Giant Tunneling Magnetoresistance, Glassiness, and the Energy Landscape at Nanoscale Cluster Coexistence

– We present microscopic results on the giant tunneling magnetoresistance that arises from the nanoscale coexistence of ferromagnetic metallic (FMM) and antiferromagnetic insulating (AFI) clusters in a disordered two dimensional electron system with competing double exchange and superexchange interactions. Our Monte Carlo study allows us to map out the different field regimes in magnetotransport and correlate it with the evolution of spatial structures. At coexistence, the isotropic O(3) model shows signs of slow relaxation, and has a high density of low energy metastable states, but no genuine glassiness. However, in the presence of weak magnetic anisotropy, and below a field dependent irreversibility temperature Tirr, the response on field cooling (FC) differs distinctly from that on zero field cooling (ZFC). We map out the phase diagram of this ‘phase coexistence glass’, highlight how its response differs from that of a standard spin glass, and compare our results with data on the manganites. Introduction. – First order phase transitions involve a regime of metastability and phase coexistence. Two phases, either both ordered, or one ordered and the other disordered, continue to be minima of the free energy and the system can get trapped in the metastable minimum, or be in a state of macroscopic coexistence of the two phases. This scenario is complicated by the presence of disorder. Disorder introduces preferential pinning or ‘nucleation’ centers for the two phases, and require us to consider the energy (E) as a functional of the full order parameter field, φr, say [1, 2, 3]. The result is a pattern of coexisting clusters in real space, and a rugged landscape for E{φr} with many deep local minima in configuration space. The non trivial energy landscape results in slow relaxation and history dependence in the response of the system, the generic signatures of ‘glassiness’. Such connection between phase coexistence and glassy effects has been explored in detail in vortex matter in superconductors [4], and more recently in the ‘colossal magnetoresistance’ manganites [5, 6, 7]. Typeset using EURO-TEX 2 EUROPHYSICS LETTERS Electron systems at coexistence, e.g, the manganites, involve charge degrees of freedom, and, in addition to glassiness, raise the possibility of a dramatic electrical response and insulator-metal transitions. It has been established that there is coexistence of ferromagnetic metallic (FMM) and charge ordered antiferromagnetic insulating (CO-AF-I) clusters in the low Tc manganites [8, 9], notably the La1−x−yPryCaxMnO3 family. These materials exhibit ‘out of equilibrium’ features like irreversibility [5], slow relaxation [6], and persistent field memory [7]. In addition, since conduction depends on electron tunneling between “half-metallic” FMM clusters, a weak magnetic field greatly enhances the conductance [8] by aligning the cluster moments. The field induced suppression of resistivity (ρ) can attain ρ(0)/ρ(h) ∼ 10, at fields h ∼ 1 Tesla, down to zero temperature. Coexistence, glassiness and giant low temperature tunneling magnetoresistance (TMR) are intimately related. A first principles theory capturing nanoscale coexistence, TMR, and the memory effects requires a method which can handle multiple interactions, quenched disorder, and thermal effects simultaneously. In this paper we use a recently developed Monte Carlo (MC) technique [10] to study a model of competing double exchange (DE) and superexchange (SE) in the background of weak disorder, and clarify the following: (i) the origin and magnitude of the large TMR at cluster coexistence and the high field evolution of the magnetic state, and (ii) the nature of the “phase coexistence glass”, that arises from a non trivial energy landscape and magnetic anisotropy, and its difference with respect to a canonical spin glass. Earlier work. – Models of competing DE and SE, in the presence of weak disorder, have been studied in the recent past via ‘exact’ simulation on small lattices [11]. These studies suggest spatial coexistence of pinned clusters of the competing ordered phases. However, being limited to very small sizes, they are unable to clarify the cluster distribution, the transport properties, or possible memory effects in the system. In the absence of a microscopic approach, a resistor network phenomenology [11] has been developed to model transport at coexistence. Although useful as a starting approximation, it is unable to take into account the ‘spin overlap’ between clusters that controls magnetotransport, or the spatial correlations in the cluster distribution. We also know of no microscopic calculation addressing the slow relaxation and glassiness in the coexistence regime. In this paper we extend our earlier study at zero field [12] to clarify the magnetotransport and explore the history dependence in the coexistence regime. Model and method. – We address the issues of TMR and ‘glassiness’ using the following model [12] of competing DE and SE in the presence of weak disorder in two dimension (2D):