Exploring the spin-1/2 frustrated square lattice model with high-field
  magnetization measurements

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Abstract

We report on high-field magnetization measurements for a number of layered vanadium phosphates that were recently recognized as spin-1/2 frustrated square lattice compounds with ferromagnetic nearest-neighbor couplings (J_1) and antiferromagnetic next-nearest-neighbor couplings (J_2). The saturation fields of the materials lie in the range from 4 to 24 T and show excellent agreement with the previous estimates of the exchange couplings deduced from low-field thermodynamic measurements. The consistency of the high-field data with the regular frustrated square lattice model provides experimental evidence for a weak impact of spatial anisotropy on the nearest-neighbor couplings in layered vanadium phosphates. The variation of the J_2/J_1 ratio within the compound family facilitates the experimental access to the evolution of the magnetization curve upon the change of the frustration magnitude. Our results support the recent theoretical prediction by Thalmeier et al. [Phys. Rev. B, 77, 104441 (2008)] and give evidence for the enhanced bending of the magnetization curves due to the increasing frustration of the underlying spin system.

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Linear Magnetic Chains with Anisotropic Coupling

Jill Bonner, Michael E. Fisher (1964)

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Generalized Directed Loop Method for Quantum Monte Carlo Simulations

Fabien Alet, Stefan Wessel, Matthias Troyer (2003)

Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local level during the loop construction by accounting for the matrix elements of the operators associated with open world-line segments. Using linear programming techniques to solve the generalized equations, we look for optimal construction schemes for directed loops. This also allows for an extension of the directed loop scheme to general lattice models, such as high-spin or bosonic models. The resulting algorithms are bounce-free in larger regions of parameter space than the original directed loop algorithm. The generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes. In contrast to general expectations, we find that minimizing bounces alone does not always lead to more efficient algorithms in terms of autocorrelations of physical observables, because of the non-uniqueness of the bounce-free solutions. We therefore propose different general strategies to further minimize autocorrelations, which can be used as supplementary requirements in any directed loop scheme. We show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency; however we find that the optimal strategy depends not only on the model parameters but also on the observable of interest.

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Magnetocaloric effect in the frustrated square lattice J1-J2 model

P Thalmeier, N. Shannon, B. Schmidt (2007)

We investigate the magnetocaloric properties of the two-dimensional frustrated J1-J2 model on a square lattice. This model describes well the magnetic behavior of two classes of quasi-two-dimensional S = 1/2 vanadates, namely the Li2VOXO4 (X = Si, Ge) and AA'VO(PO4)2 (A, A' = Pb, Zn, Sr, Ba) compounds. The magnetocaloric effect (MCE) consists in the adiabatic temperature change upon changing the external magnetic field. In frustrated systems, the MCE can be enhanced close to the saturation field because of massive degeneracies among low lying excitations. We discuss results for the MCE in the two distinct antiferromagnetic regimes of the phase diagram. Numerical finite temperature Lanczos as well as analytical methods based on the spin wave expansion are employed and results are compared. We give explicit values for the saturation fields of the vanadium compounds. We predict that at subcritical fields there is first a (positive) maximum followed by sign change of the MCE, characteristic of all magnetically ordered phases.