def multi_phase_PM_func(self, n_concentration, magnetic_field, temperature, zero_index=None):
# calc Brillouin function for multi-phase sample
num = len(self.dict_of_magnetic_phases)
len_of_x = len(magnetic_field)
# vector for magnetic calculation:
vec_x = np.zeros(len_of_x)
#concentration of Mn atoms n[1/m^3*1e27]
out = np.zeros(len_of_x)
for i in self.dict_of_magnetic_phases:
val = self.dict_of_magnetic_phases[i]
n = n_concentration[i]
J = val['data'].J_total_momentum
g = val['data'].g_factor
Mn_type = val['data'].Mn_type
spin_type = val['data'].spin_type_cfg
tmp = np.zeros(len_of_x)
# create unique x-vector for Brillouin function:
vec_x = (g * J * mu_Bohr * magnetic_field) \
/ k_b / temperature
# tmp = f_PM(x=vec_x, n=n, J=J, g_factor=g)
tmp = f_PM_with_T(B=magnetic_field, n=n, J=J, T=temperature, g_factor=g)
# fight with uncertainty in 0 vicinity:
if zero_index is not None:
tmp[zero_index] = 0
out += tmp
return out
def subtract_PM_after_calc_diff_PM(self):
if not (self.n_diffPM == 0):
B = self.struct_of_data[self.diff_PM_keyName1].xx
M = self.struct_of_data[self.diff_PM_keyName1].yy
T = self.struct_of_data[self.diff_PM_keyName1].T
J = 2.5
M_sub_PM = M - f_PM_with_T(B=B, n=self.n_diffPM, J=J, T=T)
self.ax.cla()
print('->> sub PM after diff PM have been done. For m(T={0}K) - m(T={1}K) obtained n = {2:1.3g} *1e27 [1/m^3] or {3:1.3g} % of the n(GaAs)'\
.format(self.diff_PM_keyName1, self.diff_PM_keyName2, self.n_diffPM, self.n_diffPM/22.139136*100))
# setup variables for plot:
self.suptitle_txt = 'case: {}, '.format(self.selectCase) + '$Ga_{1-x}Mn_xAs$,' \
+ ' where $x = {0:1.2g}\%$ '.format(self.how_many_Mn_in_percent)
self.ylabel_txt = '$M\,(A/m)$'
self.xlabel_txt = '$B\,(T)$'
self.setupAxes()
self.ax.plot(B, f_PM_with_T(B=B, n=self.n_diffPM, J=J, T=T), 'r-',
label='PM component $\left(T={0:1.2g}K \\right)$, '.format(T) +\
'$n_{{PM}}={:1.3g}\%$,'.format(self.n_diffPM / 22.139136 * 100) + \
'\n$n_{{[PM,\;x={0:1.3g}\%]}}={1:1.3g}\%$'.format(self.how_many_Mn_in_percent,
self.n_diffPM / 22.139136 * 100/self.how_many_Mn_in_percent*100) + \
' $J={:1.2g}(Mn^{{2+}})$'.format(J/2.5)
)
self.ax.scatter(B,
M,
label='raw $\left(T={0:1.2g}K \\right)$'.format(T),
alpha=.2,
color='g')
self.ax.scatter(B,
M_sub_PM,
label='$M_{raw}-M_{PM}$' +
' $\left(T={0:1.2g}K \\right)$'.format(T),
color='k',
alpha=.2)
self.ax.legend(shadow=True, fancybox=True, loc='upper left')
self.ax.grid(True)
plt.draw()
plt.draw()
def fun_fit(B, n, j):
# return f_SPM_with_T(B, n, J=J, T=T)
return f_PM_with_T(B, n, J=j, T=T)
def calc_SPM_Langevin(self):
# fit data by using a Langevin function:
if self.n_diffPM <= 0:
self.calc_diff_PM()
T = self.struct_of_data[self.SPM_keyName].T
def fun_fit(B, n, j):
# return f_SPM_with_T(B, n, J=J, T=T)
return f_PM_with_T(B, n, J=j, T=T)
B = self.struct_of_data[self.SPM_keyName].xx
M = self.struct_of_data[self.SPM_keyName].yy
T = self.struct_of_data[self.SPM_keyName].T
J = 2.5
eps = 0.001 * abs(abs(B[0]) - abs(B[1]))
# reduce a noise:
Mp = M[(B > eps)]
Mn = M[(B < -eps)]
M_for_fit = np.copy(M)
