Hall effects on hydromagnetic flow on an oscillating porous plate

In this paper, an analysis is made on the unsteady flow of an incompressible electrically conducting viscous fluid bounded by an infinite porous flat plate. The plate executes harmonic oscillations at a frequency n in its own plane. A uniform magnetic field Ho is imposed perpendicular to the direction of the flow. It is found that the solution also exists for blowing at the plate. The temperature distribution is also obtained by taking viscous and Joule dissipation into account. The mean wall temperature θo（O） decreases with the increase in the Hall parameter m. It is found that no temperature distribution exists for the blowing at the plate.

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number Cs for energy-bands of trilayer graphene having the essence of intrinsic spin-orbit coupling is analytically calculated. We find that for each valley and spin, Cs is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states, consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin-orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin-orbit （RSO） interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin-orbit coupling, while the other two layers have zero intrinsic spin-orbit coupling. Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.

Anomalous valley Hall effect in two-dimensional valleytronic materials

The anomalous valley Hall effect(AVHE)can be used to explore and utilize valley degrees of freedom in materials,which has potential applications in fields such as information storage,quantum computing and optoelectronics.AVHE exists in two-dimensional(2D)materials possessing valley polarization(VP),and such 2D materials usually belong to the hexagonal honeycomb lattice.Therefore,it is necessary to achieve valleytronic materials with VP that are more readily to be synthesized and applicated experimentally.In this topical review,we introduce recent developments on realizing VP as well as AVHE through different methods,i.e.,doping transition metal atoms,building ferrovalley heterostructures and searching for ferrovalley materials.Moreover,2D ferrovalley systems under external modulation are also discussed.2D valleytronic materials with AVHE demonstrate excellent performance and potential applications,which offer the possibility of realizing novel low-energy-consuming devices,facilitating further development of device technology,realizing miniaturization and enhancing functionality of them.

Enhanced anomalous Hall effect in kagome magnet YbMn_(6)Sn_(6)with intermediate-valence ytterbium

We report on the magnetization and anomalous Hall effect(AHE)in the high-quality single crystals of the kagome magnet YbMn_(6)Sn_(6),where the spins of the Mn atoms in the kagome lattice order ferromagnetically and the intermediate-valence Yb atoms are nonmagnetic.The intrinsic mechanism plays a crucial role in the AHE,leading to an enhanced anomalous Hall conductivity(AHC)compared with the other rare-earth RMn_(6)Sn_(6)compounds.Our band structure calculation reveals a strong hybridization between the 4f electrons of Yb and conduction electrons.

Spin direction dependent quantum anomalous Hall effect in two-dimensional ferromagnetic materials

We propose a scheme for realizing the spin direction-dependent quantum anomalous Hall effect(QAHE)driven by spin-orbit couplings(SOC)in two-dimensional(2D)materials.Based on the sp^(3)tight-binding(TB)model,we find that these systems can exhibit a QAHE with out-of-plane and in-plane magnetization for the weak and strong SOC,respectively,in which the mechanism of quantum transition is mainly driven by the band inversion of p_(x,y)/p_(z)orbitals.As a concrete example,based on first-principles calculations,we realize a real material of monolayer 1T-SnN_(2)/PbN_(2)exhibiting the QAHE with in-plane/out-of-plane magnetization characterized by the nonzero Chern number C and topological edge states.These findings provide useful guidance for the pursuit of a spin direction-dependent QAHE and hence stimulate immediate experimental interest.

Investigations of Soret,Joule and Hall effects on MHD rotating mixed convective flow past an infinite vertical porous plate

We made an elaborate scrutiny on the Soret and Joule effects of MHD mixed convective flow of an incompressible and electrically conducting viscous fluid past an infinite vertical porous plate taking Hall effects into account.Perturbation technique is used to solve the non-dimensional equations.The effects of the various non-dimensional parameters on velocity,temperature and concentration within the boundary layer are examined.Besides that,computational deliberations or discussions are also undertaken on the effects of the pertinent or significant parameters on the skin-friction coefficient and rates of heat and mass transfer in terms of the Nusselt and Sherwood numbers respectively.The concentration distribution increases with increase in Soret effect and decrease with increase in chemical reaction parameter.An increase in Prandtl number results to decrease the temperature distribution.Both the primary and secondary velocity components and temperature increases with increasing heat source parameter.Skin friction coefficient decreases with an increase in permeability parameter,whereas it shows reverse effect for thermal and mass Grashof numbers.Nusselt number increases with an increase in Prandtl number.Sherwood number reduces with increasing Soret number.

