Session W21: Spintronic Devices: Dynamics and Transport

Local and global energy barriers for chiral domain walls in lateral magnetic junctions

The current induced manipulation of chiral spin textures is of great interest for both fundamental research and technological applications.  Of particular interest are magnetic non-volatile memories formed from synthetic antiferromagnetic (SAF) wire in which chiral composite domain walls (DWs), that act as data bits, can be efficiently moved by current [1]. However, overcoming the trade-off between energy efficiency, namely a low threshold current density and high thermal stability, remains a major challenge for the development of integrated chips with high reliability and low power consumption.  We will show that chiral DWs in a SAF-ferromagnet (FM) lateral junction, formed by local plasma oxidation, are highly stable against large magnetic fields whilst the DWs can be efficiently moved across the junction by current [2].  Our approach takes advantage of field-induced global energy barriers in the unique energy landscape of the junction that are added to the local energy barrier.  We demonstrated that thermal fluctuations are equivalent to the magnetic field effect in the energy landscape, thereby, surprisingly, increasing the energy barrier and further stabilizing the DW in the junction at higher temperatures, which is in sharp contrast with FMs or SAFs.  We found that the threshold current density can be further decreased by tilting the junction across the wire while not affecting the high DW stability.  Furthermore, we demonstrated that chiral DWs can be robustly confined within a FM region sandwiched on both their sides by SAFs and yet can be readily injected into these regions by current. Our findings break the trade-off between efficiency and stability, allowing for diverse and versatile DW-based memory, and logic, and beyond with new functionalities.

[1] See-Hun Yang, K.-S. Ryu, and S. S. P. Parkin, “Domain-wall velocities of up to 750 m s−1 driven by exchange-coupling torque in synthetic antiferromagnets”, Nature Nanotechnology 10, 221 (2015).

[2] Jiho Yoon, See-Hun Yang (corresponding author), Jae-Chun Jeon, Andrea Migliorini, Ilya Kostanovskiy, Tianping Ma, Stuart. S. P. Parkin, “Local and global energy barriers for chiral domain walls in synthetic antiferromagnet-ferromagnet lateral junctions”, Nature Nanotechnology 17, 1183 (2022).   

One Trillion True Random Numbers Generated with FPGA-actuated Magnetic Tunnel Junction

Random numbers are crucial in a wide range of applications, from encryption to Monte Carlo simulations. We have recently shown that perpendicular nanopillar magnetic tunnel junctions (pMTJs) activated with short (nanosecond) pulses can generate truly random bits [1]. Here, we significantly accelerate the true random number generation (TRNG) of our stochastic activated MTJs (SMART-MTJs [1]) using Field Programmable Gate Arrays (FPGAs). Our previous experiments used an expensive arbitrary waveform generator (AWG) and a relatively slow (100kHz) analog-to-digital converter (ADC). Our advancement is consolidating the AWG and ADC functions into a low-cost FPGA with a custom-designed daughterboard that provides analog pulses and rapidly reads the junction resistance. With this approach, we produce TRNG at 5MHz, three orders of magnitude faster and with far lower cost instrumentation than our previous method. This has enabled us to rapidly generate over 10^12 random bits that pass the NIST Statistical Test Suite for randomness with only one XOR operation. Increasing the rate of TRNG provides the opportunity to apply the longer SMART bitstream to Monte Carlo simulations, potentially enhancing their accuracy.   

Modeling a Toffoli Gate Constructed Using Perpendicular Magnetic Tunnel Junctions Free Layers

Magnetic Tunnel Junctions (MTJs) are of great interest for non-conventional computing applications. One prominent application is reversible computing, due to its energy-efficient and information-preserving nature. The Toffoli gate plays a crucial role as a universal reversible logic gate, enabling the construction of reversible circuits. Here we present a proof-of-concept construction of a classical Toffoli gate using seven coupled uniaxial nanomagnets that could form the free layer of perpendicularly magnetized MTJs. This construction maps seven spins to three input bits, three output bits, and one ancilla bit, encoding the Toffoli gate's truth table as the system's ground state. We use Python to numerically simulate the system, with the seven coupled macrospins evolving under the stochastic Landau–Lifshitz–Gilbert (sLLG) equation and a two-stage Runge-Kutta integration scheme. Our results demonstrate that the system evolves to the Toffoli gate truth table with a thermal annealing process. Additionally, we also consider the zero temperature case, where the system’s evolution is governed solely by the LLG equation. We observe that the anisotropy energy shapes the system’s energy landscape. With very low anisotropy energy (E_A∼1k_BT), spins evolve to the ground state configurations, while higher anisotropy energy causes the spins to become trapped in metastable states. Our exploration of the rich LLG dynamical behaviors suggests significant potential for future computational applications.   

