Initial commit.

.travis.yml

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+sudo: required
+
+services:
+  - docker
+
+script:
+  - make travis-build
+
+notifications:
+  slack: joommf:eqKxGPXuUP3LxnOfxg7GWgDF

Dockerfile

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+FROM ubuntu:16.04
+
+RUN apt-get -y update
+RUN apt-get install -y git tk-dev tcl-dev
+
+# Clone OOMMF repository.
+WORKDIR /usr/local
+RUN git clone http://github.com/fangohr/oommf.git
+
+# Copy OOMMF extension repository.
+COPY . /usr/local/oommf-extension-dmi-d2d/
+WORKDIR /usr/local/oommf-extension-dmi-d2d/
+
+# Copy OOMMF extension to OOMMF directory.
+RUN cp src/* /usr/local/oommf/oommf/app/oxs/local/
+
+# Compile OOMMF.
+WORKDIR /usr/local/oommf
+RUN make
+
+# Create OOMMFTCL environment variable
+ENV OOMMFTCL /usr/local/oommf/oommf/oommf.tcl
+
+# Change working directory.
+WORKDIR /usr/local/oommf-extension-dmi-d2d

LICENSE

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+Copyright <2018> David Cortés-Ortuño, Marijan Beg, Vanessa Nehruji, Ryan A. Pepper, and Hans Fangohr, European XFEL GmbH and University of Southampton
+
+Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
+
+1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
+
+3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Makefile

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+test-all:
+	ls -lh examples
+	tclsh $(OOMMFTCL) boxsi +fg examples/isolated_sk_DMI_D2d.mif -exitondone 1
+	ls -lh examples
+	tclsh $(OOMMFTCL) boxsi +fg examples/sk_lattice_DMI_D2d_PBCs.mif -exitondone 1
+	ls -lh examples
+
+travis-build: SHELL:=/bin/bash
+travis-build:
+	docker build --no-cache -t dockertestimage .
+	docker run -ti -d --name testcontainer dockertestimage
+	docker exec testcontainer make test-all
+	docker stop testcontainer
+	docker rm testcontainer

README.md

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+[![Build Status](https://travis-ci.org/joommf/oommf-extension-dmi-d2d.svg?branch=master)](https://travis-ci.org/joommf/oommf-extension-dmi-d2d)
+[![License](https://img.shields.io/badge/License-BSD%203--Clause-blue.svg)](https://opensource.org/licenses/BSD-3-Clause)
+
+# [OOMMF](https://math.nist.gov/oommf/) extension: Dzyaloshinskii-Moriya interaction (DMI) for the crystallographic class D<sub>2d</sub>
+
+David Cortés-Ortuño<sup>1</sup>, Marijan Beg<sup>1,2</sup>, Vanessa Nehruji<sup>3</sup>, Ryan A. Pepper<sup>1</sup>, and Hans Fangohr<sup>1,2</sup>
+
+<sup>1</sup> Faculty of Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, United Kingdom  
+<sup>2</sup> European XFEL GmbH, Holzkoppel 4, 22869 Schenefeld, Germany  
+<sup>3</sup> Department of Physics, University of Durham, Durham DH1 3LE, United Kingdom
+
+## Introduction
+
+Different Dzyaloshinskii-Moriya interaction forms can be written as different combinations of Lifshitz invariants depending on the crystallographic class of the magnetic material [1].
+
+## Energy density
+
+The DMI energy density for the crystallographic class D<sub>2d</sub> as a sum of Lifshitz invariants [1] is
+
+<a href="https://www.codecogs.com/eqnedit.php?latex=\LARGE&space;w&space;=&space;D&space;\left(&space;\mathcal{L}_{xz}^{(y)}&space;&plus;&space;\mathcal{L}_{yz}^{(x)}&space;\right)&space;=&space;D&space;\mathbf{m}&space;\cdot&space;\left(&space;\frac{\partial&space;\mathbf{m}}{\partial&space;x}&space;\times&space;\hat{x}&space;-&space;\frac{\partial&space;\mathbf{m}}{\partial&space;y}&space;\times&space;\hat{y}&space;\right)" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\LARGE&space;w&space;=&space;D&space;\left(&space;\mathcal{L}_{xz}^{(y)}&space;&plus;&space;\mathcal{L}_{yz}^{(x)}&space;\right)&space;=&space;D&space;\mathbf{m}&space;\cdot&space;\left(&space;\frac{\partial&space;\mathbf{m}}{\partial&space;x}&space;\times&space;\hat{x}&space;-&space;\frac{\partial&space;\mathbf{m}}{\partial&space;y}&space;\times&space;\hat{y}&space;\right)" title="\LARGE w = D \left( \mathcal{L}_{xz}^{(y)} + \mathcal{L}_{yz}^{(x)} \right) = D \mathbf{m} \cdot \left( \frac{\partial \mathbf{m}}{\partial x} \times \hat{x} - \frac{\partial \mathbf{m}}{\partial y} \times \hat{y} \right)" /></a>
+
+where <a href="https://www.codecogs.com/eqnedit.php?latex=D&space;[\text{J}/\text{m}^{2}]" target="_blank"><img src="https://latex.codecogs.com/gif.latex?D&space;[\text{J}/\text{m}^{2}]" title="D [\text{J}/\text{m}^{2}]" /></a> is the DMI constant and <a href="https://www.codecogs.com/eqnedit.php?latex=\mathbf{m}&space;=&space;\mathbf{M}/M_\text{s}" target="_blank"><img src="https://latex.codecogs.com/gif.latex?\mathbf{m}&space;=&space;\mathbf{M}/M_\text{s}" title="\mathbf{m} = \mathbf{M}/M_\text{s}" /></a> is the normalised magnetisation field.
+
+## Periodic boundary conditions
+
+This OOMMF extension works both with and without periodic boundary conditions (PBC). Therefore, it is possible to use the same class in either kind of mesh (`Oxs_RectangularMesh` or `Oxs_PeriodicRectangularMesh`).
+
+## Installation
+
+To install this extension:
+1. Copy `DMI_D2d.cc` and `DMI_D2d.h` files from the `src` directory in this repository into the `app/oxs/local` directory in the OOMMF main directory.
+2. Recompile OOMMF, usually by running
+```
+tclsh oommf.tcl pimake distclean && tclsh oommf.tcl pimake upgrade && tclsh oommf.tcl pimake
+```
+
+## Examples
+
+Examples are provided in `.mif` files for the stabilisation of an isolated skyrmion in a confined cuboid (no periodic boundary conditions) and for the stabilisation of a skyrmion lattice in a unit cell of an infinite system (with periodic boundary conditions).
+
+## Support
+
+If you require support on installation or usage of this OOMMF extension as well as if you want to report a problem, you are welcome to raise an issue in our [joommf/help](https://github.com/joommf/help) repository.
+
+## How to cite
+
+If you use this OOMMF extension in your research, please cite it as:
+
+## License
+
+This extension is licensed under the BSD 3-Clause "New" or "Revised" License. For details, please refer to the [LICENSE](LICENSE) file.
+
+## Acknowledgements
+
+This extension was developed as a part of [OpenDreamKit](http://opendreamkit.org/) – Horizon 2020 European Research Infrastructure project (676541) and the [EPSRC Programme grant on Skyrmionics (EP/N032128/1)](https://www.skyrmions.ac.uk/).
+
+## References
+
+[1] A. Bogdanov and D. Yablonskii. Thermodynamically stable "vortices" in magnetically ordered crystals. The mixed state of magnets. [Zh. Eksp. Teor. Fiz 95, 178 (1989)](http://www.jetp.ac.ru/cgi-bin/e/index/e/68/1/p101?a=list).