# Find the intersection of two arrays to avoid conflict with numbers of elements.
# if abs(self.struct_of_data[self.SPM_keyName].Hmin) == self.struct_of_data[self.SPM_keyName].Hmax:
if len(M[(B > 0)]) != len(M[(B < 0)]):
# reduce a noise:
negVal = abs(np.min(B))
pozVal = np.max(B)
if pozVal >= negVal:
limitVal = negVal
else:
limitVal = pozVal
inx_B = np.logical_or((np.abs(B) <= limitVal + eps),
(np.abs(B) <= eps))
B = np.copy(B[inx_B])
M_for_fit = np.copy(M[inx_B])
Mp = M[np.where(B > eps)]
Mn = M[np.where(B < -eps)]
if len(M[np.where(B > 0)]) == len(M[np.where(B < 0)]):
inx_B = np.logical_or((np.abs(B) <= eps), (np.abs(B) >= eps))
B = np.copy(B[inx_B])
M_for_fit = np.copy(M[np.where(inx_B)])
# reduce a noise:
Mp = M[np.where(B > eps)]
Mn = M[np.where(B < -eps)]
M_for_fit[np.where(B > eps)] = 0.5 * (Mp + np.abs(Mn[::-1]))
M_for_fit[np.where(B < -eps)] = 0.5 * (Mn - np.abs(Mp[::-1]))
# M_for_fit[(B > 0)] = 0.5*(Mp + np.abs(Mn))
# M_for_fit[(B < 0)] = 0.5*(Mn - np.abs(Mp))
if self.SPM_field_region_for_fit[0, 0] >= B.max():
self.SPM_field_region_for_fit[0, 0] = np.fix(10 * B.max()) / 10 - \
5 * self.struct_of_data[self.SPM_keyName].Hstep
# sabtruct a PM magnetic phase which is low temperature independent:
M_for_fit = M_for_fit - f_PM_with_T(B, n=self.n_diffPM, J=J, T=T)
condlist1 = (self.SPM_field_region_for_fit[0, 0] <
B) & (self.SPM_field_region_for_fit[0, 1] > B)
initial_guess = [
0.01,
2,
]
# fit the data:
pres, pcov = curve_fit(fun_fit,
B[np.logical_or(condlist1, condlist1)],
M_for_fit[np.where(
np.logical_or(condlist1, condlist1))],
p0=initial_guess,
bounds=([
0,
0,
], [
np.inf,
np.inf,
]))
self.n_SPM = pres[0]
self.J_SPM = pres[1]
print('->> fit SPM have been done. For m(T={0}K) obtained n = {1:1.3g} *1e27 [1/m^3] or {2:1.3g} % of the n(GaAs)'\
.format(self.SPM_keyName, self.n_SPM, self.n_SPM/22.139136*100))
print('->> SPM magnetic phase has total momentum J = {0:1.3g} or {1:1.3g} numbers of J(Mn2+)'\
.format(self.J_SPM, self.J_SPM/2.5))
# setup variables for plot:
self.ax.cla()
self.suptitle_txt = 'case: {}, '.format(self.selectCase) + '$Ga_{1-x}Mn_xAs$,' \
+ ' where $x = {0:1.2g}\%$ '.format(self.how_many_Mn_in_percent)
self.ylabel_txt = '$M(T={0}K) (A/m)$'.format(T)
self.xlabel_txt = '$B (T)$'
self.setupAxes()
self.ax.scatter(
B[np.logical_or(condlist1, condlist1)],
M_for_fit[np.where(np.logical_or(condlist1, condlist1))],
label='region for $fit$',
facecolor='none',
alpha=.1,
s=200,
marker='s',
edgecolors='k',
)
self.ax.plot(B, fun_fit(B, self.n_SPM, self.J_SPM), 'r-',
label='$fit$, $n_{{SPM}}={0:1.3g}\%$, \n$J={1:1.3g}(Mn^{{2+}})$'.format(self.n_SPM/22.139136*100,
self.J_SPM/2.5)+\
', $n_{{[SPM,\;x={0:1.3g}\%]}}={1:1.3g}\%$'.format(self.how_many_Mn_in_percent,
self.n_SPM / 22.139136 * 100/self.how_many_Mn_in_percent*100)
)
self.ax.plot(B, f_PM_with_T(B, n=self.n_diffPM, J=J, T=T), 'b-',
label='$PM(T={2:1.2g}K)$, $n_{{PM}}={0:1.3g}\%$, \n$J={1:1.3g}(Mn^{{2+}})$'\
.format(self.n_diffPM/22.139136*100, 1, T, )+\
', $n_{{[PM,\;x={0:1.3g}\%]}}={1:1.3g}\%$'.format(self.how_many_Mn_in_percent,
self.n_diffPM / 22.139136 * 100/self.how_many_Mn_in_percent*100))
self.ax.scatter(B,
M[np.where(inx_B)],
label='$raw$',
alpha=.2,
