poltype_rixs = [('linear', 0, 'linear', 0),
('linear', 0, 'linear', np.pi / 2.0)] # for RIXS
# Energy grid
ominc_xas = np.linspace(off - 10, off + 20, 1000) # for XAS
ominc_rixs_L3 = np.linspace(-5.9 + off, -0.9 + off,
100) # incident energy at L3 edge
ominc_rixs_L2 = np.linspace(10.4 + off, 14.9 + off,
100) # incident energy at L3 edge
eloss = np.linspace(-0.5, 5.0, 1000) # energy loss for RIXS
# Run ED
eval_i, eval_n, trans_op = edrixs.ed_1v1c_py(('d', 'p'),
shell_level=(0.0, -off),
v_soc=(zeta_d_i, zeta_d_n),
c_soc=zeta_p_n,
v_noccu=noccu,
slater=slater,
v_cfmat=cf)
# Run XAS
xas = edrixs.xas_1v1c_py(eval_i,
eval_n,
trans_op,
ominc_xas,
gamma_c=gamma_c,
thin=thin,
phi=phi,
pol_type=poltype_xas,
gs_list=[0, 1, 2],
temperature=300)
gs_list = range(0, 2)
poltype_rixs = [('linear', 0.0, 'linear', 0.0),
('linear', 0.0, 'linear', np.pi / 2.0),
('linear', np.pi / 2.0, 'linear', 0.0),
('linear', np.pi / 2.0, 'linear', np.pi / 2.0)]
rixs = np.zeros((len(ominc), len(eloss), len(poltype_rixs), natom),
dtype=np.float)
# Loop over all the atoms
for iatom in range(natom):
print()
print("edrixs >>> atom: ", iatom)
c_name = edrixs.edge_to_shell_name('L3')
eval_i, eval_n, trans_op = edrixs.ed_1v1c_py(('t2g', c_name),
v_soc=(zeta_d, zeta_d),
v_noccu=noccu,
v_cfmat=cf,
slater=slater,
loc_axis=loc_axis[iatom])
rixs[:, :, :,
iatom] = edrixs.rixs_1v1c_py(eval_i,
eval_n,
trans_op,
ominc,
eloss,
gamma_c=gamma_c,
gamma_f=gamma_f,
thin=thin,
thout=thout,
phi=phi,
pol_type=poltype_rixs,
def do_ed(dq10=1.6, d1=0.1, d3=0.75, ex_x=0., ex_y=0., ex_z=0.):
"""
Diagonalize Hamiltonian for Ni 3d8 system in tetragonal crytals field and
applied exchange field.
Parameters
----------
dq10: float
Cubic crystal field parameter (eV)
Cubic splitting
dq1: float
Cubic crystal field parameter (eV)
t2g splitting
dq3: float
Cubic crystal field parameter (eV)
eg splitting
ex_x: float
Magnitude of the magnetic exchange field in the x direction (eV)
ex_y: float
Magnitude of the magnetic exchange field in the y direction (eV)
ex_z: float
Magnitude of the magnetic exchange field in the z direction (eV)
Returns
--------
eval_i: 1d array
Eigenvalues of initial state Hamiltonian
eval_n: 1d array
Eigenvalues of intermediate state Hamiltonian
dipole_op: 3d array
Dipole operator from 2p to 3d state
"""
# PARAMETERS:
# ------------
F2_dd, F4_dd = 12.234 * 0.65, 7.598 * 0.65
Ud_av = 0.0
F0_dd = Ud_av + edrixs.get_F0('d', F2_dd, F4_dd)
G1_dp, G3_dp = 5.787 * 0.7, 3.291 * 0.7
F2_dp = 7.721 * 0.95
Udp_av = 0.0
F0_dp = Udp_av + edrixs.get_F0('dp', G1_dp, G3_dp)
slater = (
[F0_dd, F2_dd, F4_dd], # Initial
[F0_dd, F2_dd, F4_dd, F0_dp, F2_dp, G1_dp, G3_dp] # Intermediate
)
zeta_d_i = 0.083
zeta_d_n = 0.102
zeta_p_n = 11.24
cf = edrixs.cf_tetragonal_d(dq10, d1, d3)
ext_B = np.array([ex_x, ex_y, ex_z])
result = edrixs.ed_1v1c_py(shell_name=('d', 'p'),
v_soc=(zeta_d_i, zeta_d_n),
c_soc=zeta_p_n,
v_noccu=8,
slater=slater,
ext_B=ext_B,
on_which='spin',
v_cfmat=cf)
return result
('L2', 'd', 12385 + 5),
('L3', 'd', 10871 + 5), # Keep all the 5d orbitals
('L2', 't2g', 12385 + 5),
('L3', 't2g', 10871 + 5) # Keep only t2g orbitals
]
for case, v_name, om_shift in transition:
# Run ED
c_name = edrixs.edge_to_shell_name(case)
print("edrixs >>> ", c_name, " to ", v_name)
if v_name == 'd':
eloss = np.linspace(-0.5, 5.5, 1000)
result = edrixs.ed_1v1c_py(
shell_name=(v_name, c_name),
v_soc=(zeta_d_i, zeta_d_n),
v_noccu=noccu,
slater=slater,
v_cfmat=cf # add CF
)
else:
