Spin Hall effect in a spin-1 chiral semimetal

Spin-1 chiral semimetal is a new state of quantum matter hosting unconventional chiral fermions that extend beyond the common Dirac and Weyl fermions. B20-type CoSi is a prototypal material that accommodates such an exotic quasiparticle. To date, the spin transport properties in the spin-1 chiral semimetals, have not been explored yet. In this work, we fabricated B20-CoSi thin films on sapphire c-plane substrates by magnetron sputtering and studied the spin Hall effect (SHE) by combining experiments and first-principles calculations. The SHE of CoSi using CoSi/CoFeB/MgO heterostructures was investigated via spin Hall magnetoresistance and harmonic Hall measurements. First-principles calculations yield an intrinsic spin Hall conductivity (SHC) at the Fermi level that is consistent with the experiments and reveal its unique Fermi-energy dependence. Unlike the Dirac and Weyl fermion-mediated Hall conductivities that exhibit a peak-like structure centering around the topological node, SHC of B20-CoSi is odd and crosses zero at the node with two antisymmetric local extrema of opposite sign situated below and above in energy. Hybridization between Co d-Si p orbitals and spin-orbit coupling are essential for the SHC, despite the small (~1%) weight of Si p-orbital near the Fermi level. This work expands the horizon of topological spintronics and highlights the importance of Fermi-level tuning in order to fully exploit the topology of spin-1 chiral fermions for spin current generation.

Spin current generated from the spin Hall effect (SHE) can exert spin-orbit torque (SOT) on an adjacent ferromagnetic (FM) nanolayer, which provides a promising way to manipulate the magnetization of the FM layer for high-performance spintronic devices [1,2], such as SOTmagnetoresistive random access memories (MRAMs). For applications involving SOT-based devices, it is important to find materials exhibiting large damping-like spin Hall efficiency (ξDL), i.e., the efficiency of spin-charge conversion of SHE. Heavy 5d transition metals, such as Pt, Ta, and W, are commonly known for possessing large ξDL due to their strong spin-orbit interactions and optimum d-orbital filling [3][4][5][6]. Topological insulators (TIs), such as Bi2Se3 [7][8][9][10], were reported to show even larger ξDL, which arises from the spin-momentum locking of their surface states. However, several complications hinder the integration of the TIs to the state-of-the-art electronics: First, the relatively low melting point of these Bi-based TIs is not compatible with the CMOS processing. Second, the bulk-insulating TIs are generally too resistive to be incorporated into devices, such as SOT-MRAMs. Third, in a multilayer heterostructure, the surface states may be altered when a TI is in direct contact with a ferromagnet.
The emergence of topological Weyl semimetals (WSMs) provides a promising alternative for efficient spin-current generation in SOT devices, due to the topological nature of the bulk band structures and the relatively low resistivity of WSMs compared to TIs. The WSMs hold three dimensional linearly dispersive band crossing points, where the degeneracy is lifted by breaking either the inversion symmetry or the time-reversal symmetry or both [11]. Firstprinciples calculations have predicted a large intrinsic SHE peak near the Weyl points for the TaAs family of WSMs, where the SHE is interpreted as the interplay of the large spin Berry curvature and spin-orbit coupling (SOC) near the Weyl nodes [12]. Recently, large SHE was observed in Weyl semimetal prototypes WTe2 [13,14] and Co2MnGa [15,16].
The cobalt monosilicide CoSi that crystallizes in the B20 structure is a newly discovered topological semimetal featuring unconventional chiral fermions with no counterparts in highenergy physics [17]. Left panel of Fig. 1(a) shows an illustration of the unit cell of cubic B20structured CoSi. The spin-1 chiral fermion holds a threefold degeneracy at the band-crossing node of a Dirac-like band and a flat band, which carries a topological charge of ±2 [17,18], as illustrated in the right panel of Fig. 1(a). The presence of spin-1 chiral fermions (schematic shown in the right panel of Fig. 1(a)) at the band-crossing points near the Fermi level with long Fermi arcs in the momentum space of CoSi were confirmed by angle-resolved photoemission spectroscopy experiments [19][20][21]. Fabrication of high-quality CoSi thin films and understanding the spin transport in these topological semimetal thin films are essential steps towards realizing novel spintronic devices exploiting the unique properties of unconventional chiral fermions. To date, there have been no report on the spin-transport properties of nanometer-scale CoSi thin films and it is not clear yet how does the spin-1 chiral electronic structure participate in the spin transport, e.g. spin current generation via SHE.
