<title>Finite size effects in antiferromagnetic multilayers</title>

Abstract

Since the discovery of giant magnetoresistance a great effort was made for the investigation of field-induced transitions in magnetic multilayers with antiferromagnetic exchange between magnetic layers. Two peculiarities increase the complexity of this problem. At first, the exchange energy, the anisotropy energy, and the Zeeman energy are of the same order of magnitude. At second, the values of critical fields strongly depend on the number of magnetic layers (finite size effect). Despite of a long time history of these investigations the method of analytical calculation of finite size effect is absent. In the present paper the regular method of analytical calculation of critical field values in antiferromagnetic multilayers is developed. The method is based on the using of finite difference technique. Heisenberg and biquadratic exchange interactions and uniaxial anisotropy are taken into account. Using this technique we investigate the field-induced transition from angle phase to the ferromagnetic phase for arbitrary number of magnetic layers. Exact analytical expression of the critical field value is obtained. This expression shows that critical field monotonically increases with increasing layers number. The dependence of critical field value on magnetic field orientation is discussed. Also the investigation of the stability of antiferromagnetic phase under the action of external magnetic field is made. It is shown that in this case the behavior of magnetic superlattice depends on the parity of layers number. For the even layers number the value of critical field does not depend on the layers number. For the odd layers number the value of critical field depends on the orientation of magnetic field with respect to the orientation of magnetization in the boundary layers. If external magnetic field is directed along the direction of magnetization in the boundary layers the value of critical field is decreased with increasing layers number. If external magnetic field is directed in the opposite direction the value of critical field is increased with increasing layers number. To elucidate the physical mechanism giving rise to the difference in critical field values a numerical simulation was made. It shows that difference in critical field values is concerned with nucleation of the surface spin-flop phase near the surface of magnetic superlattice if the external magnetic field has the opposite direction with respect to the orientation of magnetization in the boundary layer. As external magnetic field is increased the surface spin-flop phase spread out over full volume. Thus the surface spin-flop phase serves as mediator between antiferromagnetic and angle phases and it explains the difference in critical field values. The possible use of developed technique for the investigation of field-induced transitions in ferrimagnetic multilayers is discussed.