Current-induced spin-orbit torques (SOTs) provide a unique mechanism to manipulate the magnetization of diverse class of magnetic multilayers and devices. The core of the phenomenon is charge to spin-current conversion in ferromagnetic/heavy-metal heterostructures which is governed by spin-orbit interactions mainly through spin Hall effect in heavy metals or Rashba effect at interface with broken inversion asymmetry1. The non-equilibrium spin-current (of spin σ) interacts with local magnetic moments (m) via exchange interaction and creates two different components of spin-transfer torques: damping-like and field-like , where HDL and HFL are damping-like and field-like effective fields2. In the macrospin approach of spin-orbit torque induced dynamics, the magnetization reversal in systems with perpendicular magnetic anisotropy is governed by damping-like torque and Dzyaloshinskii-Moriya interaction3. However, recent micromagnetic studies predict a unique reversal path which is determined by interplay between damping-like and field-like torques4. In this work, we will show how the ratio of field-like torque to damping-like torque is affected by the thickness of magnetic layer. A series of samples Pt 8|Co x|Al 1.4|Pt 3 with x = 0.7, 0.9, 1.2, 1.4 (numbers are thicknesses in nm) is deposited using magnetron sputtering. 5-μm-wide Hall bar structures were fabricated using optical lithography and Ar ion-milling technique. All the devices show perpendicular magnetic anisotropy. We used AC harmonic Hall voltage measurement technique to quantify current-induced effective fields. This technique exploits a sinusoidal current (IAC) of frequency 727 Hz and simultaneous measurement of the first and second harmonics of the Hall voltage as a function of an in-plane field (H) applied along or transverse to the current direction (H || IAC and H ⊥ IAC), and extract HDL or HFL effective fields. The measured HDL and HFL increase linearly with the current for all the Co thicknesses as shown in Figure 1(a) and 1(b), respectively. Furthermore, the HDL (= m×σ) changes sign with magnetization direction whereas HFL (= σ ) is independent of magnetization direction, in agreement with literature2. Figure 2 shows the HDL and HFL for an estimated current density JPt=1011 A/m2 in seed Pt layer as a function of Co thickness. The measured HDL and HFL increase with decreasing the Co thickness. The observed behavior confirms the interfacial nature of spin-orbit torques5. Interestingly, here we observe a clear increase in the ratio of HFL/HDL with decreasing the Co thickness. To corroborate the phenomenon, we next quantify the SOTs in Pt 8|Co x|Al 1.4|Ta 5 series and the similar increasing trend in HFL/HDL is observed when the Co thickness is decreased. The results suggest for additional mechanisms of spin-current generation which will be discussed in details during the conference. Acknowledgement-French ANR grant TOPSKY (ANR-17-CE24-0025), DARPA TEE program grant (MIPR#HR0011831554) and EU grant SKYTOP (H2020 FET Proactive 824123) are acknowledged for their financial support.

**References:**

1. Garello, K. et al. Nat. Nanotechnol. 8, 587–593 (2013). 2. Hayashi, M., Kim, J., Yamanouchi, M. & Ohno, H. Phys. Rev. B 89, 1–15 (2014). 3. Lee, O. J. et al. Phys. Rev. B 89, 1–8 (2014). 4. Baumgartner, M. et al. Nat. Nanotechnol. 12, 980–986 (2017). 5. Park, Y. K. et al. NPG Asia Mater. 12, (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ea959e15ad0cfb2ba720f28f9d4b4f37.jpg)
Figure 1. Current-induced SOT effective fields (a) HDL and (b) HFL as a function of current density in seed Pt layer for various Co thicknesses.

![](https://assets.underline.io/uploads/markdown_image/1/image/883262de168f440ae01eb8bce55a8174.jpg)
Figure 2. Plot of HDL and HFL per 1011 A/m2 current density in seed Pt layer with respect to the Co thickness.

 Magnetic Layer Thickness Dependence of Spin-Orbit Torques in Pt / Co / Al / (Pt | Ta) Skyrmion Magnetic Multilayers.

