Session W42: Spin Hall Effect

Strong voltage-induced tunability of threshold current and frequency in spin Hall nano-oscillators

Spin Hall nano-oscillators (SHNOs) utilize pure spin currents to excite auto-oscillations at microwave frequencies in nanoscopic regions of magnetic thin films^1-3. Thanks to their wide frequency tunability^1,2, their robust mutual synchronization in chains as well as in 2D arrays^1,3, and their CMOS compatibility², SHNOs have recently emerged as a promising spintronic device for neuromorphic computing³. While the SHNO frequency can be tuned with both current and external field, the lack of fine individual SHNO control in synchronized networks limits cognitive tasks in oscillator-based computing. It would be highly advantageous if an energy efficient route such as electrostatic gating can independently tune the SHNO characteristics in a synchronized network to perform more complex neuromorphic tasks^3,4.

Here we demonstrate how electrostatic gating in nano-constriction based W(5nm)/CoFeB(1.7nm)/MgO(2nm) SHNOs can lead to substantial voltage-controlled tunability of threshold current and auto-oscillation frequency. High frequency microwave measurements show a large overall modulation of about 22% in threshold current with △V_G= 4V and a moderate frequency tunability of 12 MHz/V. Our detailed analysis based on ST-FMR measurements combined with micromagnetic simulations unveil that the observed tunabilities are caused by minor voltage-induced changes in the perpendicular magnetic anisotropy, which, in our case, not only tunes the frequency but also significantly modifies the localization of the auto-oscillating mode resulting in a large change of the effective damping. Our demonstration introduces a new insight to critically control the effective damping and represents a significant step towards the realization of complex neuromorphic tasks^3,4.

References
¹ A. A. Awad, et al., Nat. Phys. 13, 292-299 (2017).
² H. Fulara, et al., Sci. Adv. 5, eaax8467 (2019).
³ M. Zahedinejad, et al., arXiv:1812.09630 (2018); Nat. Nanotech., accepted.
⁴ M. Romera, et al., Nature 563, 230 (2018).   

Large spin Hall effect in room-temperature sputtered W3Ta thin films grown on SiO2 and Al2O3

The spin Hall effect (SHE), in non-magnetic (NM) metals with strong spin-orbit coupling (SOC) has received much attention due to potential technological applications like magnetic random-access memory (MRAM) and spin-logic devices. Large spin Hall angles (SHA, the ratio of J_s/J_c) have been observed in materials like Pt and the metastable phase, β-W (a.k.a. W₃W in the A15-structure). Recently, W₃Ta (and other A15 compounds) was theoretically predicted to host an even larger intrinsic SHE than β-W, originating from the large spin Berry curvature of its electronic band structure. Here we report the SHE of W_4-xTa_x films including W₃Ta, deposited by DC magnetron co-sputtering on SiO₂ and Al₂O₃ substrates. Spin-torque ferromagnetic resonance (ST-FMR) and optically detected ferromagnetic resonance (ODFMR) techniques were used to measure the SHA of various W_4-xTa_x compositions and thicknesses with CoFeB as the magnetic layer. We find that W₃Ta in the A15 structure could be stabilized on both types of substrates at room temperature and hosts a large SHA in W₃Ta similar to theoretical predictions opening the door to facile device fabrication of Pt-free spintronic devices.
  

Critical spin fluctuation mechanism for the spin Hall effect

We propose mechanisms for the spin Hall effect in metallic systems arising from the coupling between conduction electrons and local magnetic moments that are dynamically fluctuating. We consider a microscopic model proposed by Kondo [1] for the coupling between electrons and local moments and describe the fluctuation of local moments using the self-consistent renormalization method by Moriya [2]. Both a side-jump-type mechanism and a skew-scattering-type mechanism naturally arise and give rise to a nontrivial temperature dependence in the spin Hall conductivity. This leads to the enhancement in the spin Hall conductivity at non-zero temperatures near the ferromagnetic instability [3]. The proposed mechanisms could be observed in 4d or 5d metallic compounds.
[1] J. Kondo, Prog. Theor. Phys.27, 772 (1962).
[2] T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism, Solid-State Sciences 56 (Springer-Verlag, 1985).
[3] S. Okamoto, T. Egami, and N. Nagaosa, arXiv:1905.10929 (to be published).   

