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< h1 > Source code for grogupy.magnetism< / h1 > < div class = "highlight" > < pre >
< span > < / span > < span class = "c1" > # Copyright (c) [2024] []< / span >
< span class = "c1" > #< / span >
< span class = "c1" > # Permission is hereby granted, free of charge, to any person obtaining a copy< / span >
< span class = "c1" > # of this software and associated documentation files (the " Software" ), to deal< / span >
< span class = "c1" > # in the Software without restriction, including without limitation the rights< / span >
< span class = "c1" > # to use, copy, modify, merge, publish, distribute, sublicense, and/or sell< / span >
< span class = "c1" > # copies of the Software, and to permit persons to whom the Software is< / span >
< span class = "c1" > # furnished to do so, subject to the following conditions:< / span >
< span class = "c1" > #< / span >
< span class = "c1" > # The above copyright notice and this permission notice shall be included in all< / span >
< span class = "c1" > # copies or substantial portions of the Software.< / span >
< span class = "c1" > #< / span >
< span class = "c1" > # THE SOFTWARE IS PROVIDED " AS IS" , WITHOUT WARRANTY OF ANY KIND, EXPRESS OR< / span >
< span class = "c1" > # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,< / span >
< span class = "c1" > # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE< / span >
< span class = "c1" > # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER< / span >
< span class = "c1" > # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,< / span >
< span class = "c1" > # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE< / span >
< span class = "c1" > # SOFTWARE.< / span >
< span class = "sd" > " " " Docstring in magnetism.< / span >
< span class = "sd" > " " " < / span >
< span class = "kn" > import< / span > < span class = "nn" > numpy< / span > < span class = "k" > as< / span > < span class = "nn" > np< / span >
< div class = "viewcode-block" id = "blow_up_orbindx" >
< a class = "viewcode-back" href = "../../implementation/grogupy.html#grogupy.magnetism.blow_up_orbindx" > [docs]< / a >
< span class = "k" > def< / span > < span class = "nf" > blow_up_orbindx< / span > < span class = "p" > (< / span > < span class = "n" > orb_indices< / span > < span class = "p" > ):< / span >
< span class = "w" > < / span > < span class = "sd" > " " " Function to blow up orbital indices to make SPIN BOX indices.< / span >
< span class = "sd" > Args:< / span >
< span class = "sd" > orb_indices : np.array_like< / span >
< span class = "sd" > These are the indices in ORBITAL BOX< / span >
< span class = "sd" > Returns:< / span >
< span class = "sd" > orb_indices : np.array_like< / span >
< span class = "sd" > These are the indices in SPIN BOX< / span >
< span class = "sd" > " " " < / span >
< span class = "n" > orb_indices< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > array< / span > < span class = "p" > ([[< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > o< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "o" > *< / span > < span class = "n" > o< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "k" > for< / span > < span class = "n" > o< / span > < span class = "ow" > in< / span > < span class = "n" > orb_indices< / span > < span class = "p" > ])< / span > < span class = "o" > .< / span > < span class = "n" > flatten< / span > < span class = "p" > ()< / span >
< span class = "k" > return< / span > < span class = "n" > orb_indices< / span > < / div >
< div class = "viewcode-block" id = "spin_tracer" >
< a class = "viewcode-back" href = "../../implementation/grogupy.html#grogupy.magnetism.spin_tracer" > [docs]< / a >
< span class = "k" > def< / span > < span class = "nf" > spin_tracer< / span > < span class = "p" > (< / span > < span class = "n" > M< / span > < span class = "p" > ):< / span >
< span class = "w" > < / span > < span class = "sd" > " " " Spin tracer utility.< / span >
< span class = "sd" > This takes an operator with the orbital-spin sequence:< / span >
< span class = "sd" > orbital 1 up,< / span >
< span class = "sd" > orbital 1 down,< / span >
< span class = "sd" > orbital 2 up,< / span >
< span class = "sd" > orbital 2 down,< / span >
< span class = "sd" > that is in the SPIN-BOX representation,< / span >
< span class = "sd" > and extracts orbital dependent Pauli traces.< / span >
< span class = "sd" > Args:< / span >
< span class = "sd" > M : np.array_like< / span >
< span class = "sd" > Traceable matrix< / span >
< span class = "sd" > Returns:< / span >
< span class = "sd" > dict< / span >
< span class = "sd" > It contains the traced matrix with " x" , " y" , " z" and " c" < / span >
< span class = "sd" > " " " < / span >