THz spintronics emitters represent today novel sources for broadband emission using nanometer-scaled materials. We present and model the THz spintronic emission based on the spin Hall effect in 3d metals and on the inverse Rashba-Edelstein effect in the optimized topological insulator Bi1-xSbx. 1. Introduction Terahertz (THz) spintronic emitters are promising candidates for covering the so-called THz gap as they offer broadband emission going up to 30 THz [1]. Conventionally, they consist in nanometer-thin heterostructures composed by a ferromagnetic layer and a heavy metal from the 3d-5d family which, owing to their high spin-orbit coupling (SOC), allow spin-to-charge conversion (SCC) from a pure transient spin-current coming from the ferromagnetic layer into a transverse transient charge current. Efforts have been made recently to increase the output emission power of such devices by layer thickness engineering in order to optimize spin-to-charge interconversion and to reduce both THz absorption in metallic layers and spin current relaxation in thick ferromagnets. In this study, we evidence the processes timescales at stake in the emission properties of metallic THz spintronic emitters using Finite Domain Time Domain (FDTD) simulations. We evidence the main figure of merit which will permit to optimize the next generation of THz emitters. We then turn towards an alternative type of THz spintronic emitters based on topological insulators. We discuss the role of surface states in the conversion mechanisms and highlight promising THz emission in topological insulator Bi1-xSbx. 2. Optimization of THz metallic spintronic emitters based on FDTD modelling Conventional THz spintronic emitters are based on ferromagnet/heavy metal heterostructures such as Co/Pt, W/CoFeB/Pt or Fe/Pt. Shining infrared femtosecond laser pulses on the heterostructure induces a transient spin current diffusing from the ferromagnet to the heavy metal. Through spin-to-charge conversion due to the inverse spin Hall effect (ISHE), a THz wave is generated. The direction of the THz emission depends on the direction of the magnetization: the polarization can thus be easily tuned by small external magnetic field. The amplitude of the THz emission depends strongly on the amplitude of the interconversion mechanism, which is related to skew-scattering and side-jump effects in heavy metals. In first approximation, the amplitude of the emission is thus given by the spin Hall angle θSHE = jc/js, ratio between the incoming spin current and the generated charge current given by jc ∝ θSHE (js x σ) where σ is the spin accumulation orientation [2,3]. Here, we provide a comprehensive understanding of the THz emission processes using FDTD modelling, including spin-dependent timescales such as spin-flip rates in heterostructures. We obtain a good agreement between experiments obtained by THz time-domain spectroscopy (THz-TDS) and performed simulations as shown in Fig. 1. We also evidence the crucial role of the interface quality between the heavy metal and the ferromagnet, as spin backflow or interfacial spin-flip may decrease the conversion. We thus propose a figure of merit η ∝ g↑↓σSHElsfHM which defines the THz emission strength in metallic heterostructures. This product includes the spin-mixing conductance g↑↓ illustrating interface quality, spin-Hall conductivity σSHE linked to interconversion strength and spin diffusion length in the conversion material lsfHM proportional to spin-current relaxation. We believe that our results will help optimizing the next generation of THz spintronic emitters. 3. Towards surface-states mediated THz emission using topological insulators Alongside ISHE-based emitters, topological insulators (TI) are studied here as an alternative source for THz emitters. They present conductive surface-states which allow interfacial interconversion via inverse Rashba-Edelstein effect (IREE). In these systems, strong spin-to-charge conversion is expected owing to i) the Fermi velocity of interfacial carriers and ii) the insulating behaviour of the material bulk, reducing possible THz absorption in the heterostructure. Such systems have been proven to show emission in the THz range, for example with topological insulator Bi2Se3 [4]. We report in Fig. 2 emission features from Bi1-xSbx/Co interface. Experimental data are taken with standard electro optic sampling (EOS) using ZnTe(111) 500 μm thickness. Emission performance of Bi0.79Sb0.21(15)/Co(4) is about the same order of magnitude as Co(2)/Pt(4) single-ISHE conversion state-of-the-art emitter. As recovered on IREE-based emitter, THz emission phase is reversed as applied magnetic field direction is reversed. Topological insulators here illustrated by Bi1-xSbx are thus suitable candidates for strong output THz emitters.

