203 lines
6.9 KiB
ReStructuredText
203 lines
6.9 KiB
ReStructuredText
.. index:: fix precession/spin
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fix precession/spin 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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fix ID group precession/spin style args
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* ID, group are documented in :doc:`fix <fix>` command
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* precession/spin = style name of this fix command
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* style = *zeeman* or *anisotropy* or *cubic* or *stt*
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.. parsed-literal::
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*zeeman* args = H x y z
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H = intensity of the magnetic field (in Tesla)
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x y z = vector direction of the field
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*anisotropy* args = K x y z
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K = intensity of the magnetic anisotropy (in eV)
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x y z = vector direction of the anisotropy
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*cubic* args = K1 K2c n1x n1y n1x n2x n2y n2z n3x n3y n3z
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K1 and K2c = intensity of the magnetic anisotropy (in eV)
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n1x to n3z = three direction vectors of the cubic anisotropy
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*stt* args = J x y z
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J = intensity of the spin-transfer torque field
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x y z = vector direction of the field
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Examples
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""""""""
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.. code-block:: LAMMPS
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fix 1 all precession/spin zeeman 0.1 0.0 0.0 1.0
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fix 1 3 precession/spin anisotropy 0.001 0.0 0.0 1.0
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fix 1 iron precession/spin cubic 0.001 0.0005 1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 1.0
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fix 1 all precession/spin zeeman 0.1 0.0 0.0 1.0 anisotropy 0.001 0.0 0.0 1.0
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Description
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"""""""""""
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This fix applies a precession torque to each magnetic spin in the
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group.
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Style *zeeman* is used for the simulation of the interaction between
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the magnetic spins in the defined group and an external magnetic
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field:
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.. math::
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H_{Zeeman} = -g \sum_{i=0}^{N}\mu_{i}\, \vec{s}_{i} \cdot\vec{B}_{ext}
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with:
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* :math:`\vec{B}_{ext}` the external magnetic field (in T)
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* :math:`g` the Lande factor (hard-coded as :math:`g=2.0`)
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* :math:`\vec{s}_i` the unitary vector describing the orientation of spin :math:`i`
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* :math:`\mu_i` the atomic moment of spin :math:`i` given as a multiple of the
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Bohr magneton :math:`\mu_B` (for example, :math:`\mu_i \approx 2.2` in bulk iron).
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The field value in Tesla is multiplied by the gyromagnetic
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ratio, :math:`g \cdot \mu_B/\hbar`, converting it into a precession frequency in
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rad.THz (in metal units and with :math:`\mu_B = 5.788\cdot 10^{-5}`
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eV/T).
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As a comparison, the figure below displays the simulation of a single
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spin (of norm :math:`\mu_i = 1.0`) submitted to an external magnetic
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field of :math:`\vert B_{ext}\vert = 10.0\; \mathrm{Tesla}` (and
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oriented along the z axis). The upper plot shows the average
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magnetization along the external magnetic field axis and the lower
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plot the Zeeman energy, both as a function of temperature. The
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reference result is provided by the plot of the Langevin function for
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the same parameters.
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.. image:: JPG/zeeman_langevin.jpg
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:align: center
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:width: 600
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The temperature effects are accounted for by connecting the spin
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:math:`i` to a thermal bath using a Langevin thermostat (see
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:doc:`fix langevin/spin <fix_langevin_spin>` for the definition of
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this thermostat).
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Style *anisotropy* is used to simulate an easy axis or an easy plane
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for the magnetic spins in the defined group:
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.. math::
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H_{aniso} = -\sum_{{ i}=1}^{N} K_{an}(\mathbf{r}_{i})\, \left(
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\vec{s}_{i} \cdot \vec{n}_{i} \right)^2
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with :math:`n` defining the direction of the anisotropy, and :math:`K`
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(in eV) its intensity. If :math:`K > 0`, an easy axis is defined, and
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if :math:`K < 0`, an easy plane is defined.
