Spin Excitation Continuum in the Exactly Solvable Triangular-Lattice Spin Liquid CeMgAl11O19

In magnetically ordered insulators, elementary quasiparticles manifest as spin waves - collective motions of localized magnetic moments propagating through the lattice - observed via inelastic neutron scattering. In effective spin-1/2 systems where geometric frustrations suppress static magnetic order, spin excitation continua can emerge, either from degenerate classical spin ground states or from entangled quantum spins characterized by emergent gauge fields and deconfined fractionalized excitations. Comparing the spin Hamiltonian with theoretical models can unveil the microscopic origins of these zero-field spin excitation continua. Here, we use neutron scattering to study spin excitations of the two-dimensional (2D) triangular-lattice effective spin-1/2 antiferromagnet CeMgAl11O19. Analyzing the spin waves in the field-polarized ferromagnetic state, we find that the spin Hamiltonian is close to an exactly solvable 2D triangular-lattice XXZ model, where degenerate 120$^\circ$ ordered ground states - umbrella states - develop in the zero temperature limit. We then find that the observed zero-field spin excitation continuum matches the calculated ensemble of spin waves from the umbrella state manifold, and thus conclude that CeMgAl11O19 is the first example of an exactly solvable spin liquid on a triangular lattice where the spin excitation continuum arises from the ground state degeneracy.

💡 Research Summary

The authors report a comprehensive investigation of the triangular‑lattice rare‑earth compound CeMgAl₁₁O₁₉, establishing it as the first experimentally realized example of an exactly solvable spin liquid on a triangular lattice. The material hosts Ce³⁺ ions that form a Kramers doublet, giving an effective spin‑½ on each site. High‑quality single crystals were grown, and structural analysis revealed modest static disorder (≈ 7 % of Ce ions displaced within the mirror plane), but the disorder does not affect the magnetic exchange pathways appreciably.

Thermodynamic measurements (magnetic susceptibility, magnetization, specific heat) show strong antiferromagnetic correlations (Curie‑Weiss temperatures Θ‖ = +45 K, Θ⊥ = ‑110 K) and a magnetic entropy that reaches ~90 % of R ln 2 by 4 K, confirming the spin‑½ nature. No magnetic Bragg peaks are observed down to 60 mK, indicating the absence of long‑range order.

Inelastic neutron scattering (INS) was performed both in a 4 T c‑axis magnetic field (to fully polarize the spins) and at zero field. In the field‑polarized state, sharp, resolution‑limited magnon modes are observed throughout the Brillouin zone. By fitting the dispersion with linear spin‑wave theory, the nearest‑neighbor XXZ Hamiltonian parameters are extracted: J_z = ‑0.024(5) meV (ferromagnetic out‑of‑plane) and J_⊥ = 0.056(3) meV (antiferromagnetic in‑plane). The anisotropy ratio J_z/J_⊥ ≈ ‑0.43 places the system extremely close to the exactly solvable point ψ_U = π − arctan 2 (≈ 0.648π) of the triangular‑lattice XXZ model, where the ground‑state manifold consists of a continuous set of “umbrella” states that are quantum‑mechanically degenerate.

Zero‑field INS reveals a coexistence of a sharp spin‑wave‑like mode emanating from the Γ point (ℏω < 0.1 meV) and a broad continuum that is bounded by this mode at low energies but extends to the Brillouin‑zone edges (M and K points) up to ~0.3 meV. Unlike the gapless continua seen in candidate quantum spin liquids such as YbMgGaO₄, the continuum in CeMgAl₁₁O₁₉ is gapped at the zone boundaries, suggesting a different origin.

To explain the continuum, the authors calculate the linear‑spin‑wave spectra for individual umbrella states characterized by different out‑of‑plane canting angles θ. Averaging over a Gaussian distribution of θ centered at 90° with a 20° width reproduces the experimental intensity maps, including the persistent mode along Γ‑M and the strong dispersion variation along M‑K that generates the observed continuum. This agreement demonstrates that the continuum arises from the superposition of spin‑wave excitations belonging to a macroscopically degenerate set of umbrella ground states, rather than from fractionalized spinons.

The work thus provides a rare experimental platform where (i) the magnetic Hamiltonian can be precisely determined via field‑polarized magnons, (ii) the system sits at the boundary between 120° coplanar order and out‑of‑plane ferromagnetism in the XXZ phase diagram, and (iii) the zero‑field excitation continuum is a direct manifestation of exact quantum degeneracy of the umbrella manifold. Consequently, CeMgAl₁₁O₁₉ establishes a new class of spin liquid—an exactly solvable triangular‑lattice spin liquid—distinct from conventional quantum spin liquids that rely on emergent gauge fields and deconfined excitations. The findings also highlight that structural disorder in this material does not obscure the intrinsic magnetic physics, making it an ideal testbed for theoretical models of highly frustrated magnetism.