Exotic quantum phases in two-dimensional frustrated magnets

Leon Balents

Tycho Sikkenk, K. Coester, Stefan Buhrandt +2 more

The classical Ising model on the frustrated three-dimensional (3D) swedenborgite lattice has disordered spin liquid ground states for all ratios of inter- and intraplanar couplings. Quantum fluctuations due to a transverse field give rise to several exotic phenomena. In the limit of weakly coupled kagome layers we find a 3D version of disorder by disorder degeneracy lifting. For large out-of-plane couplings one-dimensional macrospins are formed, which realize a disordered macrospin liquid phase on an emerging two-dimensional triangular lattice. We speculate about a possibly exotic version of quantum criticality that connects the polarized phase to the macrospin liquid.

Wen Jin

Huan-Da Ren, Tianyu Xiong, Han-Qing Wu +2 more

Understanding disorder-induced exotic states in two-dimensional magnets is one of the central topics in the study of frustrated magnetism. Here, the authors focus on the randomness-induced disordered phase in the spin-\textonehalf{} ${J}_{1}\ensuremath{-}{J}_{2}$ square-lattice Heisenberg model with a strong bond randomness, by using large-scale density matrix renormalization group (DMRG) simulations. The results not only reveal the absent spin-glass order, but also identify the power-law decay of the average spin correlation and the exponential decay of the typical spin correlation. These all agree with the corresponding behavior in the one-dimensional random-singlet state and characterize the random-singlet nature of this disordered phase. This shows that DMRG simulations provide opportunities for exploring the disorder effect in two-dimensional magnets.

Matthew Stern, Michael D. Burke, Michel J. P. Gingras +2 more

For nearly three decades, research on frustrated magnetism in three dimensions (3D) has centered on the pyrochlore lattice of corner-sharing tetrahedra and the classical spin liquid (CSL) known as spin ice. We propose that a lattice of corner-sharing octahedra -- the octochlore lattice -- may provide a next-generation platform for 3D frustrated magnetism, with realizations in anti-perovskite and alkali-rare-earth fluoride compounds. We study the phase diagram of Ising moments on the octochlore lattice, finding a variety of frustrated phases including CSLs and phases with subextensive ground state degeneracy intermediate between spin liquids and long-range order. Utilizing a cluster multipole framework, we present a unified treatment of this variety of frustrated behaviors. In addition to a spin ice CSL, we identify a fracton CSL with excitations restricted to move along one-dimensional (1D) lines, a classical U(1) equivalent of the paradigmatic X-cube model harboring fracton topological order. These "lineon" quasiparticles carry magnetic quadrupole moments, contrasting the famous magnetic monopoles of spin ice. These two CSLs lie at the boundaries of a parent "frustrated chains" phase with subextensive degeneracy. Each CSL corresponds to a condensate of different bound states of 1D ferro-spinons, giving rise to quasi-critical dimensional crossovers near the ends of the frustrated chains phase associated to avoided Kasteleyn-like transitions. We also find a spin nematic phase whose ground states may be viewed as fracton crystals, exhibiting both uniaxial and biaxial orders. The latter is caused by spontaneous dimensional reduction owing to accidental symmetries of the subextensive ground state manifold. This work paves the way for the realization of fracton CSLs and the exploration of other exotic states in underexplored octochlore magnetic materials.

Frédéric Mila