External In-plane Magnetic Field Research Articles

Crystalline Weyl semimetal phase in Quantum Spin Hall systems under magnetic fields

We investigate an unconventional topological phase transition that occurs in quantum spin Hall (QSH) systems when applying an external in-plane magnetic field. We show that this transition between QSH and trivial insulator phases is separated by a stable topological gapless phase, which is protected by the combination of particle-hole and reflection symmetries, and thus, we dub it as crystalline Weyl semimetal. We explore the stability of this new phase when particle-hole symmetry breaking terms are present. Especially, we predict a robust unconventional topological phase transition to be visible for materials described by the Kane and Mele model even if particle-hole symmetry is significantly broken.

Magnetic field robust high quality factor NbTiN superconducting microwave resonators

We systematically study the performance of compact lumped element planar microwave Nb70Ti30N (NbTiN) resonators operating at 5 GHz in external in-plane magnetic fields up to 440 mT, a broad temperature regime from 2.2 K up to 13 K, as well as mK temperatures. For comparison, the resonators have been fabricated on thermally oxidized and pristine, (001) oriented silicon substrates. When operating the resonators in the multi-photon regime at T = 2.2 K, we find internal quality factors Q int ≃ 2 × 105 for NbTiN resonators grown on pristine Si substrates. In addition, we investigate the Q-factors of the resonators on pristine Si substrates at millikelvin temperatures to assess their applicability for quantum applications. We find Q int ≃ 2 × 105 in the single photon regime and Q int ≃ 5 × 105 in the high power regime at T = 7 mK. From the excellent performance of our resonators over a broad temperature and magnetic field range, we conclude that NbTiN deposited on Si (100) substrates, where the surface oxide has been removed, constitutes a promising material platform for electron spin resonance and ferromagnetic resonance experiments using superconducting planar microwave resonators.

Flexible room-temperature multiferroic thin film with multifield tunable coupling properties

Flexible multiferroic materials that exhibit unique properties are considered as a promising solution for electronic applications in wearable products and implantable systems. In this work, we present a high quality and large-area multiferroic (1-x)BiTi(1-y)/2FeyMg(1-y)/2O3-(x)CaTiO3(BTFM-CTO) thin films grown on mica substrate by employing the sol-gel method, while the respective ferroelectric and magnetic effects are characterized at room temperature. Compared with the flat state, the in-plane ferroelectric domains of the BTFM-CTO thin films were switched under the application of a bending radius of 9 mm. This result indicates that the applied bending strain can switch the in-plane ferroelectric domain patterns by the manifestation of the respective flexoelectricity effect, whereas the external in-plane magnetic field can also switch the ferroelectric domain patterns. Thus, it is demonstrated that the flexible BTFM-CTO thin film can achieve multifield control ferroelectric polarization properties. Our work opens new paths for the developing novel flexible multiferroic devices via mechanical bending for various applications.

Pairing symmetries in the Zeeman-coupled extended attractive Hubbard model

By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the ground state of the extended attractive Hubbard model (EAHM) exhibits rich phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders. We study the competition between these superconducting pairing symmetries invoking an unrestricted Hartree–Fock–Bogoliubov–de Gennes (HFBdG) mean-field approach, and we use the d-vector formalism to characterize the nature of the stabilized superconducting orders. We discover that, while all other types of orders are suppressed, a non-unitary triplet order dominates the phase space in the presence of an in-plane external magnetic field. We also find a transition between a non-unitary to unitary superconducting phase driven by the change in average electron density. Our results serve as a reference for identifying and understanding the nature of superconductivity based on the symmetries of the pairing correlations. The results further highlight that EAHM is a suitable effective model for describing most of the pairing symmetries discovered in different materials.

