Studies On Magnetic Configurations In Multilayers by A Quantum Spin Model
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ABSTRACT A method based on the variation of the magnetization direction of each layer and HolsteinPrimakoff transformation is presented to estimate the magnetization configuration in a superlattice of quantum ferromagnetic system with an interface between perpendicular and in-plane easy-axis layers. Numerical results on the magnetization configurations under different applied magnetic fields, critical field, and critical anisotropic parameter are given. INTRODUCTION Applying a magnetic bilayer disk of a magnetic thin film with in-plane anisotropy (capping layer) coupled to the bulk medium for memory (recording layer) with perpendicular easy axis, one can significantly improve the recording properties(1 1. Some magnetic multilayer systems have already shown to have a good potential for higher recording density and to reduce the recording time in magneto-optical recording12l. Theoretical studies have also been done for double-layer systems [3-61. Among them a theory for magnetic bilayer system has been developed by two of the present authors using classical continuum model[4]. The theory addressed the competition between the vertical anisotropy of the recording layer and the inplane one of the capping layer. It clarified the mechanism of transition between two different magnetization configurations; namely a uniformly perpendicular and a bent structures, with the variances of magnetic constants, the thickness of the capping layer, and the temperature. The critical thickness of the above transition gives the minimal thickness of capping layer 11 that shows the capping effect in multilayer structuresM . The theory explained successfully the main experimental observations. Nevertheless, it still deserves to consider the effect of quantum fluctuation and that of the discreteness of lattice structure in the spin-reorientation transition. The first effect is particularly interesting from the theoretical point of view, and the second one is important for the quantitative estimation of critical values. In the present work, we would extend the former theory to quantum case. As a first step, we consider a multilayer lattice model with an interface between perpendicular and in-plane easy axis layers. To express it explicitly, an anisotropic quantum Heisenberg ferromagnetic model is studied. HAMILTONIAN H= • where
3
H,,i(R,R') + E-[D.m(Sn(R)) 2
Hm,mi(R,R') =
Hm,,,2(R, R!) where
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hSz(R)],
(1)
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Im,m,(R, R')Sm (R) . SW (R'),
(2)
and the subscripts {m, m'} denote the layer numbers, R and R! are the vectors of a lattice site on the layer, h is related to the applied magnetic field. We only discuss the simple cubic case, in which the layers are arranged along with the [001] direction. For a ferromagnetic 265
Mat. Res. Soc. Symp. Proc. Vol. 384 01995 Materials Research Society
system, the coupling constant Im,mI in the Hamiltonian H is positive. Figure 1 shows the present geometry of the layer structure where z direction is perpendicular to the layer planes. The parameter Dm describes the anisotropy of magnetizatio
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