Modification of Magnetic Coupling in Antiferromagnetically Coupled Bilayers Due to the Existence of Ferromagnetic Pin Ho
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MODIFICATION OF MAGNETIC COUPLING IN ANTIFERROMAGNETICALLY COUPLED BILAYERS DUE TO THE EXISTENCE OF FERROMAGNETIC PIN HOLES. J.F. BOBO, H. FISCHER AND M. PIECUCH Laboratoire mixte CNRS St Gobain BP 104 54704 Pont
aMousson Cedex France.
ABSTRACT We have calculated numerical simulations and analytical solutions of the influence of a pin hole on the magnetization curves of multilayer systems. The magnetization curves we obtained can be described by a biquadratic coupling model and are close to the experimental curves. INTRODUCTION The growing interest in magnetic coupling between magnetic layers through non magnetic spacers has led in the recent years to several unexpected discoveries like giant magnetoresistance effect [1,21 and biquadratic coupling [3,4]. The question of the origin of this biquadratic coupling remains an open question. Several successful explanations have been proposed for this biquadratic coupling like interface defect [51 or intrinsic band structure effect 16,7]. More recently following the initial remark by Parkin [8] some groups have observed by transmission electron microscopy 19,101 the existence of partial contact between successive magnetic layers, the so called "pin holes". However a detailed study of the magnetic behavior of multilayers or bilayers with this kind of defects is actually lacking, this is the purpose of this paper where we investigate the magnetic properties of bilayers with pin holes. FORMULATION OF THE PROBLEM The system we studied is a trilayer consisting of two magnetic layers of thickness tm separated by a non magnetic layer of thickness tnm. We have considered that the magnetization is the same at each z inside the ferromagnetic layers and that the pinholes are not able to give a perpendicular component of the magnetization and then,that the field is in the plane of the layers. 0 and 02 are the angles of the magnetizations in the two magnetic layers with respect to H app 6in plane applied field). Since the solution is inhomogeneous, 01 and 0.2 are function of r, the position in the plane of the layer. The magnetic energy in each layer is the sum of the Zeeman energy and of the exchange energy (We have neglected the anisotropy energy). The next term is the coupling energy between the two layers. At a particular point r, the sum of these energies can be written: E(r) = Atm(V0 1) 2 + At m(V02) 2
-
H(cos0 1(r) + cos0 2(r)) - J(r) cos(0 1 (r)-0 2(r))
(Ia)
A is the usual exchange stiffness parameter, H= H M t H is the external applied field, Ms is the saturation magnetization (per unit voluXe) asnJ(r) Ve value of the magnetic coupling between the two layers at r, J(r) = -J (intrinsic antiferromagnetic coupling) at the normal sites and J(r) = Jh at the pinholes (Jh = 2A/t ) We assume a symmetric solution for the two layers 01 = -02 = 0. Then, the total energy oFP½e system can be written as: E= 2f(Atm (V0) 2 -J(r) cos 2 0(r)-Hcos0(r))d 2r
(I b)
The demagnetizing and field energy inside the pinhole have been neglected and then equation (I b) is strictly valid for a vanis
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