We report on low-temperature electron transport properties of MnSb2Te4, a candidate of ferrimagnetic Weyl semimetal. Long -range magnetic order is manifested as a nearly square-shaped hysteresis loop in the anomalous Hall resistance, as well as sharp jumps in the magnetoresistance. At temperatures below 4 K, a lnT-type upturn appears in the temperature dependence of longitudinal resistance, which can be attributed to the electron-electron interaction (EEI), since the weak localization can be excluded by the temperature dependence of magnetoresistance. Although the anomalous Hall resistance exhibits a similar lnT-type upturn in the same temperature range, such correction is absent in the anomalous Hall conductivity. Our work demonstrates that MnSb2Te4 microflakes provide an ideal system to test the theory of EEI correction to the anomalous Hall effect.
We study the spin Hall magnetoresistance effect in ferrimagnet/normal metal bilayers, comparing the response in collinear and canted magnetic phases. In the collinear magnetic phase, in which the sublattice magnetic moments are all aligned along the same axis, we observe the conventional spin Hall magnetoresistance. In contrast, in the canted phase, the magnetoresistance changes sign. Using atomistic spin model calculations of the magnetic configuration, we show that the electric transport for the different magnetic phases can be rationalized considering the individual sublattice moment orient…
Due to its transverse nature, spin Hall effects (SHE) provide the possibility to excite and detect spin currents and magnetization dynamics even in magnetic insulators. Magnetic insulators are outstanding materials for the investigation of nonlinear phenomena and for novel low power spintronics applications because of their extremely low Gilbert damping. Here, we report on the direct imaging of electrically driven spin-torque ferromagnetic resonance (ST-FMR) in the ferrimagnetic insulator Y$_3$Fe$_5$O$_{12}$ based on the excitation and detection by SHEs. The driven spin dynamics in Y$_3$Fe$_5$…
We present the Co-Gd composition dependence of the spin-Hall magnetoresistance (SMR) and anisotropic magnetoresistance (AMR) for ferrimagnetic Co100-xGdx / Pt bilayers. With Gd concentration x, its magnetic moment increasingly competes with the Co moment in the net magnetization. We find a nearly compensated ferrimagnetic state at x = 24. The AMR changes sign from positive to negative with increasing x, vanishing near the magnetization compensation. On the other hand, the SMR does not vary significantly even where the AMR vanishes. These experimental results indicate that very different scatte…
Measurements of the transverse Hall resistance are widely used to investigate electron transport, magnetization phenomena, and topological quantum states. Owing to the difficulty of probing transient changes of the transverse resistance, the vast majority of Hall effect experiments are carried out in stationary conditions using either dc or ac currents. Here we present an approach to perform time-resolved measurements of the transient Hall resistance during current-pulse injection with sub-nanosecond temporal resolution. We apply this technique to investigate in real-time the magnetization rev…
We have studied magnetoresistance and Hall effects for 1.8-nm-thick Pt films grown on a ferrimagnetic insulator Y3Fe5O12 in a wide temperature (0.46-300 K) and magnetic-field (-15-15 T) region. In the low-temperature regime where quantum corrections to conductivity are observed, weak antilocalization behavior observed in Pt films is critically suppressed when the film is attached to Y3Fe5O12. Hall resistance in the Pt film is also affected by Y3Fe5O12, and it exhibits logarithmic temperature dependence in a broad temperature range. The magnetotransport properties in the high-field range are si…
We theoretically study the thermal Hall effect by magnons in skyrmion crystal phases of ferrimagnets in the vicinity of the angular momentum compensation point (CP). To this end, we start by deriving the equation of motion for magnons in the background of an arbitrary equilibrium spin texture, which gives rise to the fictitious electromagnetic field for magnons. As the net spin density varies, the resultant equation of motion interpolates between the relativistic Klein-Gordon equation at CP and the nonrelativistic Schr{ö}dinger-like equation away from it. In skyrmion crystal phases, the right-…
Charged particles exhibit the Hall effect in the presence of magnetic fields. Analogously, ferromagnetic skyrmions with non-zero topological charges and finite fictitious magnetic fields exhibit the skyrmion Hall effect, which is detrimental for applications. The skyrmion Hall effect has been theoretically predicted to vanish for antiferromagnetic skyrmions because the fictitious magnetic field, proportional to net spin density, is zero. We experimentally confirm this prediction by observing current-driven transverse elongation of pinned ferrimagnetic bubbles. Remarkably, the skyrmion Hall eff…
Spintronics is showing promising results in the search for new materials and effects to reduce energy consumption in information technology. Among these materials, ferrimagnets are of special interest, since they can produce large spin currents that trigger the magnetization dynamics of adjacent layers or even their own magnetization. Here, we present a study of the generation of spin current by GdFeCo in a GdFeCo/Cu/NiFe trilayer where the FeCo sublattice magnetization is dominant at room temperature. Magnetic properties such as the saturation magnetization are deduced from magnetometry measu…
Flexibility for interface engineering, and access to all-optical switching of the magnetization, make synthetic ferrimagnets an interesting candidate for advanced opto-spintronic devices. Moreover, due to their layered structure and disordered interfaces they also bear promise for the emerging field of graded magnetic materials. The fastest and most efficient spin-orbit torque driven manipulation of the magnetic order in this material system generally takes place at compensation. Here, we present a systematic experimental and modeling study of the conditions for magnetization compensation and …
Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram, which exhibit a metallic phase for a finite range of energies and magnetic fields, and the calculated associated critical exponent, $ν=4/3$, agree excellently with existing numerical calculations. The implication of this work for the quantum Hall effect in three dimensions is discussed.