color='g')
self.ax.scatter(
B,
M_for_fit,
label=
'set for $fit$, $\\frac{{\left(M_++M_-\\right)}}{{2}} - PM(T={0:1.2g}K)$'
.format(T),
color='k',
alpha=.2)
self.ax.plot(B,
10 * (M_for_fit - fun_fit(B, self.n_SPM, self.J_SPM)),
'k.',
label='residuals $10*(raw - fit)$')
self.ax.legend(shadow=True, fancybox=True, loc='upper left')
self.ax.grid(True)
plt.show()
plt.draw()
def subtract_Line(self):
# try to subtract BG line: y=kx+b, which may be correspond to anisotropy effect
# and then calculate FM phase concentration
if not (self.n_diffPM == 0):
B = self.struct_of_data[self.diff_PM_keyName1].xx
M = self.struct_of_data[self.diff_PM_keyName1].yy
T = self.struct_of_data[self.diff_PM_keyName1].T
J = 2.5
M_sub_PM = M - f_PM_with_T(B=B, n=self.n_diffPM, J=J, T=T)
condlist1 = (self.FM_field_region_for_fit[0, 0] <
B) & (self.FM_field_region_for_fit[0, 1] > B)
condlist2 = (self.FM_field_region_for_fit[1, 0] <
B) & (self.FM_field_region_for_fit[1, 1] > B)
inx_condlist = np.logical_or(condlist2, condlist2)
# fit the data:
par, pcov = curve_fit(
linearFunc,
B[np.logical_or(condlist2, condlist2)],
M_sub_PM[np.logical_or(condlist2, condlist2)],
)
k = par[0]
b = par[1]
M_sub_linear = M_sub_PM - (k * B)
# calc M-saturation and FM phase concentration:
M_FM_saturation = 0.5 * (abs(np.mean(M_sub_linear[condlist2])) +
abs(np.mean(M_sub_linear[condlist1])))
self.n_FM_phase = concentration_from_Ms(Ms=M_FM_saturation,
J=2.5) * (1e-27)
print('->> subtract_Line have been done.')
print(
'For Ms, which we take from m(T={0}K)-PM-k*B we obtained n = {1:1.3g} *1e27 [1/m^3] or {2:1.3g} % of the n(GaAs)' \
.format(self.diff_PM_keyName1, self.n_FM_phase, self.n_FM_phase / 22.139136 * 100))
self.ax.cla()
# setup variables for plot:
self.suptitle_txt = 'case: {}, '.format(self.selectCase) + '$Ga_{1-x}Mn_xAs$,' \
+ ' where $x = {0:1.2g}\%$ '.format(self.how_many_Mn_in_percent)
self.ylabel_txt = '$M\, (A/m)$'
self.xlabel_txt = '$B\, (T)$'
self.setupAxes()
self.ax.plot(B, f_PM_with_T(B=B, n=self.n_diffPM, J=J, T=T), 'r-',
label='PM component $\left(T={0:1.2g}K \\right)$, '.format(T) + \
'$n_{{PM}}={:1.3g}\%$,'.format(self.n_diffPM / 22.139136 * 100) + \
'\n$n_{{[PM,\;x={0:1.3g}\%]}}={1:1.3g}\%$'.format(self.how_many_Mn_in_percent,
self.n_diffPM / 22.139136 * 100/self.how_many_Mn_in_percent*100) + \
' $J={:1.2g}(Mn^{{2+}})$'.format(J / 2.5)
)
self.ax.plot(B, (k * B), 'b-', label='line')
self.ax.scatter(B, M, label='raw', alpha=.2, color='g')
self.ax.scatter(B,
M_sub_PM,
label='$M_{raw}-M_{PM}$' +
' $\left(T={0:1.2g}K \\right)$'.format(T),
color='k',
alpha=.2)
self.ax.scatter(B, M_sub_linear, label='$M_{PM}-(kx+b)$, '+\
'$n_{{FM}}={:1.3g}\%$,\n'.format(self.n_FM_phase / 22.139136 * 100) + \
'$n_{{[FM,\;x={0:1.3g}\%]}}={1:1.3g}\%$'.format(self.how_many_Mn_in_percent,
self.n_FM_phase / 22.139136 * 100/self.how_many_Mn_in_percent*100) + \
' $J={:1.2g}(Mn^{{2+}})$'.format(J / 2.5),
color='b', s=100,
alpha=.2)
self.ax.scatter(B[inx_condlist],
M_sub_PM[inx_condlist],
label='for $linear\,fit$ $M_{raw}-M_{PM}$' +
' $\left(T={0:1.2g}K \\right)$'.format(T),
color='k',
alpha=.2,
s=70)
self.ax.legend(shadow=True, fancybox=True, loc='upper left')
self.ax.grid(True)
plt.draw()