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Spin-torque ferromagnetic resonance (ST-FMR) is a common method used to measure spin-orbit torques (SOTs) in heavy metal/ferromagnet bilayer structures. In the course of a measurement, other resonant processes such as spin pumping (SP) and heating can cause spin current or heat flows between the layers, inducing additional resonant voltage signals via the inverse spin Hall effect (ISHE) and Nernst effects (NE). In the standard ST-FMR geometry, these extra artifacts exhibit a dependence on the angle of an in-plane magnetic field that is identical to the rectification signal from the SOTs. We show experimentally that the rectification and artifact voltages can be quantified separately by measuring the ST-FMR signal transverse to the applied current (i.e., in a Hall geometry) in addition to the usual longitudinal geometry. We find that in Pt (6 nm)/CoFeB samples the contribution from the artifacts is small compared to the SOT rectification signal for CoFeB layers thinner than 6 nm, but can be significant for thicker magnetic layers. We observe a sign change in the artifact voltage as a function of CoFeB thickness that we suggest may be due to a competition between a resonant heating effect and the SP/ISHE contribution.

MMM 2020

Transverse and Longitudinal Spin-Torque Ferromagnetic Resonance for Improved Measurements of Spin-Orbit Torques

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

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

Energy-efficient control of magnetization in nanoscale is fundamental for designing future generation spintronic devices. Current-induced magnetization switching via spin-orbit torques (SOTs), realized in ferromagnet/heavy metal bilayers, has emerged as one of the most promising approaches [1]. The magnitude and the sign of the SOT can be adjusted by optimizing the parameters of the system such as the thickness and the composition of the layers [2]. In this case, however, the SOTs are fixed once the multilayer is fabricated. However, for complex switching concepts, i.e. to selectively switch parts of the ferromagnet using single pulse lines, which may lead to drastically simplified device architectures, it is necessary to locally and dynamically tune the SOTs in a system. Here we demonstrate the possible dynamic control of SOTs in perpendicularly magnetized W/Co20Fe60B20/MgO multilayers by piezoelectric strain [3]. We find that modulated by an electric field, tensile strain increases the damping-like torque by a factor of two, while the compressive strain leads to a decrease. On the contrary, the field-like torque remains largely unaffected by strain. We explain our experimental results with the help of theoretical ab initio calculations revealing the difference in the response of the SOTs to the strain.References: 1. I.M. Miron et al., Nat. Mater. 9, 230 (2010). 2. A. Manchon et al., Rev. Mod. Phys. 91, 035004 (2019). 3. M. Filianina et al., Phys. Rev. Lett. 124, 217701 (2020).

Piezoelectric Strain Control of Spin-Orbit Torques in Perpendicularly Magnetized CoFeB Thin Films

Spin Hall oscillator (SHO) is a promising spin torque oscillator (STO) having high durability due to a small driving current. However, conventional SHOs with in-plane precession (IPP) mode require bias-fields for stable oscillations [1-4], which are not favored in certain applications such as a neuromorphic computing [5]. Here, we propose and theoretically analyze a bias-field-free SHO with an in-plane hard axis and out-of-plane precession (OPP) mode by solving the macrospin Landau-Lifshitz-Gilbert-Slonczewski equation analytically and numerically. Fig. 1 shows the schematic structure of our two-terminal bias-field-free SHO. The SHO consists of a magnetic tunnel junction, a spin source layer, and a shunting resistance. Materials with a small spin Hall angle are also available for the spin source because the shunting resistance provides an in-plane charge current path for a spin current generation by the spin Hall effect. A bias-field-free OPP mode can be obtained by controlling a magnetic hard axis of free layer in the same direction of a spin polarization. In our simulations, the magnetic anisotropy was controlled by demagnetization coefficients without the loss of generality. Fig. 2 shows the typical simulation result of the magnetization dynamics in our SHOs. Bias-field-free oscillations were successfully observed. We also derived formulas for a critical current, a driving current and an oscillation frequency by using the saddle and constant energy approximations [6], and they were in good agreement with numerical simulation results. Furthermore, the drive current of our SHOs were almost ten times smaller than that of conventional bias-field-free STOs.References: [1]L. Liu, C. -F. Pai and D. C. Ralph, Phys. Rev. Lett., Vol. 109, p.186602 (2012) [2]Z. Duan, A. Smith and L. Yang, Nat. Commun., Vol. 5, p.5616 (2014) [3]V. E. Demidov, S. Urazhdin and H. Ulrichs, Nat. Mater., Vol. 11, p.1028 (2012) [4]V. E. Demidov, S. Urazhdin and A. Zholud, Appl. Phys. Lett., Vol. 105, p.172410 (2014) [5]J. Torrejon, M. Riou and F. A. Araujo, Nature, Vol. 547, p.428 (2017) [6]T. Taniguchi and H. Kubota, Phys. Rev. B, Vol. 93, p.174401 (2016)

Bias-field-free spin Hall oscillator with an out-of-plane precession mode

In the spin Hall effect (SHE), a longitudinal charge-current induced transverse pure spin current has been extensively studied for the application of magnetization switching by spin-orbit torque. However, due to the strict right-hand rule among charge current, spin current, and spin polarization, this highly attractive switching scheme is not efficient and often accompanied by an unfavorable external magnetic field in a heterostructure with perpendicular magnetization (PM). In this work, we lift the restriction by demonstrating the magnetization-dependent spin Hall effect (MDSHE) in YIG/PM heterostructure, as shown in Fig. 1. Unlike the conventional SHE with the locked orientation of spin polarization, the spin current induced by the MDSHE can be arbitrarily and independently controlled by the magnetization direction of the magnetic layer. We reported about 3.6% of injected spins experience the effective spin rotation in PM layer of Pt(2)/Co(0.5)/Pt(2). Our approach provides an explicit route in exploring the spin-to-charge conversion with controllable orientations of spin polarization, which offers significant advantages in developing energy-efficient spintronic devices.

Controllable Orientations of Spin Polarization Beyond the Spin Hall Effect

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).

Enhanced superconductivity in single layer FeTeSe/SrTiO3 heterostructures INVITED

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).

Transverse and Longitudinal Spin-Torque Ferromagnetic Resonance for Improved Measurements of Spin-Orbit Torques

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