Molecular dynamics modeling of formation processes parameters influence on a superconducting spin valve structure and morphology

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Introduction
Multilayer hybrid nanostructures "superconductor-ferromagnet" are a new type of elements of quantum electronics -spintronics based on electron spin transport.
Practice shows that the creation of multilayer superconductor-ferromagnet nanostructures with the required properties is a very complex process, therefore, as a rule, it is not possible to create an "ideal" nanosystem. Fig. 1 and Fig. 2 show real multilayer nanosystems formed from various materials [ 9 ]. It can be seen from the figures that the structure of real nanosystems is far from ideal. In particular, it can be noted that the surface separating the various nanolayers of the system is not perfectly flat. The surface has noticeable irregularities that are directed into the contacting layers. The figures also show that there is a mutual penetration of atoms of one contacting layer into another. Therefore, the layer interface has a certain (nonzero) thickness.
It should be noted that the atomic structure of each layer does not form an ideal whole nanocrystal, but a system is formed that combines nanocrystals.  It should be noted that mathematical modeling is widely used in the design and analysis of the properties of various nanosystems [15][16][17], however, in relation to the considered class of multilayer nanosystems for spintronics, the number of works is very limited. Basically, the modeling of the physical properties of ideal layered nanosystems for spintronics was carried out, in which the real structure of the nanosystem was not taken into account.
The aim of this work, as the development of previous studies of the authors on the modeling of various nanosystems [18][19][20], including for spintronics [21][22], was to study the influence of the main parameters of technological modes of the formation of layered nanosystems for spintronics: temperature, concentration and spatial distribution of deposited atoms over the surface of the nanosystem -on their structure and morphology.

Mathematical Model and Theoretical Foundations
The formation processes and the structure of multilayer systems for spintronics were studied by the molecular dynamics method [23,24]. Molecular dynamics describes the motion of each atom of a nanosystem at a certain point in time, therefore it is possible to reproduce the detailed evolution of nanoelements and their properties.
The basis of the method is the equations of motion of all atoms, supplemented by the initial conditions in the form of coordinates and velocities of atoms: where Nis the number of atoms that formed nanosystem. The molecular dynamics method is based on the concept of potential () U r , which is responsible for the nature and magnitude of the interactions of atoms of a nanosystem.
The type of potential may be different, but recently due to its accuracy and adequacy, many-particle force fields have gained great popularity. In this work, we where   The immersion function is corrected by the force field created by pair interactions and refines its value. This value is due to the presence of electron gas in the material and, in accordance with [23,24], can be calculated by the formula To calculate the background electron density at the immersion point, the following equation is used, in which all electronic orbitals of atoms of various configurations add their terms Where parameters    Spherically symmetric one-electron s-orbital and angular electron p-, d-, f-clouds are distinguished. For each orbital, its own formula is used, in accordance with which its electronic distribution density is calculated The functional   G  in equation (4) can be defined in various ways. One of the most popular formulations is written as a dependency.
The weight coefficients of the modified immersed atom method from (4) also have an additive relationship with single-electron radial functions where   0, k j tare empirical parameters that depend on the chemical type of the element.
Distance energy smoothing in MEAM is achieved by introducing a shielding function.
Using the screening function, the attenuation of the potential occurs gradually, which allows one to provide a more physically accurate description of the properties of nanomaterials and reduce computational costs during simulation where min max , CCthe parameters of the mutual influence of atoms, depending on their chemical types, are set for each triple of atoms with numbers ,, i j k ; c ris the distance at which the force field is cut off; -a parameter exceeding the cutoff distance is used to smooth the potential.

