Fluctuation-Dissipation Ratio of the Heisenberg Spin Glass

Abstract

Fluctuation-dissipation (FD) relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation. Numerically determined FD ratio exhibits a "one-step-like" behavior, the effective temperature of the spin-glass state being about twice the spin-glass transition temperature, T eff ≃ 2Tg, irrespective of the bath temperature. The results are discussed in conjunction with the recent experiment by Hérisson and Ocio, and with the chirality scenario of spin-glass transition.Off-equilibrium dynamics of spin glass (SG) has attracted much recent interest [1]. In equilibrium, there holds a relation between the response and the correlation known as the fluctuation-dissipation theorem (FDT). In off-equilibrium, relaxation of physical quantities of SG depends on its previous history. Most typically, it depends not only on the observation time t but also on the waiting time t w , i.e., exhibits aging. While in the shorttime quasi-equilibrium regime t 0 << t << t w (t 0 is a microscopic time scale), relaxation is still stationary and FDT holds, it becomes non-stationary and FDT is broken in the long-time aging regime t >> t w . In particular, the breaking pattern of FDT, and its possible relation to the static quantity, has been the subject of recent active studies.A quantity playing a central role here is the so-called fluctuation-dissipation ratio (FDR) X, which may be defined by the relation,where R(t 1 , t 2 ) is a response function measured at time t 2 to an impulse field applied at time t 1 , C(t 1 , t 2 ) is a two-time correlation function in zero field at times t 1 and t 2 , and T is the bath temperature. One may regard T /X ≡ T eff as an effective temperature. In the case FDT holds, one has X = 1 and T eff = T . Via the study of certain mean-field models, Cugliandolo and Kurchan showed that, in the limit of infinite time t 1 , t 2 → ∞, the FDR X depended on the times t 1 and t 2 only through the correlation function C(t 1 , t 2 ), i.e., X(t 1 , t 2 ) = X(C(t 1 , t 2 )) [2]. It was further suggested that X(C) could be related to an appropriate static quantity, i.e., X(C) is equivalent to the x(q)-function describing the replica-symmetry breaking (RSB) pattern in the Parisi's scheme, which is related to the overlap distribution function via P (q) = dx(q) dq [2]. This conjecture was supported both by numerical simulation [3] and analytic work [4] (see, however, also ref. [5]).Experimental studies on the FDR of SG have been hampered for a long time by the difficulty in performing high-precision measurements of correlations (noise measurements), although some interesting preliminary results were reported [6]. Recently, however, a remarkable experiment by Hérisson and Ocio for an insulating Heisenberg SG CdCr 1.7 In 0.3 S 4 has eventually opened a door to experimental access to the FDR of SG [7]. Some comparison was already made between these expeirmental results and the numerical results obtained by offequilibrium simulation on certain SG models.Meanwhile,...

Chiral anomalous Hall effect in reentrant AuFe alloys

“…Following up [16] the present data confirm that there is a major contribution to the AHE linked to the presence of chirality which persists up to T ∼ 150K and which can be interpreted satisfactorily in terms of the chiral AB-related mechanism [11,12,13].…”

“…At low temperatures, this term is large enough to dominate the KL term over almost the entire re-entrant region. Because of the clear correlation with the presence of canting, the difference term can be confidently identified with the theoretically predicted chiral or real space Berry phase term [11,12]. It can be noted that in the presence of the chiral AHE the standard Equation (1) can still be written down formally, but it loses all transparency because physical phenomena depending not only on the bulk magnetization but on the details of the transverse local spin structure and its dynamics will be hidden within the AHE parameter R s (T ).…”

“…This can be described as a physically distinct Berry phase contribution occuring in real space when the spin configuration is topologically nontrivial; data on regularly ordered systems such as magnetites and perovskites whose spins are tilted have been interpreted assuming a supplementary AHE contribution of this type in the analysis [8,9,10]. The presence of this term is remarkable because it involves the magnetization components perpendicular to M. The theoretical principles of this contribution, intrinsically linked to chirality, have now been spelt out for the specific case of disordered systems with canted spins such as spin glasses and re-entrant ferromagnets [11,12]. The coupling between the magnetization and the spin chirality through the spin-orbit interaction leads to a non-zero net chirality when there is a finite magnetization which is either induced by a magnetic field in the spin glass case, or which is spontaneous in the re-entrant case [8,11,12].…”

“…The presence of this term is remarkable because it involves the magnetization components perpendicular to M. The theoretical principles of this contribution, intrinsically linked to chirality, have now been spelt out for the specific case of disordered systems with canted spins such as spin glasses and re-entrant ferromagnets [11,12]. The coupling between the magnetization and the spin chirality through the spin-orbit interaction leads to a non-zero net chirality when there is a finite magnetization which is either induced by a magnetic field in the spin glass case, or which is spontaneous in the re-entrant case [8,11,12]. However an a priori estimate of the order of magnitude for the effect in specific cases would require complex band structure calculations.…”

Experimental investigation of the fluctuation dissipation relation in a spin glass

“…Our system has a strong heisenberg character, 28 and it has been shown that in such case, the spin glass transition should correspond to chiral ordering with one-step RSB. 28,29 Numerical simulations on an heisenberg system with weak anisotropy have been performed recently, 30 whose results are characteristic of one RSB, with T ef f higher than but independent of the bath temperature: in other words, a "universal" -constant T ef f -χ(C) curve is obtained. In a one-RSB system, it can be shown that ∆ and q EA are related simply by q EA = 1/(1 + γT /T ef f ) where γ = (1 − ∆)/∆.…”