Hidden Triakontadipole Order in the Triangular-Lattice Magnet CeMgAl$_{11}$O$_{19}$

Abstract

The absence of magnetic Bragg peaks and a broad excitation continuum are commonly recognized experimental features of a quantum spin liquid. The Ce-based triangular-lattice hexaaluminate CeMgAl$_{11}$O$_{19}$ exhibits both signatures, yet its effective model and ground state remain under debate. Experiments have variously suggested a quantum spin liquid, proximate umbrella point, and disorder-suppressed magnetic order. Here we trace these contradictions to an overlooked multipolar degree of freedom: the transverse pseudospin of the $|\pm5/2\rangle$ Kramers doublet is a rank-5 triakontadipole rather than an ordinary dipole. Analyzing the magnetization, neutron spectra, and thermodynamics on equal footing, we establish a dipole-triakontadipole XXZ model with $J_{\perp} \simeq 0.65$ K and $J_c \simeq -0.13$ K. The resulting planar triakontadipolar superfluid order is hidden from dipolar probes, explaining the absence of a magnetic Bragg peak in neutron scattering. The zero-field excitations separate into a low-energy triakontadipole wave and a broad higher-energy continuum. We further propose nuclear spin-lattice relaxation and spin-current experiments to probe the gapless excitations of this hidden triakontadipole superfluid. Our findings thus open a new avenue for high-rank multipolar physics in rare-earth triangular-lattice magnets.