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Spin current generation through the spin-orbit interaction in non-magnetic materials lies at the heart of spintronics. When the generated spin current is injected to a ferromagnet, it produces spin-orbit torque and manipulates magnetization efficiently, and the electrical generation of a spin-orbit torque through the spin Hall effect in heavy metals is intensively studied [1,2]. For the fast magnetization dynamics, however, the optical generation of a spin-orbit torque is more promising than its electrical counterpart. A prerequisite for the optical generation is the photo-spin conversion, which has been intensively studied for semiconductors such as GaAs. A well-known mechanism of the conversion is the optical orientation [3]; photo-excitation by a circularly polarized light with angular momentum along the direction σ can generate excited electrons that are spin-polarized along the direction σ. Such optically generated spins have been used to generate a spin torque in a ferromagnetic semiconductor MnGaAs [4]. In this work, we report optical spin-orbit torques in heavy metal/ferromagnet heterostructures [5]. The strong spin-orbit coupling of heavy metals induces photo-excited carriers to be spin-polarized, and their transport from heavy metals to ferromagnets induces a torque on magnetization. These results resemble, in many ways, the electrically generated spin-orbit torque that also utilizes the strong spin-orbit coupling of heavy metals. We thus call the optically generated damping-like torque in heavy metal/ferromagnet heterostructures. as optical spin-orbit torque [5].References: 1. I. M. Miron, G. Gaudin, S. Auffret, B. Rodmacq, A. Schuhl, S. Pizzini, J. Vogel, and P. Gambardella, Nature Mater, Vol. 9, p. 230 (2010). 2. L. Liu, C.-F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, R. A. Buhrman, Science, Vol. 336, p. 555 (2012). 3. F. Meier and B. P. Zakharchnya, Optical Orientation (North-Holland, Amsterdam, 1984). 4. P. Némec, E. Rozkotová, N. Tesarová, F. Trojánek, E. De Ranieri, K. Olejník, J. Zemen, V. Novák, M. Cukr, P. Malý, and T. Jungwirth, Nature Phys. Vol. 8, p. 411 (2012). 5. G.-M. Choi, J. H. Oh, D.-K. Lee, S.-W. Lee, K. W. Kim, M. Lim, B.-C. Min, K.-J. Lee, and H.-W. Lee, Nature Commun. Vol. 11, p. 1482 (2020).

MMM 2020

Optical spin-orbit torque in heavy metal-ferromagnet heterostructures INVITED

The 65th Annual Conference on Magnetism and Magnetic Materials (MMM 2020) was held in a virtual form. The COVID-19 pandemic, with its associated uncertainty about international travel and the ability to gather in large groups, meant that the Steering Committee decided to cancel the face-to-face meeting that had been planned in Palm Beach, Florida November 2-6, 2020.

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technical paper

I Introduction In order to obtain the deformation characteristic of silicon steel with yoke clamping applied under alternating magnetic field, a stress-dependent magnetostriction model of silicon steel must be construct. Due to the rotation of magnetic domain and the movement of magnetic domain wall with stress applied, the magnetostrictive deformation of the material will reverse and saturate in both magnitude and direction [1-3]. Therefore, the saturated magnetic domain wall movement effect must be considered in stress-dependent magnetostriction model. II The hysteresis stress-dependent magnetostriction model of silicon steel Based on the comparison of the measured magnetostrictive strain curves and hysteresis loops, the hysteresis effect of magnetostrictive curve is obvious even the area of hysteresis loop is small [2]. Therefore, this paper constructs the magnetization model based on the J-A hysteresis model. Then, based on the macroscopic thermodynamics and Gibbs free energy expansion, the stress-dependent magnetostriction model in the excitation state is constructed. Meanwhile, due to the pinning effect, the magnetostrictive curve of silicon steel in demagnetization process cannot return along the original path and reach the initial state. Therefore, the magnetostrictive parameter λws which express the magnetic domain wall movement under varying stress in saturated magnetization was introduced into the magnetostriction model in the demagnetization case. The parameters of the model which control the saturated magnetic domain wall movement are extracted from the measured magnetic curves of non-oriented silicon steel sheet, which are shown in Fig. 1. III Results and discussion The simulated results are shown in Fig. 2. As shown, the time when magnetostriction reaches the maximum in the simulation is consistent with the experimental results, which shows that influence of saturated magnetic domain wall movement on magnetostrictive deformation is accurately simulated in the model.References: [1] Zhu L, Li J, Yang Q, et al. An Improved Magnetostriction Model for Electrical Steel sheet Based on Jiles-Atherton Model[J]. IEEE Transactions on Magneics, 2020, 56(3):7514604. [2] Zhang Y, Zhou H, Zhou Y. Vibration suppression of cantilever laminated composite plate with nonlinear giant magnetostrictive material layers[J]. Acta Mechanica Solida Sinica, 2015, 28(1):50-61. [3] Wang Z, Zhang Y, Ren Z, et al. Modeling of Anisotropic Magnetostriction Under DC Bias Based on an Optimized BP Neural Network[J]. IEEE Transactions on Magnetics, 2020, 56(3): 7512204

