86 lines
2.4 KiB
ReStructuredText
86 lines
2.4 KiB
ReStructuredText
.. index:: pair_style spin/magelec
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pair_style spin/magelec 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/magelec 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/magelec 4.5
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pair_coeff * * magelec 4.5 0.00109 1.0 1.0 1.0
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Description
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"""""""""""
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Style *spin/me* computes a magneto-electric interaction between
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pairs of magnetic spins. According to the derivation reported in
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:ref:`(Katsura) <Katsura1>`, this interaction is defined as:
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.. math::
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\vec{\omega}_i & = -\frac{1}{\hbar} \sum_{j}^{Neighb} \vec{s}_{j}\times\vec{D}(r_{ij}) \\
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\vec{F}_i & = -\sum_{j}^{Neighb} \frac{\partial D(r_{ij})}{\partial r_{ij}} \left(\vec{s}_{i}\times \vec{s}_{j} \right) \cdot \vec{r}_{ij}
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where :math:`\vec{s}_i` and :math:`\vec{s}_j` are neighboring magnetic
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spins of two particles.
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From this magneto-electric interaction, each spin i will be submitted
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to a magnetic torque omega, and its associated atom can be submitted to a
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force F for spin-lattice calculations (see :doc:`fix nve/spin <fix_nve_spin>`),
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such as:
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.. math::
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\vec{F}^{i} & = -\sum_{j}^{Neighbor} \left( \vec{s}_{i}\times \vec{s}_{j} \right) \times \vec{E} \\
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\vec{\omega}^{i} = -\frac{1}{\hbar} \sum_{j}^{Neighbor} \vec{s}_j \times \left(\vec{E}\times r_{ij} \right)
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with h the Planck constant (in metal units) and :math:`\vec{E}` an
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electric polarization vector. The norm and direction of E are giving
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the intensity and the direction of a screened dielectric atomic
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polarization (in eV).
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More details about the derivation of these torques/forces are reported in
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:ref:`(Tranchida) <Tranchida4>`.
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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>` 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_style spin/exchange <pair_spin_exchange>`, :doc:`pair_eam <pair_eam>`,
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Default
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"""""""
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none
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----------
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.. _Katsura1:
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**(Katsura)** H. Katsura, N. Nagaosa, A.V. Balatsky. Phys. Rev. Lett., 95(5), 057205. (2005)
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.. _Tranchida4:
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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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