**References:**

[1] Seifert, T. et al., “Efficient metallic spintronic emitters of ultrabroadband terahertz radiation”, Nature Photon 10, 483–488 (2016). [2] Dang T. H., Rongione E. et al., “Ultrafast spin-currents and charge conversion at 3d-5d interfaces probed by time-domain terahertz spectroscopy”, Appl. Phys. Rev. 7 (2020) [3] Hawacker J., Rongione E. et al., “Correlation between spin-mixing-conductance, THz emission and spin-memory-loss at magnetic/heavy metal interfaces”, to be submitted [4] Wang, X. et al., “Ultrafast Spin-to-Charge Conversion at the Surface of Topological Insulator Thin Films”, Adv. Mater. 30, 1802356 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b0838de1ea6769af462c232ef2eef21b.jpg)
Fig. 1 – Comparison between experimental measurements (blue curve) and FDTD simulations (red curve) for Co(2)/Pt(4) metallic THz emitter considering an infrared excitation pulse duration about 100 fs.

![](https://assets.underline.io/uploads/markdown_image/1/image/b977da06608df08ed43adbd351f5d2ed.jpg)
Fig. 2 – Bi0.79Sb0.21/Co emission alongside metallic ISHE-based emitters for comparison (left). Magnetic field dependence of Bi0.79Sb0.21/Co emission: phase reversal with field direction change proves magnetic origin of the emission (right). Thicknesses in brackets are given in nanometers.

 Efficiency of THz spintronic emitters: from spin-Hall effect in 3d metals to surfaces states in topological insulators INVITED

We present our recent realisation of a nanomagnetic Galton board [1], a nanoscale recreation of the paradigmatic experiment in which balls travel through an array of pegs, designed by Sir Francis Galton to demonstrate the emergence of order from randomness. In our nanoscale experiment, balls are substituted by magnetic domain-walls, a honeycomb nanowire lattice recreates the peg array, and an externally applied magnetic field takes the role of gravity (Figure 1). Using high-resolution immersion Kerr microscopy, we image domain wall propagation through this nanoscale system a very large number of times (Figure 2), and demonstrate that complex domain wall dynamics can be employed to generate high-quality stochasticity suitable for computing applications. By varying the direction of the externally applied field, we were also able to demonstrate the continuous tuneability of the stochastic domain-wall decision process, a critical step to the realisation of functional computing systems. To conclude, we will discuss the technical advances that enabled this study, in which millions of domain-wall trajectories were imaged and analysed. These will be of great interest to those performing stochasticity studies in spintronics, as being able to acquire and deal with large datasets is an important experimental challenge in the field. The results demonstrated open promising paths in the design and development of spintronic devices in which the intrinsic stochasticity of domain-wall dynamics is exploited using new computing architectures.

**References:**

[1] Sanz-Hernández, Dédalo, et al. "Tunable Stochasticity in an Artificial Spin Network", DOI: 10.1002/adma.2020081

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9e8bc476a41cbcab0159a897cf862dd2.jpg)
Figure 1. Nanoscale magnetic Galton board formed by an elliptical domain-wall injection pad (top) and a bifurcating nanowire network.

![](https://assets.underline.io/uploads/markdown_image/1/image/705a04356594395b96ae40d6c0dfa320.jpg)
Figure 2. Oil-immersion longitudinal Kerr microscopy image of the board presented in Figure 1, after the injection of a domain-wall in the system. The trajectory followed by the wall is observed as a dark trace.

 Tuneable Stochastic Domain-Wall Trajectories in a Magnetic Galton Board

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CC: Spin Orbit Torques

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Magnetic Layer Thickness Dependence of Spin-Orbit Torques in Pt / Co / Al / (Pt | Ta) Skyrmion Magnetic Multilayers.

Efficiency of THz spintronic emitters: from spin-Hall effect in 3d metals to surfaces states in topological insulators INVITED

Tuneable Stochastic Domain-Wall Trajectories in a Magnetic Galton Board

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