We construct a field-theoretic description of spin waves in hexagonal antiferromagnets with three magnetic sublattices and coplanar $120^\circ$ magnetic order. The three Goldstone modes can be separated by point-group symmetry into a singlet $α_{0}$ and a doublet $(β_x,β_y)$. The $α_0$ singlet is described by the standard theory of a free relativistic scalar field. The field theory of the $(β_x,β_y)$ doublet is analogous to the theory of elasticity of a two-dimensional isotropic solid with distinct longitudinal and transverse "speeds of sound". The well-known Heisenberg models on the triangular and kagome lattices with nearest-neighbour exchange turn out to be special cases with accidental degeneracy of the spin-wave velocities. The speeds of sound can be readily calculated for any lattice model. We apply this approach to the compounds of the Mn$_3$X family with stacked kagome layers.
Spin valves consisting of heterostructures of single-layer hexagonal crystal on an antiferromagnetic substrate or of bilayer hexagonal crystal intercalated between two (anti)ferromagnetic insulators, with the current-in-plane geometry, are proposed. The two-dimensional hexagonal crystals such as graphene, silicene, germanene, and stanene are modeled by the tight binding model of honeycomb lattice. The magnetization orientation of the antiferromagnetic substrate(s) controls the band gap and topological properties of bulk, which in turn control the transport of three types of spin valve geometri…
Thin magnetic films with Dzyaloshinskii-Moriya interactions are known to host skyrmion crystals, which typically have a hexagonal lattice structure. We investigate skyrmion-lattice configurations in synthetic antiferromagnets, i.e., a bilayer of thin magnetic films that is coupled antiferromagnetically. By means of Monte-Carlo simulations, we find that by tuning the interlayer coupling the skyrmion lattice structure can be tuned from square to hexagonal. We give a simple interpretation for the existence of this transition based on the fact that for synthetic antiferromagnetic coupling the skyr…
We investigate the spin-dependent thermoelectric effect of graphene flakes with magnetic edges in the ballistic regime. Employing static, respectively, dynamic mean-field theory we first show that magnetism appears at the zigzag edges for a window of Coulomb interactions that increases significantly with increasing flake size. We then use the Landauer formalism in the framework of the non-equilibrium Green's function method to calculate the spin and charge currents in magnetic hexagonal graphene flakes by varying the temperature of the junction for different flake sizes. While in non-magnetic …
We propose a theory of spin relaxation of electrons and holes in two-dimensional hexagonal crystals such as atomic layers of transition metal dichalcogenides (MoS2, WSe2, etc). We show that even in intrinsically defectless crystals, their flexural deformations are able to generate spin relaxation of carriers. Based on symmetry analysis, we formulate a generic model for spin-lattice coupling between electrons and flexural deformations, and use it to determine temperature and material-dependent spin lifetimes in atomic crystals in ambient conditions.
We demonstrate electrical spin injection from a ferromagnet to a bilayer graphene (BLG) through a monolayer (ML) of single-crystal hexagonal boron nitride (h-BN). A Ni81Fe19/ML h-BN/BLG/h-BN structure is fabricated using a micromechanical cleavage and dry transfer technique. The transport properties across the ML h-BN layer exhibit tunnel barrier characteristics. Spin injection into BLG has been detected through non local magnetoresistance measurements.
