The magnetoresistance dependence on the number of pairs of layers, n, of superlattices is shown in Fig. 1.
The studies have shown that in the Co/Cu superlattices under study the maximum magnetoresistance is ΔR/Rs = 60.2%, and the magnetic saturation field is Hs = 15 kOe for 16 pairs of Co/Cu layers (Fig. 2).
Figure 3 demonstrates the X-ray diffraction pattern of the sample after deposition. The diffraction pattern contains only one line, which is responsible for reflection from {111} planes. Thus, an axial texture with the < 111 > axis perpendicular to the plane of the substrate is formed in the sample under study.
Figure 4 shows the results of low-angle X-ray diffraction of superlattices Glass//PyCr(5nm)/[Co (1.5nm)/Cu(1nm)]n/Cr(5nm) with n = 10, 12, 14, 16 and 20. It can be seen that the first Bragg peak for all nanostructures is located near the angle 2θ = 4.35°, which means that the superstructure periods are equal. The presence of pronounced Kessig oscillations indicates the low roughness of interfaces of the layered structure.
The roughness of the layers was determined as the geometric roughness, the numerical value of which is obtained by calculating the root-mean-square roughness [21].
Modeling of reflectograms showed that the interface roughness does not directly depend on the number of bilayers and changes from σ = 0.17 to 0.42 nm with an increase from n = 10 to n = 20, respectively (Fig. 5). Thus, it can be concluded that there is no correlation between the number of bilayers and the roughness of the interfaces. Note that for a superlattice with n = 16 having the highest magnetoresistance MR = 60.2%, the roughness of the interlayer boundaries is σ = 0.28 nm.
To understand the term “highly perfect” interface, let us simulate the crystal lattice of a periodic structure in the region of the interlayer boundary. Figure 6 shows the result of modeling the Co/Cu interface of a superlattice with an axial structure < 111 > perpendicular to the plane of the layers, in the projections from the side (Fig. 6a) and from above (Fig. 6b). In Fig. 6а, the upper atomic layer is Cu (orange balls), and the lower atomic layer is Co (blue balls). For the central atom of the cobalt layer, the bonds with atoms of the nearest environment in the copper layer are shown. It can be seen from the figure under discussion that there are only three nearest neighbors for the 59Co probe nucleus in the atomic layer of copper. It is this configuration that makes it possible to obtain a highly perfect Co/Cu interlayer interface and, as a consequence, the minimum value of the probability of electron scattering at the interface, which leads to the maximization of the GMR effect. The same element of the crystal lattice, but in the projection from above, is shown in Fig. 6b.
The NMR spectra were recorded in the frequency range 140–240 MHz. According to the previously described technique and the model used, the spectrum is decomposed into several Gaussians, each of which corresponds to a 59Co probe nucleus with a certain type of the nearest environment [12].
Figure 7 shows the normalized NMR spectra of the entire series of samples. It can be seen from the figure that the spectra are principally similar: the same spectral line width at 216 MHz (there are no copper atoms in the first coordination sphere of the probe nucleus), and the position of this line also does not change depending on the number of bilayers. The rest of the spectral lines (corresponding to a different number of copper atoms in the immediate environment of the probe nucleus) visually coincide in width and resonance frequency. Substitution of one cobalt atom for one copper atom in the nearest environment leads to a decrease in the value of the hyperfine field (HFF) at the probe nucleus and, consequently, to a decrease in the resonance frequency by 16–18 MHz [18, 22]. Thus, resonance lines with a frequency of less than 216 MHz correspond to cobalt atoms localized in the interface region.
Figure 8 demonstrates an example of the NMR spectrum modeling of the superlattice Glass//PyCr(5nm)/[Co(1.5nm/Cu(1nm)]20/Cr(5nm). The following parameters were varied when modeling the spectrum: the line width (the same for all lines), the position of the peaks, as well as their intensities. In Fig. 8, the individual spectral lines are indicated by dashed lines. The resulting spectrum is shown as a solid line. The deviation of the resonance frequency of each spectral line does not exceed ~ 1.5 MHz, which is a fairly good result of agreement between the theoretical model and experimental data. The frequency of the most intense resonance line is 216 MHz, which is close to the value obtained for bulk Co (217 MHz) [17]. Consequently, this line is formed by Co atoms located in the bulk of the layers, which have the FCC structure. The resonance line at 228 MHz, which appears in the presence of the HCP modification of Co, is absent, indicating that there is no HCP modification of Co and stacking faults in the samples under study.
