STATIC AND DYNAMIC CRITICAL BEHAVIOR IN RANDOM MAGNETS

Abstract

Experiments in recent years of critical behavior in random magnets are reviewed. Attention is focused on the random exchange (REIM) and random field (RFIM) Ising model problems, as realized in dilute, insulator antiferromagnets. The static exponents of the d = 3 REIM universality class are now measured and agree with theory. REIM to RFIM crossover scaling has been shown to govern the static and dynamic critical behavior in all d = 3 systems (Fe,Znl-,Fa, Mn,Znl-,Fa and Fe,Mgl-,C12 studied, with a universal exponent 4 = 1.42f 0.03, which satisfies the Aharony inequality 4 > y, the REIM susceptibility exponent. So extreme is the slowing down of the critical fluctuations in d = 3 RFIM systems that it is at the roots of earlier misunderstandings of what was the lower critical dimension of the RFIM and may well limit the accuracy to which the static exponents of the d = 3 RFIM universality class may be obtained. Only qualitative models and limited Monte Carlo calculations exist with which to make comparison with experiment. Introduction vance the concentration profile and how TN (2) varies In the last three years, considerable progress has been made in the understanding of random magnetic systems, both from theoretical and experimental points of view. We confine ourselves to the static and dynamic critical behavior of random systems which exhibit long range order below the magnetic phase transition in particular, the Random Exchange (REIM) and Random Field (RFIM) Ising Model systems [I]. In the main, the experimentally realizable REIM and RFIM systems all turn out to be randomly diluted, uniaxial antiferromagnets, in which a uniform, external field H, applied colinearly with the spontaneous ordering direction, generates a random field HRF, as was first predicted by Fishman and Aharony [2]. With dilution governing the degree of randomness in the exchange, and the strength of HRF a function of the dilution and H, one may externally control the region of reduced temperature in which crossover from pure Ising to REIM and the crossover from REIM ( H = 0) to RFIM (H # 0 ) take place. Since the pure Ising, REIM and RFIM systems each represent different universality classes, the scaling properties associated with the crossover between any of the three is of special interest, as are the critical exponents and amplitudes. Effects of concentration gradients The experimental situation, with respect to the critical behavior of random magnets, has been clouded by uncertainties arising from the existence of concentration gradients in any two component system. For example, we will have recourse to discuss the prototype d = 3, REIM and RFIM system Fe,Znl-,Fz. If the concentration x varied in a macroscopic (nonrandom) manner in a given crystal, then the ordering temperature TN would be position dependent. Any thermodynamic measurement (e.g. magnetic specific heat C,) will be difficult to interpret unless one knows in adwith z. A method has been developed to characterize the concentration gradient in an optically anisotropic, mixed crystal [3]. It utilizes the room temperature optical birefringence technique combined with laser scanning profiles of the crystal. The effects such inhomogeneities have on the critical behavior were explicitly determined by computer simulations of the anomaly in C, and the quasielastic neutron scattering line profile in the REIM system [4]. Examples of these are given in figures l a and lb.. The derivative of the magnetic birefringence d (An) / dT (which has been previously shown to be proportional to C, [5]) us. T is shown for the laser beam parallel and perpendicular to the gradient. An important conclusion from this study is that the peak in C, does not occur at the mean transition temperature FN, if the amplitudes A' of the divergence of C$ = A' It/- are not equal above and below TN (i.e. A+ # A-). Not understanding this point has been the origin of much of the confusion in the interpretation of REIM and RFIM experiments. REIM critical behaviour d = 3. Measurements now exist of the following REIM critical exponents: cr (C,) , v (the correlation length <' = [$ Itl-), y (staggered susceptibility X * = X$ Itl--'), and B (order parameter M = Mo 1tlP) and corresponding amplitude ratios. Those that we judge to be the most accurate [6-81 are collected in table I. Examples used to determine y and P in Fe,Znl-,F2 are shown in figures 2 and 3, respectivfely, in which particular attention was paid to using an extremely homogeneously random crystal. Theoretical predictions [9, 101 of the exponents for d = 3 REIM universality class are also given in table I, where it is seen the agreement with experiment in each case is quite good. Unfortunately, critical amplitude ratios have only been calculated in the one-loop approxiArticle published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888549