< span class = "n" > M11< / span > < span class = "o" > =< / span > < span class = "n" > M< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ::< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ::< / span > < span class = "mi" > 2< / span > < span class = "p" > ]< / span >
< span class = "n" > M12< / span > < span class = "o" > =< / span > < span class = "n" > M< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ::< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ::< / span > < span class = "mi" > 2< / span > < span class = "p" > ]< / span >
< span class = "n" > M21< / span > < span class = "o" > =< / span > < span class = "n" > M< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ::< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ::< / span > < span class = "mi" > 2< / span > < span class = "p" > ]< / span >
< span class = "n" > M22< / span > < span class = "o" > =< / span > < span class = "n" > M< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ::< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ::< / span > < span class = "mi" > 2< / span > < span class = "p" > ]< / span >
< span class = "n" > M_o< / span > < span class = "o" > =< / span > < span class = "nb" > dict< / span > < span class = "p" > ()< / span >
< span class = "n" > M_o< / span > < span class = "p" > [< / span > < span class = "s2" > " x" < / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > M12< / span > < span class = "o" > +< / span > < span class = "n" > M21< / span >
< span class = "n" > M_o< / span > < span class = "p" > [< / span > < span class = "s2" > " y" < / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "mi" > 1< / span > < span class = "n" > j< / span > < span class = "o" > *< / span > < span class = "p" > (< / span > < span class = "n" > M12< / span > < span class = "o" > -< / span > < span class = "n" > M21< / span > < span class = "p" > )< / span >
< span class = "n" > M_o< / span > < span class = "p" > [< / span > < span class = "s2" > " z" < / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > M11< / span > < span class = "o" > -< / span > < span class = "n" > M22< / span >
< span class = "n" > M_o< / span > < span class = "p" > [< / span > < span class = "s2" > " c" < / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > M11< / span > < span class = "o" > +< / span > < span class = "n" > M22< / span >
< span class = "k" > return< / span > < span class = "n" > M_o< / span > < / div >
< div class = "viewcode-block" id = "parse_magnetic_entity" >
< a class = "viewcode-back" href = "../../implementation/grogupy.html#grogupy.magnetism.parse_magnetic_entity" > [docs]< / a >
< span class = "k" > def< / span > < span class = "nf" > parse_magnetic_entity< / span > < span class = "p" > (< / span > < span class = "n" > dh< / span > < span class = "p" > ,< / span > < span class = "n" > atom< / span > < span class = "o" > =< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span > < span class = "n" > l< / span > < span class = "o" > =< / span > < span class = "kc" > None< / span > < span class = "p" > ,< / span > < span class = "o" > **< / span > < span class = "n" > kwargs< / span > < span class = "p" > ):< / span >
< span class = "w" > < / span > < span class = "sd" > " " " Function to define orbital indexes of a given magnetic entity.< / span >
< span class = "sd" > Args:< / span >
< span class = "sd" > dh : sisl.physics.Hamiltonian< / span >
< span class = "sd" > Hamiltonian from sisl< / span >
< span class = "sd" > atom : integer or list of integers, optional< / span >
< span class = "sd" > Defining atom (or atoms) in the unit cell forming the magnetic entity. Defaults to None< / span >
< span class = "sd" > l : integer, optional< / span >
< span class = "sd" > Defining the angular momentum channel. Defaults to None< / span >
< span class = "sd" > Returns:< / span >
< span class = "sd" > list< / span >
< span class = "sd" > The orbital indexes of the given magnetic entity< / span >
< span class = "sd" > " " " < / span >
< span class = "c1" > # case where we deal with more than one atom defining the magnetic entity< / span >
< span class = "k" > if< / span > < span class = "nb" > type< / span > < span class = "p" > (< / span > < span class = "n" > atom< / span > < span class = "p" > )< / span > < span class = "o" > ==< / span > < span class = "nb" > list< / span > < span class = "p" > :< / span >
< span class = "n" > dat< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< span class = "k" > for< / span > < span class = "n" > a< / span > < span class = "ow" > in< / span > < span class = "n" > atom< / span > < span class = "p" > :< / span >