An Improved Magnetostriction Model of Silicon Steel Considering the Saturated Magnetic domain Wall Movement

Recent trends in the distribution of electrical energy through medium- and low-voltage grids, involving a variety of sources and smart infrastructures, call for extensive use of medium frequency transformers, as required for conversion steps and bidirectional power transfers. The employed grain-oriented (GO) cores are subjected to kHz frequencies and harmonics-rich voltages. These are scarcely assessed working regimes, regarding both loss behavior and dynamics of the domain structure. We perform in this work a thorough investigation on the energy loss dependence on frequency f (DC – 10 kHz) and peak polarization Jp (0.25 T – 1.7 T) of high-permeability 0.29 mm thick GO steel sheets, combined with the magneto-optical Kerr analysis of the dynamics of the domain walls and the evolution of the domain structure in well-oriented grains. The predicting model starts with the determination of the induction profile across the sheet thickness at any instant of time, according to the Maxwell’s diffusion equation, which is applied using the experimental normal/anhysteretic curves as magnetic constitutive equations. The classical energy loss component Wcl is calculated versus f and Jp, together with the evolution of the hysteresis loss Wh. This, although increasing with f, is observed to provide negligible contribution in the kHz range. The Kerr images show that the regular antiparallel domain wall (dw) structure is initially preserved under increasing f, at the cost of bowing and dw densification, while the excess loss Wexc follows a regular power law. However, at sufficiently high f and Jp values, the dws meet and annihilate at the surface, while remaining stuck as cylindrical domains at the sheet midplane. It turns out that in the high (f, Jp) corner the magnetization process occurs by penetration towards the midplane of extended dws parallel to the sheet surface, with Wexc and Wh dwarfed by the classical loss component.

Domain Structure and Energy Losses up to 10 kHz in Grain-Oriented Fe-Si Sheets

Ni-rich FeNi alloy (permalloy) thin films possess high permeability, low anisotropy and low damping constant. These unique set of properties mark their importance in high frequency micro-devices. The synthesis of Fe20Ni80 films using cost-effective simple technique without involving high vacuum conditions and investigation of their magnetic behavior is of great importance for such technical applications. Fe20Ni80 films were deposited on Indium Tin Oxide (ITO) coated glass substrates by electrochemical deposition technique in potentiostatic mode using three-electrode cell. I-V characteristics measured using cyclic voltammetry revealed oxidation-reduction states and potential for onset of film deposition onto the substrate. The desired composition of Fe20Ni80 films, were prepared using calculated concentration of solutions in electrolyte. The elemental composition was confirmed by EDAX. FESEM images depict uniformly dispersed nanocubes all over the substrate. Bulk hysteresis measurement by VSM confirms low coercivity (Hc) ~ 42 Oe, high saturation magnetization (Ms) ~ 760 emu/cm3 and high remanence (Mr), with the ratio of Mr/Ms ~ 0.7 in-plane geometry (Fig.1). Reduced Mr/Ms ~ 0.2 was observed in out-plane configuration.The Mr/Ms ratio increased to 0.8 after annealing at 400 °C in Ar+H2 atmosphere while retaining low Hc for in-plane configuration. The out-plane M-H curves shows increased Hc~560 Oe attributed to pinning and Mr/Ms ~ 0.26. The surface magnetic properties observed using L-MOKE revealed similar Hc and enhanced remanence after annealing. The in-plane hysteresis curves recorded at azimuthal angles of 0°, 45°, and 90° do not show significant changes, indicating random distribution of easy axis along film plane. The magnetization reversal is directed by stripe-like domains (Fig. 2) originating due to slight perpendicular component of magnetization evidenced by non-zero remarkable remanence in out-plane hysteresis. Such domain configuration along with low Hc and high Ms makes the presented highly permeable Fe20Ni80 useful for high frequency device applications.References: 1. Cao, D., Pan, L., Liu, Q. Journal of Physics D: Applied Physics, 51(2), 025001 (2017). 2. Vashisht, G., Kumar, V., Annapoorni, S. Journal of Magnetism and Magnetic Materials, 497,166064 (2020). 3. Hubert, Alex, and Rudolf Schäfer. Springer Science & and Business Media, (2008). 4. Kainuma, S., Tsuya, N. , Journal of Applied Physics, 34. 795-799 (1963). 5. Bhatia, E., Hussain, Z., Reddy, V. R., arXiv preprint arXiv:1903.08106 (2019).