We study spin-orbit torques in two dimensional hexagonal crystals such as graphene, silicene, germanene and stanene. The torque possesses two components, a field-like term due to inverse spin galvanic effect and an antidamping torque originating from Berry curvature in mixed spin-$k$ space. In the presence of staggered potential and exchange field, the valley degeneracy can be lifted and we obtain a valley-dependent Berry curvature, leading to a tunable antidamping torque by controlling the valley degree of freedom. The valley imbalance can be as high as 100\% by tuning the bias voltage or mag…
We consider electrons on a honeycomb or triangular lattice doped to the saddle point of the bandstructure. We assume system parameters are such that spin density wave (SDW) order emerges below a temperature $T_N$ and investigate the nature of the SDW phase. We argue that at $T < T_N$ the system develops a uniaxial SDW phase whose ordering pattern breaks $O(3) \times Z_4$ symmetry and corresponds to an eight site unit cell with non-uniform spin moments on different sites. This state is a half-metal -- it preserves full original Fermi surface, but has gapless charged excitations in one spin bran…
Understanding the nature of magnetic interactions in ultra-small magnetic ensembles and their intrinsic properties is vital to uncover the dynamics therein. In this study we reveal the spin dynamics of hexagonally arranged Fe atoms on metallic surface that are triggered by magnetic pulse. The switching process among various spin configurations and their relative magnetic order is tuned by the amplitude and duration of the magnetic pulse. Even more we observe a parity effect in the switching time as the size of the cluster varies in which even number of Fe atoms shows faster dynamics. The chang…
The intrinsic spin-Hall effect in hexagon-shaped samples is investigated. To take into account the spin-orbit couplings and to fit the hexagon edges, we derive the triangular version of the tight-binding model for the linear Rashba [Sov. Phys. Solid State 2, 1109 (1960)] and Dresselhaus [Phys. Rev. 100, 580 (1955)] [001] Hamiltonians, which allow direct application of the Landauer-Keldysh non-equilibrium Green function formalism to calculating the local spin density within the hexagonal sample. Focusing on the out-of-plane component of spin, we obtain the geometry-dependent spin-Hall accumulat…
In analogy with light refraction at optical boundary, ballistic electrons also undergo refraction when propagate across a semiconductor junction. Establishing a negative refractive index in conventional optical materials is difficult, but the realization of negative refraction in electronic system is conceptually straightforward, which has been verified in graphene p-n junctions in recent experiments. Here, we propose a model to realize double refraction and double focusing of electric current by a normal-hexagonal semiconductor junction. The double refraction can be either positive or negativ…
We performed spin transport measurements on boron nitride based single layer graphene devices with mobilities up to 40 000 cm${^2}$V$^{-1}$s$^{-1}$. We could observe spin transport over lengths up to 20 μm at room temperature, the largest distance measured so far for graphene. Due to enhanced charge carrier diffusion, spin relaxation lengths are measured up to 4.5 μm. The relaxation times are similar to values for lower quality SiO$_2$ based devices, around 200 ps. We find that the relaxation rate is determined in almost equal measures by the Elliott-Yafet and D'Yakonov-Perel mechanisms.
The van der Waals heterostructures of two-dimensional (2D) atomic crystals constitute a new paradigm in nanoscience. Hybrid devices of graphene with insulating 2D hexagonal boron nitride (h-BN) have emerged as promising nanoelectronic architectures through demonstrations of ultrahigh electron motilities and charge-based tunnel transistors. Here, we expand the functional horizon of such 2D materials demonstrating the quantum tunneling of spin-polarized electrons through atomic planes of CVD grown h-BN. We report excellent tunneling behavior of h-BN layers together with tunnel spin injection and…
Negatively charged boron vacancy (VB-) centers in hexagonal boron nitride (hBN) are promising spin defects in a van der Waals crystal. Understanding the spin properties of the excited state (ES) is critical for realizing dynamic nuclear polarization. Here, we report zero-field splitting in the ES of DES = 2160 MHz and an optically detected magnetic resonance (ODMR) contrast of 12% at cryogenic temperature. The ES has a g-factor similar to the ground state. The ES photodynamics is further elucidated by measuring the level anti-crossing of the VB- defects under varying external magnetic fields. …