Spin Signal Optimization in Metallic Non-Local Spin Valves via Tuned Interface Resistance

Magnetic Tunnel Junction (MTJ)-based devices are instrumental in data storage. Due to the drive to smaller devices, however, MTJs face challenges related to high resistance-area products (RA), which limit the signal-to-noise ratio due to impedance mismatch. There thus exists a pressing need to explore all-metal spintronic devices, particularly non-local spin valves (NLSVs), although their applications are spin-signal-limited. The primary approach to enhancing signals in such NLSV devices is incorporation of tuned-RA “tunnel” contacts at the ferromagnetic/nonmagnetic interfaces, thereby mitigating back diffusion of injected spins. Here, we report on a comprehensive study of highly-spin-polarized Al/AlO_x/Co₇₅Fe₂₅-based NLSVs with RA tuned from deep in the tunneling regime (10⁶ Ωμm²) to the transparent limit via controlled Al oxidation. We determine the RA range over which non-local spin signals can be detected, characterize the interfacial barriers via voltage- and temperature-dependent measurements, and comprehensively probe the spin signal enhancement vs. RA. Surprisingly, part of the enhancement is found to derive from increased spin diffusion length in the Al channels when their surfaces are controllably oxidized. We also uncover a systematic suppression of the spin polarization at moderate RA, which appears to be the primary limiting factor in the current spin signal in such devices.   

Electron and Spin Transport in an Ultrathin Al Film for Use as a Nonlocal Spin Valve

Size effect on electron and spin relaxation in ultrathin metallic films is crucial from both scientific and technological perspectives. Our work studies the relaxation of electron and spin transport in the presence of surface and bulk defects in aluminum-based ultrathin films. The contributions from surface roughness, grain boundary scattering, vacancies and surface reconstruction to momentum and spin relaxation are investigated in the Landauer-Buttiker formalism with a Green’s function technique. Resistivity and spin diffusion length are determined assuming that both the leads and the metallic channel are made of Al with 3.6nm thickness at T=0k and embedded in vacuum.  Our calculations identify that for thin sputtered films, random point vacancies and the combined effect of point vacancies and surface corrugation are the dominant contribution to momentum and spin relaxation respectively. Predicted spin diffusion lengths and Elliott-Yafet constants are found to approximately match experimental data. In addition, our work addresses the validity of the Elliott-Yafet spin relaxation mechanism and Matthiessen’s rule in the presence of surface corrugations at sub-10nm, which has not been previously reported.  Violations of Matthiessen’s rule and Elliott-Yafet prediction of β are found in the presence of surface periodicity. However, when bulk scattering dominates, the Elliott-Yafet prediction and Matthiessen’s rule are obeyed because the symmetry breaking is closely dependent on the scattering length scale and concentration of random defects.

    

Magnetic control over the superconducting thermoelectric effect

Over the past decade, it has been shown both theoretically and experimentally that a giant thermoelectric effect can arise when superconductors are coupled to strongly spin-polarized ferromagnets. The thermopower of such devices is orders of magnitude higher than metallic thermoelectric devices at comparable temperatures, and many applications of this effect have already been proposed. Here, we demonstrate a new key advantage of superconductor-ferromagnet hybrids as a platform for novel thermoelectric devices. We experimentally show that the thermopower in V/MgO/Fe/MgO/Fe/Co superconductor-spin valve hybrids (which recently revealed equal spin superconducting triplet generation due to spin-orbit coupling and symmetry filtering [1,2]) can be controlled via the relative magnetic alignment of the ferromagnetic electrodes [3]. Importantly, we confirm the theoretical prediction that by rotating one magnetic layer we can not only substantially change the thermoelectric effect, but can even reverse its sign [3,4] with an optimum antiparallel alignment of the ferromagnetic electrodes (as confirmed by the experiments and modelling). The description of the experimental results is improved by the introduction into the model of an interfacial domain wall in the spin filter layer interfacing the superconductor. Additionally, we demonstrate the in-situ control of thermoelectric effects in Fe/MgO/V/MgO/Fe/Co junctions by the relative alignment of the two ferromagnetic electrodes, in this case one at each side of the superconductor. Our results could lead to the development of a novel kind of superconducting thermoelectric generators and sensors. [1] I. Martínez, et al, Phys. Rev. Appl. 13, 014030 (2020). [2] C. González-Ruano et al., Phys. Rev. B 102  020405(R) (2020). [3] C. González-Ruano et al., Phys. Rev. Lett., 130, 237 (2023). [4] J. A. Ouassou et al., Phys. Rev. B 106, 094514 (2022).   

