Spin Pumping through Different Spin-Orbit Coupling Interfaces in β-W/Interlayer/Co2FeAl Heterostructures.

Materials possessing pronounced spin–orbit coupling (SOC) are fundamental to the development of spin–orbit torque-driven magnetic memory devices, as they facilitate efficient manipulation of spin currents essential for device operation. Transition metal dichalcogenides are promising candidates for such applications because of their inherently high SOC strength. This work investigates the interfacial spin pumping effect between a monolayer of molybdenum disulfide (ML-MoS2) and Ni80Fe20 (Py) thin films, using broadband ferromagnetic resonance (FMR) spectroscopy. FMR measurements reveal a notable enhancement in the effective damping factor for the ML-MoS2/Py (Pt = 0 nm) interface compared to the reference Py thin films, attributed to spin pumping across the ML-MoS2/Py interface. To quantify spin pumping efficiency, we insert a high SOC platinum (Pt) interlayer at the ML-MoS2/Py interface and systematically vary its thickness (1, 2, and 5 nm). This enables the evaluation of key spin transport parameters, including the enhancement of the effective damping parameter and the effective spin mixing conductance, which reflects the transfer of spin angular momentum from Py to the ML-MoS2, thereby allowing us to determine the effective spin current density. The results indicate that ML-MoS2 in combination with Pt layers of 1, 2, and 5 nm thickness is well suited for spintronic applications with promising potential for energy-efficient memory and logic devices.

Determination of spin Hall effect and spin diffusion length of Pt from self-consistent fitting of damping enhancement and inverse spin-orbit torque measurements (Conference Presentation)

The spin Hall effect (SHE) is closely related to the spin-orbit coupling. Therefore, heavy metals are usually considered as materials of choice to obtain large spin Hall angles. Among these materials, some 5d transition metals such as Pt, Ta or W offer the largest spin-charge interconversion efficiency for spin current detections through the inverse spin Hall effect or to obtain efficient current induced magnetization switching in SOT-MRAM devices [1].Despite a weaker spin orbit coupling, spin Hall angles comparable to that of the best 5d materials has also been obtained in 3d ferromagnetic metals such as Co [2] or Ni [3]. More recently nonmagnetic alloys containing Nickel atoms such as NiCu [4] and CoNiB [5] attracted great interest for their large spin Hall angles and their potential for spintronic applications. Using the spin pumping by ferromagnetic resonance technique we could compare the spin to charge current conversion in Ni60Cu40 to the one of Pt. As can be seen in figure 1 a) the normalized spin pumping signal obtained in CFB/NiCu is comparable to that of CFB/Pt. We performed a thickness dependence shown in figure 1 b) to extract the spin Hall angle (θSHE) and spin diffusion length (λs) and obtained results comparable to the one of 5d metals using similar method with λs = 2.4 ± 0.3 nm and θSHE = 4.1 ± 0.5 % [6].Keller and coworkers [4] noticed similarities in the bandstructure of paramagnetic Nickel and Platinum possibly explaining the origin of the effect. The calculated band structure of ferromagnetic Nickel does not resemble that of Platinum and the origin of the large spin Hall effect observed in ferromagnetic Ni [3] could thus be different. The interplay between the spin-orbit coupling and magnetism is known to be at the origin of specific transport properties such as the anomalous magnetoresistance and the anomalous Hall effect. However, the link between the SHE and the magnetic order is complex and still unexplored [7].In order to study the effect of the phase transition we performed spin pumping as a function of temperature in Ni60Cu40 and Ni50Cu50 alloys above and below the Curie temperature. To avoid direct contact between the ferromagnetic spin injector CFB and the magnetic NiCu alloy that would modify CFB resonance properties due to the direct coupling [8] we used a 5 nm thick Cu interlayer. The spin pumping measurements performed in CFB\Cu\ Ni60Cu40 and CFB\Cu\ Ni50Cu50 shown in figure 2 indicate that in NiCu the SHE is insensitive to the magnetic order [6].A large variety of alloys composed of Ni, Co or Fe in the ferromagnetic or paramagnetic phase could be explored as spin current generators and detectors, extending the number of possible light metal systems with a large SHE. In particular, the large spin Hall effect in NiCu shows that it is a promising alternative to obtain large spin orbit torque without heavy metals. **

Spin-pumping-induced damping and interfacial Dzyaloshinskii–Moriya interaction (iDMI) have been studied in Pt/Co2FeAl/MgO systems grown on Si or MgO substrates as a function of Pt and Co2FeAl (CFA) thicknesses. For this, we combined vibrating sample magnetometry (VSM), microstrip ferromagnetic resonance (MS-FMR), and Brillouin light scattering (BLS). VSM measurements of the magnetic moment at saturation per unit area revealed the absence of a magnetic dead layer in both systems, with a higher magnetization at saturation obtained for CFA grown on MgO. The key parameters governing the spin-dependent transport through the Pt/CFA interface, including the spin mixing conductance and the spin diffusion length, have been determined from the CFA and the Pt thickness dependence of the damping. BLS has been used to measure the spin wave non-reciprocity via the frequency mismatch between the Stokes and anti-Stokes lines. iDMI has been separated from the contribution of the interface perpendicular anisotropy difference between Pt/CFA and CFA/MgO. Our investigation revealed that both iDMI strength and spin pumping efficiency are higher for CFA-based systems grown on MgO due to its epitaxial growth confirmed by MS-FMR measurements of the in-plane magnetic anisotropy. This suggests that CFA grown on MgO could be a promising material candidate as a spin injection source via spin pumping and for other spintronic applications.

