Small In-plane Magnetic Field Research Articles

Flavor symmetry breaking in spin-orbit coupled bilayer graphene

Recent experimental discovery of flavor symmetry breaking metallic phases in Bernal-stacked bilayer graphene points to the strongly interacting nature of electrons near the top (bottom) of its valence (conduction) band. Superconductivity was also observed in between these symmetry breaking phases when the graphene bilayer is placed under a small in-plane magnetic field or in close proximity to a monolayer WSe$_2$ substrate. Here we address the correlated nature of the band edge electrons and obtain the quantum phase diagram of their many-body ground states incorporating the effect of proximity induced spin-orbit coupling. We find that in addition to the spin/valley flavor polarized half and quarter metallic states, two types of intervalley coherent phases emerge near the phase boundaries between the flavor polarized metals. Both spin-orbit coupling and in-plane magnetic field disfavor the spin-unpolarized valley coherent phase. Our findings suggest possible competition between intervalley coherence and superconducting orders, arising from the intriguing correlation effects in bilayer graphene in the presence of spin-orbit coupling.

Performance Enhancement of a Spin-Wave-Based Reservoir Computing System Utilizing Different Physical Conditions

We numerically study how to enhance reservoir computing performance by thoroughly extracting the spin-wave device potential for higher-dimensional information generation. The reservoir device has a 1-input exciter and 120-output detectors on the top of a continuous magnetic garnet film for spin-wave transmission. For various nonlinear and fading-memory dynamic phenomena distributing in the film space, small in-plane magnetic fields are used to prepare stripe domain structures and various damping constants at the film sides and bottom are explored. The ferromagnetic resonant frequency and relaxation time of spin precession clearly characterizes the change in spin dynamics with the magnetic field and damping constant. The common input signal for reservoir computing is a 1-GHz cosine wave with random 6-valued amplitude modulation. A basic 120-dimensional reservoir output vector is obtained from time-series signals at the 120-output detectors under each of three magnetic field conditions. Then, 240- and 360-dimensional reservoir output vectors are also constructed by concatenating two and three basic ones, respectively. In nonlinear autoregressive moving average (NARMA) prediction tasks, the computational performance is enhanced as the dimension of the reservoir output vector becomes higher and a significantly low prediction error is achieved for the tenth-order NARMA task using the 360-dimensional vector and optimum damping constant. The results are clear evidence that the collection of diverse output signals efficiently increases the dimensionality of the integrated reservoir state vector (i.e. reservoir-state richness) and thereby contributes to high computational performance. This paper demonstrates that performance enhancement through various configuration settings is a practical approach for on-chip reservoir computing devices with small numbers of real output nodes.

A magnetic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2.

Quantum spin liquids (QSLs) are topologically ordered states of matter that host fractionalized excitations. A particular route towards a QSL is via strongly bond-dependent interactions on the hexagonal lattice. A number of Ru- and Ir-based candidate Kitaev QSL materials have been pursued, but all have appreciable non-Kitaev interactions. Using time-domain terahertz spectroscopy, we observed a broad magnetic continuum over a wide range of temperatures and fields in the honeycomb cobalt-based magnet BaCo2(AsO4)2, which has been proposed to be a more ideal version of a Kitaev QSL. Applying an in-plane magnetic field of ~0.5 T suppresses the magnetic order, and at higher fields, applying the field gives rise to a spin-polarized state. Under a 4 T magnetic field that was oriented principally out of plane, a broad magnetic continuum was observed that may be consistent with a field-induced QSL. Our results indicate BaCo2(AsO4)2 is a promising QSL candidate.

Aspects of long range spin–triplet correlations in superconductor/ferromagnet hetero-structures

