import numpy as np
import escape as esc
from escape.utils import show
import escape.utils.mdb as mdb
esc.require('0.9.3')

Interfacial roughness and proximity effects in superconductor/ferromagnet CuNi/Nb heterostructures

Yu. Khaydukov, R. Morari, O. Soltwedel, T. Keller, G. Christiani, G. Logvenov, M. Kupriyanov, A. Sidorenko, and B. Keimer

Citation: Journal of Applied Physics 118, 213905 (2015); doi: 10.1063/1.4936789 View online: http://dx.doi.org/10.1063/1.4936789

Here we present results of fitting of experimental data presented in the publication (see above). We have chosen data for two samples which CuNi layers differ in thickness and roughness, to present the capabilities of simultaneous fit with shared parameters. Instead of fitting of SLDs we are going to fit mass densities of layer compounds.

wlx = 1.540562

cap_density=esc.par("Cap Density", 2.32, userlim=[0.9, 2.4], units="g/cm^3")
cuni_density=esc.par("CuNi Density", 8.93, userlim=[8.5, 9.0], units="g/cm^3")
nb_density=esc.par("Nb Density", 8.57, userlim=[8.2, 8.9], units="g/cm^3")
sio2_density=esc.par("SiO2 Density", 2.62, userlim=[1.7, 2.82], units="g/cm^3")
si_density=esc.par("Si Density", 2.32, userlim=[2.2, 2.4], units="g/cm^3", fixed=True)

nb_thkn = esc.par("Nb Thkn", 10.0, units="nm", userlim=[9, 12])
cap_thkn=esc.par("Cap Thkn", 10.0, units="nm", userlim=[9, 12])
sio2_thkn=esc.par("Sio2 Thkn", 3.0, units="nm", userlim=[0, 5])

cap_rough_10 = esc.par("Cap rough 5/10", 0.2, units="nm", userlim=[0, 3])
cap_rough_21 = esc.par("Cap rough 5/21", 0.2, units="nm", userlim=[0, 3])

nb_rough = esc.par("Nb rough", 0.2, units="nm", userlim=[0, 2])
sio2_rough = esc.par("SiO2 rough", 0.2, units="nm", userlim=[0, 1])
sub_rough = esc.par("Substrate rough", 0.2, units="nm", userlim=[0, 2])

cuni_thkn_10 = esc.par("CuNi Thkn 5/10", 15.0, units="nm", userlim=[15, 25])
cuni_rough_10 = esc.par("CuNi rough 5/10", 0.2, units="nm", userlim=[0, 2])

cuni_thkn_21 = esc.par("CuNi Thkn 5/21", 30.0, units="nm", userlim=[25, 35])
cuni_rough_21 = esc.par("CuNi rough 5/21", 0.2, units="nm", userlim=[0, 2])

cap = mdb.amorphous("Si", sldscale=1e-4, density=cap_density, source=mdb.Source.XRAYS, wavelength=wlx)
cuni = mdb.amorphous("CuNi", sldscale=1e-4, density=cuni_density, source=mdb.Source.XRAYS, wavelength=wlx)
nb = mdb.amorphous("Nb", sldscale=1e-4, density=nb_density, source=mdb.Source.XRAYS, wavelength=wlx)
sio2 = mdb.amorphous("SiO2", sldscale=1e-4, density=sio2_density, source=mdb.Source.XRAYS, wavelength=wlx)
sub = mdb.amorphous("Si", sldscale=1e-4,  density=si_density, source=mdb.Source.XRAYS, wavelength=wlx)

cap_layer_10 = esc.layer("Layer: Cap 5/10", cap, cap_thkn, cap_rough_10)
cap_layer_21 = esc.layer("Layer: Cap 5/21", cap, cap_thkn, cap_rough_21)

cuni_layer_10 = esc.layer("Layer: CuNi 5/10", cuni, cuni_thkn_10, cuni_rough_10)
cuni_layer_21 = esc.layer("Layer: CuNi 5/21", cuni, cuni_thkn_21, cuni_rough_21)

