Micromagnetic simulation of nucleation and domain wall motion in small particles and wires

T Schrefl, H Forster, D Suess, W Scholz, V Tsiantos, J Fidler

Proc. of Int. Workshop on Wires (IWMW), San Sebastian, Spain, June 2001, (2001) submitted

Finite element micromagnetics is an effective tool to investigate the magnetization reversal process of small magnetic structures. A detailed understanding of the reversal process becomes increasingly important for ultra high density magnetic storage and sensor applica-tions. These applications require the control of various properties such as the switching time and the energy barrier of thermally activated reversal which both depend significantly on the reversal mode. Irregular shaped particles like polyhedral, columnar grains of perpendicular media or cylindrical wires can be easily modeled using tetrahedral finite elements. The solu-tion of the Gilbert equation of motion resolves the magnetization in space and in time during the magnetization reversal process. In addition energy barriers for thermally activated magne-tization reversal can be estimated by plotting the energy along different reversal paths or by Langevin dynamics. The deterministic Gilbert equation of motion transforms to a stochastic partial differential equation adding a random thermal field to the effective field. The space dis-cretization leads to a system of stochastic differential equations with multiplicative noise which is interpreted in the sense of Stratonovich and solved using the method of Heun. The irreversible switching of magnetic particles occurs either by the rotation of the magnetiza-tion or by the expansion of a nucleus of reverse magnetization. The numerical results show that the Gilbert damping constant, alpha, drastically changes the reversal mode of elongated particles. A Co-Cr grain of a perpendicular recording media with a column length of 40 nm rotates quasi-uniformly for alpha = 1, whereas a nucleation process occurs for alpha = 1 and alpha = 0.01 respectively. Below this critical length the maximum exchange energy found during reversal increases with the column length, indicating a smooth transition between coherent rotation and nucleation. In addition thermal fluctuation may change the reversal mode. At finite temperature inhomogeneous reversal pro-cesses become dominant if the column length exceeds 30 nm. Below this value non-uniform rotation shows a lower energy barrier than the nucleation of a reversed domain. The activation energy for Co nanowires with a diameter of 2 nm was found to depend linearly on the applied field. This behavior indicates that magnetization reversal occurs by the formation of a nucleus of reverse magnetization. The analysis of the calculated magnetization configurations as a function of time confirms a nucleation mechanism. The magnetization starts to reverse within a finite volume at one end of the wire. The calculated activation volume, v = (2.1 nm), was found to be independent of the length of the nanowire. Once a reversed domain has formed, it expands along the entire wire. Adaptive refinement schemes are used to simulate the wall motion. Thus it is possible to resolve the domain wall structure while keep the total number of finite elements to a minimum. The effect of the diameter of the wire and the Gilbert damping constant on the domain wall velocity will be discussed. The calculated wall velocity in Co wires with a diameter of 40 nm was 400 m/s for alpha = 0.1 and for an external field of 80 kA/m.

This work was supported by the Austrian Science Fund (Y-132 PHY).

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Oct. 18, 2001