In this work, we fabricated CoSi thin films by magnetron sputtering and investigated the spin-transport properties by experiments and first-principles calculations. Structural characterization indicates that the CoSi films are polycrystalline and crystallizes in the B20type structure. Spin Hall magnetoresistance (SMR) and harmonic Hall measurements show that the damping-like spin Hall efficiency of CoSi is ~3%, which is larger than the values reported in pure Co (~1%) [22] and Si (~0.01%) [23]. The first-principles calculations show that the amplitude of the spin Berry curvature depends on the k-point path and changes sign above and below the topological node hosting spin-1 chiral fermion, in contrast to a WSM. The spin Berry curvature contributes to the spin Hall conductivity (SHC) in the CoSi thin films and originates from the hybridization of d-p orbitals between Co and Si.
CoSi thin films were deposited on sapphire (Al2O3) c-plane substrates from a sintered CoSi alloy target. The composition of the CoSi films was confirmed to be 50.7:49.3 using inductively coupled plasma optical emission spectrometer (ICP-OES). The surface structure of the CoSi films was monitored by in-situ reflection high energy electron diffraction (RHEED) in the sputtering chamber. Figure 1(b) is a typical RHEED pattern for a 47-nm-thick CoSi film deposited at 550°C. The RHEED pattern shows arc-shape diffractions, indicating a polycrystalline surface. The crystal structure was further characterized by x-ray diffraction (XRD) with Cu K radiation and a monochromator. Figure 1 is also known that the CoSi film has a (210)-preferential texture. The lattice constant of the CoSi is estimated to be ~0.4435 nm. Next, a heterostructure consisting of substrate/CoSi (tCoSi: 0~11)/Co20Fe60B20 (CoFeB) (1)/MgO (2)/Ta (1) was deposited in order to evaluate the spintransport properties of the CoSi film. The surface morphology of the stack layers was measured by atomic force microscopy (AFM). As shown in Fig. 1(d), a relatively flat surface with an average roughness (Ra) ~ 0.39 nm and a peak-to-valley (P-V) ~ 3.92 nm for a 11 m 2 scan was achieved. The heterostructure with such a low roughness is essential for spin-transport measurements, which will be further elaborated in the following sections.
The multilayer stacks with the core structure of CoSi/CoFeB/MgO were patterned into Hall bars, as shown in Fig. 2(a). SMR was measured to evaluate ξDL of the CoSi thin films. In nonmagnetic/ferromagnetic (NM/FM) layered structures, when a charge current is applied, a spin current can be generated by SHE in the NM and it flows towards the FM. At the interface of the NM/FM, a part of the spin current is reflected back and it is converted to a charge current within the NM by the inverse SHE, resulting in a change of the longitudinal resistance (Rxx) in the heterostructure. The difference in the Rxx between parallel and perpendicular configurations of the FM layer magnetization (M) and the spin-current polarization (σ // y) is referred to as the SMR [24,25]. Neglecting the imaginary part of the spin mixing conductance, ξDL of the NM layer can be obtained from the NM layer thickness dependence of the SMR.
Because the M is always perpendicular to the charge current, there is no contribution of anisotropic magnetoresistance (AMR) to the resistance change. Assuming a transparent interface between CoSi and CoFeB, the SMR as a function of tCoSi can be fitted by the following equation derived from a drift-diffusion model [25][26][27], The ξDL and the spin diffusion length (λ) are used as fitting parameters. The α is given by the slope of the linear fitting curve represents the inverse of the ρCoSi. We fitted the data in an appropriate range and estimated the ρCoSi is around 341 µΩ·cm. The value of ρCoSi is relatively large compared to the reported resistivity of a bulk CoSi single crystal [28], which is attributed to the carrier scattering at the surfaces and the grain boundaries of the polycrystalline thin film.
After extracting the SMR of bilayers with different thicknesses of CoSi, we fitted the SMR as a function of tCoSi by the Eq. (1). The experimental data are well fitted, as shown in Fig. 2(d).
The ξDL and λ are obtained to be 3.4 ± 0.2 % and 4.4 ± 0.6 nm, respectively. The value of ξDL is relatively large even for a material consisting of relatively light elements. Compared to pure Co (ξDL ~ 1%) [22] and Si (ξDL ~ 0.01%) [23], the result indicates that the orbital hybridization between Co and Si orbitals may play a significant role on the SHE in the CoSi, which is supported by the first-principles calculations discussed later.