Impact of spin-orbit interaction on the phase diagram and anisotropy of the in-plane critical magnetic field at the superconducting LaAlO3/SrTiO3 interface

The two-dimensional electron gas at the interface between ${\mathrm{LaAlO}}_{3}$ and ${\mathrm{SrTiO}}_{3}$ (LAO/STO) exhibits gate-tunable superconductivity with a characteristic domelike shape of the critical temperature (${T}_{c}$) in the phase diagram. As shown recently [Phys. Rev. B 102, 085420 (2020)], such an effect can be explained as a consequence of the extended $s\text{\ensuremath{-}}\mathrm{wave}$ symmetry of the gap within an intersite real space pairing scenario, leading to a good agreement between the experiment and theory. In this work, we turn to a detailed analysis of the influence of spin-orbit coupling on the LAO/STO phase diagram by considering separately the atomic component as well as the interorbital hopping induced by the broken inversion symmetry at the interface. In particular, we analyze the optimal carrier concentration for which the maximal ${T}_{c}$ is reached relative to the Lifshitz transition point. We find that the misalignment between the two can be significantly enhanced by the spin-orbit splitting of the bands, combined with the fact that superconductivity sets in when the Fermi level passes the anticrossing induced by the spin-orbital hybridization. In the presence of the external in-plane magnetic field, our calculations show fourfold anisotropy with the paramagnetic limit largely exceeded for ${B}_{||}$ directed along the high symmetry points [01] and [01]. The obtained electron concentration dependence of ${B}_{c||}$ reproduces the characteristic domelike shape reported in experiments and the estimated value of ${B}_{c||}$ corresponds to that measured experimentally.

Magnetic domains and unusual hysteresis loops of yttrium iron garnet crystals revealed by magneto-optic effects

I present a magneto-optic effect study of magnetic domains in a ferrimagnetic yttrium iron garnet crystal at different stages of a hysteresis loop. By measuring the Faraday effect in response to the out-of-plane component and Kerr effects to the in-plane components of the sample magnetization, I examined the evolution of magnetic domains during a hysteresis loop in an in-plane external magnetic field. I found that crystalline anisotropy, magneto-static energy, and the presence of movable domain walls play indispensable roles in the domain orientation, particularly when the external field is near zero, and have led to seemingly unusual appearances of hysteresis loops.

Potential antiferromagnetic Weyl nodal line state in LiTi2O4 material

Magnetic topological semimetals have brought new insights into topological aspects because they nicely combine the band topology with intrinsic magnetic order. Comparing with ferromagnetic topological semimetals, antiferromagnetic (AFM) ones are even more special since they can break the time-reversal symmetry but show no net magnetic moment, and are highly expected for applications of topological AFM spintronics. Here, we report ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ compound is an ideal AFM Weyl nodal line semimetal. It shows time-reversal breaking Weyl nodal lines in both the spin-up and spin-down channels. Each nodal line arises from the band in one single spin channel, thus is spin-polarized. The nodal lines locate quite near the Fermi level and do not coexist with other extraneous bands. The drumhead surface state of the nodal line can be clearly identified. The nodal lines are protected by the glide mirror symmetry and are robust against spin-orbit coupling. We also show that ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ can transform into an AFM Weyl semimetal under an in-plane external magnetic field. Our results suggest ${\mathrm{LiTi}}_{2}{\mathrm{O}}_{4}$ can serve as an excellent platform to investigate AFM topological semimetals with attractive features.

In-plane magnetic field-induced skyrmion crystal in frustrated magnets with easy-plane anisotropy

We theoretically investigate the instability toward a skyrmion crystal (SkX) in frustrated triangular magnets. By performing simulated annealing and Monte Carlo simulations, we show that a frustrated spin model with easy-plane single-ion anisotropy exhibits a SkX in an in-plane external magnetic field. The emergent SkX is a counterpart of that induced by easy-axis anisotropy in an out-of-plane magnetic field, both of which show the topological Hall effect. We also find that a variety of multiple-$Q$ states distinct from the SkX are stabilized in the presence of easy-plane anisotropy. Our results provide a possibility to realize a SkX in easy-plane frustrated magnets by applying an in-plane magnetic field to in-plane cycloidal spiral magnets.