sio2_layer = esc.layer("Layer: SiO2", sio2, sio2_thkn, sio2_rough)
nb_layer = esc.layer("Layer: nb", nb, nb_thkn, nb_rough)
substr = esc.substrate("Substrate: Si", sub, sub_rough)

sample_10 = esc.multilayer("CuNi/Nb/Si_10", esc.air("Air"), substr)
sample_10.add(cap_layer_10)
sample_10.add(cuni_layer_10)
sample_10.add(nb_layer)
sample_10.add(sio2_layer)


sample_21 = esc.multilayer("CuNi/Nb/Si_21", esc.air("Air"), substr)
sample_21.add(cap_layer_21)
sample_21.add(cuni_layer_21)
sample_21.add(nb_layer)
sample_21.add(sio2_layer)

Qz=esc.var("qz")
Qz0=esc.var("qz0")
fwhm_10=esc.par("FWHM_10", 0.005, userlim=[0.003, 0.03], fixed=False)
fwhm_21=esc.par("FWHM_21", 0.005, userlim=[0.003, 0.03], fixed=False)

specrefl_10 = esc.specrefl("Specrefl_10", Qz, sample_10, "matrix")
specrefl_10 = esc.average_normal(specrefl_10, fwhm_10, Qz, Qz0)

specrefl_21 = esc.specrefl("Specrefl_21", Qz, sample_21, "matrix")
specrefl_21 = esc.average_normal(specrefl_21, fwhm_21, Qz, Qz0)

B10=esc.par("Bgr 10", 1, scale=1e-6, userlim=[0, 5])
B21=esc.par("Bgr 21", 1, scale=1e-6, userlim=[0, 5])
I10=specrefl_10+B10
I21=specrefl_21+B21

qz, y, err=np.loadtxt("data/JAP15/XRR/Silicon/s10/ASCII/Si10.dat", unpack=True, skiprows=2)
qz=qz*10
dobj10 = esc.data("S10.dat", qz, y, err, copy=True)


qz, y, err=np.loadtxt("data/JAP15/XRR/Silicon/s21/ASCII/Si21.dat", unpack=True, skiprows=2)
qz=qz*10
dobj21 = esc.data("S21.dat", qz, y, err, copy=True)

mobj10 = esc.model("Model 10", I10, dobj10, residuals_scale="q4", weight_type="data")
mobj21 = esc.model("Model 21", I21, dobj21, residuals_scale="q4", weight_type="data")

opt = esc.diffevol("DiffEvol", [mobj10, mobj21], popsize=15, maxiter=150, 
                   mutation=0.5, crossover=0.5, minconv=1e-3, nupdate=1, 
                  polish_final_maxiter=50, polish_candidate_maxiter=0)
opt()
show(opt, ylog=True)

opt

Name: DiffEvol            	Parameters number:         16
Parameter           	Value          	+-	Error     	Units     	Fixed
FWHM_10             	           0.03	+-	0         	arbitr.   	    0
Cap Thkn            	         11.767	+-	0.0076306 	nm        	    0
Cap rough 5/10      	         1.1922	+-	0.0072556 	nm        	    0
CuNi Thkn 5/10      	             15	+-	0         	nm        	    0
CuNi rough 5/10     	         1.2429	+-	0.0029998 	nm        	    0
Nb Thkn             	         10.247	+-	0.0038646 	nm        	    0
Nb rough            	        0.82993	+-	0.039391  	nm        	    0
Sio2 Thkn           	         4.5213	+-	0.036256  	nm        	    0
SiO2 rough          	        0.51451	+-	0.0025637 	nm        	    0
Substrate rough     	        0.54007	+-	0.04778   	nm        	    0
Bgr 10              	         1.1812	+-	0.16273   	x1e-06	arbitr.	    0
FWHM_21             	           0.03	+-	0         	arbitr.   	    0
Cap rough 5/21      	              3	+-	0.019528  	nm        	    0
CuNi Thkn 5/21      	          33.96	+-	0.0059434 	nm        	    0
CuNi rough 5/21     	         1.0903	+-	0.0031379 	nm        	    0
Bgr 21              	         1.9439	+-	0.2501    	x1e-06	arbitr.	    0