< span class = "n" > a_orb_idx< / span > < span class = "o" > =< / span > < span class = "n" > dh< / span > < span class = "o" > .< / span > < span class = "n" > geometry< / span > < span class = "o" > .< / span > < span class = "n" > a2o< / span > < span class = "p" > (< / span > < span class = "n" > a< / span > < span class = "p" > ,< / span > < span class = "nb" > all< / span > < span class = "o" > =< / span > < span class = "kc" > True< / span > < span class = "p" > )< / span >
< span class = "k" > if< / span > < span class = "p" > (< / span >
< span class = "nb" > type< / span > < span class = "p" > (< / span > < span class = "n" > l< / span > < span class = "p" > )< / span > < span class = "o" > ==< / span > < span class = "nb" > int< / span >
< span class = "p" > ):< / span > < span class = "c1" > # if specified we restrict to given l angular momentum channel inside each atom< / span >
< span class = "n" > a_orb_idx< / span > < span class = "o" > =< / span > < span class = "n" > a_orb_idx< / span > < span class = "p" > [[< / span > < span class = "n" > o< / span > < span class = "o" > .< / span > < span class = "n" > l< / span > < span class = "o" > ==< / span > < span class = "n" > l< / span > < span class = "k" > for< / span > < span class = "n" > o< / span > < span class = "ow" > in< / span > < span class = "n" > dh< / span > < span class = "o" > .< / span > < span class = "n" > geometry< / span > < span class = "o" > .< / span > < span class = "n" > atoms< / span > < span class = "p" > [< / span > < span class = "n" > a< / span > < span class = "p" > ]< / span > < span class = "o" > .< / span > < span class = "n" > orbitals< / span > < span class = "p" > ]]< / span >
< span class = "n" > dat< / span > < span class = "o" > .< / span > < span class = "n" > append< / span > < span class = "p" > (< / span > < span class = "n" > a_orb_idx< / span > < span class = "p" > )< / span >
< span class = "n" > orbital_indeces< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > hstack< / span > < span class = "p" > (< / span > < span class = "n" > dat< / span > < span class = "p" > )< / span >
< span class = "c1" > # case where we deal with a singel atom magnetic entity< / span >
< span class = "k" > elif< / span > < span class = "nb" > type< / span > < span class = "p" > (< / span > < span class = "n" > atom< / span > < span class = "p" > )< / span > < span class = "o" > ==< / span > < span class = "nb" > int< / span > < span class = "p" > :< / span >
< span class = "n" > orbital_indeces< / span > < span class = "o" > =< / span > < span class = "n" > dh< / span > < span class = "o" > .< / span > < span class = "n" > geometry< / span > < span class = "o" > .< / span > < span class = "n" > a2o< / span > < span class = "p" > (< / span > < span class = "n" > atom< / span > < span class = "p" > ,< / span > < span class = "nb" > all< / span > < span class = "o" > =< / span > < span class = "kc" > True< / span > < span class = "p" > )< / span >
< span class = "k" > if< / span > < span class = "p" > (< / span >
< span class = "nb" > type< / span > < span class = "p" > (< / span > < span class = "n" > l< / span > < span class = "p" > )< / span > < span class = "o" > ==< / span > < span class = "nb" > int< / span >
< span class = "p" > ):< / span > < span class = "c1" > # if specified we restrict to given l angular momentum channel< / span >
< span class = "n" > orbital_indeces< / span > < span class = "o" > =< / span > < span class = "n" > orbital_indeces< / span > < span class = "p" > [< / span >
< span class = "p" > [< / span > < span class = "n" > o< / span > < span class = "o" > .< / span > < span class = "n" > l< / span > < span class = "o" > ==< / span > < span class = "n" > l< / span > < span class = "k" > for< / span > < span class = "n" > o< / span > < span class = "ow" > in< / span > < span class = "n" > dh< / span > < span class = "o" > .< / span > < span class = "n" > geometry< / span > < span class = "o" > .< / span > < span class = "n" > atoms< / span > < span class = "p" > [< / span > < span class = "n" > atom< / span > < span class = "p" > ]< / span > < span class = "o" > .< / span > < span class = "n" > orbitals< / span > < span class = "p" > ]< / span >
< span class = "p" > ]< / span >
< span class = "k" > return< / span > < span class = "n" > orbital_indeces< / span > < span class = "c1" > # numpy array containing integers labeling orbitals associated to a magnetic entity.< / span > < / div >
< div class = "viewcode-block" id = "calculate_anisotropy_tensor" >
< a class = "viewcode-back" href = "../../implementation/grogupy.html#grogupy.magnetism.calculate_anisotropy_tensor" > [docs]< / a >
< span class = "k" > def< / span > < span class = "nf" > calculate_anisotropy_tensor< / span > < span class = "p" > (< / span > < span class = "n" > mag_ent< / span > < span class = "p" > ):< / span >
< span class = "w" > < / span > < span class = "sd" > " " " Calculates the renormalized anisotropy tensor from the energies.< / span >