Two-fold symmetric superconductivity in few-layer NbSe2

Two-dimensional transition metal dichalcogenides (TMDs) have been attracting significant interest due to a range of properties, such as layer-dependent inversion symmetry, valley-contrasted Berry curvatures, and strong spin-orbit coupling (SOC). Of particular interest is niobium diselenide (NbSe2), whose superconducting state in few-layer samples is profoundly affected by an unusual type of SOC called Ising SOC. Combined with the reduced dimensionality, the latter stabilizes the superconducting state against magnetic fields up to ~35 T and could lead to other exotic properties such as nodal and crystalline topological superconductivity. Here, we report transport measurements of few-layer NbSe$_2$ under in-plane external magnetic fields, revealing an unexpected two-fold rotational symmetry of the superconducting state. In contrast to the three-fold symmetry of the lattice, we observe that the magnetoresistance and critical field exhibit a two-fold oscillation with respect to an applied in-plane magnetic field. We find similar two-fold oscillations deep inside the superconducting state in differential conductance measurements on NbSe$_2$/CrBr$_3$ superconductor-magnet junctions. In both cases, the anisotropy vanishes in the normal state, demonstrating that it is an intrinsic property of the superconducting phase. We attribute the behavior to the mixing between two closely competing pairing instabilities, namely, the conventional s-wave instability typical of bulk NbSe$_2$ and an unconventional d- or p-wave channel that emerges in few-layer NbSe2. Our results thus demonstrate the unconventional character of the pairing interaction in a few-layer TMD, opening a new avenue to search for exotic superconductivity in this family of 2D materials.

Full spin-orbit coefficient in III-V semiconductor wires based on the anisotropy of weak localization under in-plane magnetic field

Because of the one-dimensional confinement of electron momentum in narrow semiconductor wires, spin relaxation is suppressed irrespective of the presence of spin-orbit (SO) interaction. In quantum transport, weak localization corrections to conductivity are reflected as suppressed spin relaxation, which makes quantification of the SO strength difficult because quantum correction theory requires weak antilocalization when evaluating SO coefficients. Narrow wires with strong SO interaction are potential platform for Majorana particles and parafermions for topological electronics and quantum computation, so revealing the SO strength in semiconductor wire structures is beneficial. Herein, we present quantification of the full SO coefficient under weak localization in InGaAs-based narrow wires. Using anisotropic weak localization observed under an in-plane external magnetic field with various orientations, one can ascertain the relative ratio between Rashba ($\ensuremath{\alpha}$) and linear Dresselhaus (${\ensuremath{\beta}}_{1}$) SO coefficients with no fitting. Furthermore, we find that widely tuning the potential profile of the quantum well through the top gate can expose a Rashba-predominant region in magnetoconductance, where the $\ensuremath{\alpha}$ value can be extracted reliably from two-dimensional quantum correction theory. Finally, we quantify the full SO coefficients including Rashba, linear Dresselhaus, and cubic Dresselhaus terms in the wire.

Magnetic detwinning and biquadratic magnetic interaction in EuFe2As2 revealed by Eu153 NMR

In the nematic state of iron-based superconductors, twin formation often obscures the intrinsic, anisotropic, in-plane physical properties.Relatively high in-plane external magnetic fields $H_{\rm ext}$ greater than the typical lab-scale magnetic fields 10--15 T are usually required to completely detwin a sample. However, recently a very small in-plane $H_{\rm ext} \sim$ 0.1 T was found to be sufficient for detwinning the nematic domains in EuFe$_2$As$_2$. To explain this behavior, a microscopic theory based on biquadratic magnetic interactions between the Eu and Fe spins has been proposed. Here, using $^{153}$Eu nuclear magnetic resonance (NMR) measurements below the Eu$^{2+}$ ordering temperature, we show experimental evidence of the detwinning under small in-plane $H_{\rm ext}$. Our NMR study also reveals the evolution of the angles between the Eu and Fe spins during the detwinning process, which provides the first experimental evidence for the existence of biquadratic coupling in the system.

A Josephson phase battery.

A classical battery converts chemical energy into a persistent voltage bias that can power electronic circuits. Similarly, a phase battery is a quantum device that provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on phase coherence. Here we demonstrate a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states, that is proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias φ0 across the wire, leading to the anomalous Josephson effect1,2. We apply an external in-plane magnetic field and, thereby, achieve continuous tuning of φ0. Hence, we can charge and discharge the quantum phase battery. The observed symmetries of the anomalous Josephson effect in the vectorial magnetic field are in agreement with our theoretical model. Our results demonstrate how the combined action of spin-orbit coupling and exchange interaction induces a strong coupling between charge, spin and superconducting phase, able to break the phase rigidity of the system.

Octave-Tunable Magnetostatic Wave YIG Resonators on a Chip.