We theoretically study the intrinsic thermal Hall and spin Nernst effect in collinear ferrimagnets on a honeycomb lattice with broken inversion symmetry. The broken inversion symmetry allows in-plane Dzyaloshinskii-Moriya interaction between the nearest neighbors, which does not affect the magnon spectrum in the linear spin wave theory. However, the Dzyaloshinskii-Moriya interaction can induce large Berry curvature in the magnetoelastic excitation spectrum through the magnon-phonon interaction to produce thermal Hall current. Furthermore, we find that the magnetoelastic excitations transport s…
The inverse spinel ferrimagnetic NiCo$_2$O$_4$ possesses high magnetic Curie temperature $T_C$, high spin polarization, and strain-tunable magnetic anisotropy. Understanding the thickness scaling limit of these intriguing magnetic properties in NiCo$_2$O$_4$ thin films is critical for their implementation in nanoscale spintronic applications. In this work, we report the unconventional magnetotransport properties of epitaxial (001) NiCo$_2$O$_4$ films on MgAl$_2$O$_4$ substrates in the ultrathin limit. Anomalous Hall effect measurements reveal strong perpendicular magnetic anisotropy for films …
We investigate the spectral statistics of a network model for a three dimensional layered quantum Hall system numerically. The scaling of the quantity $J_0={1/2}< s^2>$ is used to determine the critical exponent $ν$ for several interlayer coupling strengths. Furthermore, we determine the level spacing distribution $P(s)$ as well as the spectral compressibility $χ$ at criticality. We show that the tail of $P(s)$ decays as $\exp(-κs)$ with $κ=1/(2χ)$ and also numerically verify the equation $χ=(d-D_2)/(2d)$, where $D_2$ is the correlation dimension and $d=3$ the spatial dimension.
We examine the magnetic properties of the quasi 2D ferrimagnetic single crystal Mn3Si2Te6 (MST) through critical phenomena and magnetic entropy analysis in the easy axis (H || ab) as a function of proton irradiance. Employing a modified asymptotic analysis method, we find that upon proton irradiation the critical exponents do not fall into any particular universality class but lie close to mean field critical exponents (γ = 1, \b{eta} = 0.5). The presence of long-range interactions can be safely assumed for the pristine and irradiated cases of MST examined in this work. Further analysis on the…
To realize the quantum anomalous Hall effect (QAHE) at elevated temperatures, the approach of magnetic proximity effect (MPE) was adopted to break the time-reversal symmetry in the topological insulator (Bi0.3Sb0.7)2Te3 (BST) based heterostructures with a ferrimagnetic insulator europium iron garnet (EuIG) of perpendicular magnetic anisotropy. Here we demonstrate phenomenally large anomalous Hall resistance (RAHE) exceeding 8 Ω (\r{ho}AHE of 3.2 μΩ*cm) at 300 K and sustaining to 400 K in 35 BST/EuIG samples, surpassing the past record of 0.28 Ω (\r{ho}AHE of 0.14 μΩ*cm) at 300 K. The remarkabl…
Electrically Sign-Reversible Topological Hall Effect in a Top-Gated Topological Insulator (Bi,Sb)2Te3 on a Ferrimagnetic Insulator Europium Iron Garnet
Current-induced spin torques in layered magnetic heterostructures have many commonalities across broad classes of magnetic materials. These include not only collinear ferromagnets, ferrimagnets, and antiferromagnets, but also more complex noncollinear spin systems. We develop a general Lagrangian-Rayleigh approach for studying the role of dissipative torques, which can pump energy into long-wavelength magnetic dynamics, causing dynamic instabilities. While the Rayleigh structure of such torques is similar for different magnetic materials, their consequences depend sensitively on the nature of …
NbSe$_2$ is one of metallic two-dimensional (2D) transition-metal dichalcogenide (TMDC) materials. Because of broken crystal inversion symmetry, large spin splitting is induced by Ising-type spin-orbit coupling in odd-number-layered NbSe$_2$, but absent for even-number-layered NbSe$_2$ with the inversion symmetry. In this paper, we numerically calculate nonlinear optical charge and spin Hall conductivities of few-layered NbSe$_2$ based on an effective tight-binding model which includes $d_{z^2}$, $d_{x^2-y^2}$ and $d_{xy}$ orbitals of Nb atom. We show that the nonlinear optical Hall conductivi…
Here, we present a temperature ($T$) dependent comparison between field-effect and Hall mobilities in field-effect transistors based on few-layered WSe$_2$ exfoliated onto SiO$_2$. Without dielectric engineering and beyond a $T$-dependent threshold gate-voltage, we observe maximum hole mobilities approaching 350 cm$^2$/Vs at $T$=300 K. The hole Hall mobility reaches a maximum value of 650 cm$^2$/Vs as $T$ is lowered below $\sim$ 150 K, indicating that insofar WSe$_2$-based field-effect transistors (FETs) display the largest Hall mobilities among the transition metal dichalcogenides. The gate c…
Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied. The phase diagram demonstrates charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer tunnelling we find quantum Hall phases with spin Hall coefficients of 0 and 2 separated by a spin metal phase. We identify a spin metal-insulator localization exponent as well as a spin conductivity exponent of ~0.9. In presence of a Zeeman term an additional phase with spin Hall coefficient of 1 appears.
The spin Hall magnetoresistance (SMR) effect arises from spin-transfer processes across the interface between a spin Hall active metal and an insulating magnet. While the SMR response of ferrimagnetic and antiferromagnetic insulators has been studied extensively, the SMR of a paramagnetic spin ensemble is not well established. Thus, we investigate herein the magnetoresistive response of as-deposited yttrium iron garnet/platinum thin film bilayers as a function of the orientation and the amplitude of an externally applied magnetic field. Structural and magnetic characterization show no evidence…
The discovery of the anomalous Hall effect (AHE) in bulk metallic antiferromagnets (AFMs) motivates the search of the same phenomenon in two-dimensional (2D) systems, where a quantized anomalous Hall conductance can in principle be observed. Here, we present experiments on micro-fabricated devices based on Co$_{1/3}$NbS$_2$, a layered AFM that was recently found to exhibit AHE in bulk crystals below the Néel temperature T$_N$ = 29 K. Transport measurements reveal a pronounced resistivity anisotropy, indicating that upon lowering temperature the electronic coupling between individual atomic lay…
We discuss and review the basic physics that leads to superfluidity/superconductivity in certain quantum Hall states, in particular the so-called double-layered (mmm) state. In the K-matrix description of the quantum correlation in quantum Hall states, those states with det(K)=0 contain a special correlation that leads to superfluidity/superconductivity. We propose a four-terminal measurement to test the DC Josephson-like effect in interlayer tunneling, so that the superfluidity/superconductivity in the (mmm) states can be settled experimentally.
Recently, a type of Hall effect due to an unusual layer-locked Berry curvature called the layer Hall effect (LHE) has been reported in the even-layered two-dimensional antiferromagnetic (AFM) MnBi2Te4 [A. Gao et.al, Nature 595, 521 (2021)]. In this work, we report that the quantization of LHE, which we call the quantum anomalous layer Hall effect (QALHE), can be realized in MnBi2Te4. The QALHE originates from kicking a layer-locked Berry-curvature monopole out of the Fermi sea by a vertielectric cal field. Remarkably, we demonstrate that the electric-field reversal can switch the sign of the q…
The recently discovered spin Hall magnetoresistance effect electrically probes pure spin current flow across a ferrimagnetic insulator/normal metal bilayer interface. While usually the DC electrical resistance of the bilayer is measured as a function of the magnetization orientation in the magnetic insulator, we here present magnetoimpedance measurements using bias currents with frequencies up to several GHz. We find that the spin Hall magnetoresistance effect persists up to frequencies of at least 4 GHz, enabling a fast readout of the magnetization direction in magnetic insulator/normal metal…
We study the temperature dependence of the spin Hall magnetoresistance (SMR) in yttrium iron garnet/platinum hybrid structures via magnetization orientation dependent magnetoresistance measurements. Our experiments show a decrease of the SMR magnitude with decreasing temperature. Using the sensitivity of the SMR to the spin transport properties of the normal metal, we interpret our data in terms of a decrease of the spin Hall angle in platinum from 0.11 at room temperature to 0.075 at 10K, while the spin diffusion length and the spin mixing conductance of the ferrimagnetic insulator/normal met…
We have discovered two-dimensional zero-gap material with a layered structure in the organic conductor $α$-(BEDT-TTF)$_2$I$_3$ under high hydrostatic pressure. In contrast to graphene, the electron-hole symmetry is not good except at the vicinity of the Dirac points. Thus, temperature dependence of the chemical potential, $μ$, plays an important role in the transport in this system. The experimental formula of $μ$ is revealed. We succeeded in detecting the inter-band effects of a magnetic field on the Hall conductivity when $μ$ passes the Dirac point.