The notion of competing ferromagnetic (F) and superconducting (S) orders in F/S hybrid structures was transformed by the first realization of ferromagnetic Josephson π-junctions and the almost simultaneous prediction of a possibility of spin–triplet correlations in such structures, almost two decades back. Such hybrid structures in various configurations are now studied as rich sources of emergent states and new effects. Unlike the spin singlet Cooper pairs, the spin triplet Cooper pairs are much less affected by the exchange field of a ferromagnet and, therefore, immediately finds interest in the field of spintronics. Theoretically, it has been shown that the basic protocol for spin–singlet to spin–triplet supercurrent conversion is the presence of magnetic non-collinearity at the superconductor–ferromagnet interface. Therefore, almost all experiments in this direction have utilized transport measurements on F/S systems with artificial magnetic non-collinearity formed by combination of several ferromagnetic layers next to the superconducting layer. Here we highlight two aspects of studying these heterostructures. Firstly we show that natural magnetic inhomogeneities, found in domain walls of ferromagnets, can also be used to achieve singlet–triplet conversion, instead of artificial magnetic inhomoheneities. This possibility was explored via transport measurements in nano-scale planar Nb–Ni–Nb junctions and nano-SQUIDs, where a domain wall was pinned at the Josephson junction barrier. By this method we were able to show Josephson coupling across about 70 nm of strong ferromagnetic planar barrier. Secondly we show that spin–triplet correlations at the F/S interface are robust enough to be probed by the diamagnetic screening currents at the interface. This was probed by studying the change in sperconducting transition temperature of Nb/Co/Py/Nb multilayers in presence of small in-plane magnetic field. The Co/Py combination, which is a soft-hard type magnetic exchange spring, worked as magnetic inhomogeneity for triplet generation at the interface of the superconducting Nb. These observations may promote new experiments in the field of superconducting-spintronics.

Correlation-Induced Triplet Pairing Superconductivity in Graphene-Based Moiré Systems.

Motivated by the possible non-spin-singlet superconductivity in the magic-angle twisted trilayer graphene experiment, we investigate the triplet-pairing superconductivity arising from a correlation-induced spin-fermion model of Dirac fermions with spin, valley, and sublattice degrees of freedom. We find that the f-wave pairing is favored due to the valley-sublattice structure, and the superconducting state is time-reversal symmetric, fully gapped, and nontopological. With a small in-plane magnetic field, the superconducting state becomes partially polarized, and the transition temperature can be slightly enhanced. Our results apply qualitatively to Dirac fermions for the triplet-pairing superconductivity in graphene-based moiré systems, which is fundamentally distinct from triplet superconductivity in ^{3}He and ferromagnetic superconductors.

Nanometric skyrmion lattice from anisotropic exchange interactions in a centrosymmetric host

Skyrmion formation in centrosymmetric magnets without Dzyaloshinskii–Moriya interactions was originally predicted from unbiased numerical techniques. However, no attempt has yet been made, by comparison to a real material, to determine the salient interaction terms and model parameters driving spin-vortex formation. We identify a Hamiltonian with anisotropic exchange couplings, local ion anisotropy, and four-spin interactions, which is generally applicable to this class of compounds. In the representative system Gd3Ru4Al12, anisotropic exchange drives a fragile balance between helical, skyrmion lattice (SkL), and transverse conical (cycloidal) orders. The model is severely constrained by the experimentally observed collapse of the SkL with a small in-plane magnetic field. For the zero-field helical state, we further anticipate that spins can be easily rotated out of the spiral plane by a tilted magnetic field or applied current.

Asymmetric crossing of the attractive and repulsive magnetic potential by Abrikosov vortices

We present studies of Abrikosov vortex motion across the magnetically charged edges of long thin ferromagnetic stripes placed above or under a thin superconducting film. The magnetic charges at the stripe edges form attractive or repulsive potential wells for vortices. Using a relatively small in-plane magnetic field to polarize the stripe edges and normal-to-plane magnetic field to induce up or down polarized vortices, we tune the attractive or repulsive stripe-vortex interactions. Imaging of the vortex dynamics reveals that the repulsive magnetic potential ${{U}_{m}}^{+}$ acts as a robust vortex pinning barrier, while the attractive ${{U}_{m}}^{\ensuremath{-}}$ has practically no effect on the vortex motion irrespective of the position of the stripes located above or underneath the superconducting film. We analyze the observed asymmetry using equations of the overdamped vortex motion. The formal analytical solution yields an asymmetry, but the numerical modeling with and without noise terms does not confirm it. Instead, we find that the asymmetry is caused by the creation of spontaneous vortices at the maxima of ${U}_{m}$, which depends on the edge polarity and suppress ${{U}_{m}}^{\ensuremath{-}}$. Furthermore, our experiment and time-dependent Ginzburg-Landau simulations demonstrate that magnetic pinning dominates over vortex pinning due to corrugations of the superconducting layer deposited on top of the ferromagnetic stripes.

