Anisotropy-temperature phase diagram for the two-dimensional dipolar Heisenberg model with and without magnetic field

Abstract

We investigate phase transitions in the two-dimensional dipolar Heisenberg model with uniaxial anisotropy with a specific ratio between the exchange and dipolar constants, δ = 1. We obtain the η-T (anisotropy vs. temperature) phase diagrams for typical values of magnetic field by a Monte Carlo method with an O(N ) algorithm. We find that at lower fields, the η-T phase diagram consists of the planar ferromagnetic (F), (perpendicular) stripe-ordered (SO), and paramagnetic (P) phases, and is characterized by the triple point. In the SO phase realized at larger η and smaller T , the SO pattern changes depending on the field. On the other hand, we find that at higher fields, the SO phase does not exist, while the planer F phase robustly remains. We study the properties of the phase boundaries by employing finite-size-scaling analyses. We find that the slope of the spinreorientation-transition line is positive with and without field, i.e., dη dT > 0, which implies that the planar F phase changes to the SO phase with lowering temperature. In the phase diagrams we observe a characteristic shape of the P-planer F phase-transition line, whose maximum point of η is located at an intermediate temperature. This structure leads to the temperature-induced reentrant transition associated with P and planar F phases, which appears in successive phase transitions with lowering temperature: P → planar F → P → SO phase at lower fields and P → planar F → P phases at higher fields. *

Phase diagram of the dipolar Ising ferromagnet on a kagome lattice

“…Because of the long-range nature of the dipolar interaction, O(N 2 ) (N is the total number of spins) computational time, namely a high computational cost, is required. Stripe phases and SR transitions have been investigated in several parameters of the 2D dipolar Ising [18][19][20][21][22][23][24][25][26][27][28][29][30][31] and Heisenberg [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] ferromagnets, but studies on the stripe-bubble and bubble-ferromagnetic transitions are limited [14,15]. In these studies on a square lattice, the intermediate phase located between (anharmonic) stripe and saturated ferromagnetic phases was named bubble phase, in which domains were observed.…”

Phase diagram of multi-layer ferromagnet system with dipole-dipole interaction

“…Moreover, the interplay between the short-range interaction and DDI leads to more complex magnetic properties. Especially, thin-film systems have been studied both theoretically 2,[6][7][8][9][10][11][12][13][14][15] and experimentally [16][17][18][19][20] , e.g., concerning the spin reorientation transition between the in-plane ferromagnetic state and the out-of-plane ferromagnetic state 2,[13][14][15] .…”

“…Most of these theoretical works have been studied in systems with periodic boundary conditions. Under the conditions, there exist four magnetic configurations: the out-of-plane ferromagnetic state, the in-plane ferromagnetic state, the multi-domain state with stripe pattern, and the canted stripe state which has been recently discovered between the multi-domain and the in-plane ferromagnetic state 2,[8][9][10]12,15 .…”

Phase diagram of the two-dimensional dipolar Heisenberg model with the Dzyaloshinskii-Moriya interaction and the Ising anisotropy

“…The theoretical aspects of these phenomena have been often investigated by using the two-dimensional (2D) dipolar Ising [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] or Heisenberg [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] model with a magnetic anisotropy, and the phase diagrams with multiple stripe-ordered phases have been shown in several parameter regions. Reentrant transitions associated with planar ferro, stripe, and paramagnetic phases have also been presented [22,37].…”