We experimentally study the electronic spin transport in hBN encapsulated single layer graphene nonlocal spin valves. The use of top and bottom gates allows us to control the carrier density and the electric field independently. The spin relaxation times in our devices range up to 2 ns with spin relaxation lengths exceeding 12 $μ$m even at room temperature. We obtain that the ratio of the spin relaxation time for spins pointing out-of-plane to spins in-plane is $τ_{\bot} / τ_{||} \approx$ 0.75 for zero applied perpendicular electric field. By tuning the electric field this anisotropy changes t…
We study fully hexagonal boron nitride (hBN)-encapsulated graphene spin valve devices at room temperature. The device consists of a graphene channel encapsulated between two crystalline hBN flakes; thick-hBN flake as a bottom gate dielectric substrate which masks the charge impurities from SiO2/Si substrate and single-layer thin-hBN flake as a tunnel barrier. Full encapsulation prevents the graphene from coming in contact with any polymer/chemical during the lithography and thus gives homogeneous charge and spin transport properties across different regions of the encapsulated graphene. Furthe…
Zigzag nanoribbons of monolayer graphene-like two-dimensional materials host spontaneous edge magnetism at the zigzag terminations, whose configuration controls the band gap. In this article, the edge magnetism of zigzag nanoribbons of bilayer hexagonal crystals are studied. The specific models of bilayer graphene and bilayer silicene are both studied. As the gated voltage increases, the total energy level, magnetic structure and band structures of the ground state and the first quasi-stable excited state are tuned. For certain region of the gated voltage, the band gaps of spin up and down are…
We investigate the charge conductivity and current-induced spin polarization on the surface state of a three-dimensional topological insulator by including the hexagonal warping effect of Fermi surface both in classical and quantum diffusion regimes. We present general expressions of conductivity and spin polarization, which are reduced to simple forms for usual scattering potential. Due to the hexagonal warping, the conductivity and spin polarization show an additional quadratic carrier density dependence both for Boltzmann contribution and quantum correction. In the presence of warping term,…
The thermodynamic and magnetic properties of the mixed spin (1/2-1) hexagonal Ising nanowire (HIN) system with core-shell structure have been presented by means of the effective-field theory (EFT) with correlations. The effects of the physical parameters of the system on thermodynmaic and magnetic properties (magnetizations, susceptibilities, internal energies, and free energies and hysteresis curves) are investigated for both ferromagnetic and antiferromagnetic case, in detail. One can find that when the temperature increases the hysteresis loop areas decrease and the hysteresis loops disappe…
We present an experimental study of spin transport in single layer graphene using atomic sheets of hexagonal boron nitride (h-BN) as a tunnel barrier for spin injection. While h-BN is expected to be favorable for spin injection, previous experimental studies have been unable to achieve spin relaxation times in the nanosecond regime, suggesting potential problems originating from the contacts. Here, we investigate spin relaxation in graphene spin valves with h-BN barriers and observe room temperature spin lifetimes in excess of a nanosecond, which provides experimental confirmation that h-BN is…
We investigate the spin conductivity of topological insulators taking into account both the surface and quasi-two-dimensional bulk states. We apply a low-energy expansion of the Hamiltonian up to the third order in momentum and take into account the vertex corrections arising due to the short range disorder. Hexagonal warping gives rise to the additional anisotropic components in the spin conductivity tensor. Typically, isotropic part of the spin conductivity is larger than anisotropic one. The helical regime for the bulk states, in which the electrons in the Fermi level have the same projecti…
The two-dimensional atomically thin insulator hexagonal boron nitride (h-BN) constitutes a new paradigm in tunnel based devices. A large band gap along with its atomically flat nature without dangling bonds or interface trap states makes it an ideal candidate for tunnel spin transport in spintronic devices. Here, we demonstrate the tunneling of spin-polarized electrons through large area monolayer h-BN prepared by chemical vapor deposition in magnetic tunnel junctions. In ferromagnet/h-BN/ferromagnet heterostructures fabricated over a chip scale, we show tunnel magneto resistance at room tempe…
Spin-coherence characterization of boron vacancy defects in hexagonal boron nitride with broadband microwave pulses
