Oxs Extension Module: Southampton_CubicAnisotropy8

Description:

This is a generic Oxs extension object, derived from the Oxs_Energy class. It enhances the Oxs_CubicAnisotropy class as part of the standard OOMMF package by sixth and eighth order anisotropy energy terms. The energy density is computed by

E =

K₁ [ (u₁·m)² (u₂·m)² + (u₁·m)² (u₃·m)² + (u₂·m)² (u₃·m)² ] +

K₂ [ (u₁·m)² (u₂·m)² (u₃·m)² ] +

K₃ [ (u₁·m)⁴ (u₂·m)⁴ + (u₁·m)⁴ (u₃·m)⁴ + (u₂·m)⁴ (u₃·m)⁴ ]

where m is the reduced (unit) magnetization, u₁/u₂/u₃ are the first/second/third cubic anisotropy axes, and K1/K2/K3 are the fourth/sixth/eighth order phenomenological anisotropy constants.

The corresponding anisotropy field H is given by the relation

- µ₀M_sH =

2 K₁ [ { (u₂·m)² + (u₃·m)² } { (u₁·m) u₁} +
          { (u₁·m)² + (u₃·m)² } { (u₂·m) u₂} +
          { (u₁·m)² + (u₂·m)² } { (u₃·m) u₃} ] +

2 K₂ [ { (u₂·m)² (u₃·m)² } { (u₁·m) u₁} +
          { (u₁·m)² (u₃·m)² } { (u₂·m) u₂} +
          { (u₁·m)² (u₂·m)² } { (u₃·m) u₃} ] +

4 K₃ [ { (u₂·m)⁴ + (u₃·m)⁴ } { (u₁·m)³ u₁} +
          { (u₁·m)⁴ + (u₃·m)⁴ } { (u₂·m)³ u₂} +
          { (u₁·m)⁴ + (u₂·m)⁴ } { (u₃·m)³ u₃} ]

where M_s is the saturation magnetization.

Installation:

Download the header and source code files below, and follow the general Oxs extension installation instructions.

Usage:

MIF 2.x files written to use this class should include a Specify block of the form

Specify Southampton_CubicAnisotropy8:name {
K1 k1_value
K2 k2_value
K3 k3_value
axis1 anisotropy_axis_1
axis2 anisotropy_axis_2
}

The values for the K1, K2, and K3 parameters should be scalar field objects, and axis1 and axis2 should be vector field objects. The only difference with respect to the stock Oxs_CubicAnisotropy class is the inclusion of the K2 and K3 terms.

Details:

Authors: Jürgen Zimmermann, Hans Fangohr
Affiliation:School of Engineering Sciences, University of Southampton
Oxs_Ext class: Southampton_CubicAnisotropy8
OOMMF releases: 1.2a3
External libraries: none
License: Public Domain
Release date: 10/04/2007
Version: 1.0

Download:

C++ header file: cubicanisotropy8.h
C++ main source file: cubicanisotropy8.cc
Example MIF input files:
- K2/K3 = 0% of real value: cubicEight_00pc.mif
- K2/K3 = 50% of real value: cubicEight_50pc.mif
- K2/K3 = 100% of real value: cubicEight_100pc.mif
- K2/K3 = 200% of real value: cubicEight_200pc.mif

Sample results:

Output from the four example MIF files, illustrating the effect of increasing K2/K3 relative to real value:

DISCLAIMER:

This software is free to use. However, the authors do not assume responsibility whatsoever for its use, and make no guarantees, expressed or implied, about its quality, reliability, or any other characteristic.

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