Emergence of a two-dimensional macrospin liquid in a highly frustrated three-dimensional quantum magnet

Abstract

The classical Ising model on the frustrated 3d swedenborgite lattice has disordered spin liquid ground states for all ratios of inter-and intra-planar couplings. Quantum fluctuations due to a transverse field give rise to several exotic quantum phenomena. In the limit of weakly coupled Kagomé layers we find a 3d version of disorder by disorder. For large out-of-plane couplings 1d macro-spins are formed which realize a disordered macro-spin liquid on an emerging triangular lattice. Signatures of this dimensional reduction are also found in critical exponents of the quantum phase transition out of the fully polarized phase into the macro-spin liquid displaying quantum criticality typical for 2d quantum systems.Introduction: Geometrical frustration in magnetic systems can give rise to a multitude of exotic classical and quantum phases. An analysis of the classical limit often reveals a large degeneracy in the ground-state manifold, which can be lifted by quantum or thermal fluctuations thereby selecting an ordered state. This phenomenon is conventionally referred to as 'order by disorder'. A more exotic version of degeneracy lifting is called 'disorder by disorder' [1-5]: out of multiple classical ground states a disordered state is selected. Paradigmatic examples for either of the two phenomena can be found in two dimensions for the transverse field Ising model (TFIM), on the triangular and the Kagomé lattices, respectively. In both cases a polarized phase is found at high transverse fields. On the triangular lattice an infinitesimal transverse field is sufficient to select an ordered state out of the degenerate classical manifold, thereby providing an example of order by disorder. The selected state is the so-called √ 3 × √ 3-state which maximizes the number of flippable spins. The two phases are connected via a second order phase transition in the 3d XY universality class [1,4,6]. In contrast, in the case of the Kagomé lattice any finite transverse field selects the disordered polarized phase which does not break any symmetry, providing an example of disorder by disorder [1,4].Recently, it was found that interesting effects of frustrated magnetism can also be encountered in the threedimensional swedenborgite systems. For example, classical O(3) Heisenberg spins on this lattice exhibit a wide spin liquid regime for a certain parameter and temperature range and can undergo a fluctuation driven order by disorder transition to a nematic phase at very low temperatures [7]. It was also shown that the classical Ising model with and without longitudinal magnetic field boasts different phases with extensive and subextensive ground-state degeneracy [8]. Depending on system parameters, the swedenborgite structure corresponds to either a stack of weakly coupled Kagomé layers or an emergent triangular lattice of stiff macro-spins. As a result, one can speculate that the order by disorder of the triangular lattice TFIM and the disorder by disorder of the

Spin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model

“…Large strains are achievable in thin films, which for spin ice materials have recently been grown [12]. The low-energy physics of such systems is expected to be described to a good extent by the transverse-field Ising model (TFIM) on the three-dimensional pyrochlore lattice.The TFIM is one of the archetypal models used in various areas in physics and is known to host a plethora of interesting physical phenomena, especially on highly frustrated lattices [13][14][15][16]. At the same time the theoretical treatment of three-dimensional frustrated systems including TFIMs represents a notable challenge and quantitative results are hard to extract.…”

“…The TFIM is one of the archetypal models used in various areas in physics and is known to host a plethora of interesting physical phenomena, especially on highly frustrated lattices [13][14][15][16]. At the same time the theoretical treatment of three-dimensional frustrated systems including TFIMs represents a notable challenge and quantitative results are hard to extract.…”

Bilayer Kitaev models: Phase diagrams and novel phases

“…We have studied the breakdown of this topological phase and the transition to the dimer paramagnet by deriving effective models in the anisotropic limit. Additionally, two further stacking variants of the model lead to novel macro-spin phases 49,50 at finite J ⊥ /K and strong anisotropies, which can be described in terms of macro-spins emerging from interlayer chains. These macro-spins can be either coupled ferromagnetically (realizing a microscopic antiferromagnet) or remain degenerate and thus constitute a classical spin liquid.…”