The efficiency of spin-current generation from the CoSi thin films was further characterized by harmonic Hall measurements. The SOTs induced by spin current acting on a FM layer can be considered, in the quasistatic regime, as effective magnetic fields, which consist of an damping-like (HDL || M  σ) term and a field-like (HFL || −σ) term [29][30][31][32][33][34]. The effective fields modulate the orientation of M of the FM layer, resulting in a second harmonic Hall resistance.
The efficiencies of damping-like (ξDL) and field-like (ξFL) torques can be extracted from the azimuthal magnetic field angular dependence of the first (Rω) and the second (R2ω) harmonic Hall resistances. A schematic illustration of the harmonic Hall measurement is shown in Fig.   3(a). A sinusoidal charge current was applied along the x axis, and an external magnetic field Hext was applied and rotated in the xy plane, making an angle φ with the current. The Rω and  The RPHE is obtained to be 65 mΩ. R2ω as a function of φ for same the device is plotted in Fig.   3(d). The Acosφ and Bcos2φcosφ components of R2ω are extracted by fitting the experimental data using Eq. (3). The factor A as a function of Hext for the device with tCoSi = 7.2 nm is plotted in Fig. 3(e). The best fit using Eq. (3) is shown by the red line and other colored lines represent decomposition of the signal. The SOT signal dominates in the low-field regime whereas the Hext dependence of R2ω at higher fields is governed by the ONE. We note that previous report [28] has found appreciable ONE in CoSi single crystal at lower temperatures. The HDL is estimated to be 1.00 Oe. Figure 3(f) shows the dependence of the factor B against the inverse of Hext. Combining with the RPHE obtained above and the HOe evaluated by the Ampère's law, the HFL opposing to the Oersted field is estimated to be 2.25 Oe from the slope of the linear curve fit in Fig. 3(f). The ξDL and ξFL are given by [35], and finally, with = 6 nm, we obtained σDL = 45 (ℏ/e)Ω −1 cm −1 and σFL = 95 (ℏ/e)Ω −1 cm −1 .
The temperature dependence of the magneto-transport for single-layer CoSi was systematically studied. The inset of Fig. 4(a) shows the temperature T dependence of the normalized resistivity. We found the temperature coefficient of the resistivity for CoSi is negative and CoSi increases by ~10% as T is swept from 300 K to 10 K. We then extract the carrier concentration n and the electron mobility μ of CoSi from the slope of the ordinary Hall effect and the longitudinal conductivity. Results are plotted in Fig. 4(a). The temperature dependences of the two quantities are relatively weak. We next investigate the T dependence of the charge-to-spin conversion for a typical CoSi/CoFeB bilayer stack with tCoSi = 8.5 nm using the harmonic Hall technique. Hext dependence of A measured at various temperatures are plotted in Fig. 4(b). We found both the damping-like SOT contribution (exponential decay of A at low field) and ONE contribution (linear slope of A at high field) of R2ω reduce with decreasing T.
At 10K, R2ω is nearly independent of Hext. Figure 4(c) shows B as a function of 1/Hext at various temperatures. The slope of B changes sign which indicates a strong temperature dependence of ξFL. At 10K, the current-induced Oersted field is sufficient to explain the observed signal, implying that ξFL is nearly zero. While the ξFL of heavy metal/CoFeB/MgO-based heterostructures was known to show such a strong temperature dependence, the T dependence of the damping-like counterpart in those structures is relatively weak [38,39].
The scaling relationship of the damping-like spin Hall conductivity σDL against the transport lifetime τ is commonly used to separate the intrinsic (independent of τ) and the extrinsic skew scattering (proportional to τ) contributions [40]. For metals, it is convenient to assume σxx ~ τ.
However, for semimetallic CoSi, since n varies with temperature ( Fig. 4(a)), we plot μ instead of τ in the x-axis in Fig. 4(f). For the y-axis, we assume σDL may scale with n due to the thermal excitation [41]. Interestingly, the scaling analyses (whether we divide σDL by n or not) show a strong temperature dependence of σDL in CoSi, which neither follows usual intrinsic nor extrinsic skew scaling [40,42,43], as shown in Fig. 4(f). Thermal-excitation-related extra extrinsic scatterings and coupling, such as the local moments [44] of Co ions, and phonons [45], as well as the shift of Fermi level with its special electronic structures [46], may contribute to the charge-spin conversion in CoSi at elevated temperatures.
