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arXiv:1406.5856 · Physical Review B

Magnetic phases in the S=1 Shastry-Sutherland model with uniaxial anisotropy

Lei Su, Keola Wierschem, Pinaki Sengupta

Published Jun 20, 2014• 6 citations
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Abstract

We explore the field-induced magnetic phases of an $S=1$ $XXZ$ model with single-ion anisotropy and large Ising-like anisotropy on a Shastry-Sutherland lattice over a wide range of Hamiltonian parameters and applied magnetic field. The multitude of ground-state phases are characterized in detail in terms of their thermodynamic properties, and the underlying classical (Ising limit) spin arrangements for the plateau phases are identified by calculating the static structure factors. The enlarged local Hilbert space of the $S=1$ spins results in several ground state phases that are not realized for $S=1/2$ spins. These include the quantum paramagnetic state that is ubiquitous to $S=1$ spins with single-ion anisotropy, two different spin supersolid phases (with distinct longitudinal ordering), and a magnetization plateau that arises as a direct descendant of the 1/3 plateau due to quantum fluctuations that are not possible for $S=1/2$ spins. We predict the same mechanism will lead to plateaus at smaller fractions of 1/3 for higher spins. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order as well as the different longitudinal orderings.

DOI
10.1103/physrevb.89.245432

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We explore the field-induced magnetic phases of an S=1S=1S=1 XXZXXZXXZ model with single-ion anisotropy and large Ising-like anisotropy on a Shastry-Sutherland lattice over a wide range of Hamiltonian parameters and applied magnetic field. The multitude of ground-state phases are characterized in detail in terms of their thermodynamic properties, and the underlying classical (Ising limit) spin arrangements for the plateau phases are identified by calculating the static structure factors. The enlarged local Hilbert space of the S=1S=1S=1 spins results in several ground state phases that are not realized for S=1/2S=1/2S=1/2 spins. These include the quantum paramagnetic state that is ubiquitous to S=1S=1S=1 spins with single-ion anisotropy, two different spin supersolid phases (with distinct longitudinal ordering), and a magnetization plateau that arises as a direct descendant of the 1/3 plateau due to quantum fluctuations that are not possible for S=1/2S=1/2S=1/2 spins. We predict the same mechanism will lead to plateaus at smaller fractions of 1/3 for higher spins. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order as well as the different longitudinal orderings.
We examine ground-state properties of the spin-1/2 easy-axis Heisenberg model on the Shastry-Sutherland lattice with ferromagnetic transverse spin exchange using quantum Monte Carlo and degenerate perturbation theory. For vanishing transverse exchange, the model reduces to an antiferromagnetic Ising model that, besides N\'eel order, harbors regions of extensive ground-state degeneracy. In the quantum regime, we find a dimerized phase of triplet states separated from the N\'eel ordered phase by a superfluid. The quantum phase transitions between these phases are characterized. The magnetization process shows a magnetization plateau at 1/3 of the saturation value, which persists down to the Ising limit, and a further plateau at 1/2 only in the quantum regime. For both plateaus, we determine the crystalline patterns of the localized triplet excitations. No further plateaus or supersolid phases are found in this model.
We use large scale quantum Monte Carlo simulations to study an extended version of the canonical Shastry-Sutherland model--including additional interactions and exchange anisotropy--over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Working in the limit of large Ising-like exchange anisotropy, we demonstrate the stabilization of columnar antiferromagnetic order in the ground state at zero field and an extended magnetization plateau at 1/2 the saturation magnetization in the presence of an applied longitudinal magnetic field--qualitatively similar to experimentally observed low-temperature phases in ErB(4). Our results show that for an optimal range of exchange parameters, a spin supersolid ground state is realized over a finite range of an applied field between the columnar antiferromagnetic phase and the magnetization plateau. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order. Our results provide crucial guidance in designing further experiments to search for the interesting spin supersolid phase in ErB(4).