All-optical investigation of anisotropic spin pumping in W/CoFeB/W heterostructure

Analogous to the spin-Hall effect (SHE), abinitio electronic structure calculations reveal that acoustic phonons can induce charge (spin) current flowing along (normal to) its propagation direction. Using the Floquet approach we have calculated the elastodynamically induced charge and spin pumping in bulk Pt and demonstrate that (i)the longitudinal charge pumping originates from the Berry curvature, while the transverse pumped spin current is an odd function of the electronic relaxation time and diverges in the clean limit. (ii)The longitudinal charge current is of nonrelativstic origin, while the transverse spin current is a relativistic effect that to lowest order scales linearly with the spin-orbit coupling strength. (iii)Both charge and spin pumped currents have parabolic dependence on the amplitude of the elastic wave.

The dynamics of pseudo-spin-1/2 Bose-Einstein condensates with weak spin-orbit coupling through a moving obstacle potential are studied numerically. Four types of wakes are observed and the phase diagrams are determined for different spin-orbit coupling strengths. The conditions to form Bénard-von Kármán vortex street are rather rigorous, and we investigate in detail the dynamical characteristics of the vortex streets. The two point vortices in a pair rotate around their center, and the angular velocity and their distance oscillate periodically. The oscillation intensifies with increasing spin-orbit coupling strengths, and it makes part of the vortex pairs dissociate into separate vortices or combine into single ones and destroys the vortex street in the end. The width b of the street and the distance l between two consecutive vortex pairs of the same circulation are determined by the potential radius and its moving velocity, respectively. The b/l ratios are independent of the spin-orbit coupling strength and fall in the range 0.19-0.27, which is a little smaller than the stability criterion 0.28 for classical fluids. Proper b/l ratios are necessary to form Bénard-von Kármán vortex street, but the spin-orbit coupling strength affects the stability of the street patterns. Finally, we propose a protocol to experimentally realize the vortex street in ^{87}Rb spin-orbit-coupling Bose-Einstein condensates.

While the growing utilization of polymers in flexible electronic devices has sparked significant interest in polymer/metal interfaces, spintronic studies of such interfaces remain limited. Here, spin pumping across a polymer/ferromagnet metal interface is systematically studied between hydrogen silsesquioxane (HSQ) oligomer layers (tHSQ = 30, 36, 48 nm) and NiFe (tNiFe = 4, 5, 7, 10 nm) thin films. Using ferromagnetic resonance measurements, strong spin pumping (large linewidth broadening) and a giant spin mixing conductance, reaching 19.8 nm−2 for HSQ = 48 nm are observed, i.e. comparable to that of heavy metals. The results suggest efficient spin transfer across the HSQ/NiFe interface, possibly originating from a combination of spin and orbital pumping, and provide valuable insights for designing self‐powered and flexible spintronic devices utilizing polymers in combination with ferromagnetic materials.

Two-dimensional materials (2D) and their van der Waals heterostructures provide unique opportunities for the exploration of various spin-related phenomena that emerge due to their combined properties and functionalities. Spintronic devices operate based on spin, the angular momentum of an electron, which is used to transfer and store information. Apart from the requisite preservation of the spin information over a micro-meter distance, there is a need for active electrical control of the spin signal for efficient spin-logic operations. In this regard, graphene is an excellent choice of material for 2D spintronic devices as it has high charge carrier mobility and weak spin-orbit coupling (SOC), allowing for long-distance spin transport. However, for the electrical generation and/or manipulation of the spin signal, materials with strong spin-orbit or exchange coupling are required. In this thesis, we experimentally show that it is possible to induce both spin-orbit and exchange couplings in graphene by the proximity to other 2D materials. We observe that the induced SOC in graphene in the vicinity of transition metal dichalcogenides results in a strong spin lifetime anisotropy and the emergence of spin-to-charge conversion mechanisms. Furthermore, we detect a strong exchange splitting in graphene in the proximity of a 2D magnetic material, CrSBr, that results in large spin polarization of conductivity. This allows for the active electrical and thermal generation of spin currents by the magnetic graphene itself. These experimental observations open the path for the direct applications of electrically-controlled 2D spintronic and spin-caloritronic circuitries with graphene-based heterostructures.