Domain observation in electrodeposited Permalloy thin films

We present detailed experiment and simulation studies of behavior of field-dependent magnetization and magnetoresistance in the vicinity of the Curie temperature in the highly disordered dilute ferromagnetic semiconductor (Ga,Mn)As system. (Ga,Mn)As has a low saturation magnetization and relatively strong magnetocrystalline anisotropy, which inhibits domain formation. The critical behavior of (Ga,Mn)As is shown to be consistent with the three-dimensional Heisenberg model, despite the very strong disorder present in this system [1]. Clear correspondence of the magnetization and magnetoresistance is observed in the critical region. We found large anisotropy of the magnetoresistance within the critical region in our high Curie temperature (Ga,Mn)As system.References: 1. M. Wang, et.al., Phys. Rev. B 93, 184417 (2016).

Magnetism and magnetotransport around the Curie temperature in the dilute ferromagnetic semiconductor (Ga,Mn)As

An ab initio study of the stacking fault energy (SFE) curve of pure FCC Co was performed. This system was considered in order to determine a baseline for similar SFE curves calculated for Co-based alloys, particularly alloys containing Mn, Fe, or a combination of the two. The calculated SFE is normalized with respect to the number of atoms, number of faults, and interfacial area of the unit cell. All unit cells were allowed to relax to a high degree to ensure SFE calculations were performed at the lowest energy state. In addition, all cells utilized the same relaxation method to ensure uniformity. The results varied from previous results published in literature [1], which were not taking the magnetic state of the system into account. Upon investigation, it was determined that there is a strong magnetic effect on the SFE of Co, similar to results calculated for FCC Fe [2]. Subsequent calculations were performed assuming a nonmagnetic system, and results yielded the previous obtained results found in literature. Additionally, it was determined that FCC Co undergoes a magnetic phase transition, where it has the potential to become non-magnetic [3]. Analysis of the magnetic system revealed changes in the total moment of the system depending on the fault state (Fig. 1). Acknowledgements: This work was supported by NASA CAN 80NSSC18M0023. Computational support was provided by the University of Alabama High Performance Computing facilities and staff.References: [1] L.-Y. Tian, R. Lizárraga, and H. Larsson, Acta Mater., Vol. 136, p.215 (2017) [2] I. Bleskov, T. Hickel, and J. Neugebauer, Phys. Rev. B, Vol. 93 (2016) [3] V. L. Moruzzi, P. M. Marcus, and K. Schwarz, Phys. Rev. B, Vol. 34, p.1784 (1986)

Observed Effects of Magnetism on the Calculated Stacking Fault Energies of FCC Co

Substitution of copper by iron in the charge reservoir block of the YSCO cuprate superconductor brings out an appealing insight on the interplay between superconductivity and magnetism. In the resulting FeSr2YCu2O7+δ compounds, [FeO1+δ] layers and CuO2 bi-layers are alternated along the stacking direction (Figure 1a), in close analogy to the RuSr2GdCu2O8 ferromagnetic superconductor1. By modifying the hole doping level through different reducing-oxidizing treatments, we have explored the evolution from a non-superconducting phase with an AFM ordered Cu2+ sublattice for δ=0.08, to a superconducting sample with Tc= 70 K for δ=0.85, in which superconductivity coexist with Fe4+ long-range magnetic ordering (TN=110 K > Tc)2. An intermediate-doped sample, with δ=0.56, present a mixed valent Fe3.5+ state and superconductivity at a lower Tc= 30K (Figure 1b), but with no evidence of magnetic interactions in the magnetization data. However, zero-field muon spin rotation spectroscopy (ZF-μSR) reveals, for the two superconducting samples, the presence of magnetic interactions involving the copper sublattice at TFigure 1c), as previously found in YBCO by means of the same technique3. For the here described FeSr2YCu2O7+δ system, there is a clear enhancement of the magnetic interactions starting at the superconducting transition (Figure 1d). This suggests a complex interplay between, the normally exclusive phenomena, of magnetism and superconductivity4. The analysis of the μSR data will be described and the eventual interplay between the magnetic and superconducting properties discussed.References: (1) C. Bernhard, J. L. Tallon, C. Niedermayer, Phys. Rev. B, 59 (21), 14099 (1999) (2) S. A. López-Paz, X. Martínez De Irujo-Labalde, M. A. Alario-Franco, Inorg. Chem., 58 (19), 12809 (2019) (3) S. Sanna, A. D. Hillier, R. De Renzi, Phys. Rev. Lett. 12, 207001 (2004) (4) J. Chakhalian, C. Bernhard, G. Cristiani, Nat. Phys., 2 (4), 244 (2006)

