Efeitos de campos magnéticos aleatórios em sistemas de vidro de spin com clusters

Abstract

This work investigates the effects of the presence of random magnetic fields (RFs) in thermodynamic quantities that characterize the spin glass state (VS). We adopt a cluster spin model that considers long-range disordered interactions between magnetic clusters and short-range interactions (ferromagnetic, FE, or antiferromagnetic, AF) between spins belonging to the same cluster, as well as a local random magnetic field acting in each spin, which can follow a bimodal or Gaussian probability distribution. A replica approach is adopted to obtain an effective single cluster problem that is solved analytically. For the system with intracluster FE interactions, we discuss the behavior of order parameters, specific heat, nonlinear susceptibility and phase diagrams for different configurations of disorder. In the absence of a random field, the nonlinear susceptibility ( 3) exhibits a divergence in the freezing temperature (Tf ), while the specific heat shows a broad ma- ximum at a temperature T , which depends on the FE interaction. In particular, the intensity of the FE interaction is set to find T around 30% above the Tf , as expected for conventional VS systems. The presence of RFs alters this scenario, Cm still shows the maximum in T that is weakly dependent on RF intensity. However, the Tf is shifted to lower temperatures, considerably increasing the ratio T =Tf . In addition, the divergence in 3 is replaced by a maximum rounded at a temperature T , which becomes higher than Tf with increasing the RF intensity. As a consequence, we suggest that the paramagne- tic (PM) phase is unfolded in three regions: (i) a conventional paramagnetism of high temperatures (T > T ); (ii) a region with short-range order formation with spins frozen (T < T < T ) e (iii) a region with slow growth of free energy barriers that retard the spin dynamics before the transition to VS (Tf < T < T ). These results qualitatively reproduce some findings for the compound LiHoxY1�����xF4 such as the maximum rounded at 3, which is triggered by RFs and the deviation of the conventional relation between Tf and T . For the case with intracluster AF interactions, the results show that the VS region is gradually reduced with increasing the intensity of the AF couplings until only a PM phase is found. Thus, we highlight two distinct regions in relation to the disorder: (i) strong disorder one, where we have a PM/VS second-order phase transition with the RF decreasing Tf similarly to the case FE; (ii) weak disorder, where only the PM state with fully compensated clusters and no long range order is found. In this region (ii), when the RF intensity increase, we observe a VS phase induced by the random field. This result suggests that the presence of RFs can introduce a VS state in weakly disordered AF cluster system.