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arXiv:2605.15274

Unveiling Magnetic Frustration via the Elastocaloric Effect

Eric C. Andrade, Pedro M. Cônsoli, Matthias Vojta C

Published May 14, 2026• 0 citations
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Abstract

Motivated by experimental progress in pressure and strain tuning of quantum materials, we examine the thermodynamic response of frustrated magnets to uniaxial strain. Specifically, we study Ising and Heisenberg models on spatially anisotropic triangular (and, for the Ising model, also kagome) lattices. We determine the entropy as a function of temperature and strain, and use it to compute the elastic Grüneisen ratio $η$. The Ising models can be strain-tuned into and out of classical spin-liquid phases, and we show that $η$ can become arbitrarily large at low temperature $T$ near the point of maximal frustration, a universal hallmark of an extensive ground-state entropy. In contrast, the spin-$1/2$ Heisenberg model is moderately frustrated and displays multiple $T=0$ phase transitions. These transitions dominate $η$ at low $T$ while the intermediate-$T$ behavior is similar to that of the Ising model. We discuss the extent to which the elastic Grüneisen ratio can be used to deduce the phase diagram, and we connect our results to recent experiments on triangular-lattice magnets.

DOI
10.48550/arxiv.2605.15274

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Motivated by experimental progress in pressure and strain tuning of quantum materials, we examine the thermodynamic response of frustrated magnets to uniaxial strain. Specifically, we study Ising and Heisenberg models on spatially anisotropic triangular (and, for the Ising model, also kagome) lattices. We determine the entropy as a function of temperature and strain, and use it to compute the elastic Grüneisen ratio ηηη. The Ising models can be strain-tuned into and out of classical spin-liquid phases, and we show that ηηη can become arbitrarily large at low temperature TTT near the point of maximal frustration, a universal hallmark of an extensive ground-state entropy. In contrast, the spin-1/21/21/2 Heisenberg model is moderately frustrated and displays multiple T=0T=0T=0 phase transitions. These transitions dominate ηηη at low TTT while the intermediate-TTT behavior is similar to that of the Ising model. We discuss the extent to which the elastic Grüneisen ratio can be used to deduce the phase diagram, and we connect our results to recent experiments on triangular-lattice magnets.
A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of two-dimensional (2D) layers and in the quantum model from the quantum dynamics induced by a transverse field. By mapping the Ising models on a triangular lattice to elastic lattices of noncrossing strings, we derive an exact relation between the spin variables and the displacement field of the strings. Using this map for both the classical (2+1)D(2+1)\mathrm{D}(2+1)D stacked model and the quantum frustrated 2D system, we obtain a microscopic derivation of an effective Hamiltonian which was proposed before on phenomenological grounds within a Landau-Ginzburg-Wilson approach. In contrast to the latter approach, our derivation provides the coupling constants and hence the entire transverse field-versus-temperature phase diagram can be deduced, including the universality classes of both the quantum and the finite-temperature transitions. The structure of the ordered phase is obtained from a detailed entropy argument. We compare our predictions to recent simulations of the quantum system and find good agreement. We also analyze the connections to a dimer model on the hexagonal lattice and its height profile representation, providing a simple derivation of the continuum free energy and a physical explanation for the universality of the stiffness of the height profile for anisotropic couplings.
We investigate a nearest-neighbor Ising model on the kagome lattice coupled to elastic lattice distortions. By integrating out the lattice degrees of freedom, we derive an approximate spin-only description in terms of a kagome J1J_1J1​-J2J_2J2​-J3J_{3}J3​ Ising model with interactions extending to third nearest-neighbors. Using tensor network methods complemented by classical Monte Carlo simulations, we revisit its zero-temperature phase diagram and characterize the ground states studied more than thirty years ago. We discover three phases with extensive zero-temperature entropy and algebraically decaying spin correlations. Importantly, these states are not confined to fine-tuned points or frontiers between phases, but occupy extended areas of parameter space. Their quasi long-range order is reflected in Bragg-like peaks in the structure factors; we relate this, and other properties, to diverse phases found in Ising and Heisenberg models. Finally, we trace the trajectories generated by the magnetoelastic coupling through the effective-model phase diagram, explaining the emergence of self-frustration for the unfrustrated magnetoelastic model with ferromagnetic interactions.