Threshold Current Density for Perpendicular Magnetization Switching Through Spin-Orbit Torque

We theoretically investigate the threshold current density for spin-orbit-torque- (SOT) induced perpendicular magnetization switching. According to the relative sign of fieldlike torque (FLT) and dampinglike torque (DLT), we derive the corresponding analytical formulas of the threshold current density ${J}_{\mathrm{th}}$ required to switch magnetization from equilibrium states to nearly in-plane states. These formulas, which agree well with numerical results among a wide range of material parameters, indicate that SOT current density can be significantly reduced in the presence of a large FLT. The conditions are then explored to achieve complete magnetization reversal after removing the SOT currents. When the ratio of FLT to DLT \ensuremath{\eta} is negative in our sign convention, we find that SOT pulses with long enough fall time, for example, 0.2 ns in our simulations, can guarantee stable switching. In contrast, a small in-plane magnetic field or a large damping is necessary when \ensuremath{\eta} g 0. Based on the conditions, the measured threshold current densities in several reported experiments, which deviate from previous models, can be well reproduced by our derived ${J}_{\mathrm{th}}$. We further study the possible incubation delay induced by SOT, clarifying the recent contradiction on incubation time during SOT switching. Our work sheds insights on the SOT material optimization and the comprehension of magnetization switching dynamics induced by SOT.

Möbius Insulator and Higher-Order Topology in MnBi_{2n}Te_{3n+1}.

We propose MnBi_{2n}Te_{3n+1} as a magnetically tunable platform for realizing various symmetry-protected higher-order topology. Its canted antiferromagnetic phase can host exotic topological surface states with a Möbius twist that are protected by nonsymmorphic symmetry. Moreover, opposite surfaces hosting Möbius fermions are connected by one-dimensional chiral hinge modes, which offers the first material candidate of a higher-order topological Möbius insulator. We uncover a general mechanism to feasibly induce this exotic physics by applying a small in-plane magnetic field to the antiferromagnetic topological insulating phase of MnBi_{2n}Te_{3n+1}, as well as other proposed axion insulators. For other magnetic configurations, two classes of inversion-protected higher-order topological phases are ubiquitous in this system, which both manifest gapped surfaces and gapless chiral hinge modes. We systematically discuss their classification, microscopic mechanisms, and experimental signatures. Remarkably, the magnetic-field-induced transition between distinct chiral hinge mode configurations provides an effective "topological magnetic switch".

Majorana and parafermion corner states from two coupled sheets of bilayer graphene

We consider a setup consisting of two coupled sheets of bilayer graphene in the regime of strong spin-orbit interaction, where electrostatic confinement is used to create an array of effective quantum wires. We show that for suitable interwire couplings the system supports a topological insulator phase exhibiting Kramers partners of gapless helical edge states, while the additional presence of a small in-plane magnetic field and weak proximity-induced superconductivity leads to the emergence of zero-energy Majorana corner states at all four corners of a rectangular sample, indicating the transition to a second-order topological superconducting phase. The presence of strong electron-electron interactions is shown to promote the above phases to their exotic fractional counterparts. In particular, we find that the system supports a fractional topological insulator phase exhibiting fractionally charged gapless edge states and a fractional second-order topological superconducting phase exhibiting zero-energy $\mathbb{Z}_{2m}$ parafermion corner states, where $m$ is an odd integer determined by the position of the chemical potential.

Surface-Acoustic-Wave Induced Ferromagnetic Resonance in Fe Thin Films and Magnetic Field Sensing

Resonant magnetoelastic coupling (MEC) is demonstrated in an Fe thin film epitaxially grown on a piezoelectric GaAs substrate with application of subgigahertz surface acoustic waves (SAWs). The frequency at which resonant MEC is achieved is reduced far below 1 GHz by the application of a small in-plane magnetic field. Moreover, the resonance, observable by attenuation and velocity changes of the SAW, can be switched on and off by a small (0.1 oC) angular rotation of this in-plane field. This angular sensitivity makes SAW-ferromagnet devices attractive for sensing applications, such as wireless, battery-free, and interrogable magnetic-field monitors. Using a simple magnetization dynamics model that takes into account the Fe magnetic anisotropy and the softening of the magnetic precession modes, we are able to describe the observed salient features.

Spin-orbit-driven band inversion in bilayer graphene by the van der Waals proximity effect.