Interplay Between Magnetism and Superconductivity in Iron Substituted FeSr2YCu2O7+δ Cuprates Studied by μSR

For possible applications as trapped field (TF) magnets, it is essential to fabricate large, polycrystalline bulk samples from the FeSe compound, the simplest high-Tc superconductor (HTSc) possible. FeSe is relatively cheap to prepare, and does not contain any rare-earth material. The grain boundaries in this compound are not acting as weak links as it is the case for the YBCO compound. Although the transition temperature, Tc, is just below 10 K, the upper critical fields are comparable with other HTSc. Preparing the FeSe samples using solid-state sintering yields samples exhibiting strong magnetic hysteresis loops (MHLs), and the superconducting contribution is only visible after subtracting MHLs from above Tc. Due to the complicated phase diagram [1], the samples are a mixture of several phases, α-FeSe, β-FeSe, δ-FeSe (Fe7Se8) and metallic α-Fe [2]. The amount of the latter two phases depends directly on the Se loss during the sintering process. The δ-FeSe is antiferromagnetic, and α-Fe is ferromagnetic [3]. In the present contribution, we show MHLs of a variety of samples measured up to ±7 T and determine the magnetic characteristics, together with the amount of superconductivity determined from M(T) measurements. We performed a thorough analysis of the microstructures using polarization microscopy, Kerr effect, MFM, SEM, EBSD and TEM in order to establish a relation between microstructure and sample properties. To prepare good superconducting samples, the presence of the (anti)ferromagnetic phases must be reduced by carefully adjusting the Se content using Ti foils as getter materials. Measuring magnetoresistance of these samples [4] implies that the samples are always cooled in the own local field, and thus, the analysis of the resistance data calculating the fluctuation-induced conductivity above Tc [5] is strongly affected by this local magnetic field. We demonstrate the importance of preparing phase-pure FeSe samples, which are essential for the various applications envisaged. This work is part of the SUPERFOAM international project funded by ANR and DFG under the references ANR-17-CE05-0030 and DFG-ANR Ko2323-10, respectively.References: [1] H. Okamoto, J. Phase Equilibria 12, 383 (1991). [2] P. Diko et al., Physica C 476, 29 (2012). [3] A. J. Williams, T. M. McQueen, R. J. Cava, Solid State Commun.149, 1507 (2009). [4] T- Karwoth et al., J. Phys. Conf. Ser. 1054, 012018 (2018). [5] A. Almessiere et al., Mat. Chem. Phys. 243, 122665 (2020).

Magnetic phases in superconducting, polycrystalline bulk FeSe samples

Nowadays machine learning is becoming more and more popular and powerful tool for scientific research. Carrasquilla and Melko have demonstrated how neural networks can be used for classifying phases in solids [1]. Restricted Boltzmann machine (RBM), a simple stochastic neural network, is shown to reproduce ferromagnetic Ising model results if trained on the dataset obtained by Monte-Carlo (MC) method [2]. The authors calculate observable physical properties with RBMs trained at different temperatures and find good agreement with MC results for corresponding temperatures. We show that RBM is able not only to reproduce observable physical properties calculated earlier, but also to predict them. First of all, we study short-range order in binary alloys. In the simplest case, this problem can be reduced to the Ising model with spins up and down corresponding to atoms of types A and B. The dataset of 106 samples of 10x10 square matrices is calculated using the Metropolis algorithm for the alloy concentration equal to one half. We propose an algorithm which allows RBM trained on this dataset to generate new samples for any alloy concentration. In Fig. 1 the Warren-Cowley short-range order parameter is presented. It can be seen that RBM trained at one concentration can correctly predict short-range order in the full concentration range. Moreover, long range magnetic order can also be successfully predicted. Fig. 2 shows the magnetization for the 2D ferromagnetic Ising model. RBM result is obtained by training the machine for T=2.5, which is close to the critical temperature, and then scaling the weights and biases to generate data for all other temperatures. We see that RBM, based on data for only one temperature, reproduces the thermodynamic properties for the entire temperature range and correctly predicts critical temperature.References: [1] J. Carrasquilla and R.G. Melko, Nat. Phys., Vol. 13, p. 431 (2017) [2] G. Torlai and R.G. Melko, Phys. Rev. B, Vol. 94, p. 165134 (2016)

