United States

Diodes are a key component in electronics with their nature of asymmetric conduction enabling rectification in circuits. Non-linear response is one criterion to have such effects and spin waves, or the quanta magnons are known to be highly nonlinear with respect to input power or spin transfer torques (STT), which leads to microwave rectification in spin torque nano oscillators[1,2]. While non linear dynamics of magnons due to STT in confined geometry has been well studied thanks to the macrospin nature, its nonlinear nature has been so far elusive in extended films. We measure non-linear spin transport behavior of magnetic garnet thin films by spin orbit torques (SOT) in non-local geometry (Fig.1) [3] and report spin diode effect marked by a strong asymmetric conductance at large current density. Namely higher spin conductance is obtained for the polarity increasing spin fluctuations than for the opposite polarity. We demonstrate that spin diode effects are determined by the collective dynamics of magnetostatic magnons and emergence of the asymmetry requires to work in the long-range regime (large separation between the 2 electrodes &amp;gt; 2μm) to efficiently filter out the spurious symmetric contribution of the rapidly decaying thermal magnons[3]. As the intensity of the spin current increases, the transport properties of magnetostatic magnons crosses 3 different regimes. i) At low currents, it is ballistic set by the film thickness. ii) Close to the damping compensation threshold, it switches to a highly correlated dynamical regime limited by spin-spin relaxation and shows a sharp increase of the non-local conductance. iii) As the temperature of the magnons approaches the Curie temperature, it switches to a diffusive regime, where the propagation length is reduced by collisions with thermal magnons, showing negative differential spin conductance (Fig.2).

![](https://assets.underline.io/uploads/markdown_image/1/image/e9026ed56a884d6b8ad6be08af8ce715.jpg)


Fig.1. Schematics of the four-terminal diode device which consists of two Pt electrodes (Pt1 and Pt2) separated by distance d on a Yttrium Iron Garnet thin film.


![](https://assets.underline.io/uploads/markdown_image/1/image/22ad15451ed7354affa41a5500699ba1.jpg)

Fig.2. Renormalized SOT contribution of the spin conduction i2 detected in Pt2 as a function of I1, the current injected in Pt1. Here T1 is the temperature of the Pt1 and Tc is the Curie temperature.

2022 Joint MMM-INTERMAG

Spin diode effect in magnetic garnets

Diodes are a key component in electronics with their nature of asymmetric conduction enabling rectification in circuits. Non-linear response is one criterion to have such effects and spin waves, or the quanta magnons are known to be highly nonlinear with respect to input power or spin transfer torques (STT), which leads to microwave rectification in spin torque nano oscillators[1,2]. While non linear dynamics of magnons due to STT in confined geometry has been well studied thanks to the macrospin nature, its nonlinear nature has been so far elusive in extended films. We measure non-linear spin transport behavior of magnetic garnet thin films by spin orbit torques (SOT) in non-local geometry (Fig.1) [3] and report spin diode effect marked by a strong asymmetric conductance at large current density. Namely higher spin conductance is obtained for the polarity increasing spin fluctuations than for the opposite polarity. We demonstrate that spin diode effects are determined by the collective dynamics of magnetostatic magnons and emergence of the asymmetry requires to work in the long-range regime (large separation between the 2 electrodes &gt; 2μm) to efficiently filter out the spurious symmetric contribution of the rapidly decaying thermal magnons[3]. As the intensity of the spin current increases, the transport properties of magnetostatic magnons crosses 3 different regimes. i) At low currents, it is ballistic set by the film thickness. ii) Close to the damping compensation threshold, it switches to a highly correlated dynamical regime limited by spin-spin relaxation and shows a sharp increase of the non-local conductance. iii) As the temperature of the magnons approaches the Curie temperature, it switches to a diffusive regime, where the propagation length is reduced by collisions with thermal magnons, showing negative differential spin conductance (Fig.2).

![](https://assets.underline.io/uploads/markdown_image/1/image/e9026ed56a884d6b8ad6be08af8ce715.jpg)


Fig.1. Schematics of the four-terminal diode device which consists of two Pt electrodes (Pt1 and Pt2) separated by distance d on a Yttrium Iron Garnet thin film.


![](https://assets.underline.io/uploads/markdown_image/1/image/22ad15451ed7354affa41a5500699ba1.jpg)

Fig.2. Renormalized SOT contribution of the spin conduction i2 detected in Pt2 as a function of I1, the current injected in Pt1. Here T1 is the temperature of the Pt1 and Tc is the Curie temperature.