Title: Observation of spin-Hall induced auto-oscillation in Pt/lithium aluminum ferrite bilayers via inverse spin-Hall effect.

Ferrimagnetic insulators with ultra-low damping are of great interest for their potential applications in efficient spin wave devices. This study demonstrates Pt nanowire spin-Hall current induced excitation of auto-oscillation states in unpatterned novel ultra-low damping ferrimagnetic insulator Li0.5Al0.5Fe2O4 (LFO) thin films. Auto-oscillations occur for only one current polarity, indicating that these states are not primarily induced by the spin Seebeck effect (i.e., temperature gradients). In contrast to previous approaches, the high-frequency (GHz) power spectral density (PSD) electrical signals are associated with the inverse spin-Hall effect at the Pt/LFO interface. A linear dependence of the PSD dispersion curves on the magnetic field is observed with a current onset threshold related to the intrinsic magnetic anisotropy of LFO. The threshold current, however, is higher than expected from the damping of LFO, which may be related to the spin-pumping-induced additional dissipation. In addition, ferromagnetic resonance (FMR) and spin-torque FMR are conducted on LFO thin films and nano-oscillators to determine their characteristics. Micromagnetic modeling shows good agreement with the PSD dispersion curves, showing only one dominant mode. This behavior in contrast with the two modes observed in transition metal nanowire-type spin-Hall nano-oscillators. The continuous thin film ferrimagnetic insulator layer thus provides a means of coupling neighboring oscillators of interest for a variety of applications, including neuromorphic computing.   

Interfacial modification to enhance the effective spin hall angle of perpendicularly magnetized systems

Maximizing the spin-orbit torque (SOT) strength to reduce the current density of magnetization switching (J_c) in heavy metal (HM)/ferromagnet (FM)/HM based perpendicularly magnetized systems have played a key role in constructing SOT-driven memory devices. The SOT strength is proportional to the material's spin Hall angle (θ_sh). We introduced an Au layer at the HM/FM interface to manipulate θ_sh. We deposited Ta/Pt/Co/Pt, Ta/Pt/Co/Au/Pt and Ta/Pt/Au/Co/Pt systems. We observed no significant difference in J_c between Ta/Pt/Co/Pt and Ta/Pt/Co/Au/Pt systems. In contrast, J_c reduces ∽34% in the Ta/Pt/Au/Co/Pt system compared to the Ta/Pt/Co/Pt system. We also prepared Ta/Pt/Co/Au and Ta/Pt/Au/Co/Au systems. We observed a reduction of J_c upto ∽30% in the Ta/Pt/Au/Co/Au multilayer compared to the Ta/Pt/Co/Pt system. To reduce J_c further, another set of samples was prepared with Ta as a capping layer. This set consists of Ta/Pt/Co/Pt/Ta, Ta/Pt/Au/Co/Pt/Ta and Ta/Pt/Au/Co/Pt/Ta/Co/Pt samples. The J_c of the Ta/Pt/Au/Co/Pt/Ta sample was reduced upto ∽58% compared to the Ta/Pt/Co/Pt sample. Experiments show that by introducing an Au layer at the bottom Pt/Co interface, J_c can be reduced. Micromagnetic simulation suggests an increase of θ_sh for these samples. Field-free magnetization switching was realized by depositing an in-plane magnetized layer Co layer in Ta/Pt/Au/Co/Pt/Ta/Co/Pt system. Hence, our findings represent a noteworthy advancement in fabricating magnetic memory devices with reduced J_c.   

Spin accumulation without spin current

The spin Hall effect is a phenomenon in which the spin current flows perpendicular to an applied electric field and causes the spin accumulation at the boundaries. However, in the presence of spin-orbit couplings, the spin current is not well defined. Here, we calculate the spin response to an electric-field gradient, which naturally appears at the boundaries. We derive a generic formula using the Bloch wave functions and the phenomenological relaxation time. We also calculate the response for the uniform Rashba model with short-range nonmagnetic disorder within the first-order Born approximation and corresponding vertex corrections. We find the nonzero spin accumulation, although the spin Hall conductivity exactly vanishes. We may discuss the spin Nernst effect as well in terms of the spin accumulation.   

