Quantum Spin Glass and the Dipolar Interaction (original) (raw)
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Physical Review Letters, 2009
The physics of the spin glass (SG) state, with magnetic moments (spins) frozen in random orientations, is one of the most intriguing problems in condensed matter physics. While most theoretical studies have focused on the Edwards-Anderson model of Ising spins with only discrete 'up/down' directions, such Ising systems are experimentally rare. LiHoxY1−xF4, where the Ho 3+ moments are well described by Ising spins, is an almost ideal Ising SG material. In LiHoxY1−xF4, the Ho 3+ moments interact predominantly via the inherently frustrated magnetostatic dipole-dipole interactions. The random frustration causing the SG behavior originates from the random substitution of dipolecoupled Ho 3+ by non-magnetic Y 3+. In this paper, we provide compelling evidence from extensive computer simulations that a SG transition at nonzero temperature occurs in a realistic microscopic model of LiHoxY1−xF4, hence resolving the long-standing, and still ongoing, controversy about the existence of a SG transition in disordered dipolar Ising systems.
Quantum spin glass in anisotropic dipolar systems
Journal of Physics: Condensed Matter, 2007
The spin-glass phase in the LiHo x Y 1−x F 4 compound is considered. At zero transverse field this system is well described by the classical Ising model. At finite transverse field deviations from the transverse field quantum Ising model are significant, and one must take properly into account the hyperfine interactions, the off-diagonal terms in the dipolar interactions, and details of the full J = 8 spin Hamiltonian to obtain the correct physical picture. In particular, the system is not a spin glass at finite transverse fields and does not show quantum criticality.
Absence of Conventional Spin-Glass Transition in the Ising Dipolar System LiHoxY1-xF4
Physical Review Letters, 2007
The magnetic properties of single crystals of LiHoxY1−xF4 with x=16.5% and x=4.5% were recorded down to 35 mK using a micro-SQUID magnetometer. While this system is considered as the archetypal quantum spin glass, the detailed analysis of our magnetization data indicates the absence of a phase transition, not only in a transverse applied magnetic field, but also without field. A zero-Kelvin phase transition is also unlikely, as the magnetization seems to follow a noncritical exponential dependence on the temperature. Our analysis thus unmasks the true, shortranged nature of the magnetic properties of the LiHoxY1−xF4 system, validating recent theoretical investigations suggesting the lack of phase transition in this system.
Quantum critical behavior of a three-dimensional Ising spin glass in a transverse magnetic field
Physical Review Letters, 1994
The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional XY model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the 4D XY universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent ν = 1/2 violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of pc = 0.688392, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents z = 1.67(6), ν = 0.90(5), β/ν = 1.09(3), and γ/ν = 2.50(3). The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors and magnetic systems.
Induced Random Fields in the LiHoxY1-xF4 Quantum Ising Magnet in a Transverse Magnetic Field
Physical Review Letters, 2006
The LiHoxY1−xF4 magnetic material in a transverse magnetic field Bxx perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the Bx−induced magnetization along thex direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho 3+ ions, random fields along the Isingẑ direction. This identifies LiHoxY1−xF4 in Bx as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin glass transition with increasing Bx, and render the Bx−induced quantum criticality in LiHoxY1−xF4 likely inaccessible.
Behavior of Ising Spin Glasses in a Magnetic Field
Physical Review Letters, 2008
We study the existence of a spin-glass phase in a field using Monte Carlo simulations performed along a nontrivial path in the field-temperature plane that must cross any putative de Almeida-Thouless instability line. The method is first tested on the Ising spin glass on a Bethe lattice where the instability line separating the spin glass from the paramagnetic state is also computed analytically. While the instability line is reproduced by our simulations on the mean-field Bethe lattice, no such instability line can be found numerically for the short-range three-dimensional model.
Quantum phase transition in spin glasses with multi-spin interactions
Physica a, 1998
We examine the phase diagram of the p-interaction spin glass model in a transverse field. We consider a spherical version of the model and compare with results obtained in the Ising case. The analysis of the spherical model, with and without quantization, reveals a phase diagram very similar to that obtained in the Ising case. In particular, using the static approximation, reentrance is observed at low temperatures in both the quantum spherical and Ising models. This is an artifact of the approximation and disappears when the imaginary time dependence of the order parameter is taken into account. The resulting phase diagram is checked by accurate numerical investigation of the phase boundaries.
Journal of Physics A: Mathematical and General, 1998
By means of extensive computer simulations we analyze in detail the two dimensional ±J Ising spin glass with ferromagnetic next-nearest-neighbor interactions. We found a crossover from ferromagnetic to "spin glass" like order both from numerical simulations and analytical arguments. We also present evidences of a second crossover from the "spin glass" behavior to a paramagnetic phase for the largest volume studied.
Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field
The European Physical Journal B, 2006
The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising spin glass model with a local BCS pairing interaction in the presence of an applied magnetic transverse field Γ. In the present approach, spins in different sublattices interact with a Gaussian random coupling with an antiferromagnetic mean J0 and standard deviation J. The problem is formulated in the path integral formalism in which spin operators are represented by bilinear combinations of Grassmann variables. The saddle-point Grand Canonical potential is obtained within the static approximation and the replica symmetric ansatz. The results are analysed in phase diagrams in which the AF and the SG phases can occur for small g (g is the strength of the local superconductor coupling written in units of J), while the PAIR phase appears as unique solution for large g. However, there is a complex line transition separating the PAIR phase from the others. It is second order at high temperature that ends in a tricritical point. The quantum fluctuations affect deeply the transition lines and the tricritical point due to the presence of Γ.