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. 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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This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Skyrmions exhibit topologically nontrivial spin textures [1] and can be motioned by comparably small spin-polarized currents [2]. This renders them promising for the use as information carriers in future magnetic data storage and processing technologies, referred to as Skyrmionics. To better understand the physics of Skyrmions, a detailed knowledge of the real space magnetic structure of these spin solitons is mandatory. We have therefore studied the 3D magnetic textures of Skyrmion tubes (SkTs) using in-line and off-axis electron holography (EH). While the orientation of the in-plane magnetic induction B obtained from a Fe0.95Co0.05Ge nanoplate using in-line EH shows the expected hexagonal vortex-like pattern (Fig. 1), a thorough quantitative analysis implies that the underlying 3D texture deviates from that of homogeneously extended Bloch Skyrmions [3]. Low temperature holographic vector field electron tomography (VFET [4]) in an external magnetic field was therefore used to quantitatively reconstruct the full 3D magnetic texture of SkTs in an FeGe needle [5]. The resulting high-resolution 3D magnetic images (Fig. 2) reveal various previously unseen details of the SkTs. Our findings include the occurrence of local deviations from a homogeneous Bloch character within the tubes. They highlight the collapse of the Skyrmion texture upon approaching the surfaces of the needle, provide evidence for the coexistence of longitudinal and transverse Skyrmion textures, and reveal an axial modulation of the SkTs that is found to be strongly correlated among neighboring tubes in the needle. Based on the quantitative 3D magnetic induction data, we have calculated spatially resolved energy density maps across the SkTs that provide experimental evidence for the energetic stabilization of these magnetic solitons through an energy gain due to the Dzyaloshinskii-Moryia interaction, which overcompensates the exchange energy in the tube centers.

![](https://assets.underline.io/uploads/markdown_image/1/image/95d4498ede230bdf211fb866fabb1ce2.jpg)

Orientation map of the projected in-plane component of the magnetic induction in the hexagonal Skyrmion lattice of a Fe0.95Co0.05Ge nanoplate.

![](https://assets.underline.io/uploads/markdown_image/1/image/a445af1acb5f54ffe8123e81a66772df.jpg)

Morphology of an FeGe needle (left) and direction of the 3D magnetic induction B (right) as determined from holographic VFET experiments.

Unravelling the details of the magnetic texture of skyrmion tubes in three dimensions

Focused ion beam (FIB) irradiation is a versatile means to tune magnetic thin films on the nanoscale [1]. Ion irradiation can create nucleation sites for Skyrmions [2] and even establish Skyrmion-tracks [3]. In this work, we present statistical data of Skyrmion motion driven by 50 ns long current pulses in a sputtered W/CoFeB/MgO trilayer. In this layers a Skyrmion phase can be stabilized by a an oop-field in the low single digit mT regime. Furthermore, we elaborate on how Skyrmion motion can be tuned and directed by non-destructive Ga+ Ion irradiation with ultra-low doses (&lt;1e13 Ions/cm2) and high dose resolution of &lt; 1e12 Ions/cm2. First, we will give an overview of how the magnetic properties of the thin film are affected by ion irradiation. Here we analyze the average domain size, film coercivity (Hc) and relative decrease of saturation magnetization (Ms) and effective magnetization (Meff), over different irradiation steps and compare this data to stepwise annealing of the samples. Next, we track the motion of at least 50 Skyrmions for various current densities in magnetic wires, utilizing widefield magneto-optical measurements, as depicted in Figure 1. Hereby half of the wire is treated with Ga+ ions. We show that ion irradiation can be used to adjust the motion of Skyrmions towards lower velocities. While the Skyrmion velocity is very similar in the pristine parts of the wires, the velocity in the irradiated region is heavily dependent on the ion dose (see Figure 2). This lower velocity is accompanied by a significantly reduced Skyrmion Hall angle in the irradiated part, which leads to a nearly straight motion in the direction of the current flow. Beyond that, also stochastical motion due to thermal effects is largely supressed in the irradiated parts.

