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44 lines
3.9 KiB
ReStructuredText
.. _soc:
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Spin-orbit coupled calculations (single-shot)
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=============================================
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There are two main ways of including the spin-orbit coupling (SOC) term into
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DFT+DMFT calculations:
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- by performing a DFT calculation including SOC and then doing a DMFT calculation on top, or
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- by performing a DFT calculation without SOC and then adding the SOC term on the model level.
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The second variant is a bit more involved and needs quite some expertise, so this guide will cover only the first variant with SOC included in the DFT calculations.
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Treatment of SOC in DFT
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-----------------------
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For now, TRIQS/DFTTools does only work with Wien2k when performing calculations with SO.
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The treatment of SOC in the VASP package is fundamentally different to the way Wien2k treats it, and the interface does not handle that at the moment.
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Therefore, this guide describes how to do an SOC calculation using the Wien2k DFT package.
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First, a Wien2k calculation including SOC has to be performed.
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For details, we refer the reader to the documentation of Wien2k. As a matter of fact, we need the output for the DFT band structure for both spin directions explicitly. That means that one needs to do a spin-polarised DFT calculation with SOC, but, however, with magnetic moment set to zero. In the Wien2k initialisation procedure, one can choose for the option -nom when ``lstart`` is called. This means that the charge densities are initialised without magnetic splitting. The SOC calculation is then performed in a standard way as described in the Wien2k manual.
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Performing the projection
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~~~~~~~~~~~~~~~~~~~~~~~~~
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Note that the final ``x lapw2 -almd -so -up`` and ``x lapw2 -almd -so -dn`` have to be run *on a single core*, which implies that, before, ``x lapw2 -up``, ``x lapw2 -dn``, and ``x lapwso -up`` have to be run in single-core mode (at least once).
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In the ``case.indmftpr`` file, the spin-orbit flag has to be set to ``1`` for the correlated atoms.
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For example, for the compound Sr\ :sub:`2`\ MgOsO\ :sub:`6`, with the struct file :download:`Sr2MgOsO6.struct <Sr2MgOsO6/Sr2MgOsO6.struct>`, we would, e.g., use the ``indmftpr`` file :download:`found here <Sr2MgOsO6/Sr2MgOsO6_SOC.indmftpr>`.
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Then, ``dmftproj -sp -so`` has to be called.
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As usual, it is important to check for warnings (e.g., about eigenvalues of the overlap matrix) in the output of ``dmftproj`` and adapt the window until these warnings disappear.
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Note that in presence of SOC, it is not possible to project only onto the :math:`t_{2g}` subshell because it is not an irreducible representation.
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We strongly suggest using the :py:meth:`.dos_wannier_basis` functionality of the :py:class:`.SumkDFTTools` class (see :download:`calculate_dos_wannier_basis.py <Sr2RuO4/calculate_dos_wannier_basis.py>`) and compare the Wannier-projected orbitals to the original DFT DOS (they should be more or less equal).
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Note that, with SOC, there are usually off-diagonal elements of the spectral function, which can also be imaginary.
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The imaginary part can be found in the third column of the files ``DOS_wann_...``.
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After the projection, one can proceed with the DMFT calculation. However, two things need to be noted here. First, since the spin is not a good quantum number any more, there are off-diagonal elements in the hybridisation function and the local Hamiltonian coupling the two spin directions. This will eventually lead to a fermonic sign problem when QMC is used as a impurity solver. Second, although the :math:`e_{g}` subshell needs to be included in the projection, it can in many cases be neglected in the solution of the Anderson impurity model, after a transformation to a rotated local basis is done. This basis, diagonalising the local Hamiltonian in the presence of SOC, is often called the numerical j-basis. How rotations are performed is described in :ref:`basisrotation`, and the cutting of the orbitals in :ref:`blockstructure`.
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A DMFT calculation including SOC for Sr2MgOsO6 is included in the :ref:`tutorials`.
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