Spin-orbit coupling (SOC) is the key to realizing time-reversal-invariant topological phases of matter1,2. SOC was predicted by Kane and Mele3 to stabilize a quantum spin Hall insulator; however, the weak intrinsic SOC in monolayer graphene4-7 has precluded experimental observation in this material. Here we exploit a layer-selective proximity effect-achieved via a van der Waals contact with a semiconducting transition-metal dichalcogenide8-21-to engineer Kane-Mele SOC in ultra clean bilayer graphene. Using high-resolution capacitance measurements to probe the bulk electronic compressibility, we find that SOC leads to the formation of a distinct, incompressible, gapped phase at charge neutrality. The experimental data agree quantitatively with a simple theoretical model in which the new phase results from SOC-driven band inversion. In contrast to Kane-Mele SOC in monolayer graphene, the inverted phase is not expected to be a time-reversal-invariant topological insulator, despite being separated from conventional band insulators by electric-field-tuned phase transitions where crystal symmetry mandates that the bulk gap must close22. Our electrical transport measurements reveal that the inverted phase has a conductivity of approximately e2/h (where e is the electron charge and h Planck's constant), which is suppressed by exceptionally small in-plane magnetic fields. The high conductivity and anomalous magnetoresistance are consistent with theoretical models that predict helical edge states within the inverted phase that are protected from backscattering by an emergent spin symmetry that remains robust even for large Rashba SOC. Our results pave the way for proximity engineering of strong topological insulators as well as correlated quantum phases in the strong spin-orbit regime in graphene heterostructures.

Optimization of Spin-Wave Propagation with Enhanced Group Velocities by Exchange-Coupled Ferrimagnet-Ferromagnet Bilayers

We report broadband spectroscopy and numerical analysis by which we explore propagating spin waves in a magnetic bilayer consisting of a 23 nm thick permalloy film deposited on 130 nm thick $Y_{3}Fe_{5}O_{12}$. In the bilayer, we observe a characteristic mode that exhibits a considerably larger group velocity at small in-plane magnetic field than both the magnetostatic and perpendicular standing spin waves. Using the finite element method, we confirm the observations by simulating the mode profiles and dispersion relations. They illustrate the hybridization of spin wave modes due to exchange coupling at the interface. The high-speed propagating mode found in the bilayer can be utilized to configure multi-frequency spin wave channels enhancing the performance of spin wave based logic devices.

Signatures of Topological Superconductivity in Bulk-Insulating Topological Insulator BiSbTe1.25Se1.75 in Proximity with Superconducting NbSe2.

The combination of superconductivity and spin-momentum locking at the interface between an s-wave superconductor and a three-dimensional topological insulator (3D-TI) is predicted to generate exotic p-wave topological superconducting phases that can host Majorana Fermions. However, large bulk conductivities of previously investigated 3D-TI samples and Fermi level mismatches between 3D bulk superconductors and 2D topological surface states have thwarted significant progress. Here, we employ bulk-insulating topological insulators in proximity with two-dimensional superconductor NbSe2 assembled via van der Waals epitaxy. Experimentally measured differential conductance yields unusual features including a double-gap spectrum, an intrinsic asymmetry that vanishes with small in-plane magnetic fields, and differential conductance ripples at biases significantly larger than the superconducting gap. We explain our results on the basis of proximity-induced superconductivity of topological surface states, while also considering possibilities of topologically trivial superconductivity arising from Rashba-type surface states. Our work demonstrates the possibility of obtaining p-wave superconductors by proximity effects on bulk-insulating TIs.

Efficient current-induced magnetization reversal by spin-orbit torque in Pt/Co/Pt

Current-induced magnetization reversal due to spin-orbit torque is demonstrated in an anisotropy controlled Pt/Co/Pt trilayer. The samples were designed to have weak perpendicular magnetic anisotropy, with a measured anisotropy field of (1340±20) Oe. Reversal is shown to be dominated by a damping-like torque associated with the spin-Hall effect. A small in-plane magnetic field was required to break the symmetry and enable reversal. With a 273 Oe field, magnetization reversal occurred with a current density amplitude of only 5×1010 A m−2, which is shown to be consistent with a simple model. The field-like torque is negligible, so measurements indicate that the imaginary part of the spin-mixing conductance associated with Co/Pt interfaces must be negligible.

Spin Accumulation and Dynamics in Inversion-Symmetric van der Waals Crystals.

