Nonlinear susceptibility of a quantum spin glass under uniform transverse and random longitudinal magnetic fields

Abstract

The interplay between quantum fluctuations and disorder is investigated in a spin-glass model, in the presence of a uniform transverse field $\Gamma$, and a longitudinal random field following a Gaussian distribution with width $\Delta$. The model is studied through the replica formalism. This study is motivated by experimental investigations on the LiHo${}_x$Y${}_{1-x}$F${}_4$ compound, where the application of a transverse magnetic field yields rather intriguing effects, particularly related to the behavior of the nonlinear magnetic susceptibility ${\chi }_3$, which have led to a considerable experimental and theoretical debate. We analyzed two situations, namely, $\Delta$ and $\Gamma$ considered as independent, as well as these two quantities related as proposed recently by some authors. In both cases, a spin-glass phase transition is found at a temperature $T_f$; moreover, $T_f$ decreases by increasing $\Gamma$ towards a quantum critical point at zero temperature. The situation where $\Delta$ and $\Gamma$ are related appears to reproduce better the experimental observations on the LiHo${}_x$Y${}_{1-x}$F${}_4$ compound, with the theoretical results coinciding qualitatively with measurements of the nonlinear susceptibility. In this later case, by increasing $\Gamma$, ${\chi }_3$ becomes progressively rounded, presenting a maximum at a temperature $T^{\ast }$ ($T^{\ast }>T_f$). Moreover, we also show that the random field is the main responsible for the smearing of the nonlinear susceptibility, acting significantly inside the paramagnetic phase, leading to two regimes delimited by the temperature $T^{\ast }$, one for $T_f<T<T^{\ast }$, and another one for $T>T^{\ast }$. It is argued that the conventional paramagnetic state corresponds to $T>T^{\ast }$, whereas the temperature region $T_f<T<T^{\ast }$ may be characterized by a rather unusual dynamics, possibly including Griffiths singularities.

accepted for publication in PRB

References in corpus (7)

• Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses
• Induced Random Fields in the LiHo${}_x$Y${}_{1-x}$F${}_4$ Quantum Ising Magnet in a Transverse Magnetic Field
• Quantum and Classical Glass Transitions in $LiH{o}_x{Y}_{1-x}{F}_4$
• Absence of Conventional Spin-Glass Transition in the Ising Dipolar System LiHo_xY_{1-x}F_4
• Effective Spin-1/2 Description of Transverse-Field-Induced Random Fields in Dipolar Spin Glasses with Strong Single-Ion Anisotropy
• Low-temperature spin-glass behaviour in a diluted dipolar Ising system
• One-step replica symmetry breaking solution for fermionic Ising spin glass in a transverse field

Cited by in corpus (1)

• Specific heat and non-linear susceptibility in spin glasses with random fields