Giant interfacial spin-Hall angle from Rashba-Edelstein effect revealed by the spin-Hall Hanle processes

The Rashba-Edelstein effect (REE), which generates interfacial spin polarization and subsequent spin current, is a compelling spin-charge conversion mechanism for spintronics applications, since it is not limited by the elemental spin-orbit coupling. In this work, we demonstrate REE at Pt/ferroelectric interfaces using the recently elucidated spin-Hall Hanle effects (SHHE), in which a Larmor precession of spin polarization in a diffusion process from the interface manifest as magnetoresistance and Hall effect. We show that REE leads to a three-fold enhancement of the effective spin Hall angle in ferroelectric interface Pt/h-LuFeO3 compared to that of Pt /Al2O3, although the difference in the spin relaxation time is negligible. Modeling using SHHEs involving REE as an additional source of interfacial polarization suggests that REE can lead to an interfacial spin Hall angle (~0.3) that is one order of magnitude larger than the bulk value of Pt. Our results demonstrate that a ferroelectric interface can produce large spin-charge conversion and that SHHEs are a sensitive tool for characterizing interfacial spin transport properties.   

First principles calculation and experimental study of the self spin pumping in La0.67Sr0.33MnO3

In spintronics research, the efficient generation of spin currents and spin torques is an important subject and the spin Hall effect is one of the most important mechanisms to generate spin currents in spintronic devices. Recently, experiments have shown that anti-damping spin torques and the inverse spin Hall effect occur simultaneously in the La_0.67Sr_0.33MnO₃ (LSMO)/Pt heterostructures [1]. In this talk, we discuss theoretical calculations and experimental measurements of the inverse spin Hall effect (ISHE) in single layer LSMO films. In order to evaluate the appreciable ISHE from the experiment, we compute the spin Hall conductivity of bulk LSMO using first principles calculations. First, the ground state electronic structure of bulk LSMO is obtained from density functional theory. Next, we interpolate the calculated electronic structure into the orbital-based Wannier functions basis. Finally, using the Kubo formalism, we compute the full spin Hall conductivity tensor of bulk LSMO. The calculated spin Hall conductivity values for bulk LSMO are on the order of 10 S/cm, in reasonable agreement with the experimental results.   

Spin Transport in All-Metallic Al2Cu-Based Non-Local Spin Valves

As microelectronic components scale down, new materials must be used to mitigate the negative effects of size reduction, such as increasing resistivity in interconnects. One promising material in this regard is the ordered metallic alloy θ-phase Al₂Cu. With growing interest in spintronic devices, including for interconnect applications, it is important to understand not only charge transport in such materials, but also spin transport. There is a complete dearth of knowledge and understanding of spin transport in light-metal alloys, however, despite their potential to outperform metals such as Al. We address this here through the first study of ordered-alloy-based all-metallic non-local spin valves, focusing on θ-Al₂Cu. X-ray diffraction confirms the formation of 112-oriented polycrystalline θ-Al₂Cu films which we have optimized via thickness, composition, and post-deposition annealing. Optimized films have been incorporated in non-local spin valves, enabling temperature-dependent measurements of the spin signal and θ-Al₂Cu spin diffusion length. Elliot-Yafet spin relaxation probabilities are found to be close to those of Al, much improved over Cu, and with no evidence of Kondo spin relaxation. This suggests promise for the incorporation of θ-Al₂Cu in metallic spin transport devices.   

Critical enhancement of the spin Hall effect by spin fluctuations

The spin Hall (SH) effect, the conversion of the electric current to the spin current along the transverse direction, relies on the relativistic spin-orbit coupling (SOC). Here, we develop microscopic mechanisms of the SH effect in magnetic metals, where itinerant electrons are coupled with localized magnetic moments via the Hund exchange interaction and the SOC [1]. Both antiferromagnetic metals and ferromagnetic metals are considered. It is shown that the SH conductivity can be significantly enhanced by dynamical spin fluctuations when approaching the magnetic transition temperature of both cases. For antiferromagnetic metals, the pure SH effect appears in entire temperature range, while for ferromagnetic metals, the pure SH effect is expected to be replaced by the anomalous Hall effect below the transition temperature. When the magnetic transition temperature is tuned to zero temperature, i.e., approaching a quantum critical point, nontrivial temperature dependence of the SH conductivity is predicted for both ferromagnetic metals and antiferromagnetic metals. We discuss possible experimental realizations of the predicted SH effect induced by the dynamical spin fluctuations, such as antiferromagnetic metal Cr [2].

Reference

[1] S. Okamoto and N. Nagaosa, arXiv:2308.09636

[2] C. Fang, C. Wan, X. Zhang, S. Okamoto, T. Ma, J. Qin, X. Wang, C. Guo, J. Dong, G. Yu, Z. Wen, N. Tang, S. S. P. Parkin, N. Nagaosa, Y. Lu, and X. Han, arXiv:2304.13400.