![](https://assets.underline.io/uploads/markdown_image/1/image/bb1f0be62208fad403370b509e76634d.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/82950f12d80d3940195e22e18676c0c9.jpg)

Influence of Ga+ Ion Irradiation on Skyrmion Motion

Influence of Ga+ Ion Irradiation on Skyrmion Motion

Skyrmions are topologically protected chiral spin textures that have shown promise as data carriers in future spintronic applications. They can be stabilized by the interfacial Dzyaloshinskii-Moriya interaction (iDMI) in material systems with inversion asymmetry and spin-orbit coupling, such as Ir/Co/Pt multilayers [1]. The ability to locally (at the nanoscale) tune such interface interactions, and hence the skyrmion energy, could lead to novel ways to optimise the nucleation and control of skyrmions. In this contribution we investigate the local tuning of the iDMI and the perpendicular magnetic anisotropy (PMA) using Ga+ ion irradiation, as well as its effect on skyrmion nucleation. Ga+ ion irradiation affects the coordination of atoms at the interfaces (Fig. 1a), which is expected to decrease both PMA and iDMI [2]. From Fig. 1b, we find that the reduction in PMA and iDMI are correlated, suggesting that both effects depend similarly on the interface quality. This reduces the energy cost of domain walls but does not affect their chirality. Hence, we expect that this will also facilitate the nucleation of more complicated chiral textures, such as skyrmions. To confirm this, we studied for the first time the current driven nucleation of skyrmions [3] in identical devices with and without Ga+ ion irradiation. We find that the ion irradiation indeed affects skyrmion nucleation, see Fig. 2. The critical current density required for nucleation is reduced by almost 30% and the number of skyrmions is doubled by irradiation. Thus, we argue that ion irradiation can be used to facilitate and control the nucleation of skyrmions in novel devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/3e984d72283a4626aa9f30b40e9bb2d9.jpg)

Fig. 1 a) Illustration: Ion irradiation causes intermixing at interfaces (left to right). b) Plot of the strength of the iDMI Ds against the strength of the interface PMA Ks, both Ds and Ks decrease when the Ga+ dose is increased, as indicated by the arrow.


![](https://assets.underline.io/uploads/markdown_image/1/image/920cf7b2d1c34d1c6fbb082d4a8f6f88.jpg)

Fig. 2 Number of skyrmions nucleated in our devices after applying 1000 50 ns pulses with current density J. In an irradiated device the number of skyrmions is increased and the current density required for nucleation is lowered. Black lines are fits to the data with the error function. Top: MFM scans of the devices.

Facilitating Skyrmion Nucleation in Ir/Co/Pt Multilayers With Ga+ Ion Irradiation

Anisotropic magnetoresistance (AMR) is a ubiquitous and versatile probe of magnetic order in contemporary spintronics research [1]. It arises from the dependence of the resistance of a magnetically ordered solid on the relative angle between the applied electric field and the magnetization vector independent of their polarity. The origins of the AMR are usually ascribed to extrinsic effects (i.e. spin-dependent electron scattering), whereas intrinsic (i.e. scattering-independent) contributions are neglected [2]. Here, we perform a broadband measurement of the AMR of prototypical ferromagnets such as Co, Ni or NiFe alloys in a frequency range from DC to 28 THz [3]. The large bandwidth covers the regimes of both diffusive and ballistic intraband electron transport and, thus, allows us to separate extrinsic and intrinsic AMR components. Analysis of the THz response based on Boltzmann transport theory reveals that the AMR of the Ni and NiFe alloys is of predominantly extrinsic nature. However, the Co thin film exhibits a sizeable intrinsic, frequency-independent AMR contribution, which amounts to more than 2/3 of the DC AMR contrast of 1%. These features are attributed to the lower symmetry of the hexagonal structure of Co crystallites which allows for larger anisotropies in their bandstructure. The new insight into the nature of AMR is not only relevant for the fundamental understanding of the magnetotransport but might also advance the ultrafast probing techniques in spintronic devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/b939fa383f615a86b5ac200134a15b4d.jpg)

Fig. 1. THz detection of the AMR. The incident THz pulse applies transient electric field in the direction of polarization, in which, as a consequence of the AMR, the electrical resistance and the transmission of the THz pulse depend on the angle of the magnetization. Variations in transmitted amplitude allow us to calculate the AMR contrast.


![](https://assets.underline.io/uploads/markdown_image/1/image/584dca932356943c776e64e9fc76bbd6.jpg)

Fig. 2. Spectral composition of the AMR in different metals. (a) The absolute value of the AMR contrast in permalloy versus frequency is well described within the Drude formalism (curve) assuming only magnetization-dependent electron scattering rates. (b) The same measurement for a cobalt sample shows a scalable frequency-independent offset which witnesses the intrinsic contribution to the AMR.

