Mechanisms for the multistep spin reorientation of ultrathin Fe films on Gd A. P. Popov and A. V. Anisimov Department of Molecular Physics, Moscow State Engineering Physics Institute, 115407, Moscow, Kashirskoe shosse, 31, Russia D. P. Pappas National Institute of Standards and Technology, Boulder, Colorado80305 Received 7 October 2002; published 31 March 2003 The multistep spin reorientation transition of ultrathin iron films on bulk gadolinium is described theoreti- cally. We find that it is necessary to include cubic terms in the magnetic anisotropy energy expansion in order to explain this phenomenon. Furthermore, the signs of the anisotropy coefficients required to explain the coexistence of both first- and second-order phase transitions in this spin reorientation transition are obtained. We can then model this system using either a surface or a bulk driven model, or a combination of both. DOI: 10.1103/PhysRevB.67.094428 PACS numbers: 75.70.Rf I. INTRODUCTION Phase transitions are a common phenomenon encountered in nearly every branch of physics. 1 Modeling the driving forces and the order of the transition often leads to a deeper understanding of the underlying physical processes involved. Magnetism, in particular, is a rich field in this regard due to the vector nature of the order parameter. Integral to this is the concept of magnetic anisotropy, i.e., the difference in energy for various orientations of the magnetization with respect to a sample. The anisotropy plays a role in every magnetic device, 2 and applications have allowed, for example, magneto-optical devices to surpass the diffraction limit of magneto-optical storage devices. These ‘‘super-resolution’’ devices rely on a temperature-driven spin-reorientation tran- sition, where the magnetization of a thin film rotates from in-plane to perpendicular with increasing temperature. 3 An understanding of these spin reorientation transitions is an important source of knowledge regarding magnetic anisot- ropy. This information is invaluable because ab initio calcu- lations in even the simplest systems are difficult, 4 and it is currently not feasible to predict, from first principles, the behavior of complicated alloys and multilayered systems. For the most part, single magnetic films supported on nonmagnetic substrates have been investigated. 5,6 In these systems, the magnetization vector reorients from in the plane of the film to perpendicular as the temperature changes. This phenomenon can occur either as the temperature increases or decreases. For example, in Fe and Co films the magnetiza- tion rotates into the plane as the temperature ramps up, 7–9 while in films of Ni grown on Cu it rotates out of the plane. 10,11 All of these spin reorientation transitions are single step, continuous transitions, and can be understood using only the linear ( K 1 ) and quadratic ( K 2 ) terms of the anisotropy energy expansion for a single magnetic film. In addition, these films are thin enough that the entire film mag- netization rotates uniformly across the thickness of the film. However, devices are generally composed of many differ- ent magnetic layers that can have significantly different mag- netic orientations and properties. These properties include the Curie temperature, higher order anisotropies, interlayer and intralayer exchange, and crystal structure. In order to begin understanding these systems, it is necessary to inves- tigate the properties of more complicated, magnetic multilayer structures. Recently, we reported experimental evidence of a multi- step spin reorientation transition in a magnetic bilayer sys- tem consisting of an ultrathin 1.5 atomic layers amorphous film of Fe on a thick, bulklike Gd0001 film. 12 The first step in this unique spin reorientation transition is a continuous, reversible transition as the temperature increases from an in- plane orientation of Fe-rich surface magnetization into a slightly canted, out-of-plane state. The next step occurs at still higher temperature, and is a discontinuous, hysteretic transition of the surface magnetization to a nearly perpen- dicular, out-of-plane state. Both steps take place in the tem- perature interval from 260 to 280 K, i.e., below the Gd Curie point, T C,Gd =292.5 K. Subsequent magnetic studies using the polar magneto-optic Kerr effect, 13 have shown that the Gd layers near the interface participate in the spin reorienta- tion transition. However, it was not possible to determine to what extent these interfacial layers are perturbed from the data at hand. The goals of the present work are 1 to reveal the physi- cal mechanisms underlying these two phase transitions, 2 to find the area in parameter space in terms of the magnetic properties of both films required for both a first order and second order phase transition to occur, and 3 to understand and model the extent to which the Gd interfacial layers par- ticipate in the spin reorientation transition. The approach used is based on the accepted viewpoint that magnetic spin reorientations are physical realizations of phase transitions as described by Landau theory. 14–16 We take the perpendicular component of the surface layer vector magnetization as an order parameter and model the behavior of the entire system as the temperature changes, taking into account the layer dependent magnetization properties. II. FIRST STEP—CONTINUOUS PHASE TRANSITION FROM IN-PLANE TO CANTED Here we discuss the physical mechanism that gives rise to the continuous, low temperature transition from the in-plane to canted magnetization state of the Fe-rich surface. This PHYSICAL REVIEW B 67, 094428 2003 0163-1829/2003/679/0944286/$20.00 67 094428-1