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arXiv:0910.4162 · Physical Review B

Magnetic properties of the spin- 12 XXZ model on the Shastry-Sutherland lattice: Effect of long-range interactions

Takahumi Suzuki, Yusuke Tomita, Naoki Kawashima

Published Nov 5, 2009• 35 citations
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Abstract

We study magnetic properties of the spin-$\frac{1}{2}$ 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 ${\text{TmB}}_{4}$.

DOI
10.1103/physrevb.80.180405

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We study the magnetization for the classical antiferromagnetic Ising model on the Shastry-Sutherland lattice using the tensor renormalization-group approach. With this method, one can probe large spin systems with little finite-size effect. For a range of temperature and coupling constant, a single magnetization plateau at one third of the saturation value is found. We investigate the dependence of the plateau width on temperature and on the strength of magnetic frustration. Furthermore, the spin configuration of the plateau state at zero temperature is determined.
Magnetization dependence on the external magnetic field was studied in a system with the Shastry–Sutherland lattice using exact diagonalization method at zero temperature within the xxz-model with spin S = 1/2. It was found that contrary to the classical Heisenberg model, the magnetization plateaus corresponding to m* = m/msat = 1/4, 1/3, and 1/2 (here msat is the saturation magnetization) exist even in the case of isotropic exchange interactions. The effect of exchange interaction on the width of the plateaus was studied. It was shown that depending on the ratio of exchange constants, there exist three regions corresponding to different types of the behavior of the system: the regions of a Neel-like antiferromagnet, a “dimer” antiferromagnet, and an intermediate region where the unique properties of Shastry–Sutherland lattices are most pronounced. The boundaries of these regions were also determined.
We study the finite-temperature transition to the 1/2 magnetization plateau in a model of interacting S = 1/2 spins with longer range interactions and strong exchange anisotropy on the geometrically frustrated Shastry-Sutherland lattice. In previous studies, it was obtained from Monte Carlo calculations that the transition to the plateau state occurs via two successive transitions with the two-dimensional Ising universality class, when the quantum exchange interactions are finite, while a single phase transition takes place in the purely Ising limit[l]. To understand these behaviors, we introduce the generalized four-state chiral clock model and perform Monte Carlo calculations for this model. By comparing the phase diagrams of the two models, we find that the topology of the thermal phase diagram is the same each other - the criticality of the thermal phase transition in the original model can be well explained by that of the generalized four-state chiral clock model.
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.
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.