Broadband terahertz spectroscopy of anisotropic magnetoresistance reveals intrinsic contributions

Spin torque ferromagnetic resonance (ST-FMR)1 has widely been used for evaluation of the spin Hall effect (SHE) of the nonmagnetic metal (NM) in an NM/ferromagnetic metal (FM) bilayer structure. Figure 1 shows a schematic of the measurement setup of the ST-FMR. DC voltage, VDC, is monitored under a microwave irradiation with sweeping the external magnetic field, Bext. VDC-Bext curve in the ST-FMR measurement is composed of symmetric and anti-symmetric Lorentzian functions. In the simplest case, efficiency of the SHE, which is especially called spin Hall angle (SHA), can be estimated by taking the amplitude ratio between two Lorentzian functions. However, unwanted effects such as the spin pumping, the anomalous Nernst effect, and non-uniform flow of the charge current impede a precise estimation of SHA. Therefore, a cross-check of the obtained SHA by using another methodology is desired. In this study, we found an additional signal related to the SHA in the ST-FMR spectrum2. Figure 2 shows the ST-FMR spectrum of a tantalum (Ta)/cobalt (Co) sample, where the microwave frequency, f, was 12 GHz and the microwave power, P, was 5 dBm. l, w, and q defined as shown in Fig. 1 were 5 μm, 5 μm, and 45°, respectively. In addition to the conventional Lorentzian functions which correspond to the ST-FMR, a magnetization-dependent background (BG) signal was also observed. From the Bext, P, f , temperature and NM material dependences, we conclude that the BG signal is mainly generated by the spin-dependent unidirectional spin Hall magnetoresistance (SD-USMR)3, the origin of which is the spin-dependent electron mobility in the FM. From the magnitude of the BG signal, SHA of Ta was estimated to be -0.042±0.006, which is consistent with the previous works. The ST-FMR spectrum is produced by the spin orbit torque, whereas the BG signal is produced by the spin accumulation. Therefore, our finding provides an effective cross-check of the SHA, which are obtained from two different physical origins by using only one ST-FMR spectrum.


![](https://assets.underline.io/uploads/markdown_image/1/image/a0a14efb8444390cd598c3d1052c95a2.jpg)

A schematic of the device and the electrical circuit used in the ST-FMR measurement


![](https://assets.underline.io/uploads/markdown_image/1/image/d505d560f88dbba485e85162b710bd64.jpg)

ST-FMR spectra with the BG signal originating from the SD-USMR for Ta/Co.

DC voltage generated by the unidirectional spin Hall magnetoresistance in the spin torque ferromagnetic resonance spectrum

Pure spin currents produced by the spin Hall effect(SHE) in a nonmagnetic heavy metal has the potential to drive ultra-fast, energy-efficient spintronic devices such as spin Hall nano-oscillators(SHNOs)[1-3], spin-orbit torque based magnetic random access memory(SOT-MRAM), and spin logic devices[4,5]. One key challenge in such emerging devices remains to reduce their high current densities(Jc) and energy consumption to drive magnetization switching and auto oscillations in the adjacent ferromagnets. Efforts have been made to increase the SOT efficiency(ζSOT) by choosing suitable material combinations and/or use oxygen incorporation[6]. However, the increased ζSOT is observed at the expense of an equivalent increase in the longitudinal resistivity(ρ), which essentially cancels out any reduction in the power consumption. A more successful direction is instead to alloy elements, which are in themselves already good SOT material[7]. Here, we demonstrate such alloying of W with Ta to obtain a simultaneous increase of both the ζSOT and the spin Hall conductivity(σSH), which in turn substantially reduces the Jc in W100-xTax(5nm)/CoFeB(tCFB=1.4 to 2 nm)/MgO(2nm) SHNOs. First, we performed STFMR measurements on microbars (6 ×18 µm2, 6 ×12 µm2) to determine their magnetodynamical properties such as current induced ζSOT and σSH. The ζSOT varies from maximum ~ -0.57(x=10%) to ~-0.18(x = 50%) as compared to pure β-W, ~-0.36(x=0). Thanks to a reduced resistivity of W100-xTax, the increased ζSOT is accompanied with a significant increase of the σSH of about ~140% as compared to pure β-W. Finally, we investigated the alloying effect on the auto-oscillation threshold current(Ith) densities by fabricating SHNOs of different widths varying from 10nm to 150nm on a 4 × 14 µm2 mesa[1] and observed about 40% reduction in Ith (at x=12%) as compared to pure β-W measured. The trade-off between ζSOT, ρ, and σSH demonstrates the promising aspects of a W-Ta alloying approach for energy-efficient operation of emerging spintronic devices