Predicting Long- and Short-Range Order with Restricted Boltzmann Machine

Manipulation of the magnetization state of spintronic devices can be achieved by spin-orbit torque (SOT). SOT can be induced by Rashba effect1 or Spin Hall effect2, which are both originated from the spin-orbit (SO) coupling. Therefore, to enhance SOT, materials with strong SO coupling are favored. Weyl semimetals are predicted to be a good candidate for achieving an efficient charge to spin interconversion driven by spin-galvanic effect3. Crystalline Weyl semimetals (e.g., WTe2) also provide an exciting possibility of generating out-of-plane (OOP) anti-damping SOT. The presence of strong OOP anti-damping SOT in WTe2/Py heterostructure, originated from the broken 2-fold rotational symmetry at the interface of WTe2, has been demonstrated by spin-torque ferromagnetic resonance4. Unlike conventional heavy metals such as Pt and Ta that only allow in-plane AD SOT, WTe2 can be more efficient for perpendicular magnetization switching. The 2D ferromagnet Fe3GeTe2 (FGT) has been reported to possess strong perpendicular anisotropy at temperatures below TC ~ 230 K5. Anomalous Hall effect can be utilized to monitor the magnetization state of FGT flake during the switching measurements. SOT switching of perpendicular magnetization has been realized in Pt/FGT semi van der Waals (vdW) heterostructure6-7. However, SOT switching in a complete vdW heterostructure still needs to be demonstrated to fill the gap. As shown in Fig.1, we demonstrated SOT switching of perpendicular magnetization in WTe2/FGT vdW heterostructure, and the chirality of SOT switching was found to switch with the direction of the in-plane field. The current density threshold is plotted in Fig.2 as a function of temperature, where the magnitude required for switching is one order smaller than the previously reported value in conventional heavy metal system Pt/FGT6.References: 1. I. M .Miron, G. Gaudin and S. Auffret, Nat. Mater., Vol. 9, p.230 (2010) 2. K. Ando, S. Takahashi and K. Harii, Phys. Rev. Lett., Vol. 101, p.036601 (2008) 3. A. Johansson, J. Henk and I. Mertig, Phys. Rev. B, Vol. 97, p. 085417 (2018) 4. J. Jiang, F. Tang and X. C. Pan, Phys. Rev. Lett., Vol. 115, p.166601 (2015) 5. D. MacNeill, G. M. Stiehl and M. H. D. Guimarães, Nat. Phys., Vol. 13, p. 300 (2017) 6. M. Alghamdi, M. Lohmann and J. Li, Nano Lett., Vol. 19, p.4400 (2019) 7. X. Wang, J. Tang and X. Xia, Sci. Adv., Vol. 5, p.eaaw8904 (2019)

Efficient spin-orbit torque in vdW heterostructure of 2D itinerant ferromagnet and Weyl semimetal

Bulk FeTe exhibits a bicollinear (BCL) antiferromagnetic (AFM) ordering that can be suppressed by Se alloying, where superconductivity emerges with TC=10K at 30% Se. We explore reduced dimensionality on AFM ordering & superconductivity in nanoribbons of single layer FeTe1-xSex grown on SrTiO3 by MBE. Using scanning tunneling microscopy, we find 1D superconducting channel at ribbon edge with a TC of 42K for x<0.1, coexisting with BCL AFM ordered interior. Calculations indicate Se incorporation and presence of the edge destabilize the BCL magnetic order, resulting in a paramagnetic region near the edge with local checkerboard fluctuations conducive to superconductivity. These results show an effective route towards stabilizing superconductivity in Fe-based superconductors at reduced dimensions.1 Furthermore, we show the Tc of single layer FeSe/SrTiO3 can be enhanced by UV light, attributed to a metastable polar distortion at the interface. The enhancement is also nonvolatile and persists even when the light is removed, and is reversible with a voltage pulse (Fig.1),2 paving a path towards high-speed superconducting switches with infinite on/off ratio.References: 1. “Superconductivity on edge: Evidence of one-dimensional superconducting channel on the edges of antiferromagnetic single layer FeTeSe nanoribbons”, ACS Nano, DOI:10.1021/acsnano.9b08726. 2. “Light induced non-volatile switching of superconductivity in single layer FeSe on SrTiO3 substrate”, Nat. Commun. 10, 85 (2019).

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An Improved Magnetostriction Model of Silicon Steel Considering the Saturated Magnetic domain Wall Movement

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