Problem Statement and Software
The influence of the formation processes parameters of the spin system hybrid structures "superconductor-ferromagnet" is studied for a multilayer nanosystem based on cobalt and niobium. This system is a functional material demonstrated a giant spin-valve effect, theoretically and experimentally investigated in [25][26][27]. In these works the authors proposed a new design and performed the calculation of a spin valve consisting of superconducting plates and an artificial magnetic metamaterial placed between them, formed by periodically alternating thin and thick nanolayers of a ferromagnetic metal. The thickness of the layers affects the magnetic exchange interaction between ferromagnet layers, that gives the possibility of design of artificial magnetic metamaterials with tunable properties .
The choice of niobium and cobalt as the metals forming nanolayers is dictated by the wide potential of using these elements in spintronics. At the moment, not only research were carried out on spintronic devices involving these metals [28,29], but also new patents are being issued [30][31][32].
The general scheme of the investigated nanosystem is presented in Figure 3. Nevertheless, the processes of formation are similar to each other. Therefore, in this work, we consider the deposition of only the first four layers of cobalt and niobium.
The general statement of the problem of modeling the multilayer nanosystem formation processes is presented in Figure 4.  Also, modeling of nanocomposite formation processes was performed on a scale reduced by 4 times.

Results and Discussion
In this case, the number of deposited atoms in each layer was proportionally reduced so that the thickness of the formed nanofilms did not change. The temperature is 300 K.
The influence of the area of the deposition flow and the size of the modeling region on the relative layer-by-layer composition of the nanosystem are shown in Figure 9. pronounced. The conducted studies indicate the presence of a certain critical deposition rate, the excess of which leads to the formation of a nanomaterial of a different structure. Since in real technological processes deposition is carried out with a sufficiently low intensity (about 1000 nm per hour), in order to obtain physically adequate research results, the deposition processes must be simulated at a speed not exceeding this critical value. On the other hand, there is no need to increase the duration of the stages of nanofilm growth, maximally approximating its real value, since, as the graphs in Fig. 10, the structure and composition in this case are similar. Figure 11: The percentage composition of the Nb-Co multilayer nanosystem formed at a substrate temperature of 300, 500, and 800 K, respectively A series of computational experiments was carried out in which the formation of Nb-Co multilayer nanosystems was studied in the temperature range 300-800 K, for substrate temperatures of 300, 500, and 800 K, respectively. The simulation results are presented in Figure 11 in the form of a percentage composition graph of this nanosystem. The calculations showed that the temperature of the substrate significantly affects the formation of the structure of the nanosystem. An increase in temperature leads to an increase in the total thickness of the nanosystem (at 800 K, this value increased by 0.3 nm compared with a temperature of 300 K). The region of mutual penetration of Nb atoms into the layers of the system consisting of Co, and vice versa, is also increasing, which is clearly seen in the graphs in Figure 11.

Conclusion
The paper proposes a technique and describes a mathematical model for studying technological modes and parameters in the manufacture of multilayer nanosystems.
The model was tested in the study of the processes of formation of a nanosystem based on niobium and cobalt hybrid structure with the spin valve design. The influence of various technological parameters was investigated: substrate temperature, deposition flow rate and density, nanosystem sizes. Briefly, we consider the main results of the calculations. An analysis of the coordination number distribution in the material showed that when multilayer nanofilms are formed under normal conditions, the layers have a different structure. The structure of the niobium substrate is close to crystalline; cobalt nanofilms are characterized by an amorphous-like structure.
In the thickened niobium layer, crystallization zones are observed located in places of direct contact with the cobalt nanolayer. The mismatch of the crystal lattices of the starting metals causes mutual rearrangements of atoms and the transformation of the structure inside the nanosystem.

2.
A decrease in the area of the deposition flux and the simulation region by 75%

4.
In order to obtain physically adequate research results that correspond to real technological processes, the growth mechanisms of nanoscale films and layers must be modeled with a deposition rate not exceeding the critical value of clustering.

5.
The temperature of the substrate is a leading factor affecting the formation of multilayer nanosystems, the atomic structure of the contact areas of the interface, as well as the composition and structure of the multilayer nanosystem as a whole.
The simulation allows us to obtain detailed information on the structure and composition of multilayer nanosystems, on the mechanisms of formation of individual nanolayers and contact areas under various technological manufacturing conditions.
The obtained data can be used as a supporting tool during experimental tests and for adjusting and optimizing technological processes for producing multilayer nanosystems and devices for spintronics.