Impact of impurities on the spin Hall conductivity in β -W

Abstract

While the metastable β (A15) phase of tungsten has one of the largest spin Hall angles measured, the origin of this high spin Hall conductivity is still unclear. Since large concentrations of oxygen and nitrogen are often used to stabilize β tungsten, it is not obvious whether the high spin Hall conductivity is due to an intrinsic or extrinsic effect. In this work, we have examined the influence of O and N dopants on the spin Hall conductivity and spin Hall angle of β-W. Using multiple first principles approaches, we examine both the intrinsic and extrinsic (skew scattering) contributions to spin Hall conductivity. We find that intrinsic spin Hall conductivity calculations for pristine β-W are in excellent agreement with experiment. However, when the effect of high concentrations (11 at.%) of O or N interstitials on the electronic structures is taken into account, the predicted intrinsic spin Hall conductivity is significantly reduced. Skew scattering calculations for O and N interstitials in β-W indicate that extrinsic contributions have a limited impact on the total spin Hall conductivity. However, we find that the spin-flip scattering at O and N impurities can well explain the experimentally found spin-diffusion length within the range of 1-5 nm. To explain these findings, we propose that dopants (O and N) help to stabilize β-W grains during film deposition and afterwards segregate to the grain boundaries. This process leads to films of relatively pristine small β-W grains and grain boundaries with high concentrations of O or N scattering sites. This combination provides high spin Hall conductivity and large electrical resistance, leading to high spin Hall angles. This work shows that engineering grain boundary properties in other high spin Hall conductivity materials could provide an effective way to boost the spin Hall angle.

Probing the Spin Hall Characteristics of W/CoFeB/MgO Based Heterostructures for Spin‐Orbit Torque Based Magnetic Random Access Memory Application

“…[ 13–15 ] Even though, part of such variation can be attributed to different experimental techniques [ 14 ] and the use of different models for data analysis, such a high degree of discrepancy requires deeper probing. On the other hand, the theoretical studies show much better consistency with σ SH for β‐W ≈ 1500–2000 ℏ/e S cm −1 as reported by various groups [ 16,17 ] and can be used as a benchmark.…”

“…[13][14][15] Even though, part of such variation can be attributed to different experimental techniques [14] and the use of different models for data analysis, such a high degree of discrepancy requires deeper probing. On the other hand, the theoretical studies show much better consistency with σ SH for β-W ≈ 1500-2000 ℏ/e S cm −1 as reported by various groups [16,17] and can be used as a benchmark.In the first part of this work, we focus on minimizing the growth and fabricationrelated uncertainties and carry out systematic characterization of SOT using the anomalous Hall harmonics analysis method. [18] We perform in-depth analysis considering various factors and conform our experimentally extracted parameters with the same evaluated using the ab initio method to establish a robust protocol.…”

Highly Energy‐Efficient Spin‐Orbit‐Torque Magnetoresistive Memory with Amorphous W─Ta─B Alloys

“…Therefore, the intrinsic spin Hall effect in W─Ta─B may originate from the short-range order of the 𝛽-phase W. In Figure 3d, we also observed an increase in |𝜉 E SHE | (|𝜉 Our interpretation is that the enhancement of the spin Hall effect originates from the effect on the Fermi-level tuning of W by Ta substitutional doping. [27][28][29]49,50] According to the first-principles calculation for 𝛽-W, the spin Hall effect based on the intrinsic mechanism shows a maximum at 0.4-0.5 eV below the Fermi level. [27][28][29] Substitutional doping of Ta into W corresponds to effective hole doping.…”

“…Typical candidate materials with large spin Hall angles are Pt (or its binary alloys), [16][17][18] 𝛽-phase W (𝛽-W), [19][20][21][22][23] 𝛽-phase Ta (𝛽-Ta), [6] and topological insulators. [24,25] All these materials have polycrystalline (textured) or single-crystal structures, in which a large spin Hall effect is theoretically expected by an intrinsic mechanism based on the band structure of materials with long-range crystal order [26][27][28][29] . As a result of extensive experimental studies, some such materials exhibiting large spin Hall angles have been observed, and with these j c0 < 1 × 10 7 A cm −2 could be achieved [30][31][32][33][34][35] .…”

Advanced modeling of materials with PAOFLOW 2.0: New features and software design

“…The code has been employed in multiple areas of materials science since its initial release in 2016. In particular, several groups used it to compute the (spin) Berry curvature as well as spin and/or anomalous Hall conductivity (SHC and AHC) in a variety of materials, ranging from β-W to magnetic antiperovskites [4][5][6][7][8]. Transport quantities, such as the electrical and thermal conductivity, were also computed in order to analyze carrier mobility in thermoelectrics [9,10].…”