Magnetic properties of exchange-biased three-layer films in a perpendicular magnetic field

We study by Monte Carlo (MC) simulations and Green-function (GF) method some properties of a system composed of three thin ferromagnetic films coupled to each other by an antiferromagnetic (AF) interface exchange interaction. This model simulates the so-called “exchange-biased” layers. The films have the triangular lattice structure with Ising spins. Due to the AF interface interaction at zero temperature, $T=0,$ the first and third films have up spins, while the middle one has down spins (or vice versa). A uniform magnetic field H is applied along the spin axis, i.e., perpendicular to the film surfaces. In the simplest case where all interactions except for interface ones are ferromagnetic and taken to be equal to $J=1,$ and the interface interactions between the second (middle) film and its neighboring first and third films, $J_{12}$ and $J_{23},$ are equal to $-1,$ we obtained by Monte Carlo simulation a phase diagram in the $\mathrm{}(T,H)\mathrm{}$ space which shows several interesting behaviors. For H smaller than the critical value $H_t,$ we observe a second-order phase transition at a finite T from the AF ordering to paramagnetic phase. For $H>\mathrm{}{H}_t,$ there is a crossover: the transition becomes of first order as shown by the double-peak structure in the energy histogram taken at the transition temperature. The value of $H_t$ decreases with decreasing the interface coupling strength and with increasing the film’s thickness. The hysteresis cycle, measured in the transition region by field heating and field cooling, shows a two-step cycle which may have important practical applications in magnetic recording. We have also performed an analytical calculation by the GF method using an Ising-like model for the same system. Self-consistent calculations for layer magnetizations are carried out. The GF results are shown and compared to the MC ones.