Low-temperature magnetization curves and thermodynamics of a frustrated spin-12\frac{1}{2}21​ Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-12\frac{1}{2}21​ Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-12\frac{1}{2}21​ Ising model in a field. A description based on the effective Ising model implies that the frustrated Heisenberg triangular bilayer with the ferromagnetic interdimer coupling displays in a zero-temperature magnetization curve discontinuous magnetization jump, which is reduced upon increasing of temperature until a continuous field-driven phase transition from the Ising universality class is reached at a certain critical temperature. The frustrated Heisenberg triangular bilayer with the antiferromagnetic interdimer coupling contrarily exhibits multistep magnetization curve with intermediate plateaus at 13\frac{1}{3}31​ and 23\frac{2}{3}32​ of the saturation magnetization, whereas discontinuous magnetization jumps observable at zero temperature change to continuous field-driven phase transitions from the universality class of three-state Potts model at sufficiently low temperatures. Exact results and Monte Carlo simulations of the effective Ising model are confronted with full exact diagonalization data for the Heisenberg triangular bilayer in order to corroborate these findings.
The spin-12\frac{1}{2}21​ Ising-Heisenberg model on two geometrically related triangles-in-triangles lattices is exactly solved through the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the effective spin-12\frac{1}{2}21​ Ising model on a triangular lattice. Basic thermodynamic quantities were exactly calculated within this rigorous mapping method along with the ground-state and finite-temperature phase diagrams. Apart from the classical ferromagnetic phase, both investigated models exhibit several unconventional quantum ordered and disordered ground states. A mutual competition between two ferromagnetic interactions of basically different character generically leads to the emergence of a quantum ferromagnetic phase, in which a symmetric quantum superposition of three up-up-down states of the Heisenberg trimers accompanies a perfect alignment of all Ising spins. In the highly frustrated regime, we have either found the disordered quantum paramagnetic phase with a substantial residual entropy or a similar but spontaneously ordered phase with a nontrivial criticality at finite temperatures. The latter quantum ground state exhibits a striking coexistence of imperfect spontaneous order with partial disorder, which is evidenced by a quantum reduction of the spontaneous magnetization of Heisenberg spins that indirectly causes a small reduction of the spontaneous magnetization of otherwise classical Ising spins.
The spin-1/2 Ising-Heisenberg model on martini and martini-diced lattices is exactly solved using a star-triangle transformation, which affords an exact mapping correspondence to an effective spin-1/2 Ising model on a triangular lattice. The ground-state phase diagram of both investigated quantum spin models display two spontaneously ordered ferromagnetic phases and one macroscopically degenerate disordered phase. In contrast to a classical ferromagnetic phase where the spontaneous magnetization of the Ising as well as Heisenberg spins acquire fully saturated values, the spontaneous magnetization of the Heisenberg spins is subject to a quantum reduction to one-third of its saturated value within a quantum ferromagnetic phase. The spontaneous magnetization and logarithmic divergence of the specific heat as the most essential features of both ferromagnetic phases disappear whenever the investigated quantum spin model is driven to the highly degenerate disordered phase. The disordered phase with nonzero residual entropy originates either from a geometric spin frustration caused by antiferromagnetic interactions or more strikingly it may also alternatively arise from a competition of the ferromagnetic Ising and Heisenberg interactions of easy-axis and easy-plane type, respectively. All three available ground states coexist together at a single triple point, around which anomalous magnetic and thermodynamic behavior can be detected.
The spin-1/2 Ising-Heisenberg model on martini and martini-diced lattice is exactly solved using a star-triangle transformation, which affords an exact mapping correspondence to an effective spin-1/2 Ising model on a triangular lattice. The ground-state phase diagram of both investigated quantum spin models display two spontaneously ordered ferromagnetic phases and one macroscopically degenerate disordered phase. In contrast to a classical ferromagnetic phase where the spontaneous magnetization of the Ising as well as Heisenberg spins acquire fully saturated values the spontaneous magnetization of the Heisenberg spins is subject to a quantum reduction to one-third of its saturated value within a quantum ferromagnetic phase. The spontaneous magnetization and logarithmic divergence of the specific heat as the most essential features of both ferromagnetic phases disappear whenever the investigated quantum spin model is driven to the highly degenerate disordered phase. The disordered phase with nonzero residual entropy originates either from a geometric spin frustration caused by antiferromagnetic interactions or more strikingly it may also alternatively arise from a competition of the ferromagnetic Ising and Heisenberg interactions of easy-axis and easy-plane type, respectively. All three available ground states coexist together at a single triple point, around which anomalous magnetic and thermodynamic behavior can be detected.