Controlling the magnetic state of the proximate quantum spin liquid α-RuCl₃ with an optical cavity

The realization of magnetic van der Waals (vdW) materials with thicknesses down to the monolayer limit has sparked a new interest in fundamental aspects of two-dimensional magnetism. Due to a competition of strong anisotropy, fluctuations, and spin-orbit effects, vdW materials are prime candidates to host exotic phenomena such as topological phase transitions, magnetic skyrmions, and quantum spin liquids. In addition, the electronic, magnetic, and optical properties of these materials are sensitive to a wide range of material engineering techniques such as strain, nanostructuring, electric fields, and moiré twisting, allowing their state to be tuned with high precision. Recent progress has also established optical engineering techniques as a method to functionalize quantum materials and to reach exotic (out-of-equilibrium) topological phases. However, driving a system with lasers is associated with excessive heating when the frequency becomes multi-photon resonant with electronic transitions. A way to circumvent this problem is to embed the system in an optical cavity, where the effective light-matter coupling is enhanced via mode volume compression and the state of the material can be modified in an equilibrium setting. Due to the strong interaction between light and charged excitations, polaritonic control of material and chemical properties via the cavity vacuum has so far focused on electronic and phonon mediated phase transitions. Alternatively, to address magnetic systems, optical cavities have been combined with external drives, or been used to modify a system's excited state properties. While currently efforts are made to extend the cavity framework to a broader class of materials, and to construct a unified first principles description of cavity quantum fluctuations and quantum matter, experiments demonstrating polaritonic control of materials are scarce. Therefore, to transform this promising approach into a powerful experimental tool, it is of key importance to identify candidate materials where cavity engineering techniques can be explored. Here, we extend the concept of cavity quantum electrodynamics (c-QED) engineering into the magnetic regime and identify such a candidate system, by demonstrating how an optical cavity can be used to control the magnetic ground state of the proximate quantum spin liquid α-RuCl3 via shaping the quantum fluctuations of the cavity. Depending on the cavity frequency, photon occupation, and the strength of the effective light-matter coupling, we find that it is possible to transform the equilibrium zigzag antiferromagnetic order into any of the magnetic phases supported by the extended Kitaev model. As a key result we find that for frequencies of a few THz and for moderate light-matter couplings, the interaction between the magnetic system and the vacuum fluctuations of the cavity is sufficient to transform α-RuCl3 from a zigzag antiferromagnet to a ferromagnet. In contrast to the meta-stable states obtained by driving the system with classical light, the magnetic state resulting from the interaction with the quantum fluctuations of the cavity is a true equilibrium state denoted the photo ground state (PGS). Pumping the cavity in the few photon regime, it is further possible to push the system into the Kitaev quantum spin liquid state and to retrieve the non-equilibrium phase diagram of the semi-classical limit. Our results pave the way for utilizing c-QED to induce and control long-lived exotic states in quantum materials.

The paper situates itself within recent advances in two-dimensional van der Waals magnets and their tunability via strain, nanostructuring, electric fields, and moiré engineering. Prior optical engineering has realized out-of-equilibrium topological phases but suffers from heating under strong laser drives. Cavity quantum electrodynamics offers enhanced light-matter coupling via mode volume compression, enabling equilibrium modifications of material states. Previous cavity work largely focused on electronic and phonon-mediated phenomena, with relatively few demonstrations in magnetic systems. Efforts combining cavities with external drives or targeting excited-state properties in magnets have been reported, and a broader first-principles framework for cavity quantum materials is being developed. Experimental demonstrations of polaritonic control remain scarce, motivating identification of candidate materials where cavity engineering can achieve robust, equilibrium control of magnetic phases.

- Model and approach: The authors study α-RuCl3, a proximate Kitaev quantum spin liquid on a honeycomb lattice, described by an extended Kitaev spin model derived from an underlying multiorbital electronic Hamiltonian. The system is embedded in a Fabry-Pérot cavity and coupled to a single effective circularly polarized in-plane cavity mode (or equivalently two degenerate linear in-plane modes to restore rotational symmetry). The photo ground state (PGS) of the coupled spin-photon system is computed. - Exact diagonalization: They obtain the magnetic phase diagram and PGS by exact diagonalization of the cavity-coupled spin Hamiltonian on a 24-site honeycomb spin cluster that preserves all sublattice symmetries. They analyze the evolution of magnetic order as a function of effective light-matter coupling geff and cavity photon energy Ω, tracking spin-spin correlations and the plaquette flux operator Wp to diagnose phases including quantum spin liquids. - Treatment of cavity and dissipation: The principal results assume an ideal (lossless) cavity to define an equilibrium PGS where the photon population remains close to the vacuum. They argue dark-cavity results are robust to losses, as the phase transitions emerge predominantly within the n=0–1 photon sectors. For driven cavities (finite photon occupation), they discuss required cavity quality factors (Q ≈ Ω/κ ≳ 1000 in the optical regime) to observe phase transitions given light-induced parameter changes of order 1–10 meV. Coupling to collective spin excitations at q≈0 is neglected, expected to be suppressed except near ferromagnetic order. - Photon state and high-frequency approximation: For few-photon driving, they approximate quasi-stationary photon populations over timescale κ−1 and evaluate observables in photon number states, justified by weak dependence of expectation values on photon number compared to Poissonian weights of a coherent state in the high-frequency limit with negligible cross-coupling between photon-number sectors. - First-principles downfolding: Electronic parameters for α-RuCl3 are obtained from first-principles DFT+U calculations with OCTOPUS and Wannier90. A 1×√3 supercell (zigzag order), experimental lattice parameters a=5.98 Å and b=10.35 Å, mixed boundary conditions (periodic in-plane, open out-of-plane), and a 15 Å vacuum are used. The k-point grid is 8×8 with real-space grid spacing 0.3 Bohr. Using the ACBNO DFT+U functional, self-consistent Ueff=U−JH is determined on Ru and Cl; Kanamori U and JH are extracted after convergence. Wannierization of Ru 4d and Cl 3p states provides tight-binding parameters (Table 1). These are downfolded to equilibrium spin couplings (Table 2) used as a baseline for cavity-induced renormalizations. - Cavity parameters: For a two-dimensional cavity, the lowest photon mode frequency is Ω=πc/Lz. The effective single-mode light-matter coupling is given as g=0.12 under the assumption ax ay=a2 (expression provided in the text), and geff is varied in calculations up to ≈0.5 to trace phase evolution. Polarization considerations are discussed: a single linearly polarized mode breaks rotational symmetry; two degenerate in-plane modes or one circularly polarized mode restore C3 symmetry.

