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arXiv:0911.1133 · Physical Review B

Nonequilibrium quantum criticality in bilayer itinerant ferromagnets

So Takei, William Witczak‐Krempa, Yong Baek Kim

Published Mar 25, 2010• 10 citations
arXivHTMLPDF

Abstract

We present a theory of nonequilibrium quantum criticality in a coupled bilayer system of itinerant electron magnets. The model studied consists of the first layer subjected to an in-plane current and open to an external substrate. The second layer is subject to no direct external drive, but couples to the first layer via short-ranged spin-exchange interaction. No particle exchange is assumed between the layers. Starting from a microscopic fermionic model, we derive an effective action in terms of two coupled bosonic fields which are related to the magnetization fluctuations of the two layers. When there is no interlayer coupling, the two bosonic modes possess different dynamical critical exponents $z$ with $z=2$ $(z=3)$ for the first (second) layer. This results in multiscale quantum criticality in the coupled system. It is shown that the linear coupling between the two fields leads to a low-energy fixed point characterized by the larger dynamical critical exponent $z=3$. We compute the correlation length in the quantum disordered and quantum critical regimes for both the nonequilibrium case and in thermal equilibrium where the whole system is held at a common temperature $T$. We identify an effective temperature scale ${T}_{\text{eff}}$ with which we define a quantum-to-classical crossover that is in exact analogy with the thermal equilibrium case but with $T$ replaced by ${T}_{\text{eff}}$. However, we find that the leading correction to the correlation length in the quantum critical regime scales differently with respect to $T$ and ${T}_{\text{eff}}$. We also note that the current in the lower layer generates a drift of the magnetization fluctuations, manifesting itself as a parity-breaking contribution to the effective action of the bosonic modes. In this sense, the nonequilibrium drive in this system plays a role which is distinct from $T$ in the thermal equilibrium case. We also derive the stochastic dynamics obeyed by the critical fluctuations in the quantum critical regime and find that they do not fall into the previously identified dynamical universality classes.

DOI
10.1103/physrevb.81.125430

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We study the out-of-equilibrium steady-state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low-energy excitations. This model describes the destruction of the Kondo effect as the coupling to the bosons is increased. Its phase diagram comprises three non-trivial fixed points. Using a dynamical large- N approach on the Keldysh contour, we study two different non-equilibrium setups: a) a finite bias voltage and b) a finite temperature gradient, imposed across the leads. The scaling behavior of the charge and energy currents is identified and characterized for all fixed points. We report the existence of a fixed-point–dependent effective temperature, defined though the fluctuation-dissipation relations of the local spin-susceptibility in the scaling regime, which permits to recover the equilibrium behavior of both dynamical and static spin-susceptibilities.
We study the out-of-equilibrium steady-state properties of the Bose-Fermi-Kondo model, describing a local magnetic moment coupled to two ferromagnetic leads that support bosonic (magnons) and fermionic (Stoner continuum electrons) low-energy excitations. This model describes the destruction of the Kondo effect as the coupling to the bosons is increased. Its phase diagram comprises three non-trivial fixed points. Using a dynamical large-N approach on the Keldysh contour, we study two different non-equilibrium setups: a) a finite bias voltage and b) a finite temperature gradient, imposed across the leads. The scaling behavior of the charge and energy currents is identified and characterized for all fixed points. We report the existence of a fixed-point-dependent effective temperature, defined though the fluctuation-dissipation relations of the local spin-susceptibility in the scaling regime, which permits to recover the equilibrium behavior of both dynamical and static spin-susceptibilities. Copyright (c) EPLA, 2013
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Critical properties of an Ising bilayer system, consisting of two triangular planes with antiferromagnetic (AF) JAJ_{\rm A}JA​ and ferromagnetic (FM) JBJ_{\rm B}JB​ exchange interactions, coupled by the interlayer exchange JABJ_{\rm AB}JAB​, are studied by Monte Carlo simulation. The FM plane is found to induce in the AF one some effects similar to those resulting from the joint presence of a next-nearest-neighbor FM coupling and an external magnetic field in the single triangular lattice Ising antiferromagnet. The similarities include the appearance of the quasi-long-range-order BKT phase with algebraically decaying correlations for smaller JABJ_{\rm AB}JAB​, as well as the phase transitions belonging to the three-state Potts universality class for larger JABJ_{\rm AB}JAB​. On the other hand, no first-order phase transitions are observed. A new phenomenon is a cross-over from the BKT to the Wannier state at higher temperatures, that can be stabilized over a relatively wide temperature range. In the strong JABJ_{\rm AB}JAB​ limit, the critical behavior of the entire bilayer is governed by the behavior of the plane with a dominant intraplane interaction. If JAJ_{\rm A}JA​ is dominant, then the strong JABJ_{\rm AB}JAB​ coupling makes the system kinetically freeze at lower temperatures.
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