Cavity control of multiferroic order in single-layer NiI$_2$

Controlling materials through their interactions with electromagnetic vacuum fluctuations is an emergent frontier in material engineering. Although recent experiments have demonstrated dark cavity effects for electronic material phases, like superconductivity, ferroelectricity and charge density waves, a smoking gun experiment for magnetic systems is lacking. Largely, this comes from the focus on phase transitions, where a large critical light-matter coupling is needed to observe cavity modifications. Here, we propose spiral magnets, where even a small cavity-mediated change in magnetic interactions is reflected in a change of the spiral wavelength, as a promising platform to observe cavity effects. We focus on the single-layer multiferroic NiI$_2$, interacting with electric field fluctuations from surface phonon polaritons of the paraelectric substrate SrTiO$_3$. With decreasing substrate-material distance, the ratio of nearest and third nearest neighbor exchange interactions reduces, leading to an increase of the spiral wavelength and an eventual transition into a ferromagnetic state. Our work identifies a realistic platform to observe cavity vacuum renormalization effects in magnetic systems.

💡 Research Summary

This paper proposes a concrete platform for observing cavity‑vacuum renormalization effects in magnetic systems, focusing on the single‑layer multiferroic NiI₂ interfaced with a paraelectric SrTiO₃ substrate. The authors argue that while dark‑cavity modifications have been demonstrated for electronic phases such as superconductivity, charge‑density waves, and ferroelectricity, magnetic systems have lacked a clear experimental signature because most proposals rely on phase transitions that require a large light‑matter coupling to become observable. Spiral magnets, however, offer a more sensitive probe: a modest cavity‑induced change in magnetic exchange interactions directly translates into a measurable shift of the spiral wavelength.

NiI₂ is a van‑der‑Waals material with a triangular lattice of Ni²⁺ ions surrounded by edge‑sharing I⁻ octahedra. The Ni d‑orbitals split into a fully filled t₂g manifold and an e_g manifold that hosts two electrons forming an S = 1 local moment via Hund’s coupling. Using a Hubbard‑Kanamori description (U, U′ = U − 2J_H, J_H, spin‑orbit λ) and a fourth‑order strong‑coupling expansion, the authors derive an effective spin Hamiltonian that includes nearest‑neighbor Heisenberg exchange J₁, third‑nearest‑neighbor exchange J₃, a Kitaev term K, and small anisotropies Γ, Γ′. First‑principles calculations give J₁ ≈ ‑4.24 meV, J₃ ≈ 2.54 meV, K ≈ 1.06 meV, Γ ≈ 0.02 meV, Γ′ ≈ 0.06 meV. The comparable magnitude of |J₁| and J₃ is responsible for the helical magnetic ground state observed experimentally in bulk and monolayer NiI₂.

Because the helical order breaks inversion symmetry, NiI₂ becomes type‑I multiferroic: the electric polarization is odd under inversion and can be expressed as P_ij = P (x̂ + ŷ)