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Weyl semimetals (WSMs) are a newly discovered class of quantum materials which can host a number of massless quasiparticles called Weyl fermions. One of the most unique properties of WSMs is the chiral anomaly – a pair of Weyl nodes of opposite chirality acts as source and drain of electrons in the presence of non-perpendicular electric and magnetic fields. To date, the most remarkable phenomenon induced by the chiral anomaly is the longitudinal negative magnetoresistance, which is a linear response effect. In this work, we theoretically investigate the transport properties of WSMs in the nonlinear regime and predict a novel nonlinear Hall effect in tilted non-centrosymmetric Weyl semimetals. Intuitively, a steady-state density difference between a pair of Weyl nodes is established when the chiral pumping and internode relaxation reach a balance, which conspires with the anomalous velocity to give rise to this nonlinear Hall effect. Taking the semiclassical Boltzmann approach, we find that the nonlinear Hall conductivity scales linearly with both the electric and magnetic fields, and depends critically on the tilting of the Weyl cones in both type-I and type-II WSMs. For a pair of Weyl cones that are un-tilted or oppositely tilted, the chiral-anomaly-induced nonlinear Hall current vanishes because it is forbidden by a mirror symmetry. We also show that this effect does not rely on a finite Berry curvature dipole, in contrast to the intrinsic quantum nonlinear Hall effect that was proposed to occur in time-reversal invariant materials [1].References: [1] I. Sodemann and L. Fu, Phys. Rev. Lett. 115, 216806 (2015).

MMM 2020

Chiral-Anomaly-Induced Nonlinear Hall Effect in Tilted Weyl Semimetals

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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MMM 2022

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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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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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

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.

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

Using the first-principles non-equilibrium Green’s function technique [1] with supercell disorder averaging, we study the influence of interfacial intermixing on the spin-orbit torque in Co/Pt (111) bilayers. The interlayer distances are optimized, several models of intermixing are considered, and atomic potentials in the intermixed layers are obtained using the coherent potential approximation. The magnitude and thickness dependence of the damping-like torque are similar to earlier results for the Co/Pt (001) interface [1,2] and rather insensitive to intermixing. In contrast, the field-like torque, which is small in the case of an ideal interface, is strongly enhanced by intermixing.References: [1] K. D. Belashchenko, A. A. Kovalev, and M. van Schilfgaarde, Phys. Rev. Mater. 3, 011401 (2019). [2] K. D. Belashchenko, A. A. Kovalev, and M. van Schilfgaarde, arXiv:1908.02680.

Effect of interfacial intermixing on spin-orbit torque in Co/Pt bilayers

Weyl semimetals combine both topological and semimetallic effects in their transport of fermions through both bulk and surface states, making them excellent candidates for transverse thermomagnetic transport via the Nernst effect. The Nernst effect is a thermoelectric phenomenon requiring a magnetic field. A temperature gradient is applied to a sample, and the sample is placed in an external magnetic field orthogonal to the temperature gradient. The charge carriers, moving parallel to the temperature gradient, now experience a Lorentz force due to the cross product of the magnetic field and the temperature gradient. An electric field is produced in the mutually perpendicular direction. Single-crystal NbP has shown an unprecedentedly large Nernst thermopower at high magnetic fields, exceeding 800 μV K-1 at 109 K and 9 T [1]. Bulk polycrystalline NbP maintains a large Nernst thermopower, although its magnitude is decreased by approximately a factor of 8 under similar circumstances. Due to the high electrical conductivity of the material, polycrystalline NbP’s Nernst power factor is determined to be 35 x 10-4 W m-1 K-2 at 9 T and 136 K, which is comparable to that of state-of-the-art thermoelectric materials [2]. This high conversion of thermal-to-electrical energy in NbP has been determined as due to the chemical potential’s location near linear, Dirac band crossing points (called Weyl points), giving access to many mobile holes and electrons. These initial results of transverse thermomagnetic transport in both single-crystal and polycrystalline NbP motivate further study to elucidate Weyl fermion transport and the length scales over which it is effective and dominant. Here, we present a grain size study on bulk polycrystalline samples of NbP, where different annealing times result in different grain sizes. Via microstructural characterization and thermomagnetic transport measurements, we can begin to determine the effects of grain size on transport in Weyl semimetals.References: [1] S. J. Watzman et al. Phys. Rev. B 97(16), 161404(R) (2018). [2] C. Fu et al. Energy Environ. Sci. 11(10), 2813-2830 (2018).

Grain Size Dependence of Transverse Thermomagnetic Transport in the Weyl Semimetal NbP

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).

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