A method for computing the microwave absorption spectrum in a discrete model of a ferromagnetic

Abstract

An effective method based on linearization of the Landau-Lifshitz equation has been developed to determine normal magnetization oscillation modes in a discrete model of a condensed medium. The possibility to calculate microwave absorption spectra for ferromagnetic specimens of any shape is shown.The fundamental equation that describes the dynamics of a magnetic system under the action of external constant and variable magnetic fields is the Landau-Lifshitz nonlinear differential equation. For a discretized model of an inhomogeneous medium, it is necessary to solve a system of connected nonlinear differential equations. To solve systems of this type, numerical integration based on an algorithm similar to the Runge-Kutta algorithm is widely used [1]. The main advantage of this approach is the possibility to predict the evolution of a magnetic system, starting from the initial distribution of magnetic moments in the discrete model. The main disadvantages of this type of algorithm are substantial computational burden and the inconstancy of the magnetic moment vector in discrete elements in iterative calculations, which in fact gives no way of investigating systems that consist of a large number of elements. Therefore, undoubtedly, the search for new approaches and algorithms which would allow one to solve complicated problems of this type is of importance and urgency in modern physics. The potentialities of multilayer magnetic structures used in microelectronic devices also promote the extension of related research works.In recent years, to study microdiscrete models of complicated magnetic structures, approaches have been developed that have been actively used in optics [2][3][4]. They are based on a description of the motion of magnetic moments as the sum of the natural oscillations of the normal magnetic modes for the overall system. In this paper, the idea described elsewhere [2] is developed as applied to a discrete model [5], which has shown rather high efficiency.A ferromagnetic is represented as a discrete medium consisting of N identical (of volume V 0 ) dipoles μ (i) (i = 1, 2, …, N) that, having a constant saturation magnetization M s , fill uniformly the whole of the body. Denoting the direction of the ith dipole by M (i) , we write an expression for the free energy density of the system, F, taking into account the Zeeman energy, the exchange and dipole interaction energies, and the energy of uniaxial magnetic anisotropy:

Micromagnetic Simulation of Magnetization Reversal Processes in Thin Obliquely Deposited Films

“…Obtained samples exhibited tilted columnar microstructure reproducing that of experimental obliquely deposited films [8]. In order to study numerically magnetic properties of these simulated oblique films we employed our micromagnetic simulation software [9,10]. In micromagnetic analysis, each cell of the three-dimensional array occupied by a particle was characterized by an averaged value of a magnetic moment M with the magnetization saturation M s (for unoccupied cells M s = 0).…”

Numerical Simulation of Magnetic Microstructure in Nanocrystalline Thin Films with the Random Anisotropy

“…We used our micromagnetic modeling software [5,6] to study the magnetic microstructure of thin nanocrystalline films. The investigated films were monolayers of close-packed nanoparticles with a random distribution of anisotropy axes, where the number of the particles was 2048×2048×1.…”