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

Physics of surfaces has been intensively developed overthe past 30 years.¹ Many spectacular properties due to the presence of surfaces have been discovered and used in industrial devices. In particular, physics of magnetic thin films and multilayers has been a subject of intensive investigations during the last decades. This is due, on the one hand, to numerous recording applications and, on the other hand, to fundamental interests in understanding physical mechanisms involved in those small-scale systems which are quite differ-ent from bulk properties.² For magnetic thin films, it has been shown a long time ago that low-lying-energy surface-localized modes play an important role in thermodynamic properties of thin films at low temperature.^{3 - 5} One of the effects of these surface modes is the low surface magnetiza-tion with respect to the bulk one. One has to bear this in mind while analyzing numerical results as well as analytical ones presented in this paper. Another interesting phenom-enon which has been observed in thin films is that the film magnetization, which is perpendicular to the film surface at low temperature (T ) , can change into parallel configuration at intermediate T before becoming disordered at higher T. This ‘‘magnetization reorientation’’ has been shown to be a consequence of the competition between perpendicular an-isotropy and long-range dipolar interaction.⁶ For multilayers, one of their important properties is the magnetoresistance hysteresis shape of the system under an applied field.^{2,7 - 10} Besides, let us note that in magnetic films as well as in mul-tilayers, there exists in many materials a perpendicular an isotropy when the system thickness becomes very small.2,11

In this work, we are interested in a magnetic system madeof three ferromagnetic films coupled antiferromagnetically to each other. Such a system has been subject to many experi-mental studies.¹² The nanometer scale of the total thickness of such a trilayer makes it possible for magneto-optic signals from each of the magnetic films to be additive. Depending on the geometry of the composed trilayer, one can have very interesting effects which have been used, for example, for magnetic sensors and pickup heads.^13,14

The paper is organized as follows. In Sec. II, we describe the model used for Monte Carlo (MC) simulation. The spin model is the Ising one. We carry out (MC) simulations to study the phase transition and the phase diagram in the (T ,H ) space, where T is the temperature and H is the mag-netic field applied along the z direction, i.e., perpendicular to the surface of coupled films. The simulation results are pre-sented and discussed in Sec. III. In Sec. IV, we show an analytical calculation based on the Green-function technique for the Ising-like spin model. The results obtained are then compared to the MC ones. We find a good agreement be-tween the two methods. Concluding remarks are given in Sec. V. A part of this work has been just reported elsewhere.¹⁵

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