The University of Tokyo（东京大学）；National Institute for Materials Science（国立材料研究所）；Tokyo University of Technology（东京都立科学技术大学）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
Effects of electron-electron and spin-orbit interactions on the ground-state magnetic configuration and on the corresponding thermoelectric and spin thermoelectric properties in zigzag nanoribbons of two-dimensional hexagonal crystals are analyzed theoretically. Thermoelectric properties of quasi-stable magnetic states are also considered. Of particular interest is the influence of Coulomb and spin-orbit interactions on the topological edge states and on the transition between the topological insulator and conventional gap insulator states. It is shown that the interplay of both interactions h…
Hexagonal boron nitride is an ideal dielectric to form two-dimensional heterostructures due to the fact that it can be exfoliated to be just few atoms thick and its a very low density of defects. By placing graphene nanoribbons on high quality hexagonal boron nitride it is possible to create ideal quasi one dimensional (1D) systems with very high mobility. The availability of high quality one-dimensional electronic systems is of great interest also given that when in proximity to a superconductor they can be effectively engineered to realize Majorana bound states. In this work we study how a b…
The mixed spin-1/2 Ising model and spin-1 Blume-Capel model in an hexagonal nanowire structure under the presence of crystal field is considered. The free energy is obtained through the transfer matrix technique, which is solved numerically. Our main result lies in the presence of pseudo-transition in low temperature region near the ferrimagnetic/ferromagnetic boundary, due to the influence of a crystal field. The evidence of a pseudo-transition is observed in several quantities. Free energy first derivative quantities like entropy and internal energy show an abrupt but continuous jump, wherea…
Optically active spin defects in wide-bandgap materials have many potential applications in quantum information and quantum sensing. Spin defects in two-dimensional layered van der Waals materials are just emerging to be investigated. Here we demonstrate that optically-addressable spin ensembles in hexagonal boron nitride (hBN) can be generated by femtosecond laser irradiation. We observe optically detected magnetic resonance (ODMR) of hBN spin defects created by laser irradiation. We show that the creation of spin defects in hBN is strongly affected by the pulse energy of the femtosecond lase…
Theoretical and numerical studies on curved magnetic nano-objects predict numerous exciting effects that can be referred to as magneto-chiral effects, which do not originate from the intrinsic Dzyaloshinskii-Moriya interaction or surface-induced anisotropies. The origin of these chiral effects is the isotropic exchange or the dipole-dipole interaction present in all magnetic materials but renormalized by the curvature. Here, we demonstrate experimentally that curvature induced effects originating from the dipole-dipole interaction are directly observable by measuring spin-wave propagation in m…
The recently discovered spin defects in hexagonal boron nitride (hBN), a layered van der Waals material, have great potential in quantum sensing. However, the photoluminescence and the contrast of the optically detected magnetic resonance (ODMR) of hBN spin defects are relatively low so far, which limits their sensitivity. Here we report a record-high ODMR contrast of 46$\%$ at room temperature, and simultaneous enhancement of the photoluminescence of hBN spin defects by up to 17-fold by the surface plasmon of a gold-film microwave waveguide. Our results are obtained with shallow boron vacancy…
The topological protected electronic states on the surface of a topological insulator can progressively change their Fermi cross-section from circular to a snowflake shape as the chemical potential is increased above the Dirac point because of an hexagonal warping term in the Hamiltonian. Another effect of warping is to change the spin texture which exists when a finite gap is included by magnetic doping, although the in-plane spin component remains locked perpendicular to momentum. It also changes the orbital magnetic moment, the matrix element for optical absorption and the circular dichrois…
The current research in graphene spintronics strives for achieving a long spin lifetime, and efficient spin injection and detection in graphene. In this article, we review how hexagonal boron nitride (hBN) has evolved as a crucial substrate, as an encapsulation layer, and as a tunnel barrier for manipulation and control of spin lifetimes and spin injection/detection polarizations in graphene spin valve devices. First, we give an overview of the challenges due to conventional SiO$_2$ substrate for spin transport in graphene followed by the progress made in hBN based graphene heterostructures. T…