examples/isolated_sk_DMI_D2d.mif

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+# MIF 2.1 ---------------------------------------------------------------------
+
+# Generate an isolated skyrmion with interfacial (C_nv) DMI
+#
+# Authors: D. Cortes, M. Beg, H.Fangohr (2018)
+
+set PI [expr {4 * atan(1.)}]
+set MU0 [expr {4 * $PI * 1e-7}]
+
+# -----------------------------------------------------------------------------
+# PdFe on Ir(111) [PRL, 114(17):1-5, 2015]
+# This is an interfacial system but the parameters should work similarly for 
+# the D2d symmetry. Spins only change the sense of rotation
+set Ms [expr {1.1e6}]
+set A  [expr {2e-12}]
+set D  [expr {3.9e-3}]
+set KU [expr {2.5e6}]
+set BZ [expr {1.0}]
+
+set XL [expr {15e-9}]
+set YL [expr {$XL}]
+set ZL [expr {2e-9}]
+
+set xcell [expr {$XL / 20}]
+set ycell [expr {$YL / 20}]
+set zcell [expr {2e-9}]
+
+# -----------------------------------------------------------------------------
+
+# BoxAtlas
+Specify Oxs_BoxAtlas:atlas [subst {
+  xrange {0 $XL}
+  yrange {0 $YL}
+  zrange {0 $ZL}
+  name atlas
+}]
+
+# RectangularMesh
+Specify Oxs_RectangularMesh:mesh [subst {
+  cellsize {$xcell $ycell $zcell}
+  atlas Oxs_BoxAtlas:atlas
+}]
+
+# UniformExchange
+Specify Oxs_UniformExchange [subst {
+  A $A
+}]
+
+# Uniaxial Anisotropy
+Specify Oxs_UniaxialAnisotropy:Anisotropy [subst {
+	axis { 0 0 1 }
+	K1 $KU
+}]
+
+# D_2d DMI
+Specify Oxs_DMI_D2d [subst {
+  default_D $D
+  atlas :atlas
+  D {
+    atlas atlas $D
+  }
+}]
+
+Specify Oxs_FixedZeeman:Bfield [subst {
+  comment {Field values in Tesla; scale to A/m}
+  multiplier [expr {1 / $MU0}]
+  field {0.0 0.0 $BZ}
+}]
+
+# CGEvolver
+Specify Oxs_CGEvolve {}
+
+# MinDriver
+Specify Oxs_MinDriver [subst {
+  evolver Oxs_CGEvolve
+  stopping_mxHxm 0.01
+  mesh :mesh
+  Ms $Ms
+  m0 { Oxs_ScriptVectorField {
+     atlas :atlas
+     script { dot }
+     norm 1.0
+     script_args { relpt }
+  }}
+
+  basename isolated_sk_D2d
+  scalar_field_output_format {text %\#.15g}
+  vector_field_output_format {text %\#.15g}
+}]
+
+Destination table mmArchive
+Destination mags mmArchive
+
+Schedule DataTable table Stage 1
+Schedule Oxs_MinDriver::Magnetization mags Stage 1
+
+# =============================================================================
+
+proc dot { x y z } {
+	set xnorm  [expr {(2 * $x - 1)}]
+	set ynorm  [expr {(2 * $y - 1)}]
+    set radius [expr {sqrt($xnorm * $xnorm + $ynorm * $ynorm)}]
+    if {$radius < 0.2} { return [list 0 0 -1] }
+    return [list 0 0 1]
+}