Using the parton construction, we build a three-dimensional (3D) multilayer fractional quantum Hall state with average filling ν= 1/3 per layer that is qualitatively distinct from a stacking of weakly coupled Laughlin states. The state supports gapped charge e/3 fermionic quasiparticles that can propagate both within and between the layers, in contrast to the quasiparticles in a multilayer Laughlin state which are confined within each layer. Moreover, the state has gapless neutral collective modes, a manifestation of an emergent "photon", which is minimally coupled to the fermionic quasipartic…
Anomalous Hall-like signals in platinum in contact with magnetic insulators are common observations that could be explained by either proximity magnetization or spin Hall magnetoresistance. In this work, longitudinal and transverse magnetoresistances are measured in a pure gold thin film on the ferrimagnetic insulator Y$_3$Fe$_5$O$_{12}$ (Yttrium Iron Garnet, YIG). We show that both the longitudinal and transverse magnetoresistances have quantitatively consistent scaling in YIG/Au and in a YIG/Pt reference system when applying the Spin Hall magnetoresistance framework. No contribution of an an…
Among van der Waals (vdW) layered ferromagnets, Fe3GeTe2 (FGT) is an excellent candidate material to form FGT/heavy metal heterostructures for studying the effect of spin-orbit torques (SOT). Its metallicity, strong perpendicular magnetic anisotropy built in the single atomic layers, relatively high Curie temperature (Tc about 225 K) and electrostatic gate tunability offer a tantalizing possibility of achieving the ultimate high SOT limit in monolayer all-vdW nanodevices. The spin current generated in Pt exerts a damping-like SOT on FGT magnetization. At about 2.5x1011 A/m2 current density,SOT…
We study theoretically and experimentally the spin pumping signals induced by the resonance of canted antiferromagnets with Dzyaloshinskii-Moriya interaction and demonstrate that they can generate easily observable inverse spin-Hall voltages. Using a bilayer of hematite/heavy metal as a model system, we measure at room temperature the antiferromagnetic resonance and an associated inverse spin-Hall voltage, as large as in collinear antiferromagnets. As expected for coherent spin-pumping, we observe that the sign of the inverse spin-Hall voltage provides direct information about the mode handedn…
Quantum spin Hall (QSH) insulators are materials that feature an insulating bulk and host edge states protected by time-reversal symmetry. The helical locking of spin and momentum in these states suppresses backscattering of charge carriers, promising applications from low-power electronics to quantum computing. A major challenge for applications is the identification of large gap QSH materials, which would enable room temperature dissipationless transport in their edge states. Here we show that the layered mineral jacutingaite (Pt$_2$HgSe$_3$) is a candidate QSH material, realizing the long s…
Prediction of two-dimensional $π$-electron half-metallic ferrimagnets
International Iberian Nanotechnology Laboratory（伊比利亚纳米技术国际实验室）；Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；Universidad de Alicante（阿利坎特大学）；University of Minho（米尼奥大学）
We proposed a theory of quantum anomalous Hall effect in a flat-band ferromagnet on a two-dimensional (2D) decorated lattice with spin-orbit coupling. Free electrons on the lattice have dispersionless flat bands, and the ground state is highly degenerate when each lattice site is occupied averagely by one electron, i.e., the system is at half filling. The on-site Coulomb interaction can remove the degeneracy and give rise to the ferrimagnetism, which is the coexistence of the ferromagnetic and antiferromagnetic long-range orders. On the other hand the spin-orbit coupling makes the band structu…
We report magnetoresistance measurements on thin Pt bars grown on epitaxial (001) and (111) CoFe2O4 (CFO) ferrimagnetic insulating films. The results can be described in terms of the recently discovered spin Hall magnetoresistance (SMR). The magnitude of the SMR depends on the interface preparation conditions, being optimal when Pt/CFO samples are prepared in situ, in a single process. The spin-mixing interface conductance, the key parameter governing SMR and other relevant spin-dependent phenomena such as spin pumping or spin Seebeck effect, is found to be different depending on the crystallo…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave functions for the incompressible quantum fluid states are presented and the cohesive and the excitation energies are given.