< span class = "sd" > It uses the grogu convention for output.< / span >
< span class = "sd" > Args:< / span >
< span class = "sd" > mag_ent : dict< / span >
< span class = "sd" > An element from the magnetic entities< / span >
< span class = "sd" > Returns:< / span >
< span class = "sd" > K : np.array_like< / span >
< span class = "sd" > elements of the anisotropy tensor< / span >
< span class = "sd" > " " " < / span >
< span class = "c1" > # get the energies< / span >
< span class = "n" > energies< / span > < span class = "o" > =< / span > < span class = "n" > mag_ent< / span > < span class = "p" > [< / span > < span class = "s2" > " energies" < / span > < span class = "p" > ]< / span >
< span class = "c1" > # calculate the diagonal tensor elements< / span >
< span class = "n" > Kxx< / span > < span class = "o" > =< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "o" > -< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span >
< span class = "n" > Kyy< / span > < span class = "o" > =< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "o" > -< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span >
< span class = "n" > Kzz< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< span class = "c1" > # perform consistency check< / span >
< span class = "n" > calculated_diff< / span > < span class = "o" > =< / span > < span class = "n" > Kyy< / span > < span class = "o" > -< / span > < span class = "n" > Kxx< / span >
< span class = "n" > expected_diff< / span > < span class = "o" > =< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > -< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< span class = "n" > consistency_check< / span > < span class = "o" > =< / span > < span class = "nb" > abs< / span > < span class = "p" > (< / span > < span class = "n" > calculated_diff< / span > < span class = "o" > -< / span > < span class = "n" > expected_diff< / span > < span class = "p" > )< / span >
< span class = "k" > return< / span > < span class = "n" > Kxx< / span > < span class = "p" > ,< / span > < span class = "n" > Kyy< / span > < span class = "p" > ,< / span > < span class = "n" > Kzz< / span > < span class = "p" > ,< / span > < span class = "n" > consistency_check< / span > < / div >
< div class = "viewcode-block" id = "calculate_exchange_tensor" >
< a class = "viewcode-back" href = "../../implementation/grogupy.html#grogupy.magnetism.calculate_exchange_tensor" > [docs]< / a >
< span class = "k" > def< / span > < span class = "nf" > calculate_exchange_tensor< / span > < span class = "p" > (< / span > < span class = "n" > pair< / span > < span class = "p" > ):< / span >
< span class = "w" > < / span > < span class = "sd" > " " " Calculates the exchange tensor from the energies.< / span >
< span class = "sd" > It produces the isotropic exchange, the relevant elements< / span >
< span class = "sd" > from the Dzyaloshinskii-Morilla (Dm) tensor, the symmetric-anisotropy< / span >
< span class = "sd" > and the complete exchange tensor.< / span >
< span class = "sd" > Args:< / span >
< span class = "sd" > pair : dict< / span >
< span class = "sd" > An element from the pairs< / span >
< span class = "sd" > Returns:< / span >
< span class = "sd" > J_iso : float< / span >
< span class = "sd" > Isotropic exchange (Tr[J] / 3)< / span >
< span class = "sd" > J_S : np.array_like< / span >
< span class = "sd" > Symmetric-anisotropy (J_S = J - J_iso * I – – > Jxx, Jyy, Jxy, Jxz, Jyz)< / span >
< span class = "sd" > D : np.array_like< / span >
< span class = "sd" > DM elements (Dx, Dy, Dz)< / span >
< span class = "sd" > J : np.array_like< / span >
< span class = "sd" > Complete exchange tensor flattened (Jxx, Jxy, Jxz, Jyx, Jyy, Jyz, Jzx, Jzy, Jzz)< / span >
< span class = "sd" > " " " < / span >
< span class = "c1" > # energies from rotations< / span >
< span class = "n" > energies< / span > < span class = "o" > =< / span > < span class = "n" > pair< / span > < span class = "p" > [< / span > < span class = "s2" > " energies" < / span > < span class = "p" > ]< / span >
< span class = "c1" > # Initialize output arrays< / span >
< span class = "n" > J< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > zeros< / span > < span class = "p" > ((< / span > < span class = "mi" > 3< / span > < span class = "p" > ,< / span > < span class = "mi" > 3< / span > < span class = "p" > ))< / span >
< span class = "n" > D< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > zeros< / span > < span class = "p" > (< / span > < span class = "mi" > 3< / span > < span class = "p" > )< / span >
< span class = "c1" > # J matrix calculations< / span >
< span class = "c1" > # J(1,1) = mean([DEij(2,2,2), DEij(2,2,3)])< / span >