examples/sk_lattice_DMI_D2d_PBCs.mif

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+# MIF 2.1 ---------------------------------------------------------------------
+
+# Generate a skyrmion lattice in a "unit cell" with Periodic Boundaries
+#
+# Authors: D. Cortes, M. Beg, H.Fangohr (2018)
+
+set PI [expr {4 * atan(1.)}]
+set MU0 [expr {4 * $PI * 1e-7}]
+
+# -----------------------------------------------------------------------------
+# PdFe on Ir(111) [PRL, 114(17):1-5, 2015]
+# This is an interfacial system but parameters should work similarly for D2d 
+# symmetry. Spins only change the sense of rotation for the skyrmion
+set Ms [expr {1.1e6}]
+set A  [expr {2e-12}]
+set D  [expr {3.9e-3}]
+set KU [expr {2.5e6}]
+set BZ [expr {1.0}]
+
+set XL [expr {15e-9}]
+set YL [expr {$XL / sqrt(3)}]
+set ZL [expr {2e-9}]
+
+set xcell [expr {$XL / 64}]
+set ycell [expr {$YL / 32}]
+set zcell [expr {2e-9}]
+
+# -----------------------------------------------------------------------------
+
+# BoxAtlas
+Specify Oxs_BoxAtlas:atlas [subst {
+  xrange {0 $XL}
+  yrange {0 $YL}
+  zrange {0 $ZL}
+  name atlas
+}]
+
+# RectangularMesh
+Specify Oxs_PeriodicRectangularMesh:mesh [subst {
+  cellsize {$xcell $ycell $zcell}
+  atlas Oxs_BoxAtlas:atlas
+  periodic "xy"
+}]
+
+# UniformExchange
+Specify Oxs_UniformExchange [subst {
+  A $A
+}]
+
+# Uniaxial Anisotropy
+Specify Oxs_UniaxialAnisotropy:Anisotropy [subst {
+	axis { 0 0 1 }
+	K1 $KU
+}]
+
+# D_2d DMI
+Specify Oxs_DMI_D2d [subst {
+  default_D $D
+  atlas :atlas
+  D {
+    atlas atlas $D
+  }
+}]
+
+Specify Oxs_FixedZeeman:Bfield [subst {
+  comment {Field values in Tesla; scale to A/m}
+  multiplier [expr {1 / $MU0}]
+  field {0.0 0.0 $BZ}
+}]
+
+# CGEvolver
+Specify Oxs_CGEvolve {}
+
+# MinDriver
+Specify Oxs_MinDriver [subst {
+  evolver Oxs_CGEvolve
+  stopping_mxHxm 0.01
+  mesh :mesh
+  Ms $Ms
+  m0 { Oxs_ScriptVectorField {
+     atlas :atlas
+     script { skX }
+     norm 1.0
+     script_args { relpt }
+  }}
+
+  basename skL_D2d_PBCs
+  scalar_field_output_format {text %\#.15g}
+  vector_field_output_format {text %\#.15g}
+}]
+
+Destination table mmArchive
+Destination mags mmArchive
+
+Schedule DataTable table Stage 1
+Schedule Oxs_MinDriver::Magnetization mags Stage 1
+
+# =============================================================================
+
+proc skX { x y z } {
+	set xnorm  [expr {(2 * $x - 1)}]
+	set ynorm  [expr {(2 * $y - 1)}]
+
+    foreach xsk [list -1.0 1.0 -1.0 1.0 0.0] ysk [list -1.0 -1.0 1.0 1.0 0.0] {
+
+        set xrel [expr {$xnorm - $xsk}]
+        set yrel [expr {$ynorm - $ysk}]
+        set radius [expr {sqrt($xrel * $xrel + $yrel * $yrel)}]
+
+        if {$radius < 0.3} { return [list 0 0 -1] }
+
+    }
+
+    return [list 0 0 1]
+}