We investigate the coherent transport properties of electrons in a side terminal of a four-terminal nano device made of quantum wires with Rashba spin-orbit (SO) coupling in the presence of magnetic filed. We numerically calculate the charge and spin conductances dependent on SO coupling strength and reduced flux. The results imply that the coherent transport in this device is determined by the interplay of Rashba SO coupling and magnetic filed. For specific values of magnetic flux and SO coupling strength, a complete blocking can take place. It also shows that there is a de-blocking phenomenon induced by the interplay of magnetic flux and SO coupling. Such a 4-terminal and multi-channel structure may provide more options of controlling methods for the coherent charge and spin transport.

Most of the low-energy effective descriptions of spin-orbit driven Mott insulators consider spin orbit coupling (SOC) as a second order perturbation to electron-electron interactions. However, when SOC is comparable to anisotropic Hund's coupling, such as in Ir, validity of this formally weak-SOC approach is not a priori known. Depending on the relative strength of SOC and anisotropic Hund's coupling, different descriptions of the multiplet structure should be employed in the weak and strong SOC limits, \textit{viz.} \textit{LS} and \textit{jj} coupling schemes, respectively. We investigate the implications of both the coupling schemes on the low-energy effective $t-J$ model and calculate the angle resolved photoemission (ARPES) spectra using self-consistent Born approximation. In particular, we obtain the ARPES spectra of quasi-two-dimensional square-lattice iridate ${\rm Sr_2IrO_4}$ in both weak and strong SOC limits. The differences in the limiting cases are understood in terms of the composition and relative energy splittings of the multiplet structure. Our results indicate that the LS coupling scheme yields better agreement with the experiment, thus providing an indirect evidence for the validity of LS coupling scheme for iridates. We also discuss the implications for other metal ions with strong SOC.

Generation of terahertz transients from Co2Fe0.4Mn0.6Si Heusler alloy/heavy-metal bilayers

We develop path-integral Monte Carlo simulations for a parabolic two-dimensional (2D) quantum dot containing $N$ interacting electrons in the presence of Dresselhaus and/or Rashba spin-orbit couplings. Our method solves in a natural way the spin contamination problem and allows for numerically exact finite-temperature results at weak spin-orbit coupling. For $N<10$ electrons, we present data for the addition energy, the particle density, and the total spin $S$ in the Wigner molecule regime of strong Coulomb interactions. We identify magic numbers at N=3 and N=7 via a peak in the addition energy. These magic numbers differ both from weak-interaction and classical predictions, and are stable with respect to (weak) spin-orbit couplings.

We present a detailed analysis of spin-orbit coupling (SOC) in $\ensuremath{\pi}$-conjugated organic materials and its effects on spin characteristics including the spin-relaxation time, spin-diffusion length, and $g$ factor. While $\ensuremath{\pi}$ electrons are responsible for low-energy electrical and optical processes in $\ensuremath{\pi}$-conjugated organic solids, $\ensuremath{\sigma}$ electrons must be explicitly included to properly describe the SOC. The SOC mixes up- and down-spin states and, in the context of spintronics, can be quantified by an admixture parameter in the electron and hole polaron states in $\ensuremath{\pi}$-conjugated organics. Molecular geometry fluctuations such as ring torsion, which are common in soft organic materials and may depend on sample preparation, are found to have a strong effect on the spin mixing. The SOC-induced spin mixing leads to spin flips as polarons hop from one molecule to another, giving rise to spin relaxation and diffusion, which are examined by the time-dependent perturbation theory and density-matrix theory. The spin-relaxation rate is found to be proportional to the carrier hopping rate, or equivalently, carrier mobility. The spin-diffusion length depends on the spin mixing and hopping distance but is insensitive to the carrier mobility. An applied electric field causes spin drift and gives rise to upstream and downstream spin-diffusion lengths in the hopping-conduction regime. The SOC influences the $g$ factor of the polaron state and makes it deviate from the free-electron value. The deviation is due to the mixing of different orbitals in the polaron state, which does not include the spin mixing within the same orbital, and therefore underestimates the SOC strength. In particular, the $g$ factor is not sensitive to the molecular geometry fluctuations, where the spin mixing within the same orbital is dominant. The SOCs in tris-(8-hydroxyquinoline) aluminum (Alq${}_{3}$) and in copper phthalocyanine (CuPc) are particularly strong, due to the orthogonal arrangement of the three ligands in the former and Cu $3d$ orbitals in the latter. The theory quantitatively explains the recent measured spin-diffusion lengths in Alq${}_{3}$ from muon spin rotation and in CuPc from spin-polarized two-photon photoemission.

We study the two-body and three-body bound states in ultracold atomic mixtures with one of the atoms subjected to an isotropic spin-orbit (SO) coupling. We consider a system of two identical fermions interacting with one SO coupled atom. It is found that there can exist two types of three-body bound states, Efimov trimers and universal trimers. The Efimov trimers are energetically less favored by the SO coupling, which will finally merge into the atom-dimer threshold as increasing the SO coupling strength. Nevertheless, these trimers exhibit a new kind of discrete scaling law incorporating the SO coupling effect. On the other hand, the universal trimers are more favored by the SO coupling. They can be induced at negative s-wave scattering lengths and with smaller mass ratios than those without SO coupling. These results are obtained by both the Born-Oppenheimer approximation and exact solutions from three-body equations.