Magnon-Phonon Coupling of Synthetic Antiferromagnets in a Surface Acoustic Wave Cavity Resonator.

We used a surface acoustic wave (SAW) cavity resonator to study the coupling of acoustic magnons in a synthetic antiferromagnet (SAF) and phonons carried by SAWs. The SAF is composed of a CoFeB/Ru/CoFeB trilayer, and the scattering matrix of the SAW resonator is studied to assess the coupling. We find that the spectral line width of the SAW resonator is modulated when the frequency of the excited magnons approaches the SAW resonance frequency. Such a change in the spectral linewidth can be well reproduced using macrospin-like model calculations. From the model analyses, we estimate the magnon-phonon coupling strength to be ∼9.9 MHz at a SAW resonance frequency of 1.8 GHz: the corresponding magnomechanical cooperativity is ∼0.66. As the spectral shape hardly changes in a CoFeB single-layer reference sample, these results show that SAF provides an ideal platform to study magnon-phonon coupling in an SAW cavity resonator.

Switchable generation of azimuthally- and radially-polarized terahertz beams from a spintronic terahertz emitter.

We propose and demonstrate a method of generating two fundamental terahertz cylindrical vector beams (THz-CVBs), namely the azimuthally- and radially-polarized THz pulses, from a spintronic THz emitter. We begin by presenting that the spintronic emitter generates the HE21 mode, a quadrupole like polarization distribution, when placed between two magnets with opposing polarity. By providing an appropriate mode conversion using a triangular Si prism, we show both from experiment and numerical calculation that we obtain azimuthal and radial THz vector beams. The proposed method facilitates the access of CVBs and paves the way toward sophisticated polarization control in the THz regime.

Current-Induced Modulation of the Interfacial Dzyaloshinskii-Moriya Interaction.

The Dzyaloshinskii-Moriya (DM) interaction is an antisymmetric exchange interaction that is responsible for the emergence of chiral magnetism. The origin of the DM interaction, however, remains to be identified albeit the large number of studies reported on related effects. It has been recently suggested that the DM interaction is equivalent to an equilibrium spin current density originating from spin-orbit coupling, an effect referred to as the spin Doppler effect. The model predicts that the DM interaction can be controlled by spin current injected externally. Here we show that the DM exchange constant (D) in W/CoFeB-based heterostructures can be modulated with external current passed along the film plane. At higher current, D decreases with increasing current, which we infer is partly due to the adiabatic spin transfer torque. At lower current, D increases linearly with current regardless of the polarity of current flow. The rate of increase in D with the current density agrees with that predicted by the model based on the spin Doppler effect. These results imply that the DM interaction at the heavy-metal-ferromagnetic-metal interface partly originates from an equilibrium interface spin (polarized) current which can be modulated externally.

Current-Induced Generation and Synchronous Motion of Highly Packed Coupled Chiral Domain Walls.

Chiral domain walls of Neel type emerge in heterostructures that include heavy metal (HM) and ferromagnetic metal (FM) layers owing to the Dzyaloshinskii-Moriya (DM) interaction at the HM/FM interface. In developing storage class memories based on the current induced motion of chiral domain walls, it remains to be seen how dense such domain walls can be packed together. Here we show that a universal short-range repulsion that scales with the strength of the DM interaction exists among chiral domain walls. The distance between the two walls can be reduced with the application of the out-of-plane field, allowing the formation of coupled domain walls. Surprisingly, the current driven velocity of such coupled walls is independent of the out-of-plane field, enabling manipulation of significantly compressed coupled domain walls using current pulses. Moreover, we find that a single current pulse with optimum amplitude can create a large number of closely spaced domain walls. These features allow current induced generation and synchronous motion of highly packed chiral domain walls, a key feature essential for developing domain wall based storage devices.

Spin Hall Magnetoresistance in Metallic Bilayers.

Spin Hall magnetoresistance (SMR) is studied in metallic bilayers that consist of a heavy metal (HM) layer and a ferromagnetic metal (FM) layer. We find a nearly tenfold increase of SMR in W/CoFeB compared to previously studied HM/ferromagnetic insulator systems. The SMR increases with decreasing temperature despite the negligible change in the W layer resistivity. A model is developed to account for the absorption of the longitudinal spin current to the FM layer, one of the key characteristics of a metallic ferromagnet. We find that the model not only quantitatively describes the HM layer thickness dependence of SMR, allowing accurate estimation of the spin Hall angle and the spin diffusion length of the HM layer, but also can account for the temperature dependence of SMR by assuming a temperature dependent spin polarization of the FM layer. These results illustrate the unique role a metallic ferromagnetic layer plays in defining spin transmission across the HM/FM interface.

