Equilibrium domain structure in vicinity of elliptical magnetic impurity in iron–garnet magnetic films

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Abstract

The given work is devoted to the research of distortion of the shape of the isolated stripe domain in the presence of two-dimensional magnetic impurity with sizes of the order of width of this domain. The analysis is based on the developed analytical theory of mixed domain structures. The equation, describing the equilibrium domain wall profile in the vicinity of an elliptical magnetic impurity, had been derived. Calculations were performed for a magnetic film with its parameters typical for the magnetic memory application. The mixed domain structure, consisting of the stripe domains with the elliptical domain at the center of one of them, was nucleated in an iron–garnet film with (2 1 0) orientation. Results of calculations are consistent with experimental observations performed on this film.

Introduction

The study of magnetic ordering is justified by a wide implementation of magnetic materials in a variety of devices (radio devices, computers, etc…). In recent years, great achievements were made in the area of magnetic information storage. Magnetic storage devices size increased from megabytes to hundreds of gigabytes. These breakthroughs would be impossible without work and achievements in theoretical and experimental physics of spin self-ordering in magnetic films. Today, microelectronics is concurring technologies based on magnetic nanostructures. This drives a fundamental theoretical and modeling research. Discovery of new fundamental effects, such as giant magnetoresistance of thin multilayer films, spin-polarized tunneling in ferromagnetic micro-contacts, giant magnetoimpedance in thin amorphous ferromagnetic conductors, form a base for new precise sensors, writing and storing information, applications of new technologies in nano-electronics, computers, and communication devices. Modern methods of electrical lithography allow existence of plane ferromagnetic nanoelements with controlled magnetic properties. Generation and a control of magnetic structures can be achieved by external electromagnetic excitation. Understanding of these processes, from Physics perspective, will potentially allow a control over generation and dynamics of magnetic structures, which is essential for modern technology based on magnetic nanostructures.

Although, the active study of magnetic spin systems have been conducted for almost hundred of years, the interest in these systems is evident in modern times. First of all, the interest is based on fundamental scientific curiosity towards existence of various collective structures and unstable structures and control over these systems. Second, the interest is based on development of reliable, compact and vast magnetic memory devices, magnetic micro-sensors, microwave elements such as filters, rectifiers, spin transistors, resonators, and so etc.

Spin ordering in magnetic systems is one of the main features of the system, which determines most properties of its behavior. For example, stripe or cylindrical magnetic domains are known to occur in ferromagnetic materials to decrease magnetostatic energy of a sample [1], [2]. Recently, experiments showed that a stable mixed domain structure, consisting of stripe domains with magnetic impurities of cylindrical or elliptical shape can be generated in some magnetic films as well [3], [4].

This paper is devoted to the research of mixed domain structure in an iron–garnet magnetic film with (2 1 0) orientation focusing on distortion of the shape of a stripe domain in vicinity of a magnetic impurity located at the center of the domain. The analysis is based on the developed analytical theory of mixed domain structures. Calculations were performed for a magnetic film with its parameters typical for the magnetic memory application. The mixed domain structure, consisting of stripe domains with the elliptical domain at the center of one of them, was observed experimentally.

Section snippets

Experimental procedure

The experimental observation of a mixed domain structure was conducted in an iron–garnet magnetic film of composition (Bi0.7,Lu0.3)3(Fe0.8,Ga0.2)5O12 with orientation (2 1 0) and following parameters: thickness, h=13.0 μm; saturation magnetization, 4πMs=60.0 Gs; the field of an orthorhombic anisotropy, HK=1400 Oe; Gilbert damping constant, α=0.01; the angle of the easy magnetization axis from the normal to the film surface, θ=30°; the equilibrium period of stripe domains, W=26.0 μm. A traditional

Theory of mixed domain structure

For simplicity, let us consider the individual isolated stripe domain and the magnetic impurity, such as an elliptical magnetic domain, inside the isolated stripe domain. Let us choose the origin of the coordinate system at the center of the elliptic area, as shown in Fig. 2. The isolated stripe domain of width w=2a is extended along the X-axis in the infinite film of thickness h. The Z-axis is directed perpendicularly to the plane of the film, and the Y-axis is perpendicular to domain walls.

Conclusions

A stable mixed domain structure, consisting of stripe domains with magnetic impurity of elliptical shape was observed in iron–garnet magnetic films with tilted anisotropy. To explain the observed structures, the theoretical analysis based on the magnetostatic energy minimization was performed. The equations describing the equilibrium shape of domain walls of a stripe domain in vicinity of the elliptical impurity were derived. The analysis of the theoretical results supports existence of a

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