Emergent color centers with accessible spins hosted by van der Waals materials have attracted substantial interest in recent years due to their significant potential for implementing transformative quantum sensing technologies. Hexagonal boron nitride (hBN) is naturally relevant in this context due to its remarkable ease of integration into devices consisting of low-dimensional materials. Taking advantage of boron vacancy spin defects in hBN, we report nanoscale quantum imaging of low-dimensional ferromagnetism sustained in Fe3GeTe2/hBN van der Waals heterostructures. Exploiting spin relaxomet…
We consider the mechanical motion of a system of six macroscopic pendula which are connected with springs and arranged in a hexagonal geometry. When the springs are pre-tensioned, the coupling between neighbouring pendula along the longitudinal (L) and the transverse (T) directions are different: identifying the motion along the L and T directions as a spin-like degree of freedom, we theoretically and experimentally verify that the pre-tensioned springs result in a tunable spin-orbit coupling. We elucidate the structure of such a spin-orbit coupling in the extended two-dimensional honeycomb la…
We analyze the detailed structure of topological edge mode protection occuring in hexagonal quantum spin Hall (QSH) materials. We focus on bismuthene, antimonene, and arsenene on a SiC substrate, which, due to their large bulk gap, may offer new opportunities for room-temperature QSH applications. While time reversal symmetry is responsible for the principal symmetry protected character of QSH states, the hexagonal edge terminations yield further aspects of crystal symmetry which affect the topological protection. We show that armchair QSH edge states remain gapless under an in-plane magnetic …
Optically active defects in solids with accessible spin states are promising candidates for solid state quantum information and sensing applications. To employ these defects as quantum building blocks, coherent manipulation of their spin state is required. Here we realize coherent control of ensembles of boron vacancy (V$_B^-$) centers in hexagonal boron nitride (hBN). Specifically, by applying pulsed spin resonance protocols, we measure spin-lattice relaxation time ($T_1$) of 18 $μ$s and spin coherence time ($T_2$) of 2 $μ$s at room temperature. The spin-lattice relaxation time increases by t…
The quantum tunneling of the magnetization vector are studied theoretically in single-domain ferromagnetic nanoparticles placed in an external magnetic field at an arbitrarily directed angle in the $ZX$ plane. We consider the magnetocrystalline anisotropy with trigonal and hexagonal crystal symmetry, respectively. By applying the instanton technique in the spin-coherent-state path-integral representation, we calculate the tunnel splittings, the tunneling rates and the crossover temperatures in the low barrier limit for different angle ranges of the external magnetic field ($θ_{H}=π/2$, $π/2\ll…
Recently observed quantum emitters in hexagonal boron nitride (hBN) membranes have a potential for achieving high accessibility and controllability thanks to the lower spatial dimension. Moreover, these objects naturally have a high sensitivity to vibrations of the hosting membrane due to its low mass density and high elasticity modulus. Here, we propose and analyze a spin-mechanical system based on color centers in a suspended hBN mechanical resonator. Through group theoretical analyses and ab-initio calculation of the electronic and spin properties of such a system, we identify a spin double…
Novel materials with tunable magnetic states play a significant role in the development of next-generation spintronic devices. In this paper, we examine the role of biaxial strain on the electronic properties of vacancy-decorated hexagonal boron nitride (h-BN) monolayers using density functional theory calculations. We found that the strain can lead to switching of the magnetic state for h-BN monolayers with boron vacancy or divacancy. Our findings promise a new route for the operation of low-dimensional spintronic devices.
Using topological band theory analysis we show that the nonsymmorphic symmetry operations in hexagonal lattices enforce Weyl points at the screw-invariant high-symmetry lines of the band structure. The corepresentation theory and connectivity group theory show that Weyl points are generated by band crossings in accordion-like and hourglass-like dispersion relations. These Weyl points are stable against weak perturbations and are protected by the screw rotation symmetry. Based on first-principles calculations we found a complete agreement between the topological predicted energy dispersion rela…