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Style *cubic* is used to simulate a cubic anisotropy, with three
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possible easy axis for the magnetic spins in the defined group:
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.. math::
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H_{cubic} = -\sum_{{ i}=1}^{N} K_{1}
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\Big[
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\left(\vec{s}_{i} \cdot \vec{n}_1 \right)^2
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\left(\vec{s}_{i} \cdot \vec{n}_2 \right)^2 +
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\left(\vec{s}_{i} \cdot \vec{n}_2 \right)^2
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\left(\vec{s}_{i} \cdot \vec{n}_3 \right)^2 +
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\left(\vec{s}_{i} \cdot \vec{n}_1 \right)^2
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\left(\vec{s}_{i} \cdot \vec{n}_3 \right)^2 \Big]
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+K_{2}^{(c)} \left(\vec{s}_{i} \cdot \vec{n}_1 \right)^2
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\left(\vec{s}_{i} \cdot \vec{n}_2 \right)^2
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\left(\vec{s}_{i} \cdot \vec{n}_3 \right)^2
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with :math:`K_1` and :math:`K_{2c}` (in eV) the intensity coefficients
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and :math:`\vec{n}_1`, :math:`\vec{n}_2` and :math:`\vec{n}_3`
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defining the three anisotropic directions defined by the command (from
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*n1x* to *n3z*). For :math:`\vec{n}_1 = (1 0 0)`, :math:`\vec{n}_2 =
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(0 1 0)`, and :math:`\vec{n}_3 = (0 0 1)`, :math:`K_1 < 0` defines an
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iron type anisotropy (easy axis along the :math:`(0 0 1)`-type cube
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edges), and :math:`K_1 > 0` defines a nickel type anisotropy (easy
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axis along the :math:`(1 1 1)`-type cube diagonals). :math:`K_2^c >
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0` also defines easy axis along the :math:`(1 1 1)`-type cube
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diagonals. See chapter 2 of :ref:`(Skomski) <Skomski1>` for more
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details on cubic anisotropies.
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Style *stt* is used to simulate the interaction between the spins and
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a spin-transfer torque.
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See equation (7) of :ref:`(Chirac) <Chirac1>` for more details about the
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implemented spin-transfer torque term.
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In all cases, the choice of :math:`(x y z)` only imposes the vector
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directions for the forces. Only the direction of the vector is
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important; its length is ignored (the entered vectors are
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normalized).
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Those styles can be combined within one single command line.
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.. note::
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The norm of all vectors defined with the precession/spin command
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have to be non-zero. For example, defining
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"fix 1 all precession/spin zeeman 0.1 0.0 0.0 0.0" would result
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in an error message.
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Since those vector components are used to compute the inverse of the
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field (or anisotropy) vector norm, setting a zero-vector would result
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in a division by zero.
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----------
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Restart, fix_modify, output, run start/stop, minimize info
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"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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No information about this fix is written to :doc:`binary restart files
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<restart>`.
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The :doc:`fix_modify <fix_modify>` *energy* option is supported by
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this fix to add the energy associated with the spin precession
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torque to the global potential energy of the system as part of
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:doc:`thermodynamic output <thermo_style>`. The default setting for
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this fix is :doc:`fix_modify energy no <fix_modify>`.
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This fix computes a global scalar which can be accessed by various
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:doc:`output commands <Howto_output>`. The scalar is the potential
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energy (in energy units) discussed in the previous paragraph. The
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scalar value is an "extensive" quantity.
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No information about this fix is written to :doc:`binary restart files
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<restart>`.
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Restrictions
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""""""""""""
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The *precession/spin* style is part of the SPIN package. This style
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is 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
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<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>`
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Default
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"""""""
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none
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----------
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.. _Skomski1:
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**(Skomski)** Skomski, R. (2008). Simple models of magnetism.
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Oxford University Press.
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.. _Chirac1:
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**(Chirac)** Chirac, Theophile, et al. Ultrafast antiferromagnetic
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switching in NiO induced by spin transfer torques.
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Physical Review B 102.13 (2020): 134415.
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