Natural convection flow of a couple stress fluid between two vertical parallel plates with Hall and ion-slip effects

The Hall and ion-slip effects on fully developed electrically conducting couple stress fluid flow between vertical parallel plates in the presence of a temperature dependent heat source are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the homotopy analysis method （HAM）. The effects of the magnetic parameter, Hall parameter, ion-slip parameter and couple stress fluid parameter on velocity and temperature are discussed and shown graphically

Semiclassical Boltzmann theory of spin Hall effects in giant Rashba systems

For the spin Hall effect arising from strong band-structure spin-orbit coupling, a semiclassical Boltz- mann theory reasonably addressing the intriguing disorder effect called side-jump has not yet been developed. This paper describes such a theory in which the key ingredient is the spin-current counter- part of the semiclassical side-jump velocity （introduced in the context of the anomalous Hall effect）. Applying this theory to spin Hall effects in a two-dimensional electron gas with giant Rashba spin-orbit coupling, largely enhanced spin Hall angle is found in the presence of magnetic impurities when only the lower Rashba band is partially occupied.

Experimental observation of topological Hall effects in compensated ferrimagnet-heavy metal layered structures

The topological Hall effect(THE) as a powerful probe for the experimental observation of topological spin textures, such as magnetic skyrmions, has been observed in a wide variety of distinct material systems. However, limited experimental observations have been reported for antiferromagnetic(AFM) materials. Here, the THE signals in the AFM state were observed in compensated ferrimagnetic thin films interfaced with heavy metals at the magnetization compensation temperature(TM).Ferrimagnetic CoTb thin films grown on Pt thin films were used in the experiments. The Co Tb films exhibited a magnetization compensation point at which the moments of Co and Tb sublattices canceled each other, giving rise to the AFM state. The temperature(T)-dependent Hall measurements showed anomalous Hall effect(AHE) and THE responses at T≠T_(M) but pure THE responses at T=T_(M). Control measurements and analyses suggest that the THE responses are associated with interfacial Dzyaloshinskii-Moriya interaction(DMI) rather than the overlapping of different AHE signals in the structure. This work presents the first-ever observation of interfacial DMI-induced THE in AFM metal trilayered systems and demonstrates a new approach for electrical reading of chiral spin textures in AFM thin film-based heterostructures.

Vectorial spin-orbital Hall effect of light upon tight focusing and its experimental observation in azopolymer films

Hall effect of light is a result of symmetry breaking in spin and/or orbital angular momentum(OAM)possessing optical system and is caused by e.g.refractive index gradient/interface between media or focusing of a spatially asymmetrical beam,similar to the electric field breaking the symmetry in spin Hall effect for electrons.The angular momentum(AM)conservation law in the ensuing asymmetric system dictates redistribution of spin and orbital angular momentum,and is manifested in spin-orbit,orbit-orbit,and orbit-spin conversions and reorganization,i.e.spin-orbit and orbit-orbit interaction.This AM restructuring in turn requires shifts of the barycenter of the electric field of light.In the present study we show,both analytically and by numerical simulation,how different electric field components are displaced upon tight focusing of an asymmetric light beam having OAM and spin.The relation between field components shifts and the AM components shifts/redistribution is presented too.Moreover,we experimentally demonstrate,for the first time,to the best of our knowledge,the spin-orbit Hall effect of light upon tight focusing in free space.This is achieved using azopolymers as a media detecting longitudinal or z component of the electrical field of light.These findings elucidate the Hall effect of light and may broaden the spectrum of its applications.

Nonmonotonic anomalous Hall effect and anisotropic magnetoresistance in SrRuO_(3)/PbZr_(0.52)Ti_(0.48)O_(3)heterostructures

We fabricate SrRuO_(3)/PbZr_(0.52)Ti_(0.48)O_(3)heterostructures each with an in-plane tensile-strained SrRuO_(3)layer and investigate the effect of an applied electric field on anomalous Hall effect.The four-fold symmetry of anisotropic magnetoresistance and the nonmonotonic variation of anomalous Hall resistivity are observed.By applying positive electric field or negative electric field,the intersecting hump-like feature is suppressed or enhanced,respectively.The sign and magnitude of the anomalous Hall conductivity can be effectively controlled with an electric field under a high magnetic field.The electric-field-modulated anomalous Hall effect is associated with the magnetization rotation in SrRuO_(3).The experimental results are helpful in modulating the magnetization rotation in spintronic devices based on SrRuO_(3)heterostructures.