Layer thickness dependence of the current-induced effective field vector in Ta|CoFeB|MgO.

Current-induced effective magnetic fields can provide efficient ways of electrically manipulating the magnetization of ultrathin magnetic heterostructures. Two effects, known as the Rashba spin orbit field and the spin Hall spin torque, have been reported to be responsible for the generation of the effective field. However, a quantitative understanding of the effective field, including its direction with respect to the current flow, is lacking. Here we describe vector measurements of the current-induced effective field in Ta|CoFeB|MgO heterostructrures. The effective field exhibits a significant dependence on the Ta and CoFeB layer thicknesses. In particular, a 1 nm thickness variation of the Ta layer can change the magnitude of the effective field by nearly two orders of magnitude. Moreover, its sign changes when the Ta layer thickness is reduced, indicating that there are two competing effects contributing to it. Our results illustrate that the presence of atomically thin metals can profoundly change the landscape for controlling magnetic moments in magnetic heterostructures electrically.

Decoding the magnetic bit positioning error in a ferrimagnetic racetrack.

Current-driven motion of magnetic domain walls is one of the key technologies for developing storage class memory devices. Extensive studies have revealed a variety of material systems that exhibit high-speed and/or lower power propagation of the domain walls driven by electric current. However, few studies have assessed the reliability of the operations of the memory technology. Here, we decode the errors associated with writing and shifting domain walls using nanosecond current pulses in a ~5-micrometer-wide wire composed of a Pt/GdFeCo bilayer. We find that writing a domain wall at the edge of the wire causes a bit positioning error of ~0.3 micrometers, whereas the shifting process induces an error of ~0.1 micrometers per a 2-nanosecond-long current pulse. The error correlation among successive shifting is negligible when the current drive is sufficiently large. These features allow reliable operation of highly packed domain walls in a ferrimagnetic racetrack.

Time-domain observation of the spinmotive force in permalloy nanowires.

The spinmotive force associated with a moving domain wall is observed directly in Permalloy nanowires using real time voltage measurements with proper subtraction of the electromotive force. Whereas the wall velocity exhibits nonlinear dependence on magnetic field, the generated voltage increases linearly with the field. We show that the sign of the voltage reverses when the wall propagation direction is altered. Numerical simulations explain quantitatively these features of spinmotive force and indicate that it scales with the field even in a field range where the wall motion is no longer associated with periodic angular rotation of the wall magnetization.

Oscillatory dependence of current-driven magnetic domain wall motion on current pulse length.

Magnetic domain walls, in which the magnetization direction varies continuously from one direction to another, have long been objects of considerable interest. New concepts for devices based on such domain walls are made possible by the direct manipulation of the walls using spin-polarized electrical current through the phenomenon of spin momentum transfer. Most experiments to date have considered the current-driven motion of domain walls under quasi-static conditions, whereas for technological applications, the walls must be moved on much shorter timescales. Here we show that the motion of domain walls under nanosecond-long current pulses is surprisingly sensitive to the pulse length. In particular, we find that the probability of dislodging a domain wall, confined to a pinning site in a permalloy nanowire, oscillates with the length of the current pulse, with a period of just a few nanoseconds. Using an analytical model and micromagnetic simulations, we show that this behaviour is connected to a current-induced oscillatory motion of the domain wall. The period is determined by the wall's mass and the slope of the confining potential. When the current is turned off during phases of the domain wall motion when it has enough momentum, the domain wall is driven out of the confining potential in the opposite direction to the flow of spin angular momentum. This dynamic amplification effect could be exploited in magnetic nanodevices based on domain wall motion.

Acoustic spin Hall effect in strong spin-orbit metals.

We report on the observation of the acoustic spin Hall effect that facilitates lattice motion-induced spin current via spin-orbit interaction (SOI). Under excitation of surface acoustic wave (SAW), we find that a spin current flows orthogonal to the SAW propagation in nonmagnetic metals (NMs). The acoustic spin Hall effect manifests itself in a field-dependent acoustic voltage in NM/ferromagnetic metal bilayers. The acoustic voltage takes a maximum when the NM layer thickness is close to its spin diffusion length, vanishes for NM layers with weak SOI, and increases linearly with the SAW frequency. To account for these results, we find that the spin current must scale with the SOI and the time derivative of the lattice displacement. These results, which imply the strong coupling of electron spins with rotating lattices via the SOI, show the potential of lattice dynamics to supply spin current in strong spin-orbit metals.

Spin-orbit torque driven magnetization switching in W/CoFeB/MgO-based type-Y three terminal magnetic tunnel junctions.

