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 =

K_{1} [
(u_{1}·m)^{2}
(u_{2}·m)^{2} +
(u_{1}·m)^{2}
(u_{3}·m)^{2} +
(u_{2}·m)^{2}
(u_{3}·m)^{2}
] +

K_{2} [
(u_{1}·m)^{2}
(u_{2}·m)^{2}
(u_{3}·m)^{2}
] +

K_{3} [
(u_{1}·m)^{4}
(u_{2}·m)^{4} +
(u_{1}·m)^{4}
(u_{3}·m)^{4} +
(u_{2}·m)^{4}
(u_{3}·m)^{4}
]
where m is the reduced (unit) magnetization,
u_{1}/u_{2}/u_{3} 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

 µ_{0}M_{s}H =

2 K_{1} [
{ (u_{2}·m)^{2} +
(u_{3}·m)^{2} }
{ (u_{1}·m) u_{1}} +
{ (u_{1}·m)^{2} +
(u_{3}·m)^{2} }
{ (u_{2}·m) u_{2}} +
{ (u_{1}·m)^{2} +
(u_{2}·m)^{2} }
{ (u_{3}·m) u_{3}}
] +

2 K_{2} [
{ (u_{2}·m)^{2}
(u_{3}·m)^{2} }
{ (u_{1}·m) u_{1}} +
{ (u_{1}·m)^{2}
(u_{3}·m)^{2} }
{ (u_{2}·m) u_{2}} +
{ (u_{1}·m)^{2}
(u_{2}·m)^{2} }
{ (u_{3}·m) u_{3}}
] +

4 K_{3} [
{ (u_{2}·m)^{4} +
(u_{3}·m)^{4} }
{ (u_{1}·m)^{3} u_{1}} +
{ (u_{1}·m)^{4} +
(u_{3}·m)^{4} }
{ (u_{2}·m)^{3} u_{2}} +
{ (u_{1}·m)^{4} +
(u_{2}·m)^{4} }
{ (u_{3}·m)^{3} u_{3}}
]
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:
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.