- Equilibrium cavity control: Embedding α-RuCl3 in a Fabry-Pérot cavity enables equilibrium control of its magnetic ground state via quantum vacuum fluctuations and few-photon populations, without the heating associated with strong classical drives. - Phase stabilization across extended Kitaev model: By tuning cavity frequency, photon occupation, and light-matter coupling, the system can be driven across the magnetic phases supported by the extended Kitaev model, including zigzag antiferromagnet, ferromagnet, stripe, Néel, and quantum spin-liquid regimes. - Vacuum-induced phase transition in THz regime: For frequencies of a few THz and moderate light-matter coupling, cavity vacuum fluctuations alone are sufficient to transform α-RuCl3 from its equilibrium zigzag antiferromagnetic order to a ferromagnetic state, establishing a true photo ground state (PGS). - Few-photon access to Kitaev QSL: With external pumping in the few-photon limit, the system can be pushed into the antiferromagnetic Kitaev quantum spin liquid state, recovering aspects of previously reported semi-classical non-equilibrium phase diagrams. - Microscopic insights: Low-photon-energy processes enhance the Heisenberg J via fourth-order direct Ru–Ru virtual transitions, while ligand-mediated processes introduce a low-frequency cutoff for the Kitaev K term, shaping the cavity-renormalized spin couplings and thus the phase diagram. - Practical requirements: In driven cavities, cavity-induced changes to magnetic parameters are of order 1–10 meV. Observability requires cavity decay rates κ ≲ 1 meV, corresponding to quality factors Q=Ω/κ ≈ 1000 or higher in the optical regime, which are achievable with current technology. Dark-cavity results are expected to be insensitive to typical cavity losses.

The study demonstrates that cavity quantum electrodynamics provides a viable equilibrium pathway to manipulate the magnetic ground state of a correlated quantum magnet. By modifying the effective spin interactions through coupling to vacuum and few-photon cavity fields, the approach navigates the extended Kitaev phase diagram, achieving transitions inaccessible or unstable under classical periodic driving due to heating. The identification of conditions—few-THz frequencies and moderate coupling—for vacuum-induced transitions, and the few-photon route to an antiferromagnetic Kitaev quantum spin liquid, highlights the sensitivity of α-RuCl3 to cavity quantum fluctuations. The results underscore the concept of a photo ground state as a long-lived equilibrium state of the coupled matter-photon system. Considerations of polarization show that symmetry can be preserved with appropriate cavity mode choices. While dissipation is neglected in the main calculations, the analysis indicates robustness for dark cavities and provides quantitative Q-factor thresholds for driven settings, supporting experimental feasibility. Overall, the findings extend c-QED engineering into magnetic regimes, offering a route to stabilize and control exotic magnetic states in vdW materials.

This work extends cavity quantum electrodynamical materials engineering to correlated magnetic systems, identifying α-RuCl3 as a prime platform where an optical cavity can deterministically control magnetic order. Theoretical calculations combining first-principles downfolding with exact diagonalization of a cavity-coupled extended Kitaev model show that cavity vacuum fluctuations at THz frequencies can drive the system from zigzag antiferromagnetism to ferromagnetism, and few-photon pumping can access the antiferromagnetic Kitaev quantum spin liquid. The concept of an equilibrium photo ground state is central, enabling long-lived phase control without heating. The study provides practical criteria (e.g., Q≳1000 for driven regimes) and symmetry considerations for cavity design. Future work should incorporate dissipation quantitatively, include couplings to collective spin excitations in the macroscopic limit, and develop advanced computational methods (e.g., tensor networks or quantum Monte Carlo) to capture larger systems and dynamics, guiding experimental realization of cavity-controlled magnetic phases.

- Idealized cavity: Main calculations assume a perfect (lossless) cavity. While dark-cavity results are argued to be robust, a full quantitative treatment for driven cavities requires inclusion of dissipation and photon leakage. - Neglected collective spin-photon couplings: Coupling to collective spin excitations at q≈0 is neglected, expected to be suppressed except near ferromagnetic order. Including these effects could modify phase boundaries in macroscopic samples with long-range order. - Finite-size effects: Exact diagonalization is restricted to a 24-site cluster, which, while symmetry-respecting, may not capture all finite-size and long-wavelength physics. - Photon-state approximation: For driven cases, the quasi-stationary few-photon assumption and evaluation in number states rely on a high-frequency limit with negligible cross-coupling between photon-number sectors. - Parameter uncertainties: Downfolded spin parameters depend on DFT+U choices and Wannierization; while carefully obtained, uncertainties may shift quantitative phase boundaries. Observation of driven-cavity transitions requires κ≲1 meV (Q≈Ω/κ≳1000).