1. ABOUT THE DATASET -------------------- Title: Data and code associated with "Skyrmion motion in synthetic antiferromagnets and ferrimagnets driven by asymmetric spin wave emission" Creator(s): Christopher E A Barker [1], Charles Parton-Barr [2], Christopher H Marrows [2], Olga Kazakova [1,3], Craig Barton [1] Organisation(s): 1. National Physical Laboratory 2. University of Leeds. 3. University of Manchester Rights-holder(s):Unless otherwise stated, Copyright 2025 University of Leeds Publication Year: 2025 Description: Data generated from micromagnetic simulations of skyrmion breathing modes in a synthetic antiferromagnet. Data is composed of simulation scripts, and their associated outputs. Most data represents sets of simulations of the motions of the skyrmions, where the skyrmion is excited with some drive, and the motion recorded over a period of typically 10 ns. Over this period snapshots of the magnetisation are take from wich position can be extracted and velocity calculated given the time interval. These calculations are performed as a function of frequency, amplitude and for different excitation types to support each section of the paper. Cite as: Barker, Christopher E A and Parton-Barr, Charles and Marrows, Christopher H and Kazakova, Olga and Barton, Craig (2021): Dataset for 'Skyrmion motion in synthetic antiferromagnets and ferrimagnets driven by asymmetric spin wave emission'. University of Leeds. [Dataset] https://doi.org/10.5518/1742 Related publication: Barker, Christopher E A and Parton-Barr, Charles and Marrows, Christopher H and Kazakova, Olga and Barton, Craig, "Skyrmion motion in synthetic antiferromagnets and ferrimagnets driven by asymmetric spin wave emission", Physical Review B 112, 104438 (2025). Contact: Christopher H Marrows, christopher.h.marrows@leeds.ac.uk 2. TERMS OF USE --------------- Copyright 2025 University of Leeds, National Physical Laboratory, University of Manchester. Unless otherwise stated, this dataset is licensed under a Creative Commons Attribution 4.0 International Licence: https://creativecommons.org/licenses/by/4.0/. 3. PROJECT AND FUNDING INFORMATION ---------------------------------- Title: National Measurement Service (Metrology of complex systems for low energy computation) Dates: Apr 2024 - Mar 2025 Funding organisation: UK Government Department for Science, Innovation and Technology Grant no.: N/A 4. CONTENTS ----------- File listing 1. Static Skyrmion Characterisation.zip This is the data that contributes to Figure 1. Contains .mx3 mumax script files initialising the pair of skyrmions in the synthetic antiferromagnet and relaxing them in a given field. Also contains .out folders with the relaxed texture as a .npy file. The skyrmions in this file were analysed to extract their radii. 2. Skyrmion breathing mode characterisation.zip Contains .mx3 mumax script files that initialise the pair of skyrmions in the synthetic antiferromagnet and relaxes them in a 50 mT field along the z axis. A sinc pulse is then excited and the system allowed to run collecting the magnetisation in the file table.txt. These table.txt files are then captured and used to calculate the data shown in Figure 2. The table contains data for the entire system (m) as well as layer 1 (m_zrange0) and layer 2 (m_zrange2). 3. Skyrmion motion intro data.zip This is the data that contributes to Figure 3. The folder here contains the simulation script used to generate this data. The skyrmion was initialised in the synthetic antiferromagnet in a static out of plane field of 50 mT, and allowed to relax. Then a sinusoidal field of amplitude 20 mT was added at a frequency of 57.4 GHz (the out of phase skyrmion breathing mode resonant frequency) and the simulation allowed to run for 10 ns, collecting snapshots of the magnetisation every 0.05 ns. The snapshots of the magnetisation are contained in the subfolder "Mumax Simulation Results" with each number corresponding to the snapshot number, i.e. m000000 is at 0 ns, and m000200 is at 10 ns. Each of these snapshots was then looped over, and the skyrmion guiding centre calculated for each layer in the SAF. These guiding centres are saved to a csv file that was used for analysis of the position as a function of time, and therefore the velocity. This python file is called skyrmion_position_processor.py. The calculated skyrmion positions are in a file called Sk_Positions.csv. ***Note, for all subsequent position as a function of time datasets, given the vast volume of data, the scripts used to generate the data will be given, and the calculated skyrmion guiding centres will also be given, following the above method.*** 4. Skyrmion velocity as a function of frequency.zip This is the data that contributes to Figure 4. The simulation scripts repeat the form of 3. but do it over a range of frequencies from 6 GHz to 97 GHz. Each .out file contains a .csv with skyrmion positions as a function of time, from which a velocity is then calculated and presented as a function of frequency in Figure 4 of the main manuscript. 