Quantum anomalous Hall state is expected to emerge in Dirac electron systems such as graphene under both sufficiently strong exchange and spin-orbit interactions. In pristine graphene, neither interaction exists; however, both interactions can be acquired by coupling graphene to a magnetic insulator (MI) as revealed by the anomalous Hall effect. Here, we show enhanced magnetic proximity coupling by sandwiching graphene between a ferrimagnetic insulator yttrium iron garnet (YIG) and hexagonal-boron nitride (h-BN) which also serves as a top gate dielectric. By sweeping the top-gate voltage, we o…
Bi2Se3 is an important semiconductor thermoelectric material and a prototype topological insulator. Here we report observation of Shubnikov-de Hass (SdH) oscillations accompanied by quantized Hall resistances (Rxy) in highly-doped n-type Bi2Se3 with bulk carrier concentrations of few 10^19 cm^-3. Measurements under tilted magnetic fields show that the magnetotransport is 2D-like, where only the c-axis component of the magnetic field controls the Landau level formation. The quantized step size in 1/Rxy is found to scale with the sample thickness, and average ~e2/h per quintuple layer (QL). We s…
The large magnetic anisotropy in the layered ferromagnet Fe_{1/4}TaS_2 leads to very sharp reversals of the magnetization $\bf M$ at the coercive field. We have exploited this feature to measure the anomalous Hall effect (AHE), focussing on the AHE conductivity $σ^A_{xy}$ in the inelastic regime. At low temperature T (5-50 K), $σ^A_{xy}$ is T-independent, consistent with the Berry-phase/Karplus-Luttinger theory. Above 50 K, we extract an inelastic AHE conductivity $σ^{in}_{xy}$ that scales as the square of $Δρ$ (the T dependent part of the resistivity $ρ$). The term $σ^{in}_{xy}$ clarifies the…
We measure the ordinary and the anomalous Hall effect in a set of yttrium iron garnet$|$platinum (YIG$|$Pt) bilayers via magnetization orientation dependent magnetoresistance experiments. Our data show that the presence of the ferrimagnetic insulator YIG leads to an anomalous Hall like signature in Pt, sensitive to both Pt thickness and temperature. Interpretation of the experimental findings in terms of the spin Hall anomalous Hall effect indicates that the imaginary part of the spin mixing interface conductance $G_{\mathrm{i}}$ plays a crucial role in YIG$|$Pt bilayers. In particular, our da…
Factors affecting the topological Hall effect in strongly correlated layered magnets: spin of the magnetic atoms, polar and azimuthal angle subtended by the spin texture
We present a theory of the magneto-optical Faraday and Kerr effects of topological insulator (TI) films. For film thicknesses short compared to wavelength, we find that the low-frequency Faraday effect in ideal systems is quantized at integer multiples of the fine structure constant, and that the Kerr effect exhibits a giant $π/2$ rotation for either normal or oblique incidence. For thick films that contain an integer number of half wavelengths, we find that the Faraday and Kerr effects are both quantized at integer multiples of the fine structure constant. For TI films with bulk parallel cond…
We investigate the magnetic response in the quantum spin Hall phase of the layered Kane-Mele model with Hubbard interaction, and argue a condition to obtain the Meissner effect. The effect of Rashba spin orbit coupling is also discussed.
We report the magnetic and electronic transport properties of the inversion and time-reversal symmetry breaking Weyl semimetal NdAlGe. This material is analogous to NdAlSi, whose helical magnetism presents a rare example of a Weyl-mediated collective phenomenon, but with a larger spin-orbit coupling. Our neutron diffraction experiments revealed that NdAlGe, similar to NdAlSi, supports an incommensurate Ising spin density wave ($T_{\text{inc}}=6.8$ K) with a small helical spin canting of 3$^\circ$ and a long-wavelength of $\sim$ 35 nm, which transitions to a commensurate ferrimagnetic state bel…