We have designed, fabricated, and characterized magnetostatic wave (MSW) resonators on a chip. The resonators are fabricated by patterning single-crystal yttrium iron garnet (YIG) film on a gadolinium gallium garnet (GGG) substrate and excited by loop-inductor transducers. We achieved this technology breakthrough by developing a YIG film etching process and fabricating thick aluminum coplanar waveguide (CPW) inductor loop around each resonator to individually address and excite MSWs. At 4.77 GHz, the 0.68-mm2 resonator achieves a quality factor ( with a bias field of 987 Oe. We also demonstrate YIG resonator tuning by more than one octave from 3.63 to 7.63 GHz by applying an in-plane external magnetic field. The measured quality factor of the resonator is consistently over 3000 above 4 GHz. The micromachining technology enables the fabrication of multiple single- and two-port YIG resonators on the same chip with all resonators demonstrating octave tunability and high Q .

Room temperature multiferroic properties of electrospun gallium ferrite nanofibers

Gallium ferrite (GaFeO3) is a promising multiferroic material for multifunctional device applications. Compared with bulk and thin film materials, nanofibers are possible to magnify the magnetostriction or piezoelectric effect due to their large length–diameter ratio, thus improving the performance of the material. In this work, GaxFe2 – xO3 (GFO) nanofibers have been synthesized by sol-gel based electrospinning. With the increasing Fe ion content, the room-temperature antiferromagnetic to ferromagnetic transition of GFO nanofibers has been confirmed by magnetic hysteresis loops; and the corresponding temperature dependent magnetization curves show that the ferromagnetic–paramagnetic transition temperature (Tc) is above room temperature and increases from around 292 K to above 400 K. Ferroelectricity of GFO nanofibers has been confirmed by second harmonic generation and piezoresponse force microscopy. Magnetoelectric (ME) coupling has been further measured by dual amplitude resonance tracking piezoresponse force microscopy and sequential excitation piezoresponse force microscopy under an in-plane external magnetic field. The newly developed SE-PFM method reduces the crosstalk of morphology, confirming that no obvious intrinsic ME coupling appears in the GFO nanofibers.

Inelastic light scattering by intrasubband spin-density excitations in GaAs-AlGaAs quantum wells with balanced Bychkov-Rashba and Dresselhaus spin-orbit interaction: Quantitative determination of the spin-orbit field

Inelastic light scattering experiments on low-energy intrasubband spin-density excitations (SDEs) are performed in (001)-grown modulation-doped GaAs-AlGaAs single quantum wells in in-plane external magnetic fields. The investigated samples possess balanced linear Bychkov-Rashba (α) and Dresselhaus (β) spin-orbit strengths in two different configurations, α=β and α=−β. Both configurations lead to an extreme anisotropy of the spin splitting of the conduction band, where the in-plane directions of maximum spin splitting for both configurations are perpendicular to each other. The spin splitting asymmetry can be directly detected via the SDE by breaking of the time-reversal symmetry due to transfer of a momentum q in the quantum-well plane. In addition, the application of an in-plane magnetic field Bext⊥q allows us to modulate the effective magnetic field. Via a numerical line-shape analysis of the experimental SDE spectra, we determine the relevant parameters of the samples. We find that the linear spin-orbit strength |α|=β is comparable for both samples, while the electron g factors are markedly different. Furthermore, we experimentally quantify the values of the maximum internal spin-orbit fields, which are as high as Bso∼18T for both samples.

Magnetization switching in bistable nanomagnets by picosecond pulses of surface acoustic waves

We perform a theoretical investigation of the magnetization switching in polycrystalline Ni nanoparticles induced by ultrashort pulses of surface acoustic waves via magnetoelastic interactions. In our numerical simulations, a Ni nanoparticle is modeled as an ellipsoidal disk deposited on a dielectric substrate. The in-plane external magnetic field breaks the symmetry and allows us to adjust the height of the energy barrier between two metastable magnetization states of the free-energy density and dramatically lower the amplitude of elastic strain pulses required for magnetization switching. The switching threshold is shown to depend on the duration of an acoustic pulse, the magnetic shape anisotropy of an elliptical nanoparticle, the amplitude of the external magnetic field, and the magnetostriction coefficient. We introduce the magnetoelastic switching diagram, allowing for the simultaneous visualization of the switching threshold and its characteristic timescale as a function of various physical parameters.