5. Func Amp.zip This is the data that contributes to Figure 5. This is split up into a number of subfolders, outlined here: a_b_c_d. SAF_Sky_Motion_RKKY_-0.0003_50mT_f57.4GHz_A_19.99mT.out: Full simulation output for the case when driving the skyrmion motion with a field of 20 mT at the resonant frequency of the out-of-phase skyrmion breathing mode, from which snapshots were taken in panels a and b in Figure 5, and from these line cuts in panes c and d. e_f. SAF_Sky_Breathing_RKKY_-0.0003_50mT_f57.4GHz_A_19.99mT.out: Full simulation output for the case when driving the skyrmion breathing at the resonant frequency of the out-of-phase skyrmion breathing mode, without an in-plane field, from which line cuts in panels e and f were taken. g_h_i_j. SAF_Sky_Motion_RKKY_-0.00030_50mT_f14.0.out: Full simulation output for the case when driving the skyrmion motion with a field of 20 mT at the resonant frequency of the in-phase skyrmion breathing mode, from which snapshots were taken in panels g and h, and from these line cuts in panels i and j. k_l. SAF_Sky_Breathing_RKKY_-0.0003_50mT_f14.3GHz_A_19.99mT.out: Full simulation output for the case when driving the skyrmion breathing at the resonant frequency of the in-phase skyrmion breathing mode, without an in-plane field, from which line cuts in panels k and l were taken. m. Velocity: Simulation scripts and resulting position vs time data for simulations on resonance where the amplitude of the driving field is varied. This data goes into Figure 5 (m). n. Breathing Amp: Mumax scripts used to run the skyrmion breathing mode simulation on the out-of-phase breathing mode resonant frequency at a range of amplitudes. .out files contain the results of fitting the m_x and m_y profiles of the skyrmions in each layer to the derivative of a gaussian. This data as a function of time was used to calculate the average variation in the skyrmion radius shown in Figure 5 (n), as discussed in detail in the supplementary information. 6. Function of RKKY.zip This is the data that corresponds to Figure 6 The directory contains 14 subfolders labelled RKKY_XXe-5 where XX is the magnitude of the antiferromagnetic interlayer exchange coupling. In each of these subfolders are the .mx3 scripts used to run the simulation, and the .out folders containing a csv of the skyrmion positions as a function of time. In the Subfolder "Analysed Velocities" a csv file can be found which holds the calculated velocity as a function of frequency for each of the previous subfolders. These csvs contain the data that is plotted in Figure 6 a, from which fits to asymmetric lorentzians determine the peak velocities that are shown in Figure 6b. 7. Ferrimagnets.zip This is the data that corresponds to Figure 7 This data is split into a number of subfolders: 7.1 RKKY_1e-4_Breathing: mumax simulation scripts and .out files for stimulating the breathing modes in a synthetic antiferromagnet. This was done holding either the Ms of layer 1 or layer 2 fixed to the original value, and varying the Ms of the other layer around the original value. Files are named with the convention MsXi_YYY, where X is the number of the layer that is being varied, and YYY is a multiplication factor of the original Ms. Therefore Ms1i_1.35 means that the Ms of Layer 1 is 135% of the original Ms value. Each .out file contains the table from which the PSD is calculated. Also included are two .csv files with fit results for the amplitude and frequency of the two peaks. 7.2 RKKY_3e-4_Breathing: Same as above but with an antiferromagnetic interlayer exchange coupling strength of 3x10^-4 J/m^2. This data is presented in the supplementary information. 7.3 RKKY_1e-4_Motion: .mx3 scripts and .out folders containing skyrmion positions as a function of time for simulations of motion done for a range of frequencies for each value of Ms1i and Ms2i. The subfolder "Analysed Velocities" contains the results of calculating the skyrmion velocity at each drive frequency, with a separate .csv file for each value of Ms1i. The Skyrmion_Peak_Velocities_RKKY_-0.00010_50mT_Fn_Ms1i.csv contains the results of fitting asymmetric lorentzians to the data in the above .csv files to extract peak velocities for each of these. 7.4 RKKY_3e-4_Motion: Same as above but with an antiferromagnetic interlayer exchange coupling strength of 3x10^-4 J/m^2. 8. Electric Field.zip This is the data that corresponds to Figure 8. The data is split into the following subfolders: 8.1 Skyrmion Motion: .mx3 files and processed skyrmion positions for sweeping the frequency of an electric field and driving the skyrmion motion. This data is presented in Figure 8. 8.2 Simulation .out file containing the results of running the system with a sinc pulse in E field to measure the PSD. Also in the file is the .mx3 script used to generate the data. 8.3 Skyrmion Radius Tests: .mx3 scripts and simuulation .out files containing tables of the magnetisation that can be used to calculate the skyrmion radius, with the simulation being run with a sinusoidal electric field driven at the two resonant frequencies. 9. STT.zip This is the data that corresponds to Figure 9. The data is split into the following subfolders. 9.1 STT Breathing: .mx3 file and .out simulation output for running the system with a sinc pulse in current from which the PSD can be calculated. This data contributes to Figure 9(b). 9.2 Motion vs Current Density: .mx3 files and .out simulations running the system and driving with a sinusoidal current density on resonance and varying the magnitude of the current density. This data contributes to Figure 9(c) 9.3 Motion vs Frequency: .mx3 files and .out simulation outputs containing .csv files with the processed skyrmion positions. This data contains sweeps where each .mx3 file drives the skyrmion with a current density of a fixed magnitude varying the frequency. This is done for current densities of 5e10, 1e11 and 2.5e11 A/m2. The resulting data from this is shown in Figure 9(d). 5. METHODS ---------- All data was generated using the software package MuMax3 as discussed in the associated manuscript.