Inversion-symmetric materials are forbidden to show an overall spin texture in their band structure in the presence of time-reversal symmetry. However, in van der Waals materials which lack inversion symmetry within a single layer, it has been proposed that a layer-dependent spin texture can arise leading to a coupled spin-layer degree of freedom. Here we use time-resolved Kerr rotation in inversion-symmetric WSe_{2} and MoSe_{2} bulk crystals to study this spin-layer polarization and unveil its dynamics. Our measurements show that the spin-layer relaxation time in WSe_{2} is limited by phonon scattering at high temperatures and that the interlayer hopping can be tuned by a small in-plane magnetic field at low temperatures, enhancing the relaxation rates. We find a significantly lower lifetime for MoSe_{2} which agrees with theoretical expectations of a spin-layer polarization stabilized by the larger spin-orbit coupling in WSe_{2}.

Effects of flow on the dynamics of a ferromagnetic nematic liquid crystal.

We investigate the effects of flow on the dynamics of ferromagnetic nematic liquid crystals. As a model, we study the coupled dynamics of the magnetization, M, the director field, n, associated with the liquid crystalline orientational order, and the velocity field, v. We evaluate how simple shear flow in a ferromagnetic nematic is modified in the presence of small external magnetic fields, and we make experimentally testable predictions for the resulting effective shear viscosity: an increase by a factor of 2 in a magnetic field of about 20 mT. Flow alignment, a characteristic feature of classical uniaxial nematic liquid crystals, is analyzed for ferromagnetic nematics for the two cases of magnetization in or perpendicular to the shear plane. In the former case, we find that small in-plane magnetic fields are sufficient to suppress tumbling and thus that the boundary between flow alignment and tumbling can be controlled easily. In the latter case, we furthermore find a possibility of flow alignment in a regime for which one obtains tumbling for the pure nematic component. We derive the analogs of the three Miesowicz viscosities well-known from usual nematic liquid crystals, corresponding to nine different configurations. Combinations of these can be used to determine several dynamic coefficients experimentally.

Internal flux dynamics and stray field-mediated coupling in the AC susceptibility response of Nb/Ni thin-film bilayers

The in-phase ac magnetic susceptibility (X′) of Nb/Ni bilayers was measured using a small in-plane magnetic field (the drive field). The sample’s response changes considerably in the presence of perpendicular stray fields that arise during magnetization reversal of the Ni film. The interplay between stray fields and flux lines inside the superconductor is associated to an enhancement of vortex entrance and exit, suggesting an effective magnetic coupling of the ferromagnetic and superconducting components. As a DC field probes the different configurations of the Ni layer throughout its hysteresis loop, the X′ signal traces a curve with irreversible features that are analogous to those of well-known magnetoresistance measurements. A modification of the measuring temperature provides access to various kinds of superconductor/ferromagnet interaction.

Magnetic gates and guides for superconducting vortices

We image the motion of superconducting vortices in niobium film covered with a regular array of thin permalloy strips. By altering the magnetization orientation in the strips using a small in-plane magnetic field, we can tune the strength of interactions between vortices and the strip edges, enabling acceleration or retardation of the superconducting vortices in the sample and consequently introducing strong tunable anisotropy into the vortex dynamics. We discuss our observations in terms of the attraction/repulsion between point magnetic charges carried by vortices and lines of magnetic charges at the strip edges and derive analytical formulas for the vortex-magnetic strips coupling. Our approach demonstrates the analogy between the vortex motion regulated by the magnetic strip array and electric carrier flow in gated semiconducting devices. Scaling down the geometrical features of the proposed design may enable controlled manipulation of single vortices, paving the way for Abrikosov vortex microcircuits and memories.

Spin-orbit torque induced magnetization switching in Ta/Co20Fe60B20/MgO structures under small in-plane magnetic fields

Spin-orbit torque (SOT)-induced magnetization switching under small in-plane magnetic fields in as-deposited and annealed Ta/CoFeB/MgO structures is studied. For the as-deposited samples, partial SOT-induced switching behavior is observed under an in-plane field of less than 100 Oe. Conversely, for the annealed samples, an in-plane field of 10 Oe is large enough to achieve full deterministic magnetization switching. The Dzyaloshinskii-Moriya interaction at the Ta/CoFeB interface is believed to be the main reason for the discrepancy of the requisite in-plane magnetic fields for switching in the as-deposited and annealed samples. In addition, asymmetric field dependence behavior of SOT-induced magnetization switching is observed in the annealed samples. Deterministic magnetization switching in the absence of an external magnetic field is obtained in the annealed samples, which is extremely important to develop SOT-based magnetoresistive random access memory.