We have studied current induced magnetization switching in W/CoFeB/MgO based three terminal magnetic tunnel junctions. The switching driven by spin-orbit torque (SOT) is evaluated in the so-called type-Y structure, in which the magnetic easy-axis of the CoFeB layer lies in the film plane and is orthogonal to the current flow. The effective spin Hall angle estimated from the bias field dependence of critical current (Ic) is ~ 0.07. The field and current dependence of the switching probability are studied. The field and DC current induced switching can be described using a model based on thermally assisted magnetization switching. In contrast, the 50 ns long pulse current dependence of the switching probability shows significant deviation from the model, even if contribution from the field-like torque is included. The deviation is particularly evident when the threshold switching current is larger. These results show that conventional thermally assisted magnetization switching model cannot be used to describe SOT induced switching using short current pulses.

The spin Hall effect of Bi-Sb alloys driven by thermally excited Dirac-like electrons.

We have studied the charge to spin conversion in Bi1-x Sb x /CoFeB heterostructures. The spin Hall conductivity (SHC) of the sputter-deposited heterostructures exhibits a high plateau at Bi-rich compositions, corresponding to the topological insulator phase, followed by a decrease of SHC for Sb-richer alloys, in agreement with the calculated intrinsic spin Hall effect of Bi1-x Sb x . The SHC increases with increasing Bi1-x Sb x thickness before it saturates, indicating that it is the bulk of the alloy that predominantly contributes to the generation of spin current; the topological surface states, if present, play little role. Unexpectedly, the SHC is found to increase with increasing temperature, following the trend of carrier density. These results suggest that the large SHC at room temperature, with a spin Hall efficiency exceeding 1 and an extremely large spin current mobility, is due to increased number of thermally excited Dirac-like electrons in the L valley of the narrow gap Bi1-x Sb x alloy.

Interference induced enhancement of magneto-optical Kerr effect in ultrathin magnetic films.

We have studied the magneto-optical spectra of ultrathin magnetic films deposited on Si substrates coated with an oxide layer (SiOx). We find that the Kerr rotation angle and the ellipticity of ~1 nm thick CoFeB thin films, almost transparent to visible light, show a strong dependence on the thickness of the SiOx layer. The Kerr signal from the 1 nm CoFeB thin film can be larger than that of ~100 nm thick CoFeB films for a given SiOx thickness and light wavelength. The enhancement of the Kerr signal occurs when optical interference takes place within the SiOx layer. Interestingly, under such resonance condition, the measured Kerr signal is in some cases larger than the estimation despite the good agreement of the measured and calculated reflection amplitude. We infer the discrepancy originates from interface states that are distinct from the bulk characteristics. These results show that optical interference effect can be utilized to study the magneto-optical properties of ultrathin films.

The spin Nernst effect in tungsten.

The spin Hall effect allows the generation of spin current when charge current is passed along materials with large spin-orbit coupling. It has been recently predicted that heat current in a nonmagnetic metal can be converted into spin current via a process referred to as the spin Nernst effect. We report the observation of the spin Nernst effect in W. In W/CoFeB/MgO heterostructures, we find changes in the longitudinal and transverse voltages with magnetic field when temperature gradient is applied across the film. The field dependence of the voltage resembles that of the spin Hall magnetoresistance. A comparison of the temperature gradient-induced voltage and the spin Hall magnetoresistance allows direct estimation of the spin Nernst angle. We find the spin Nernst angle of W to be similar in magnitude but opposite in sign to its spin Hall angle. Under an open-circuit condition, this sign difference results in the spin current generation larger than otherwise. These results highlight the distinct characteristics of the spin Nernst and spin Hall effects, providing pathways to explore materials with unique band structures that may generate large spin current with high efficiency.

Tunable inertia of chiral magnetic domain walls.

The time it takes to accelerate an object from zero to a given velocity depends on the applied force and the environment. If the force ceases, it takes exactly the same time to completely decelerate. A magnetic domain wall is a topological object that has been observed to follow this behaviour. Here we show that acceleration and deceleration times of chiral Neel walls driven by current are different in a system with low damping and moderate Dzyaloshinskii-Moriya exchange constant. The time needed to accelerate a domain wall with current via the spin Hall torque is much faster than the time it needs to decelerate once the current is turned off. The deceleration time is defined by the Dzyaloshinskii-Moriya exchange constant whereas the acceleration time depends on the spin Hall torque, enabling tunable inertia of chiral domain walls. Such unique feature of chiral domain walls can be utilized to move and position domain walls with lower current, key to the development of storage class memory devices.

Giant nonreciprocal emission of spin waves in Ta/Py bilayers.