Quantiative X-ray Imaging of Spin Accumulation due to the Spin Hall Effect in NixCu1-x Nanowires

We recently reported a spin Hall ratio θ_SH = 1.05 ± 0.18 in Ni₆₀Cu₄₀, an alloy that is nonmagnetic at room temperature, based on FMR measurements of unpatterned Ni₈₀Fe₂₀ films deposited in a bilayer with the alloy [1]. Like previous studies of spin Hall effect (SHE) in heavy metals such as Pt and W, this work inferred spin accumulation indirectly, in this case from its effect on the FMR resonance. An alloy containing Ni enables scanning transmission x-ray microscopy (STXM) to directly image spin accumulation using circularly polarized x-rays tuned to the Ni L3 absorption edge. Importantly, this technique can quantify the spin accumulation without resorting to a theoretical model of spin transport. In wires of Ni₆₀Cu₃₅Al₅ with a cross section ≈ 80 nm x 30 nm and driven at a current density ≈ 5 x 10¹¹ A/m², fabricated on Si₃N₄ membranes, we observed spin polarization along each wire edge in normal-incidence STXM images. The amount of spin accumulation is consistent with θ_SH ≈ 1 and it obeys three symmetries expected for SHE measured via STXM: 1) opposite sign on opposite edges of the wire, 2) opposite sign with reversal of the driving current, and 3) opposite sign with opposite x-ray helicity.
[1] M.W. Keller et al., Phys. Rev. B 99, 214411 (2019).   

Mutually synchronized 2D spin Hall nano-oscillator arrays with quality factors up to 170,000

Nano-constriction based Spin Hall nano-oscillators (SHNOs) have emerged as an attractive alternative to spin torque nano-oscillators [1,2], as their auto-oscillating mode exhibits substantial spatial expansion in out-of-plane fields [3], propagating spin waves can be generated [4], and long chains of nano-constrictions can be mutually synchronized [5]. Here we demonstrate that it is also possible to synchronize nano-constriction SHNOs in two dimensions. We fabricate 2D square SHNO arrays ranging from 2 x 2 to 10 x 10 constrictions and study their microwave signal properties in out-of-plane fields using both electrical measurements and Brillouin Light Scattering microscopy. We observe robust mutual synchronization in up to 8 x 8 arrays and find that their quality factor, Q = f/Δf, increases in direct proportion to the number of mutually synchronized constrictions, with the largest arrays showing Q = 170,000.

[1] T. Chen et al., Proc. IEEE 104, 1919 (2016)
[2] V. Demidov et al., Appl. Phys. Lett. 105, 172410 (2014)
[3] M. Dvornik, A. A. Awad, and J. Åkerman, Phys. Rev. Appl. 9, 014017 (2018)
[4] H. Fulara et al., Sci. Adv. 5, eaax8467 (2019)
[5] A. A. Awad et al., Nature Physics 13, 292–299 (2017)
[6] M. Zahedinejad et al., Nature Nanotechnology, accepted (2019); arXiv:1812.06350   

Magnetization-Independent Spin Hall Effect in Ferromagnetic Metals

The anomalous spin Hall effect, which creates charge-to-spin conversion in metallic ferromagnets, offers an exciting opportunity to generate spin currents for which the spin direction is controllable. Here we report spin-torque ferromagnetic resonance measurements of current-induced torques in ferromagnet-spacer-ferromagnet trilayers with NiFe, Co and CoFeB as our magnetic layers, allowing us to clearly separate signals from the different ferromagnetic layers. We observe signals with the symmetry of a magnetization-independent spin Hall effect with spin-to-charge efficiencies as large as 10% in NiFe, which is comparable to heavy metal-ferromagnet bilayers investigated previously. This research illustrates some of the competing effects which must be considered when investigating spin-to-charge conversion in ferromagnets, and also confirms that the spin current polarization and local magnetic moment in a ferromagnet do not need to be aligned.   

