation (Go et al., 19 Jan 2026).

Generalized magnetoelectronic circuit theory incorporates interfacial spin-orbit coupling via a tensorial conductance formalism, replacing scalar spin-mixing conductances with full $G_{i\alpha\beta}$ and $\sigma_{i\alpha}$ tensors. The new boundary conditions describe how in-plane electric fields and spin accumulations promote spin and charge currents of arbitrary polarization, impacting spin transfer, spin pumping, and spin memory loss phenomena (Amin et al., 2016).

3. Experimental Signatures and Quantification

Raman and infrared spectroscopies provide primary evidence for interfacial spin-lattice coupling. In Bi$_2$Te$_3$/FePS$_3$ heterostructures, departures from phonon anharmonicity under cooling, alongside excess linewidth broadening and magnon energy softening, quantitatively support interfacial coupling with $\Delta\omega \sim 1.5$–3 cm$^{-1}$ and strain-induced suppression of Néel temperature from 120 K to 65 K (Maity et al., 2022). Fe–S–Fe bond angles contract by $\sim$10° under 0.5% strain, as confirmed by DFT exchange mapping.

In Sr$_3$NiIrO$_6$, three infrared-active phonons (133, 310, 534 cm$^{-1}$) exhibit coupling constants up to 10 cm$^{-1}$. Their displacement patterns favor the modulation of both intra-chain and inter-chain exchange, yielding observable frequency shifts and reduced switching barriers under magnetic field sweeps to 48 T (O'Neal et al., 2019).

Spin pumping, memory loss, and torque signatures in ferromagnet/heavy-metal bilayers are influenced by interfacial SOC, as shown in experiments that report thickness-dependent spin Hall magnetoresistance and modified spin torque behavior (Amin et al., 2016).

4. Emergent Nonreciprocal and Hybrid Excitations

Interfacial spin-lattice coupling gives rise to hybridized magnon–phonon modes, nonreciprocal phonon propagation, and directional absorption. In Rashba-active systems, transverse phonon dispersion is modified as

$\omega_T(k) \simeq c_T |k| + \frac{\eta}{2\rho} k,$

leading to an asymmetry in group velocity $\Delta v = v_T(+|k|) - v_T(-|k|) = \eta/\rho$ (Go et al., 19 Jan 2026). Dramatic contrasts in phonon attenuation and propagation length for opposite wavevectors arise from directional hybridization gaps at anti-crossings, controlled by $$\Delta_{gap}(k)\propto |\omega \lambda_{SL} - b_2 k|$$.

The hybridized magnon–phonon spectrum can be tuned via interface engineering. Spacer layers such as bulk or few-layer hBN restore phonon anharmonicity, suppressing interfacial coupling by decoupling spin fluctuations from the lattice (Maity et al., 2022).

In oxide chains, nonzero components of displacement eigenvectors across chains (e.g., $Q_{310}^{(ab)}$) establish microscopic bridges, enabling interfacial damping, magnon entanglement, and vibronic activation of on-site transitions (O'Neal et al., 2019).

5. Materials Engineering and Device Implications

Precisely controlling interfacial spin-lattice coupling allows for the design of devices utilizing nonreciprocal phonon transport, ultrahigh coercivity, surface-code spin logic, and spin–orbit torque functionalities.

Key parameters include maximizing $\lambda_{SL}$ via material selection (heavy-element substrates, strong band-mismatch), orienting magnetization in the propagation direction, and choosing appropriate phonon modes (shear horizontal surface waves). Spacer layers (e.g., hBN) provide on-demand switching for spin-phonon coupling, crucial for hybrid magnon–phonon qubits and surface-code architectures operating in the $\sim$3–5 THz regime with switching energies down to 2 meV (Maity et al., 2022, Go et al., 19 Jan 2026).

In Sr$_3$NiIrO$_6$, spin–charge–lattice entanglement resulting from strong interfacial coupling facilitates ultra-high coercive fields and novel mechanisms for topological exchange anisotropy and vibronic behavior (O'Neal et al., 2019).

Spin transport models incorporating interfacial SOC elucidate spin transfer torque, spin pumping, and spin Hall magnetoresistance, predicting modifications in experimentally obtained spin Hall angles and damping factors (Amin et al., 2016).

6. Design Principles and Future Directions

Optimal design of interfacial spin-lattice coupling requires:

• Selecting materials with large Rashba coefficients and strong spin-orbit coupling.
• Engineering biaxial strain and bond-angle environments to tune exchange interactions (e.g., FePS$_3$/Bi$_2$Te$_3$ interfaces).
• Utilizing interface orientation, material band-structure, and atomically flat spacers to control coupling strength and hybridization.
• Applying magnetoelectronic circuit theory to extract tensorial conductances in experimental spin transport setups.

Potentially, these principles enable directional acoustic devices, tunable magnon-phonon entanglement, and robust topological quantum architectures. Spacer-controlled spin-lattice coupling provides a reconfigurable platform for future spintronic and phononic applications, subject to further elucidation of the underlying microscopic mechanisms and quantum statistics.

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Key Reference Table: Experimental Systems Exhibiting Interfacial Spin-Lattice Coupling

System	Coupling Manifestation	Quantified Parameters
Bi$_2$Te$_3$/FePS$_3$ (vdW stack)	Raman mode shifts, magnon softening	$\Delta\omega$ 1.5–3 cm$^{-1}$; $T_N$↓120→65 K
Sr$_3$NiIrO$_6$ (3$d$/5$d$ oxide)	IR-phonon–exchange modulation, vibronics	$g_\beta$≈10 cm$^{-1}$, coercivity~48–55 T
FM/heavy-metal interfaces (SOC)	Spin torque, spin Hall magnetoresistance	Mixing conductance tensors, SML

These systems serve as platforms for elucidating interfacial spin-lattice coupling mechanisms, quantifying coupling strengths, and translating fundamental understanding into device-level implementation.