Language: C++

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The SPIN-Ga/Gr software package implements the construction of magnetic moment reversal domains in the φ0 Josephson junction model on the model parameter plane.

The dynamics of the magnetization in ferromagnetic layer in the φ₀ - Josephson junctions is described by the Landau-Lifshitz-Gilbert equation:

             (1)

where α is damping parameter, ω_F is normalized frequency of ferromagnetic resonance. Here is effective magnetic field with the components

             (2)

where G – relation of Josephson energy to energy of magnetic anisotropy, r – the spin-orbit coupling parameter, m_x,y,z is x,y,z - component of magnetic moment . Initial conditions: m_x(0) = 0, m_y(0) = 0, m_z(0) = 1.

The Josephson phase difference φ(t) can be found using equation

             (3)

Here I_pulse is the pulse current, A_s is the amplitude of the pulse current, and Δt is the time interval, in which the pulse current is applied, t0 is the time point the maximal amplitude.

In the presented programs, the numerical solution of the initial problem (1-3) for a system of ordinary differential equations is implemented both on the basis of the explicit 4-step Runge–Kutta method, and using the implicit Runge–Kutta scheme, also called the Gauss–Legendre method. In this case, the calculation is carried out on the plane of parameters (G, α) or (G, r), where the parameters G, α or G, r change in a given range with a certain step. During the calculations, for each pair of parameter values on the scanned plane, a reversal of the magnetic moment is identified (if the initial value m_z(0) = +1 during the simulation changes sign and takes the value m_z(t) = –1) or the absence of a reversal (the sign of z - components of the magnetic moment m_z(t) = +1).

A detailed presentation of the mathematical formulation of the problem, the computational scheme and the algorithm for identifying the magnetic moment reversal is presented in [1]. The parallel implementation scheme and the results of acceleration calculations depending on the number of MPI processes and OpenMP threads are presented in [2].

The SPIN-Ga/Gr software package implements the construction of magnetic moment reversal domains in a φ0 Josephson junction and combines four versions of programs for the (G, α) and (G, r) planes:

•  parallel version developed using MPI technology and implemented by the 4th order Runge - Kutta method,

•  parallel version developed using MPI technology and implemented by the Gauss - Legendre method,

•  parallel version developed using OpenMP technology and implemented by the 4th order Runge - Kutta method,

•  parallel version developed using OpenMP technology and implemented by the Gauss - Legendre method.

In SPIN-Ga/Gr, input parameters are specified through a special input file, the name of which can be arbitrary and is specified when starting the task. In this file, in any order, the following are specified:

•  Normalized magnetic resonance frequency (OmegaF),

•  Minimum value of the dissipation parameter (alpha_min) (only for G, α),

•  Maximum value of the dissipation parameter(alpha_max) (only for G, α),

•  Dissipation parameter step (alpha_step) (only for G, α),

•  Minimum value of the spin-orbit coupling parameter (r_min) (only for G, r),

•  Maximum value of the spin-orbit coupling parameter (r_max) (only for G, r),

•  Spin-orbit coupling parameter step (r_step) (only for G, r),

•  Minimum ratio of Josephson energy to magnetic anisotropy energy (G_min),

•  Maximum ratio of Josephson energy to magnetic anisotropy energy(G_max),

•  Step of the ratio of Josephson energy to magnetic anisotropy energy(G_step).

Other parameters can be changed directly in the program source code.

The results of the program execution are written, depending on the choice of the calculation plane, into the files points_GA_mz_m1.dat or points_Gr_mz_m1.dat and contain the coordinates of points on the parameter plane, respectively (G, α) or (G r), in which the magnetic moment is reversed. The files points_GA_mz_p1.dat or points_Gr_mz_p1.dat contain points where the flip is not detected. The first column of the files of both versions contains the values of the ratio of Josephson energy to the magnetic anisotropy energy G, the second column contains the values of the dissipation parameter alpha (only for the case of calculations on the (G, α) plane) or the values of the spin-orbit coupling parameter r (only for calculations on the plane (G, r)). The third column contains the absolute values of the magnetic moment.

The archive includes programs in MPI-C++ and OpenMP-C++, a script for compiling and running the program, the result of the program in the form of output files with data obtained for the input parameters specified as an example, as well as a readme file with a detailed description of the launch order and an explanation for example.

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References:

1. Atanasova P.K., Panayotova S.A., Rahmonov I.R. Shukrinov Yu.M., Zemlyanaya E.V., Bashashin, M.V. Periodicity in the Appearance of Intervals of the Reversal of the Magnetic Moment of a φ0 Josephson Junction. Jetp Lett. 110, 722–726, 2019.
2. Bashashin M.V., Zemlyanaya E.V. Comparative Performance Analysis of MPI- and OpenMP-Programs on the Example of Parallel Calculations in the Framework of the Nucleus-Nucleus Potential Model and the φ0-Spintronic Model. Modern Information Technologies and IT-Education, 18(3), 545-557, 2022.

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