Maximizing the spin Hall ratio of Pt: Trade-off between intrinsic spin Hall conductivity and carrier lifetime

Spin Hall metals with high spin-torque efficiencies and relatively low resistivities are key for developing practical spin-orbit torque technologies (e.g. memories, oscillators, and logic). Pt-based spin Hall metals are the most attractive for such applications due to their relatively low resistivity, giant intrinsic spin Hall conductivity, easy growth, and ability to be readily integrated into experimental and/or manufacturing processes. This talk will report on an unambiguous determination of the intrinsic nature of spin Hall effect in Pt [1] and how the intrinsic spin Hall conductivity and spin Hall ratio of Pt varies with carrier lifetime, strain, and interruption of crystal order [2,3]. Based on this physical understanding, we have developed several low-resistivity spin Hall metals for spin-orbit torque technologies whose power consumption is estimated to be only 1% of that of the topological insulator Bi_xSe_1-x [4] based devices.
[1] L. Zhu et al., Sci Adv. 5, eaav8025 (2019).
[2] L. Zhu et al., Phys. Rev. Appl. 11, 061004 (2019).
[3] L. Zhu, R.A. Buhrman, Phys. Rev. Appl. (2019), in press. arXiv:1908.06528.
[4] M. DC et al., Nat. Mater. 17,800-807 (2018)   

Spin pumping and non-uniform magnetic excitation in spin-torque FMR studies of the spin Hall effect

Early on, spin-torque ferromagnetic resonance (ST-FMR) was used to establish an initially surprisingly strong spin Hall effect (SHE) in certain heavy metals (HM), and has since been widely deployed in the study of spin-orbit torques in HM/FM bilayers. However, there are questions as to whether ST-FMR always provides accurate, quantitative measures of the dampinglike spin-torque efficiency ξ_DL, principally because of the unsettled role of spin-pumping and the inverse SHE in ST-FMR, but also because of the assumption that only the uniform mode is excited. Here we report on an extensive ST-FMR study of Pt/FM and β-W/FM bilayers and HM/spacer/FM trilayers chosen such that the spin pumping effect is both strong and variable. We show that spin pumping, when significant, subtracts from the antidamping torque signal, resulting in ξ_FMR<ξ_DL. In conjunction with the spin pumping model, the FMR studies also clearly indicate that there can be significant coupling of the incident spin current to non-uniform modes in the FM layer, which also contributes to a lower apparent ξ_DL. These results explain why ST-FMR often underestimates ξ_DL in comparison to quasi-static second harmonic results, the latter of which are generally confirmed by ST switching of MTJs.   

Electrical Measurement of Thermally Driven Spin Hall Voltage in Platinum with Permalloy contacts

A group of effects coupling spin current with heat has drawn considerable attention due to their large potential for applications in spincaloritronics[1]. Recently, a new member of the family which converts thermal gradient into pure spin current in nonmagnetic conductors, named the spin Nernst effect, was observed. Here, we report a surprisingly large magnetic-field dependent voltage (<800 nV) across two permalloy contacts on a platinum channel patterned into a cross shape, while in the orthogonal channel, electrical current is utilized to create local thermal gradient by Joule heating. From finite element analysis as well as local electrical transport thermometry measurements, we estimate thermal gradients to be 1.5 K/micron near the permalloy contacts at electrical current of 10 mA. We will further discuss the origins of the large observed voltage by presenting several experimental results which we strongly feel rules out any unintended electrical effects such as spin Hall effect.
[1] G. E. W. Bauer et al., Nat. Mat., 11, 391 (2012).   

