def rixs(eval_i, eval_n, T_abs, T_emi):
gs = list(range(0, 3))
prob = edrixs.boltz_dist([eval_i[i] for i in gs], 300)
off = 857.4
phi, thin, thout = 0, 15 / 180.0 * np.pi, 75 / 180.0 * np.pi
Gam_c, Gam = 0.2, 0.1 # core-hole life-time and RIXS resolution
pol = [(0, 0), (0, np.pi / 2.0)] # pi-pi and pi-sigma polarization
omega = np.linspace(-5.9, -0.9, 100)
eloss = np.linspace(-0.5, 5.0, 1000)
rixs = np.zeros((len(pol), len(eloss), len(omega)), dtype=np.float)
# Calculate RIXS
for i, om in enumerate(omega):
F_fi = edrixs.scattering_mat(eval_i, eval_n, T_abs[:, :, gs], T_emi,
om, Gam_c)
for j, (alpha, beta) in enumerate(pol):
ei, ef = edrixs.dipole_polvec_rixs(thin, thout, phi, alpha, beta)
F_mag = np.zeros((len(eval_i), len(gs)), dtype=np.complex)
for m in range(3):
for n in range(3):
F_mag[:, :] += ef[m] * F_fi[m, n] * ei[n]
for m in gs:
for n in range(len(eval_i)):
rixs[j, :, i] += (prob[m] * np.abs(F_mag[n, m])**2 * Gam /
np.pi /
((eloss -
(eval_i[n] - eval_i[m]))**2 + Gam**2))
# plot RIXS map
plt.figure()
ax = plt.subplot(1, 1, 1)
a, b, c, d = min(omega) + off, max(omega) + off, min(eloss), max(eloss)
plt.imshow(rixs[0] + rixs[1],
extent=[a, b, c, d],
origin='lower',
aspect='auto',
cmap='rainbow',
interpolation='bicubic')
ax.xaxis.set_major_locator(MultipleLocator(1))
ax.xaxis.set_minor_locator(MultipleLocator(0.5))
ax.yaxis.set_major_locator(MultipleLocator(1))
ax.yaxis.set_minor_locator(MultipleLocator(0.5))
plt.xlabel(r'Energy of incident photon (eV)')
plt.ylabel(r'Energy loss (eV)')
plt.text(851.6, 4.5, r'(b)', fontsize=25)
plt.subplots_adjust(left=0.1,
right=0.95,
bottom=0.13,
top=0.95,
wspace=0.05,
hspace=0.00)
plt.savefig("rixs_map_ni.pdf")
def get_transop(loc, pos):
# get dipole transition operator in local axis
dop = edrixs.get_trans_oper('t2gp32')
dop_g = np.zeros((2, 3, 6, 4), dtype=np.complex)
# transform to golobal axis
for i in range(2):
for j in range(3):
for k in range(3):
dop_g[i, j] += loc[i, j, k] * dop[k]
# RIXS settings
thin, thout, phi = 30 / 180.0 * np.pi, 60 / 180.0 * np.pi, 0.0
ein, eout = 11215.0, 11215.0 # eV
# Wavevector
kin, kout = edrixs.get_wavevector_rixs(thin, thout, phi, ein, eout)
# polarization pi-pi and pi-sigma
for key, alpha, beta in [('pp', 0, 0), ('ps', 0, np.pi / 2.0)]:
ei, ef = edrixs.dipole_polvec_rixs(thin, thout, phi, alpha, beta)
T_i = np.zeros((2, 6, 4), dtype=np.complex)
T_f = np.zeros((2, 4, 6), dtype=np.complex)
for i in range(2):
for j in range(3):
T_i[i] += dop_g[i, j] * ei[j]
T_f[i] += np.conj(np.transpose(dop_g[i, j] * ef[j]))
# multiply phase factor
T_i[i] = T_i[i] * np.exp(+1j * np.dot(pos[i], kin))
T_f[i] = T_f[i] * np.exp(-1j * np.dot(pos[i], kout))
transop_rixs_i = np.zeros((20, 20), dtype=np.complex)
transop_rixs_f = np.zeros((20, 20), dtype=np.complex)
for i in range(2):
off1, off2 = i * 6, 12 + i * 4
transop_rixs_i[off1:off1 + 6, off2:off2 + 4] = T_i[i]
transop_rixs_f[off2:off2 + 4, off1:off1 + 6] = T_f[i]
# write to file
edrixs.write_emat(transop_rixs_i, "rixs_" + key + "/transop_rixs_i.in")
edrixs.write_emat(transop_rixs_f, "rixs_" + key + "/transop_rixs_f.in")
# For XAS, use isotropic polarization
ei = np.array([1, 1, 1]) / np.sqrt(3.0)
T_i = np.zeros((2, 6, 4), dtype=np.complex)
for i in range(2):
for j in range(3):
T_i[i] += dop_g[i, j] * ei[j]
transop_xas = np.zeros((20, 20), dtype=np.complex128)
for i in range(2):
off1, off2 = i * 6, 12 + i * 4
transop_xas[off1:off1 + 6, off2:off2 + 4] = T_i[i]
edrixs.write_emat(transop_xas, "xas/transop_xas.in")
def get_transop(loc, pos):
dop = edrixs.get_trans_oper('t2gp')
dop_g = np.zeros((2, 3, 6, 6), dtype=np.complex)
for i in range(2):
