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Article Dans Une Revue Physical Review E Année : 2020

Effective negative specific heat by destabilization of metastable states in dipolar systems

Résumé

We study dipolarly coupled three-dimensional spin systems in both the microcanonical and the canonical ensembles by introducing appropriate numerical methods to determine the microcanonical temperature and by realizing a canonical model of heat bath. In the microcanonical ensemble, we show the existence of a branch of stable antiferromagnetic states in the low-energy region. Other metastable ferromagnetic states exist in this region: by externally perturbing them, an effective negative specific heat is obtained. In the canonical ensemble, for low temperatures, the same metastable states are unstable and reach a new branch of more robust metastable states which is distinct from the stable one. Our statistical physics approach allows us to put some order in the complex structure of stable and metastable states of dipolar systems. For long-range interactions [1,2], the dimensionality of the sample is larger than or equal to the decay exponent of the power-law interaction itself. Among the most exotic manifestations of long-range interactions is negative specific heat. As an example, for self-gravitating systems there is an energy region where temperature increases with a loss of energy [3-5]. Experimental observations of negative specific heat have been reported for atomic clusters near phase transitions [6,7]. On the theoretical side, two-dimensional systems [8] and mean-field models [1] have been shown to display negative specific heat in the microcanonical ensemble. On the other hand, it has been observed that the phenomenon of negative specific heat is tightly related with the general notion of inequivalence of ensembles [9,10]. However, there is not yet a clear laboratory experiment which shows negative specific heat for samples of macroscopic size, where one could directly study the phenomenon and devise possible applications. Dipolar forces are marginal examples among long-range interacting systems, because the interaction strength among spins decays as 1/r 3 in three dimensions. There is an open question whether such forces could induce negative specific heat and ensemble inequivalence. Previously, another feature of long-range interactions, i.e., ergodicity breaking, was shown for a model of dipolar spins by reducing it to an effective mean-field model [11,12]. Numerical simulations show that this exotic feature appears only for needle-shaped samples (i.e., when the aspect ratio is large) and when, additionally , one has spontaneous magnetization in zero field. However, it has been argued in Ref. [12] that, in the thermo-dynamic limit [13], the ferromagnetic state survives only in the case of a body-centered-cubic lattice. Despite this fact, we show in the present Rapid Communication that, when considering a finite simple cubic lattice with 2 × 2 base and a large aspect ratio ergodicity breaking and negative specific heat are found. By slightly increasing the base size to 3 × 3, the sample loses all these features, which are therefore absent also in the thermodynamic limit. However, we show below that the simple cubic lattice displays also a ferrimagnetic (only partially magnetized) state which could persist also in the thermodynamic limit and show some of the exotic properties of long-range interactions. Realizing the microcanonical ensemble for spin systems is straightforward by the direct integration of the Hamiltonian equations of motion. On the contrary, the realization of canon-ical ensemble is more complex. It requires the introduction of the Landau-Gilbert damping term in the equations of motion and the coupling with a Nosé-Hoover thermostat adapted to spin variables [14]. In this Rapid Communication, we consider dipolarly coupled spin systems and we study them in both the micro-canonical and canonical ensembles. These systems could be experimentally realized using, e.g., cobalt nanoparticles [15]. In particular, we consider a setup, in which a magnetized dipolar system with a simple cubic lattice structure interacts with a short-range spin chain (see Fig. 1). Due to the interaction , the magnetized state is destabilized and converts into an antiferromagnetic one. If one defines the specific heat of the system in this particular process as the ratio between the exchanged energy and the microcanonical temperature difference, the effective specific heat takes negative values depending on the size of the sample. The same process, when observed in the canonical ensemble, follows a completely different pathway which leads in some cases to a metastable partially ferromagnetic state. The Hamiltonian of our system consists of classical spins interacting through dipolar forces and can be written
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hal-02994117 , version 1 (07-11-2020)

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Vazha Loladze, Thierry Dauxois, Ramaz Khomeriki, Stefano Ruffo. Effective negative specific heat by destabilization of metastable states in dipolar systems. Physical Review E , 2020, 101, ⟨10.1103/physreve.101.030102⟩. ⟨hal-02994117⟩
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