111 lines
3.5 KiB
ReStructuredText
111 lines
3.5 KiB
ReStructuredText
.. index:: pair_style spin/neel
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pair_style spin/neel command
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============================
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Syntax
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""""""
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.. code-block:: LAMMPS
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pair_style spin/neel cutoff
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* cutoff = global cutoff pair (distance in metal units)
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Examples
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""""""""
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.. code-block:: LAMMPS
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pair_style spin/neel 4.0
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pair_coeff * * neel 4.0 0.0048 0.234 1.168 2.6905 0.705 0.652
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pair_coeff 1 2 neel 4.0 0.0048 0.234 1.168 0.0 0.0 1.0
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Description
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"""""""""""
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Style *spin/neel* computes the Neel pair anisotropy model
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between pairs of magnetic spins:
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.. math::
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\mathcal{H}_{N\acute{e}el}=-\sum_{{ i,j=1,i\neq j}}^N g_1(r_{ij})\left(({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{i})({\mathbf{e}}_{ij}
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\cdot {\mathbf{s}}_{j})-\frac{{\mathbf{s}}_{i}\cdot{\mathbf{s}}_{j}}{3} \right)
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+q_1(r_{ij})\left( ({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{i})^2 -\frac{{\mathbf{s}}_{i}\cdot{\mathbf{s}}_{j}}{3}\right)
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\left( ({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{i})^2 -\frac{{\mathbf{s}}_{i}\cdot{\mathbf{s}}_{j}}{3} \right)
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+ q_2(r_{ij}) \Big( ({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{i}) ({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{j})^3 + ({\mathbf{e}}_{ij}\cdot
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{\mathbf{s}}_{j}) ({\mathbf{e}}_{ij}\cdot {\mathbf{s}}_{i})^3\Big)
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where :math:`\mathbf{s}_i` and :math:`\mathbf{s}_j` are two neighboring magnetic spins of two particles,
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:math:`r_{ij} = \vert \mathbf{r}_i - \mathbf{r}_j \vert` is the inter-atomic distance between the two particles,
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:math:`\mathbf{e}_{ij} = \frac{\mathbf{r}_i - \mathbf{r}_j}{\vert \mathbf{r}_i - \mathbf{r}_j\vert}` is their normalized separation vector and :math:`g_1`,
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:math:`q_1` and :math:`q_2` are three functions defining the intensity of the dipolar
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and quadrupolar contributions, with:
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.. math::
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g_1(r_{ij}) &= g(r_{ij}) + \frac{12}{35} q(r_{ij}) \\
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q_1(r_{ij}) &= \frac{9}{5} q(r_{ij}) \\
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q_2(r_{ij}) &= - \frac{2}{5} q(r_{ij})
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With the functions :math:`g(r_{ij})` and :math:`q(r_{ij})` defined and fitted according to
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the same Bethe-Slater function used to fit the exchange interaction:
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.. math::
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{J}\left( r_{ij} \right) = 4 a \left( \frac{r_{ij}}{d} \right)^2 \left( 1 - b \left( \frac{r_{ij}}{d} \right)^2 \right) e^{-\left( \frac{r_{ij}}{d} \right)^2 }\Theta (R_c - r_{ij})
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where :math:`a`, :math:`b` and :math:`d` are the three constant coefficients defined in the
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associated "pair\_coeff" command.
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The coefficients :math:`a`, :math:`b`, and :math:`d` need to be fitted so that the function
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above matches with the values of the magneto-elastic constant of the
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materials at stake.
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Examples and more explanations about this function and its
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parameterization are reported in :ref:`(Tranchida) <Tranchida6>`. More
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examples of parameterization will be provided in future work.
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From this DM interaction, each spin :math:`i` will be submitted to a magnetic
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torque :math:`\mathbf{\omega}` and its associated atom to a force :math:`\mathbf{F}` (for spin-lattice
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calculations only).
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More details about the derivation of these torques/forces are reported
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in :ref:`(Tranchida) <Tranchida6>`.
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----------
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Restrictions
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""""""""""""
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All the *pair/spin* styles are part of the SPIN package. These styles
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are only enabled if LAMMPS was built with this package, and if the
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atom\_style "spin" was declared. See the :doc:`Build package <Build_package>` doc page for more info.
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Related commands
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""""""""""""""""
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:doc:`atom_style spin <atom_style>`, :doc:`pair_coeff <pair_coeff>`,
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:doc:`pair_eam <pair_eam>`,
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**Default:**
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none
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----------
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.. _Tranchida6:
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**(Tranchida)** Tranchida, Plimpton, Thibaudeau and Thompson,
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Journal of Computational Physics, 372, 406-425, (2018).
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