dop_g[i, 0] = loc[i, 0, 0] * dop[0] + loc[i, 0, 1] * dop[1] + loc[
i, 0, 2] * dop[2]
dop_g[i, 1] = loc[i, 1, 0] * dop[0] + loc[i, 1, 1] * dop[1] + loc[
i, 1, 2] * dop[2]
dop_g[i, 2] = loc[i, 2, 0] * dop[0] + loc[i, 2, 1] * dop[1] + loc[
i, 2, 2] * dop[2]
# for RIXS
thin, thout, phi = 30 / 180.0 * np.pi, 60 / 180.0 * np.pi, 0.0
ein, eout = 11215.0, 11215.0 # eV
kin, kout = edrixs.get_wavevector_rixs(thin, thout, phi, ein, eout)
# polarization pi-pi and pi-sigma
for key, alpha, beta in [('pp', 0, 0), ('ps', 0, np.pi)]:
ei, ef = edrixs.dipole_polvec_rixs(thin, thout, phi, alpha, beta)
T_i = np.zeros((2, 6, 6), dtype=np.complex)
T_o = np.zeros((2, 6, 6), dtype=np.complex)
for i in range(2):
T_i[i] = (dop_g[i, 0] * ei[0] + dop_g[i, 1] * ei[1] +
dop_g[i, 2] * ei[2]) * np.exp(1j * np.dot(pos[i], kin))
T_o[i] = np.exp(-1j * np.dot(pos[i], kout)) * np.conj(
np.transpose(dop_g[i, 0] * ef[0] + dop_g[i, 1] * ef[1] +
dop_g[i, 2] * ef[2]))
transop_rixs_i = np.zeros((24, 24), dtype=np.complex)
transop_rixs_f = np.zeros((24, 24), dtype=np.complex)
for i in range(2):
off1, off2 = i * 6, 12 + i * 6
transop_rixs_i[off1:off1 + 6, off2:off2 + 6] = T_i[i]
transop_rixs_f[off2:off2 + 6, off1:off1 + 6] = T_o[i]
edrixs.write_emat(transop_rixs_i, "rixs_" + key + "/transop_rixs_i.in")
edrixs.write_emat(transop_rixs_f, "rixs_" + key + "/transop_rixs_f.in")
# For XAS
ei = np.array([1, 1, 1]) / np.sqrt(3.0)
T_i = np.zeros((2, 6, 6), dtype=np.complex)
for i in range(2):
T_i[i] = dop_g[i, 0] * ei[0] + dop_g[i, 1] * ei[1] + dop_g[i,
2] * ei[2]
transop_xas = np.zeros((24, 24), dtype=np.complex128)
for i in range(2):
off1, off2 = i * 6, 12 + i * 6
transop_xas[off1:off1 + 6, off2:off2 + 6] = T_i[i]
edrixs.write_emat(transop_xas, "xas/transop_xas.in")
def get_transop():
tmp = edrixs.get_trans_oper('t2gp')
dipole = np.zeros((3, 28, 28), dtype=np.complex)
for i in range(3):
tmp[i] = edrixs.cb_op2(tmp[i], edrixs.tmat_c2j(1), edrixs.tmat_c2j(1))
dipole[i, 0:6, 24:28] = tmp[i, 0:6, 2:6]
# for RIXS
thin, thout, phi = 45 / 180.0 * np.pi, 45 / 180.0 * np.pi, 0.0
# polarization pi-pi and pi-sigma
for key, alpha, beta in [('pp', 0, 0), ('ps', 0, np.pi)]:
ei, ef = edrixs.dipole_polvec_rixs(thin, thout, phi, alpha, beta)
transop_rixs_i = dipole[0] * ei[0] + dipole[1] * ei[1] + dipole[
2] * ei[2]
transop_rixs_f = np.conj(
np.transpose(dipole[0] * ef[0] + dipole[1] * ef[1] +
dipole[2] * ef[2]))
edrixs.write_emat(transop_rixs_i, "rixs_" + key + "/transop_rixs_i.in")
edrixs.write_emat(transop_rixs_f, "rixs_" + key + "/transop_rixs_f.in")
# For XAS
ei = np.array([1, 1, 1]) / np.sqrt(3.0)
transop_xas = dipole[0] * ei[0] + dipole[1] * ei[1] + dipole[2] * ei[2]
edrixs.write_emat(transop_xas, "xas/transop_xas.in")
for omi_ind, omi in enumerate(omi_mesh):
print(omi_ind, omi, omi + omi_shift)
Ffg_Ir = np.zeros((2, 3, 3, ncfgs_gs, len(gs_list)),
dtype=np.complex128)
for i in range(0, 2):
abs_trans = copy.deepcopy(trans_mat_abs[i])
emi_trans = copy.deepcopy(trans_mat_emi[i])
Ffg_Ir[i] = edrixs.scattering_mat(eval_gs, eval_ex[i],
abs_trans[:, :, gs_list],
emi_trans, omi, gamma_c)
print('------------------------')
for ipol, (alpha, beta) in enumerate(pol_vec):
ein, eout = omi + omi_shift, omi + omi_shift
ei, ef = edrixs.dipole_polvec_rixs(thin,
thout,
phi,
alpha,
beta,
local_axis=np.eye(3))
kin, kout = edrixs.get_wavevector_rixs(thin,
thout,
phi,
ein,
eout,
local_axis=np.eye(3))
Q = kout - kin
phase_Ir = np.zeros(2, dtype=np.complex128)
for i in range(0, 2):
phase_Ir[i] = np.exp(-1j * np.dot(Q, Ir_pos[i]))
Ffg = np.zeros((ncfgs_gs, len(gs_list)), dtype=np.complex128)
for i in range(0, 2):
for j in range(3):