eloss = np.linspace(-0.5, 2, 1000)
result = edrixs.ed_1v1c_py(
shell_name=(v_name, c_name),
v_soc=(zeta_d_i, zeta_d_n),
v_noccu=noccu,
slater=slater # NO CF
)
eval_i, eval_n, trans_op = result
# Run RIXS
rixs = edrixs.rixs_1v1c_py(eval_i,
################################################################################
# Diagonalization
# ------------------------------------------------------------------------------
# We obtain the ground and intermediate state eigenenergies and the transition
# operators via matrix diagonalization. Note that the calculation does not know
# the core hole energy, so we need to adjust the energy that the resonance will
# appear at by hand. We know empirically that the resonance is at 11215 eV
# and that putting four electrons into the valance band costs about
# :math:`4 F^0_d\approx6` eV. In this case
# we are assuming a perfectly cubic crystal field, which we have already
# implemented when we specified the use of the :math:`t_{2g}` subshell only
# so we do not need to pass an additional :code:`v_cfmat` matrix.
off = 11215 - 6
out = edrixs.ed_1v1c_py(shell_name, shell_level=(0, -off), v_soc=v_soc,
c_soc=info['c_soc'], v_noccu=v_noccu, slater=slater)
eval_i, eval_n, trans_op = out
################################################################################
# Compute XAS
# ------------------------------------------------------------------------------
# To calculate XAS we need to correctly specify the orientation of the x-rays
# with respect to the sample. By default, the :math:`x, y, z` coordinates
# of the sample's crystal field, will be aligned with our lab frame, passing
# :code:`loc_axis` to :code:`ed_1v1c_py` can be used to specify a different
# convention. The experimental geometry is specified following the angles
# shown in Figure 1 of Y. Wang et al.,
# `Computer Physics Communications 243, 151-165 (2019)
# <https://doi.org/10.1016/j.cpc.2019.04.018>`_. The default
# setting has x-rays along :math:`z` for :math:`\theta=\pi` rad
# and the x-ray beam along :math:`-x` for
# L3-edge
gamma_c, gamma_f = 0.275, 0.1
ominc_rixs = np.linspace(-5.9 + off, -0.9 + off, 100)
# L2-edge
# gamma_c, gamma_f = 0.7, 0.1
# ominc_rixs = np.linspace(10.9 + off, 14.9 + off, 100)
eloss = np.linspace(-0.5, 5.0, 1000)
poltype_rixs = [('linear', 0, 'linear', 0),
('linear', 0, 'linear', np.pi / 2.0),
('linear', np.pi / 2.0, 'linear', 0.0),
('linear', np.pi / 2.0, 'linear', np.pi / 2.0)]
# Run ED
eval_i, eval_n, trans_op = edrixs.ed_1v1c_py(shell_name=('d', 'p'),
shell_level=(0, -off),
v_soc=(zeta_d_i, zeta_d_n),
c_soc=zeta_p_n,
v_noccu=8,
slater=slater,
v_cfmat=cf,
verbose=1)
# Run XAS
xas = edrixs.xas_1v1c_py(eval_i,
eval_n,
trans_op,
ominc_xas,
gamma_c=gamma_c,
thin=thin,
phi=phi,
pol_type=poltype_xas,
gs_list=[0, 1, 2],
temperature=300)
gamma_c[i] = 1.05 / 2.0 + step * (i - last_one)
else:
gamma_c[i] = 6.5 / 2.0
poltype_xas = [('isotropic', 0.0)]
poltype_rixs = [('linear', 0.0, 'linear', 0.0),
('linear', 0.0, 'linear', np.pi / 2.0),
('linear', np.pi / 2.0, 'linear', 0.0),
('linear', np.pi / 2.0, 'linear', np.pi / 2.0)]
# END of Parameters
# ------------------
# Run ED
eval_i, eval_n, trans_op = edrixs.ed_1v1c_py(('f', 'd'),
shell_level=(0, -om_shift),
v_soc=(zeta_f_i, zeta_f_n),
c_soc=zeta_d_n,
v_noccu=noccu,
slater=slater)
# Run XAS
xas = edrixs.xas_1v1c_py(eval_i,
eval_n,
trans_op,
ominc,
gamma_c=gamma_c,
thin=thin,
phi=phi,
pol_type=poltype_xas,
gs_list=gs_list,
temperature=300)