![](https://assets.underline.io/uploads/markdown_image/1/image/5e590e6a057e20864ec79b7e0c117dad.jpg)

Fig.1: (a) Variation of ρ(blue) and σSH(red) vs. W100-xTax alloy composition. (b-c) Power spectral densities showing a 40% reduction in the SHNO Ith for two SHNOs with identical constriction width of 50nm.

Alloying effect on auto-oscillation properties of W100-xTax/CoFeB/MgO spin Hall nano-oscillators

Rare earth-transition metal (RETM)-based ferrimagnets are known to exhibit strong bulk perpendicular magnetic anisotropy and bulk Dzyaloshinskii-Moriya interaction [1]. These properties make RETM ferrimagnets a model system to study exciting magnetic phenomena such as magnetic skyrmion [2,3], chiral domain wall [3], all-optical switching [4], spin-orbit torque switching [5] and canted magnetic moments. Here, we demonstrate a field-free spin-orbit torque-driven multistate switching of a nearly compensated GdCo ferrimagnet sandwiched between Ta and Pt. We show that our GdCo film exhibits a strong canting of magnetic moments, and the canted moments can be deterministically switched among three stable states using a current-driven spin-orbit torque, even in the absence of a magnetic field. We further show that the three states persist in the presence of an in-plane magnetic field and the levels of the three states can be tuned with the magnitude of the magnetic field. We consider various possible origins of the canting, including concentration gradient, Dzyaloshinskii - Moriya interaction, and balanced pair-correlations of unlike atoms versus like atoms in the growth direction, and discuss various methods to differentiate among these mechanisms. Furthermore, we discuss the possibility of domain formations to explain the observed multistate. Our results provide a new perspective to study the competing magnetic interaction in RETM-based ferrimagnetic alloys at the near-compensation point, and enable a new pathway to achieve multistate spin-orbit torque devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/df0a749c720a6befff1af56d0b3f65bb.jpg)

Multistate switching of canted GdCo moments via spin-orbit torque with zero in-plane symmetry breaking field.


Field-free Spin-orbit Torque-driven Multistate Switching of Canted GdCo Moments

BiSb topological insulator is a promising candidate for spin-orbit-torque (SOT) magnetoresistive random-access memory (MRAM). A giant spin Hall angle θSH up to 52 and 10.7 has been observed for BiSb deposited by MBE on GaAs(111) [1] and by sputtering on c-plane Al2O3 [2] substrates, respectively. In realistic MRAM, however, magnetic tunnel junctions whose core structure includes an MgO barrier layer and a free ferromagnetic layer on top have to be deposited on Si/SiOx substrates. In this work, we demonstrate the large θSH = 2.4 of BiSb in all-sputtered BiSb/CoPt/MgO multilayers on Si/SiOx substrates, and investigate the SOT magnetization switching behaviors. Low power and fast switching is attained, demonstrating the robustness and reliability of BiSb as a spin current source. We deposited BiSb(10)/Pt(0.8)/Co(0.6)/Pt(0.8)/MgO(10) (Fig. 1(a)), from top to bottom on Si/SiOx substrates at room temperature (thickness in nm). The Pt/Co/Pt trilayers are perpendicularly magnetized with a large anisotropy field of 4.5 kOe (Fig. 1 (b)(c)). Fig. 1(d) shows 2nd harmonic Hall resistance R2ω - field Hx characteristics at different current density JBiSb, and a representative fitting curve (dashed) for evaluation of the antidamping-like field HAD. Fig. 1(e) shows the estimated HAD at various JBiSb, which yields θSH = 2.4. Fig. 2(a) shows the pulse width τ dependence SOT switching loop. The magnetization of CoPt trilayers can be efficiently switched by a small threshold current density JthBiSb = 2.3 MAcm-2 at pulse width of 50 ms. The JthBiSb - τ characteristics yields the thermal stability factor Δ = 32 (Fig. 2(b)). We also demonstrate robust switching by consecutive pulses (Fig. 2(c)) and fast switching down to 100 ns (Fig. 2(d)). Our work shows that it is possible to implement ultralow power SOT-MRAM using BiSb on Si/SiOx substrates.