To compare the state of interlayer boundaries, the NMR spectrum of a Co/Cu superlattice with the structural formula Al2O3//Nb(3nm)Cu(2nm)/[Co(1.5nm)/Cr(0.9nm)]20 prepared by the method of molecular beam epitaxy (MBE) was taken from [23] and simulated according to the technique used to simulate the NMR spectra of the investigated series of superlattices. Both multilayer superstructures have the < 111 > texture. The inset in Fig. 7 shows the NMR spectra (normalized to unity) for superlattices Glass//PyCr(5nm)/[Co(1.5nm)/Cu(1nm)]20/Cr(5nm) and Al2O3//Nb(3nm)Cu(2nm)/[Co(1.5nm)/Cr(0.9nm)]20 [23]. It can be noted that the width of the resonance line at 216 MHz is practically identical for both spectra. This suggests that superlattices prepared by magnetron sputtering have a high degree of structural homogeneity within the Co layer. The NMR spectrum of the superlattice prepared by the MBE method contains two resonance lines: ~ 216 MHz (a probe core with no copper atoms in its immediate environment - inside the Co layer) and ~ 168 MHz (a probe core with three atoms of Cu).
The internal structure of interlayer boundaries can be characterized by the proportion of areas of "perfect" conjugation in the total interface surface. The presence of the < 111 > texture means that the "perfect" conjugation corresponds to the situation when the boundary coincides with the {111} crystallographic plane. In this case, each Co atom located at the boundary corresponds to three Cu atoms in the nearest environment.
The resonance line at a frequency of ~ 168 MHz is formed by the nuclei of Co atoms of a highly perfect Co/Cu interface, which coincides with the close-packed < 111 > plane of the FCC lattice, when each Co atom has three Cu atoms in the nearest environment. Consequently, the fraction of interface atoms surrounded by three copper atoms, and hence the fraction of highly perfect interlayer boundaries, can be determined as
, where i corresponds to the number of copper atoms in the immediate environment of the probe nucleus. Modeling of NMR spectra makes it possible to quantify the proportion of highly perfect boundaries (Fig. 9).
According to Fig. 9, the proportion of highly perfect interlayer boundaries varies in the range from 38 to 46%. For a superlattice with n = 16, which has the greatest GMR effect, the fraction of highly perfect boundaries is 46%. In the superlattice from [23], only highly perfect interlayer boundaries are formed, which is probably due to preparation by molecular beam epitaxy.
The state of interlayer boundaries can also be characterized by the fraction of Co atoms localized at the interfaces. The fraction of such atoms can be determined as the ratio of the total intensity of resonance lines formed by atoms located in the interfaces to the total intensity of all resonance lines, that is
, see Fig. 10, columns. Figure 10 also demonstrates the fraction of Co atoms involved in the formation of highly perfect interfaces:
for superlattices Glass//PyCr(5nm)/[Co(1.5нм)/Cu(1nm)]n/Cr(5nm) (shaded columns) and Al2O3//Nb(3nm)Cu(2nm)/[Co(1.5нм)/Cr(0.9нмm)]20 [23] (solid horizontal line).
Modeling of NMR spectra made it possible to establish that the fraction of cobalt atoms forming interlayer boundaries varies from 28 to 38%. The absence of a significant change in the number of cobalt atoms localized in the interface region is in agreement with the data on similar magnetic superlattices CoFe/Cu [23]: an increase in the coherent scattering region in the direction perpendicular to the film plane with an increase in the number of bilayers n. Note that in the case of a superlattice with MR = 60.2%, the fraction of Co atoms localized at the interfaces is 29%. Figure 10 shows that the number of atoms forming highly perfect boundaries varies from 10 to 13% and practically coincides with the number of atoms forming highly perfect boundaries in a superlattice fabricated by the MBE method. Consequently, the fraction of atoms that do not form highly perfect interfaces characterizes the degree of roughness of the interlayer boundaries. Since this quantity is not zero, we can conclude that interlayer boundaries of the diffuse type are formed in the superlattices under study.