Current induced domain wall motion with a Ta/Gd-Fe/Si-N magnetic nanowire for a magneto-optical light modulator

We investigated a magnetic nanowire device for a light modulator which is very important for 3D holography display application. It has a Si-N/Ta/Gd-Fe/Si-N nanowire with 0.5 × 17 μm2 dimension and a Co/Pd multilayer hard magnet with its size of 0.5 × 3 μm2 which is attached underneath the nanowire for initial domain nucleation. Both the nanowire and the hard magnet have perpendicular anisotropy. An initial domain was successfully nucleated by pulse current and found spin-orbit torque from Ta and local magnetic field from the nanomagnet was responsible for the domain nucleation. Current induced domain wall (DW) motion was observed and the DW moved along current direction without magnetic field. DW velocity was significantly enhanced with in-plane magnetic field (Hinp) of 25mT and velocity more than 200 m/s was obtained, which was more than 25 times faster than that without magnetic field. We also show that the fast DW velocity is attributed to chiral Neel domain wall induced by external in-plane magnetic field. This fast DW motion is very useful for large scale light modulator which refreshes large number of pixels, such as 10K × 10K pixels, over a limited time scale of 8 ∼ 16.7 ms which corresponds to TV frame rate of 120 or 60 Hz.

Bulk Rashba effect in multiferroics: A theoretical prediction for BiCoO3

We put forward the concept of a bulk Rashba effect emerging in a multiferroic material, such as an antiferromagnetic system with a polar crystal structure. According to symmetry considerations, while time-reversal and space-inversion symmetries are both broken, there exist specific spin flipping operations that relate opposite spin sites in the magnetic crystal structure. As a consequence, at certain high-symmetry points in the momentum space, the magnetic point group allows the spin angular momentum to be locked to the linear momentum, a typical feature of the Rashba effect. In such a case, spin-splitting effects induced by spin-orbit coupling can arise, similar to what happens in nonmagnetic Rashba systems. As a prototypical example, ab initio calculations of antiferromagnetic ${\mathrm{BiCoO}}_{3}$ in the polar structure reveal that a large Rashba-like band and spin splitting occurs at the conduction-band bottom, having a large weight from $\mathrm{Bi}\ensuremath{-}p$ orbital states. Moreover, we show that the spin texture of such a multiferroic can be modulated by applying a magnetic field. In particular, an external in-plane magnetic field is predicted not only to induce spin canting, but also a distortion of the energy isocontours and a shift of the spin vortex (centered on the high-symmetry point and characteristic of Rashba effect) along a direction perpendicular to the applied field.

Methods for reducing write error rate in voltage-induced switching having prolonged tolerance of voltage-pulse duration

Simulating the magnetization dynamics in a perpendicularly-magnetized free layer with Langevin equation, we investigated methods for reducing write error rate (WER) in voltage-induced switching with long tolerance of voltage-pulse duration (tp). The simulation results show that WER can be reduced by increasing the perpendicular anisotropy (Ku) before and after the application of voltage or by increasing both Ku and the in-plane external magnetic field.

Evolution of topological superconductivity by orbital-selective confinement in oxide nanowires

We determine the optimal conditions to achieve topological superconducting phases having spin-singlet pairing for a planar nanowire with finite lateral width in the presence of an in-plane external magnetic field. We employ a microscopic description that is based on a three-band electronic model including both the atomic spin-orbit coupling and the inversion asymmetric potential at the interface between oxide band-gap insulators. We consider amplitudes of the pairing gap, spin-orbit interactions and electronic parameters that are directly applicable to nanowires of LaAlO$_3$-SrTiO$_3$. The lateral confinement introduces a splitting of the $d$-orbitals that alters the orbital energy hierarchy and significantly affects the electron filling dependence of the topological phase diagram. Due to the orbital directionality of the $t_{2g}$-states, we find that in the regime of strong confinement the onset of topological phases is pinned at electron filling where the quasi flat heavy bands start to get populated. The increase of the nanowire thickness leads to a changeover from sparse-to-dense distribution of topologically non-trivial domains which occurs at the cross-over associated to the orbital population inversion. These findings are corroborated by a detailed analysis of the most favorable topological superconducting phases in the electron doping-magnetic field plane highlighting the role of orbital selective confinement.