The phase behavior of ferromagnetic thin films is studied by Monte Carlo simulations, modeling it as a classical two-dimensional anisotropic Heisenberg model with dipolar interactions. Its phase diagram reveals a rich phenomenology that includes low-temperature phases characterized by stripe-ordered domains (SO), oriented along the anisotropy axis, perpendicular to the film, and planar ferromagnetic domains (FM). The apparition of these phases depend on the magnitude of anisotropy term in the Hamiltonian. Furthermore, a PM phase is present at high temperatures.

The stripe width (h) in the SO phase depends on the relation between the exchange (J) and dipolar (g) constants, $\delta=J/g$ [1, 2]. A fixed value $\delta$ = 1 is considered, that corresponds to h=1. For this value the phase transitions in the plane $\eta-T$ have been largely determined. The reorientation transition line SO-FM has been reported as first order, while the transition lines FM-PM and SO-PM as continuous [1]. The critical behavior of the SO-PM transition has not yet been fully characterized, and there is still an ongoing controversy regarding the nature of the transitions near the triple point, including the existence of a reentrant region and a possible tricritical point.

Appropriated order parameters are selected with the aim to determine the transition lines between the above mentioned phases, determine their character, and estimate the critical exponents in the case of continuous transitions. The dynamic evolution of the order parameters and their moments, in the short-time regime, is analyzed for selected values of ($\eta$,T). To consider finite size effects due to the cutoff in the range of dipolar interactions, periodic boundary conditions were implemented using Ewald sums.

The critical temperatures ($T_{c}$) and the dynamical critical exponents of the observables are determined for continuous transitions (FM-PM, SO-PM), while the spinodal points are found for the SO-FM first order line. The $T_{c}$ obtained for the SO-PM transitions, increases with $\eta$, and converges to the value corresponding to the $\eta \rigtharrow \infty$ limit, i.e., to the Ising model with dipolar interactions. Moreover, it was found that the distance between the spinodal points decreases when the control parameters approaches the triple point, indicating a weakening of the first order transitions. Furthermore, the transition line FM-PM remains continuous, providing evidence of reentrant behavior.

References

[1] H. Komatsu, Y. Nonomura y M. Nishino, Phys. Rev. B 100, (2019).

[2] M. Carubelli, O.V. Billoni, S.A. Pighin, S.A. Cannas, D.A. Stariolo y F.A. Tamarit, Phys. Rev. B 77 (2008).

[3] C. M. Horowitz, M. A. Bab, M. Mazzini, M. L. Rubio Puzzo, y G. P. Saracco, Phys. Rev. E, 92,04127 (2015).