Thermal Hall effect and the Wiedemann–Franz law in Chern insulator

Thermal Hall effect, where a transverse temperature difference is generated by implementing a longitudinal temperature gradient and an external magnetic field in the perpendicular direction to systems, is a useful tool to reveal transport properties of quantum materials. A systematic study of the thermal Hall effect in a Chern insulator is still lacking. Here,using the Landauer–Büttiker formula, we investigated the thermal Hall transport of the Harper–Hofstadter model with flux φ= 1/2 and its generalizations. We demonstrated that the Wiedemann–Franz law, which states that the thermal Hall conductivity is linearly proportional to the quantum Hall conductivity in the low temperature limit, is still valid in this Chern insulator, and that the thermal Hall conductivity can be used to characterize the topological properties of quantum materials.

Anomalous Hall effect in ferromagnetic LaCo_(2)As_(2) and ferrimagnetic NdCo_(2)As_(2)

We conducted a comparative study of the magnetic and transport properties of single-crystalline LaCo_(2)As_(2) and NdCo_(2)As_(2).LaCo_(2)As_(2) is a soft metallic ferromagnet which exhibits purely intrinsic anomalous Hall effect(AHE) due to Co-3d electrons. With Nd-4f electronic magnetism, ferrimagnetic NdCo_(2)As_(2) manifests pronounced sign reversal and multiple hysteresis loops in temperature-and field-dependent magnetization, Hall resistivity, and magnetoresistance, due to complicated magnetic structural changes. We reveal that the AHE for NdCo_(2)As_(2) is stemming from the Co sub-lattice and deduce its phase diagram which includes magnetic compensation and two meta-magnetic phase transitions. The sensitivity of the Hall effect on the details of the magnetic structures in ferrimagnetic NdCo_(2)As_(2) provides a unique opportunity to explore the magnetic interaction between 4f and 3d electrons and its impact on the electronic structure.

Effects of oxygen/nitrogen co-incorporation on regulation of growth and properties of boron-doped diamond films

Regulation with nitrogen and oxygen co-doping on growth and properties of boron doped diamond films is studied by using laughing gas as dopant. As the concentration of laughing gas(N2O/C) increases from 0 to 10%, the growth rate of diamond film decreases gradually, and the nitrogen-vacancy(NV) center luminescence intensity increases first and then weakens. The results show that oxygen in laughing gas has a strong inhibitory effect on formation of NV centers, and the inhibitory effect would be stronger as the concentration of laughing gas increases. As a result, the film growth rate and nitrogen-related compensation donor decrease, beneficial to increase the acceptor concentration(~3.2×10^(19)cm^(-3)) in the film. Moreover, it is found that the optimal regulation with the quality and electrical properties of boron doped diamond films could be realized by adding appropriate laughing gas, especially the hole mobility(~700cm^(2)/V·s), which is beneficial to the realization of high-quality boron doped diamond films and high-level optoelectronic device applications in the future.

Coexistence of giant Rashba spin splitting and quantum spin Hall effect in H–Pb–F

Rashba spin splitting(RSS)and quantum spin Hall effect(QSHE)have attracted enormous interest due to their great significance in the application of spintronics.In this work,we theoretically proposed a new two-dimensional(2D)material H–Pb–F with coexistence of giant RSS and quantum spin Hall effec by using the ab initio calculations.Our results show that H–Pb–F possesses giant RSS(1.21 eV·A)and the RSS can be tuned up to 4.16 e V·A by in-plane biaxial strain,which is a huge value among 2D materials.Furthermore,we also noticed that H–Pb–F is a 2D topological insulator(TI)duo to the strong spin–orbit coupling(SOC)interaction,and the large topological gap is up to 1.35 e V,which is large enough for for the observation of topological edge states at room temperature.The coexistence of giant RSS and quantum spin Hall effect greatly broadens the potential application of H–Pb–F in the field of spintronic devices.