We study magnetic properties of the spin-12\frac{1}{2}21​ Ising-like XXZ model on the Shastry-Sutherland lattices with long-range interactions, using the quantum Monte Carlo method. This model shows magnetization plateau phases at one-half and one-third of the saturation magnetization when additional couplings are considered. We investigate the finite temperature transition to one-half and one-third plateau phases. The obtained results suggest that the former case is of the first order and the latter case is of the second order. We also find that the system undergoes two successive transitions with the two-dimensional Ising model universality although there is a single phase transition in the Ising limit case. Finally, we estimate the coupling ratio to explain the magnetization process observed in TmB4{\text{TmB}}_{4}TmB4​.
We study the spin-3/23/23/2 Heisenberg model including easy-plane and exchange anisotropies in one and two dimensions. In the Ising limit, when the off-diagonal exchange interaction JJJ is zero, the phase diagram in magnetic field is characterized by magnetization plateaus that are either translationally invariant or have a two-sublattice order, with phase boundaries that are macroscopically degenerate. Using a site-factorized variational wave function and perturbational expansion around the Ising limit, we find that superfluid and supersolid phases emerge between the plateaus for small finite values of JJJ. The variational approach is complemented by a density matrix renormalization group study of a one-dimensional chain and exact diagonalization calculations on small clusters of a square lattice. The studied model may serve as a minimal model for the layered Ba2{}_{2}2​CoGe2{}_{2}2​O7{}_{7}7​ material compound, and we believe that the vicinity of the uniform 1/3 plateau in the model parameter space can be observed as an anomaly in the measured magnetization curve.
Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intradimer and Ising interdimer couplings are found by two independent rigorous procedures. The first method uses a unitary transformation to establish a mapping correspondence with an effective classical spin model, while the second method relies on the derivation of an effective hard-core boson model by continuous unitary transformations. Both methods lead to equivalent effective Hamiltonians providing a convincing proof that the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice exhibits a zero-temperature magnetization curve with just two intermediate plateaus at one-third and one-half of the saturation magnetization, which correspond to stripe and checkerboard orderings of singlets and polarized triplets, respectively. The nature of the remarkable stripe order relevant to the one-third plateau is thoroughly investigated with the help of the corresponding exact eigenvector. The rigorous results for the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice are compared with the analogous results for the purely classical Ising and fully quantum Heisenberg models. Finally, we discuss to what extent the critical fields of SrCu2(BO3)2{\mathrm{SrCu}}_{2}{(\mathrm{BO}}_{3}){}_{2}SrCu2​(BO3​)2​ and (CuCl)Ca2Nb3O10{(\mathrm{CuCl})\mathrm{Ca}}_{2}{\mathrm{Nb}}_{3}{\mathrm{O}}_{10}(CuCl)Ca2​Nb3​O10​ can be described within the suggested Ising-Heisenberg model.
Frustrated magnets host rich emergent behavior because competing interactions generate dense manifolds of low-energy states. The Ising Shastry-Sutherland model is a paradigmatic setting, motivated experimentally by Ising-like rare-earth tetraborides such as TmB4_44​ and ErB4_44​, whose field-induced magnetization plateaus have motivated extensive microscopic modeling. Yet how tunable quantum fluctuations reorganize this material-motivated phase diagram remains largely unexplored. Here, we realize a transverse- and longitudinal-field Ising model on the Shastry-Sutherland lattice using a programmable Rydberg-atom array. We map its quantum phase diagram using density matrix renormalization group calculations and probe corresponding signatures experimentally in arrays containing more than 110 atoms. Beyond the established classical phases, the calculations identify two regimes absent in the classical limit and stabilized at finite transverse field: a 2/52/52/5 filling plateau whose finite stability region emerges from a classically degenerate phase boundary and a symmetry-preserving quantum-dimer regime replacing classically selected collinear order. Experiments on finite open arrays reveal signatures consistent with these regimes across three boundary-pinning conditions, with the resulting response maps agreeing qualitatively with the calculated phase diagram. Our results establish programmable Rydberg-atom arrays as tools for exploring frustrated, material-motivated Hamiltonians and motivate searches for new, quantum-driven magnetization plateaus and quantum-dimer behavior in ErB4_44​ under a transverse field or in strain-tuned TmB4_44​.