Dipolar needles in the microcanonical ensemble: evidence of spontaneous magnetization and ergodicity breaking

We have studied needle shaped three-dimensional classical spin systems with purely dipolar interactions in the microcanonical ensemble, using both numerical simulations and analytical approximations. We have observed spontaneous magnetization for different finite cubic lattices. The transition from the paramagnetic to the ferromagnetic phase is shown to be first-order. For two lattice types we have observed magnetization flips in the phase transition region. In some cases, gaps in the accessible values of magnetization appear, a signature of the ergodicity breaking found for systems with long-range interactions. We analytically explain these effects by performing a nontrivial mapping of the model Hamiltonian onto a one-dimensional Ising model with competing antiferromagnetic nearest-neighbor and ferromagnetic mean-field interactions. These results hint at performing experiments on isolated dipolar needles in order to verify some of the exotic properties of systems with long-range interactions in the microcanonical ensemble. Systems with long-range interactions, such as gravitational, Coulomb and magnetic systems, are of fundamental and practical interest because of their exotic statistical properties including ensemble inequivalence, negative specific heat, temperature jumps, ergodicity breaking, etc. [1] Recently, a number of mean-field type models have been developed which are very convenient for analytical understanding [2,3]. However, up to now, the connection to real physical systems has not been seriously addressed (see, however, Refs. [4–6] for some progress in this direction). It is therefore crucial to propose experimentally testable effects. Dipolar force is one of the best candidates for experimental and theoretical studies of long-range interactions [7]. For instance, experimental studies have been performed on layered spin structures [8]. For these systems, intralayer exchange is much larger than the interlayer one: hence, every layer can be identified as a single macroscopic spin. As a consequence, dipolar forces between layers are dominant and one can describe the system with an effective long-range one-dimensional model [5]. However, in order to perform a careful study of the statistical properties of such samples, one should simulate all the spins in each layer, which is computationally heavy. Alternatively, one can consider purely dipolar systems known as dipolar ferromagnets [9, 10], where dipolar effects prevail over short-range exchange interactions. Longrange dipolar orientational order is also found theoretically for dipolar fluids confined in ellipsoidal geometries [11]. More recently, dipolar ferromagnetism has also been measured at ambient temperature in assemblies of closelyspaced cobalt nanoparticles [12]. It has been pointed out long ago [13] that body centered cubic (bcc) or face centered cubic (fcc) needle like samples should display spontaneous magnetization, while simple cubic (sc) lattices can be ordered only antiferromagnetically. On the other hand, it was later argued that dipolar systems cannot show nonzero magnetization in the ther-