Phase transition in bilayer quantum Hall system with opposite magnetic field

We construct a mapped bilayer quantum Hall system to realize the proposal that two nearly flatbands have opposite Chern numbers.For the C=±1 case,the two Landau levels of the bilayer experience opposite magnetic fields.We consider a mapped bilayer quantum Hall system at total fillingν_(t)=1/2+1/2where the intralayer interaction is repulsive and the interlayer interaction is attractive.We take exact diagonalization(ED)calculations on a torus to study the phase transition when the separation distance d/l_(B)is driven.The critical point at d_(c)/l_(B)=0.68 is characterized by a collapse of degeneracy and a crossing of energy levels.In the region d/l_(B)<d_(c)/l_(B),the states of each level are highly degenerate.The pair-correlation function indicates electrons with opposite pseudo-spins are strong correlated at r=0.We find an exciton stripe phase composed of bound pairs.The ferromagnetic ground state is destroyed by the strong effective attractive potential.An electron composite-Fermion(eCF)and a hole composite Fermion(hCF)are tightly bound.In the region d/lB>d_(c)/l_(B),a crossover from the d→d_(c)limit to the large d limit is observed.The electron and hole composite Fermion liquids(CFL)are realized by composite Fermions(CF)which attach opposite fluxes,respectively.

Recent progress on the planar Hall effect in quantum materials

The planar Hall effect(PHE),which originates from anisotropic magnetoresistance,presents a qualitative and simple approach to characterize electronic structures of quantum materials by applying an in-plane rotating magnetic field to induce identical oscillations in both longitudinal and transverse resistances.In this review,we focus on the recent research on the PHE in various quantum materials,including ferromagnetic materials,topological insulators,Weyl semimetals,and orbital anisotropic matters.Firstly,we briefly introduce the family of Hall effect and give a basic deduction of PHE formula with the second-order resistance tensor,showing the mechanism of the characteristicπ-period oscillation in trigonometric function form with aπ/4 phase delay between the longitudinal and transverse resistances.Then,we will introduce the four main mechanisms to realize PHE in quantum materials.After that,the origin of the anomalous planar Hall effect(APHE)results,of which the curve shapes deviate from that of PHE,will be reviewed and discussed.Finally,the challenges and prospects for this field of study are discussed.

Stability analysis of magnetization in a perpendicular magnetic layer driven by spin Hall effect

We investigate the stability of magnetization in free layer where the spin torque is induced by the spin Hall effect.In terms of the Landau–Liftshitz–Gilbert equation,we find the low-energy and high-energy equilibrium states,as well as the saddle points.The stability region is defined in the phase diagram spanned by the current density and the spin Hall angle.The spin Hall effect makes the previous saddle point into a stable state above a critical current.However,in the presence of magnetic field,the spin Hall effect leads to the opposite changes in the stable regions of the two low-energy states.

Doping tuned anomalous Hall effect in the van der Waals magnetic topological phases Mn(Sb_(1-x)Bi_(x))_(4)Te_(7)

The van der Waals(vdW)MnSb4Te7is a newly synthesized antiferromagnetic(AFM)topological insulator hosting a robust axion insulator state irrelative to the specific spin structure.However,the intrinsic hole doped character of MnSb_4Te_7makes the Fermi level far away from the Dirac point of about 180 meV,which is unfavorable for the exploration of exotic topological properties such as the quantum anomalous Hall effect(QAHE).To shift up the Fermi level close to the Dirac point,the strategy of partially replacing Sb with Bi as Mn(Sb_(1-x)Bi_(x))_(4)Te_(7)was tried and the magnetotransport properties,in particular,the anomalous Hall effect,were measured and analyzed.Through the electron doping,the anomalous Hall conductanceσAH changes from negative to positive between x=0.3 and 0.5,indicative of a possible topological transition.Besides,a charge neutrality point(CNP)also appears between x=0.6 and 0.7.The results would be instructive for further understanding the interplay between nontrivial topological states and the magnetism,as well as for the exploration of exotic topological properties.

Engineered photonic spin Hall effect of Gaussian beam in antisymmetric parity-time metamaterials

A model of the photonic spin Hall effect(PSHE)in antisymmetric parity-time(APT)metamaterials with incidence of Gaussian beams is proposed here.We derive the displacement expression of the PSHE in APT metamaterials based on the transport properties of Gaussian beams in positive and negative refractive index materials.Furthermore,detailed discussions are provided on the APT scattering matrix,eigenstate ratio,and response near exceptional points in the case of loss or gain.In contrast to the unidirectional non-reflection in parity-time(PT)symmetric systems,the transverse shift that arises from both sides of the APT structure is consistent.By effectively adjusting the parameters of APT materials,we achieve giant displacements of the transverse shift.Finally,we present a multi-layer APT structure consisting of alternating left-handed and right-handed materials.By increasing the number of layers,Bragg oscillations can be generated,leading to an increase in resonant peaks in transverse shift.This study presents a new approach to achieving giant transverse shifts in the APT structure.This lays a theoretical foundation for the fabrication of related nano-optical devices.