< span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > mean< / span > < span class = "p" > ([< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 3< / span > < span class = "p" > ],< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 3< / span > < span class = "p" > ]])< / span >
< span class = "c1" > # J(1,2) = -mean([DEij(1,2,3), DEij(2,1,3)])< / span >
< span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "o" > -< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > mean< / span > < span class = "p" > ([< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]])< / span >
< span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< span class = "c1" > # J(1,3) = -mean([DEij(1,2,2), DEij(2,1,2)])< / span >
< span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "o" > -< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > mean< / span > < span class = "p" > ([< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]])< / span >
< span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]< / span >
< span class = "c1" > # J(2,2) = mean([DEij(2,2,1), DEij(1,1,3)])< / span >
< span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > mean< / span > < span class = "p" > ([< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 3< / span > < span class = "p" > ],< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ]])< / span >
< span class = "c1" > # J(2,3) = -mean([DEij(1,2,1), DEij(2,1,1)])< / span >
< span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "o" > -< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > mean< / span > < span class = "p" > ([< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]])< / span >
< span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]< / span >
< span class = "c1" > # J(3,3) = mean([DEij(1,1,1), DEij(1,1,2)])< / span >
< span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > mean< / span > < span class = "p" > ([< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ],< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ]])< / span >
< span class = "c1" > # D vector calculations< / span >
< span class = "c1" > # D(1) = mean([DEij(1,2,1), -DEij(2,1,1)])< / span >
< span class = "n" > D< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > mean< / span > < span class = "p" > ([< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "o" > -< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]])< / span >
< span class = "c1" > # D(2) = mean([DEij(2,1,2), -DEij(1,2,2)])< / span >
< span class = "n" > D< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > mean< / span > < span class = "p" > ([< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ],< / span > < span class = "o" > -< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ]])< / span >
< span class = "c1" > # D(3) = mean([DEij(1,2,3), -DEij(2,1,3)])< / span >
< span class = "n" > D< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > mean< / span > < span class = "p" > ([< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "o" > -< / span > < span class = "n" > energies< / span > < span class = "p" > [< / span > < span class = "mi" > 2< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]])< / span >
< span class = "n" > J_iso< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > trace< / span > < span class = "p" > (< / span > < span class = "n" > J< / span > < span class = "p" > )< / span > < span class = "o" > /< / span > < span class = "mi" > 3< / span >
< span class = "c1" > # based on the grogu output pdf< / span >
< span class = "c1" > # traceless symmetric exchange matrix:< / span >
< span class = "c1" > # Jxx, Jyy, Jxy, Jxz, Jyz< / span >
< span class = "n" > J_S< / span > < span class = "o" > =< / span > < span class = "n" > np< / span > < span class = "o" > .< / span > < span class = "n" > array< / span > < span class = "p" > ([< / span > < span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 0< / span > < span class = "p" > ]< / span > < span class = "o" > -< / span > < span class = "n" > J_iso< / span > < span class = "p" > ,< / span > < span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span > < span class = "o" > -< / span > < span class = "n" > J_iso< / span > < span class = "p" > ,< / span > < span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span > < span class = "p" > ],< / span > < span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ],< / span > < span class = "n" > J< / span > < span class = "p" > [< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "mi" > 2< / span > < span class = "p" > ]])< / span >
< span class = "k" > return< / span > < span class = "n" > J_iso< / span > < span class = "p" > ,< / span > < span class = "n" > J_S< / span > < span class = "p" > ,< / span > < span class = "n" > D< / span > < span class = "p" > ,< / span > < span class = "n" > J< / span > < / div >
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