![](https://assets.underline.io/uploads/markdown_image/1/image/377dc47146e78726a8fbab3cddd96e54.jpg)

Fig. 1 (a) Schematic structure. (b)(c) Hall resistance measured with magnetic field perpendicular to the film plane and in-plane along the current direction. (d) R2ω as a function of Hx at different JBiSb. (e) HAD as a function of JBiSb.

![](https://assets.underline.io/uploads/markdown_image/1/image/0dfa12a8b5145229ef559ecc86b500d1.jpg)

Fig. 2 (a) SOT switching loops at different τ. (b) JthBiSb as a function of τ. (c) Robust switching by 100 μs pulse currents. (d) Switching loops by short pulses.

Low power spin-orbit torque magnetization switching in all-sputtered BiSb topological insulator / perpendicularly magnetized CoPt / MgO multilayers on Si substrate

Efficient modulation of electrically-injected spin signals that is suitable for modern-day transistor functionality is yet to be established. In this work, we demonstrate in detail the fabrication of Fe/n-GaAs spin injection device and the experimental setup for an optical gating of the non-local spin transport signal. Three- and four-terminal Hanle measurements confirm successful spin injection into n-GaAs, with strong interfacial spin dephasing at high magnetic fields. Tunable-wavelength, time-resolved pump-probe Kerr rotation [1] was used to verify the strongest photoexcitation signal with 822 nm and the long spin relaxation time of ~ 2.4 ns in the channel n-GaAs layer. As seen in Figure 1, changes in the non-local spin transport signal, V3-4, were measured with the modulation light with opposite helicity illuminated in the region of pure spin current. The helicity-dependent optical modulation efficiency, calculated as the ratio between the difference and the sum of the signals at the opposite helicity, of (0.4 ± 0.3)% was obtained at 30 K at the maximum available laser power of 7 mW. Furthermore, in-situ scanning electron microscope interface imaging, developed by authors [2], was used to reveal the correlation between the contrast inhomogeneity of the Fe/n-GaAs injector interface and the injection current, as displayed in Figure 2. The larger contrast inhomogeneity observed at lower injection currents suggest “pin-hole” type charge transport at bias voltage lower than the Schottky barrier height.

![](https://assets.underline.io/uploads/markdown_image/1/image/1fb23f3b9f343fc75dd41d8812ec204e.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/d955ce302deb8d7f30dd574b818b0b9c.jpg)

Development of an Optically-Gated Fe/n-GaAs Spin-Polarised Transistor

Development of an Optically-Gated Fe/n-GaAs Spin-Polarised Transistor

Nonreciprocal electrical transport responses arise in materials with broken inversion and time-reversal symmetries [1]. Although these nonlinear magnetoresistance or Hall effects are typically weak compared with their linear analogs, they can be used to probe exotic properties like spin-orbit interaction, spin textures and superconductivity. At the surface of the 3D topological insulator (TI) Bi2Se3, a nonlinear planar Hall effect (NPHE) was reported to exist due to the hexagonally warped spin structures [2]. This NPHE is expected to be small at low carrier densities because the hexagonal warping effect is negligible at the Dirac point. In this study, we observed a similar NPHE in Bi2Se3/CoFeB and magnetic insulator/Bi2Se3 heterostructures. Though with a lower carrier density, the NPHE in these systems is two orders of magnitude larger than the previously reported one. Moreover, the strength of this NPHE scales inversely with carrier density. This suggests that the intrinsic hexagonal warping is not the dominant mechanism for the observed NPHE. Instead, we attribute this large NPHE to the recently proposed extrinsic mechanism based on the interplay between current-induced spin-polarization and scattering from spin-momentum locking inhomogeneities [3]. Our results provide experimental evidence for this new mechanism and show that the NPHE can be enhanced by disorder engineering.

![](https://assets.underline.io/uploads/markdown_image/1/image/a5ea6152d1cf679c7030c2ca6f2fb62d.jpg)

Fig. 1 Nonlinear planar Hall effect in a YIG(2.46m)/Bi2Se3(8nm) sample.

![](https://assets.underline.io/uploads/markdown_image/1/image/895b64111427635788c6e4f435603dcd.jpg)

Fig. 2 Carrier density dependence of the nonlinear planar Hall effect.

Spin diode effect in magnetic garnets

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