2010-08-25
10:15 at HCI J 574

A micromagnetic study on magnetization behavior of two interacting magnetic particles

Andrei-Valentin Plamadă

Department of Physics, Alexandru Ioan Cuza University, 700506 Iasi, Romania

The two-particle system (2PS) can be solved with high accuracy and may therefore serve as a benchmark for more complicated particle arrays. An example of 2PS is the synthetic antiferromagnet (SAF) structure. The SAF structure is a system of two ferromagnetic layers antiferromagnetically coupled through a nonmagnetic metallic spacer layer. SAF structures received great interest due to their application in magnetoresistance sensors, spin electronics, high-density recording technology, as active parts of toggle magnetic random access memory. Using the single domain assumption the exact expressions for the switching fields were derived and the switching behavior was analyzed [1-5]. When the field is applied along the easy axis the energy barriers are obtained analytically only on certain intervals of applied field, and numerical calculations are needed to fully characterize the system [1]. In Refs. [2, 5] the analyses are based on the hysteresis loops without debating neither the possible jumps nor the energy barriers. Mainly, to understand the magnetic response of a 2PS one must analyze the free energy landscape with its local minima, and how the configuration of minima is altered as the field changes. To estimate the influence of thermal fluctuations on the system, the activation energies for all the energy barriers are necessary. So it is essentially to have a clear idea about the system minima, as well as about the corresponding saddle points and which minima make them available. The energy barriers are defined as the energy differences between the local minimum where the system is currently in and all the saddle points which can link the local minimum with another distinct equilibrium state. The activation energy is the lowest energy barrier. The equilibrium state solutions are found from the minima of the system’s free energy. Both minima and saddle points of free energy are particular cases of critical points. The second derivative test is used to distinguish between them. In this work we use a decoupling method to convert the critical points problem into an algebraic equation, and for the particular case of a field applied along the easy axis we show that the two particle system is completely analytically solvable [6, 7]. For this case, the switching diagram as a function of coupling parameters is presented. We present an elegant way to understand the key elements - the hysteresis loops and energy barriers by introducing a simple method, representing the energy as a function of magnetic field. We have derived the exact expressions for the energy's critical points, energy barriers, and we have identified all the possible hysteresis loops. We have also identified all the possible jumps as consequence of thermal fluctuations, these results being useful in the rate equation formalism. References [1] D. C. Worledge, Applied Physics Letters 84 (2004) 4559. [2] D. C. Worledge, Applied Physics Letters 84 (2004) 2847. [3] S.Y. Wang and H. Fujiwara, Journal of Magnetism and Magnetic Materials 286 (2005) 27. [4] H. Rohrer and H. Thomas, Journal of Applied Physics 40 (1969) 1025. [5] D. M. Forrester, E. K. Karl, and F. V. Kusmartsev, Physical Review B (Condensed Matter and Materials Physics) 76 (2007) 134404. [6] A. V. Plamada and A. Stancu, Magnetics, IEEE Transactions on 45 (2009) 3796. [7] A.-V. Plamada, D. Cimpoesu, and A. Stancu, Applied Physics Letters 96 (2010) 122505.