In order to shed light on the mechanism of the spin-current generation in CoSi thin films, first-principles calculations based on the density-functional theory (DFT) [47][48][49] were carried out to evaluate the intrinsic SHC in the B20-type CoSi. The relativistic band structures along high-symmetry k paths are presented in Fig. 5(a). Band crossings with high-fold degeneracy are confirmed at Γ (near the Fermi energy) and R (at 0.2 eV below the Fermi energy) in the Brillouin zone (BZ) as reported previously [19][20][21]. These states were identified as the spin-1 chiral fermions and the double Weyl fermions, respectively [18]. The degeneracy of these states, as shown in Fig. 5(a) with inset, is reduced by the spin-orbit coupling (SOC) and the split bands might be an origin of the enhanced SHC in CoSi. Figure 5 Interestingly, SHC vanishes at the spin-1 band crossing and changes its sign above and below the topological node, whereas rather a peak-like structure of SHC was observed around the double Weyl point (Fig. 5(c)). The distinct odd-function-like energy dependence of SHC for the spin-1 chiral fermion clearly distinguishes itself from others (e.g. massive Dirac fermion [50], inversion asymmetric Weyl fermion [12], magnetic Weyl fermion [51], and Dirac fermion from the topological surface states [46]) where the Fermi energy dependence of the (anomalous and spin) Hall conductivities are rather even-like.
To provide more insights into this unique character, we show the contributions of Ω on the slices of BZ (kxky plane at kz=0) at varying energies of 0.24, 0.12, 0.06, 0.03, 0, and −0.03 eV in Figs. 6(a)−6(f), respectively. At the spin-1 chiral band crossing point (0.03 eV; Fig. 6(d)), the positive contribution of Ω is found around Γ point with two-fold symmetry. When the energy shifts upward to 0.06 eV (Fig. 6(c)), the negative Ω appears along Γ -X' line. With further increasing the energy to 0.12( Fig. 6(b)) and to 0.24 eV (Fig. 6(a)), the negative contribution of Ω is increased and eventually, the value of SHC reaches to the minimum value, to SHC is small. The local derivative in energy of SHC / is however robust near the topological node and may be exploited for thermal spin current generation via the spin Nernst effect [53,54]. Furthermore, it would be interesting to investigate the isostructural B20 PtAl [55] for which dramatic enhancement of SOC is expected to boost up / at the crossing and peaks of slightly away from the crossing. K. Tang, Y.L. and K.N. contributed equally to this work.

Film deposition, characterizations, and device fabrication
The CoSi thin films were deposited using magnetron sputtering at the substrate temperature of 550℃ in a high-vacuum sputter chamber. The base and deposition pressures were 2  10 −6 Pa and 0.7 Pa (Ar gas), respectively. The sputtering power of CoSi was set at 20 W generated by a direct current (dc) source for a 76.2 mm diameter Co50Si50 target. The crystal structure was characterized using the out-of-plane XRD measurement with Cu Kα radiation (λ = 0.15418 nm).
The surface structure and morphology were evaluated using RHEED and AFM, respectively.
Ta(5)/Au(150 nm) layers were then deposited on the Hall bars as electrodes using lift-off process.

SMR and harmonic Hall measurements
Magneto-transport properties were characterized in a physical properties measurement system (PPMS) at room temperature. For the SMR measurement, a magnetic field of 20 kOe was applied to saturate the magnetization of the FM layer. For the harmonic Hall measurement, a sinusoidal signal of constant amplitude and frequency of 172.1 Hz was applied by a Keithley 6221 current source meter. The first-and second-harmonic Hall voltages were simultaneously measured by two lock-in amplifiers (nf LI5660).

The first-principles calculations
The first-principles calculations were performed based on the generalized gradient approximation [56] using the full-potential linearized augmented plane-wave (FLAPW) method [47][48][49]. The cubic B20-type crystal structure of stoichiometric CoSi was modelled by using the experimental lattice constant, in which all the atomic positions were fully relaxed by the force calculations [57]. Muffin-tin (MT) radii of 2.40 and 1.80 aB were employed for Co and Si, respectively. The LAPW basis for the wave function in the interstitial region has a cutoff of | + | ≤ 4.5 −1 , and the angular momentum expansion inside the MT sphere is truncated at ℓ = 8 for the Co and at 6 for the O. The SOC was incorporated by the second variational method [58]. The intrinsic SHC was evaluated by means of the Kubo formula in the static limit (ω = 0) [59,60], where the spin Berry curvature Ω ( ) is given by Here