Spin waves are propagating disturbances in the magnetization of magnetic materials. One of their interesting properties is nonreciprocity, exhibiting that their amplitude depends on the magnetization direction. Nonreciprocity in spin waves is of great interest in both fundamental science and applications because it offers an extra knob to control the flow of waves for the technological fields of logics and switch applications. We show a high nonreciprocity in spin waves from Ta/Py bilayer systems with out-of-plane magnetic fields. The nonreciprocity depends on the thickness of Ta underlayer, which is found to induce an interfacial anisotropy. The origin of observed high nonreciprocity is twofold: different polarities of the in-plane magnetization due to different angles of canted out-of-plane anisotropy and the spin pumping effect at the Ta/Py interface. Our findings provide an opportunity to engineer highly efficient, nonreciprocal spin wave-based applications, such as nonreciprocal microwave devices, magnonic logic gates, and information transports.

Enhanced orbital magnetic moments in magnetic heterostructures with interface perpendicular magnetic anisotropy.

We have studied the magnetic layer thickness dependence of the orbital magnetic moment in magnetic heterostructures to identify contributions from interfaces. Three different heterostructures, Ta/CoFeB/MgO, Pt/Co/AlOx and Pt/Co/Pt, which possess significant interface contribution to the perpendicular magnetic anisotropy, are studied as model systems. X-ray magnetic circular dichroism spectroscopy is used to evaluate the relative orbital moment, i.e. the ratio of the orbital to spin moments, of the magnetic elements constituting the heterostructures. We find that the relative orbital moment of Co in Pt/Co/Pt remains constant against its thickness whereas the moment increases with decreasing Co layer thickness for Pt/Co/AlOx, suggesting that a non-zero interface orbital moment exists for the latter system. For Ta/CoFeB/MgO, a non-zero interface orbital moment is found only for Fe. X-ray absorption spectra shows that a particular oxidized Co state in Pt/Co/AlOx, absent in other heterosturctures, may give rise to the interface orbital moment in this system. These results show element specific contributions to the interface orbital magnetic moments in ultrathin magnetic heterostructures.

Interface control of the magnetic chirality in CoFeB/MgO heterostructures with heavy-metal underlayers.

Recent advances in the understanding of spin orbital effects in ultrathin magnetic heterostructures have opened new paradigms to control magnetic moments electrically. The Dzyaloshinskii-Moriya interaction (DMI) is said to play a key role in forming a Néel-type domain wall that can be driven by the spin Hall torque. Here we show that the strength and sign of the DMI can be changed by modifying the adjacent heavy-metal underlayer (X) in perpendicularly magnetized X/CoFeB/MgO heterostructures. The sense of rotation of a domain wall spiral is reversed when the underlayer is changed from Hf, Ta to W and the strength of DMI varies as the filling of 5d orbitals, or the electronegativity, of the heavy-metal layer changes. The DMI can even be tuned by adding nitrogen to the underlayer, thus allowing interface engineering of the magnetic texture in ultrathin magnetic heterostructures.

Topological repulsion between domain walls in magnetic nanowires leading to the formation of bound states.

Head-to-head and tail-to-tail magnetic domain walls in nanowires behave as free magnetic monopoles carrying a single magnetic charge. Since adjacent walls always carry opposite charges, they attract one another. In most cases this long-range attractive interaction leads to annihilation of the two domain walls. Here, we show that, in some cases, a short-range repulsive interaction suppresses annihilation of the walls, even though the lowest energy state is without any domain walls. This repulsive interaction is a consequence of topological edge defects that have the same winding number. We show that the competition between the attractive and repulsive interactions leads to the formation of metastable bound states made up of two or more domain walls. We have created bound states formed from up to eight domain walls, corresponding to the magnetization winding up over four complete 360° rotations.

Domain wall dynamics driven by spin transfer torque and the spin-orbit field.

We have studied current-driven dynamics of domain walls when an in-plane magnetic field is present in perpendicularly magnetized nanowires using an analytical model and micromagnetic simulations. We model an experimentally studied system, ultrathin magnetic nanowires with perpendicular anisotropy, where an effective in-plane magnetic field is developed when current is passed along the nanowire due to the Rashba-like spin-orbit coupling. Using a one-dimensional model of a domain wall together with micromagnetic simulations, we show that the existence of such in-plane magnetic fields can either lower or raise the threshold current needed to cause domain wall motion. In the presence of the in-plane field, the threshold current differs for positive and negative currents for a given wall chirality, and the wall motion becomes sensitive to out-of-plane magnetic fields. We show that large non-adiabatic spin torque can counteract the effect of the in-plane field.