Anomalous Spin Hall Effect in Iron Rhodium for Driving Spin Torque Oscillators

Ferromagnetic materials can generate spin currents with controllable spin polarization via the anomalous spin Hall effect, a property potentially useful for driving spin torque oscillators (STOs), which have recently found applications for performing neurotrophic tasks. Iron rhodium (FeRh) exhibits a transition between a low-temperature antiferromagnetic (AFM) state and a high-temperature ferromagnetic (FM) state. For appropriate growth parameters, this transition can be found close to 300K, such that both the FM and AFM states are stable at room temperature, making it an ideal material to compare the effectiveness of FM and AFM spin sources for STOs. The transition also provides a high level of versatility for device design. We present measurements of the spin torque efficiency in iron rhodium as the temperature is varied to drive the FeRh through its magnetic transition. We compare FeRh's efficiency for driving STOs in the stable AFM and FM states at the same temperature, and compare the effectiveness of FeRh as a spin source with ordinary spin Hall materials.   

Very high spin Hall conductivities and spin Hall ratios in epitaxial Iridium di-oxide films

New metallic materials with exceptionally high spin Hall conductivities and accompanying high spin Hall ratios are desirable both to produce more efficient systems for spin-orbit torque applications and to further test the fundamental understanding of intrinsic spin-orbit interactions. A particularly interesting candidate for such research is the metallic rutile oxide Iridium di-oxide which angle resolved photoemission spectroscopy studies have shown exhibits Dirac nodal lines in the band structure, a feature that could enable a very high . Here we report spin-torque ferromagnetic resonance studies of the damping-like and field-like torques exerted on an adjacent ferromagnetic layer as the result of current flowing in epitaxial (110) and (001) IrO₂ films. The (110) films exhibit a damping-like torque efficiency ≈ 0.18 at 293 K, which sets a lower bound for the spin Hall conductivity . The higher resistivity (~ 300 µΩ-cm) (001) films exhibit even stronger spin-orbit torques, with ranging from ~0.45 at 293K to 0.8 at 30 K as decreases, behavior indicative of the dirty metal regime. The very high value for (001) IrO₂, ≥ , is both a challenge for current theoretical understanding and an exciting prospect for more efficient SOT applications.   

Extrinsic Spin Hall Effect in Inhomogeneous Systems

Interconversion between spin and charge signals is one of the most important processes in spintronics. This is done most commonly by the direct and inverse spin Hall effects (SHE). Recently, An et al. observed an enhanced charge-to-spin conversion, comparable to heavy metals, in naturally oxidized Cu (nox-Cu) [1]. Okano et al. reported a non-reciprocal charge-spin interconversion in nox-Cu [2]. The so-called spin-vorticity coupling (SVC) was suggested as the origin of these results.

In this work, we take a different approach and study the problem in terms of the extrinsic SHE in a inhomogeneous system. We model the nox-Cu system by nearly free electrons subject to impurities with spin-orbit interaction and with spatially modulated distribution. We calculate spin accumulation and spin current induced by an electric field using Kubo formula and discuss the relation between them. The results are summarized by a generalized spin diffusion equation with a spin source term given by the divergence of the spin Hall current. This source term can be put in a form of SVC only if the spin Hall angle is independent of impurity concentration, as in the case of skew scattering.

[1] H. An et al., Nat. Commun. 7, 12069 (2016).
[2] G. Okano et al., Phys. Rev. Lett. 122, 217701 (2019).   

Large Spin Hall and Edelstein effects in Weyl semimetal WTe2 up to Room Temperature

The discovery of topological semimetals has revealed the opportunities to realize several extraordinary physical phenomena in condensed matter physics. Here, we report current-induced spin polarization, i.e. the spin Hall effect [1] and the Edelstein effect [2] and its inverse phenomenon in type-II Weyl semimetal WTe2 up to room temperature. In addition, to spin Hall and Rashba-Edelstein effects, our measurements also show an out-of-plane electrical field-induced spin polarization in WTe2 due to spin momentum locking of the spin-polarized bulk Fermi states [2]. These findings open opportunities for spin-orbit based spintronic technologies and possibilities for the realization of new states of topological matter with novel spin textures.
1. Observation of Spin Hall Effect in Weyl Semimetal WTe2, arXiv:1812.02113 (2019).
2. Edelstein Effect in Type-II Weyl Semimetal WTe2, arXiv:1910.06225 (2019).