The anomalous Hall effect has been indispensable in our understanding of numerous magnetic phenomena. This concerns both ferromagnetic materials, as well as diverse classes of antiferromagnets, where in addition to the anomalous and crystal Hall effects, the topological Hall effect in non-coplanar antiferromagnets has been a subject of intensive research in the past decades. Here, we uncover a new flavour of the anomalous Hall effect in canted spin systems. Using advanced theoretical tools we demonstrate that upon canting, the anomalous Hall effect acquires a contribution which is sensitive to the sense of imprinted vector chirality among spins. We explore the origins and basic properties of corresponding chiral Hall effect, and closely tie it to the symmetry properties of the system. Our findings suggest that the chiral Hall effect and corresponding chiral magneto-optical effects emerge as novel versatile tools in characterizing an interplay of structure and chirality in complex magnets, as well as in tracking their chiral dynamics and fluctuations.
Most canted antiferromagnets are also anomalous Hall antiferromagnets (AHE AFMs), i.e. they have an anomalous Hall response and other responses with the same symmetry requirements. We suggest that AHE AFMs are promising materials as hosts for high-temperature quantum anomalous Hall effects. By considering models of two-dimensional (001) perovskite layers with strong spin-orbit coupling that isolates an effective total angular momentum $\tilde{j}= \frac{1}{2}$ subspace of the $t_{2g}$ manifold, we propose a strategy to engineering quantum anomalous Hall antiferromagnets.
Spin superfluid is a novel emerging quantum matter arising from the Bose-Einstein condensate (BEC) of spin-1 bosons. We demonstrate the spin superfluid ground state in canted antiferromagnetic Cr2O3 thin film at low temperatures via nonlocal spin transport. A large enhancement of the nonlocal spin signal is observed below ~ 20 K, and it saturates from ~ 5 K down to 2 K. We show that the spins can propagate over very long distances (~ 20 micro meters) in such spin superfluid ground state and the nonlocal spin signal decreases very slowly as the spacing increases with an inverse relationship, wh…
In the quantum Hall regime of graphene, antiferromagnetic and spin-polarized ferromagnetic states at the zeroth Landau level compete, leading to a canted antiferromagnetic state depending on the direction and magnitude of an applied magnetic field. Here, we investigate this transition at 2.7 K in graphene Hall bars that are proximity coupled to the ferrimagnetic insulator Y$_{3}$Fe$_{5}$O$_{12}$. From nonlocal transport measurements, we demonstrate an induced magnetic exchange field in graphene, which lowers the magnetic field required to modulate the magnetic state in graphene. These results …
Antiferromagnets have recently been propelled to the forefront of spintronics by their high potential for revolutionizing memory technologies. For this, understanding the formation and driving mechanisms of the domain structure is paramount. In this work, we investigate the domain structure in a thin-film canted antiferromagnet $α$-Fe$_2$O$_3$. We find that the internal destressing fields driving the formation of domains do not follow the crystal symmetry of $α$-Fe$_2$O$_3$, but fluctuate due to substrate clamping. This leads to an overall isotropic distribution of the Néel order with locally …
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…
The spin and layer (pseudospin) degrees of freedom are entangled coherently in the canted antiferromagnetic phase of the bilayer quantum Hall system at the filling factor $ν=2$. There emerges a complex Goldstone mode describing such a combined degree of freedom. In the zero tunneling-interaction limit ($Δ_{\text{SAS}}\rightarrow 0$), its phase field provokes a supercurrent carrying both spin and charge within each layer. The Hall resistance is predicted to become anomalous precisely as in the $ν=1$ bilayer system in the counterflow and drag experiments. Furthermore, it is shown that the total …
Magnetotransport properties are investigated in the bilayer quantum Hall state at the total filling factor $ν=2$. We measured the activation energy elaborately as a function of the total electron density and the density difference between the two layers. Our experimental data demonstrate clearly the emergence of the canted antiferromagnetic (CAF) phase between the ferromagnetic phase and the spin-singlet phase. The stability of the CAF phase is discussed by the comparison between experimental results and theoretical calculations using a Hartree-Fock approximation and an exact diagonalization s…
Motivated by experimental studies of graphene in the quantum Hall regime, we revisit the phase diagram of a single sheet of graphene at charge neutrality. Because of spin and valley degeneracies, interactions play a crucial role in determining the nature of ground state. We show that, generically, in the regime of interest there is a region of coexistence between magnetic and bond orders in the phase diagram. We demonstrate this result both in continuum and lattice models, and argue that the coexistence phase naturally provides an explanation for unreconciled experimental observations on the q…
In bilayer quantum Hall (BLQH) systems at $ν$=2, three different kinds of ground states are expected to be realized, i.e. a spin polarized phase (spin phase), a pseudospin polarized phase (ppin phase) and a canted antiferromagnetic phase (C-phase). An SU(4) scheme gives a powerful tool to investigate BLQH systems which have not only the spin SU(2) but also the layer (pseudospin) SU(2) degrees of freedom. In this paper, we discuss an origin of the C-phase in the SU(4) context and investigate SU(4) coherent effects to it. We show peculiar operators in the SU(4) group which do not exist in SU$_{\…
In antiferromagnets, the efficient propagation of spin-waves has until now only been observed in the insulating antiferromagnet hematite, where circularly (or a superposition of pairs of linearly) polarized spin-waves propagate over long distances. Here, we report long-distance spin-transport in the antiferromagnetic orthoferrite YFeO$_3$, where a different transport mechanism is enabled by the combined presence of the Dzyaloshinskii-Moriya interaction and externally applied fields. The magnon decay length is shown to exceed hundreds of nano-meters, in line with resonance measurements that hig…
We present details of earlier studies (Zheng et al, Phys. Rev. Lett. 78, 310 (1997) and Das Sarma et al, ibid 79, 917 (1997)) and additional new results on double-layer quantum Hall systems at a total filling ν= 2 ν_1, where a single layer at filling ν_1 forms a ferromagnetic, fully spin-polarized, gapped incompressible quantum Hall state. For the case ν_1 = 1, a detailed Hartree-Fock analysis is carried out on a realistic, microscopic Hamiltonian. Apart from the state continuously connected to the ground state of two well separated layers, we find two double-layer quantum Hall phases: one wit…
The ground state of a graphene sheet at charge neutrality in a perpendicular magnetic field remains enigmatic, with various experiments supporting canted antiferromagnetic, bond ordered, and even charge density wave phases. A promising avenue to elucidating the nature of this state is to sandwich it between regions of different filling factors, and study spin-dependent tunneling across the edge modes at the interfaces. Here we report on tunnel transport through a $ν=0$ region in a graphite-gated, hexagonal boron nitride ($hBN$) encapsulated monolayer graphene device, with the $ν=0$ strip sandw…
A low energy action for double-layer quantum Hall systems at filling fractions $ν= 2/m$ ($m$ an odd integer) is introduced. Interlayer antiferromagnetic exchange induces a phase with canted spin order, and also a spin-singlet phase. Universal properties of zero and finite temperature transitions are obtained. We compute the critical temperature at which the canted order vanishes in a Kosterlitz-Thouless transition. Implications for recent light scattering experiments at $ν= 2$ are noted.
Magnetic skyrmions are quasiparticle configurations in a magnetic film that can act as information carrying bits for ultrasmall, all-electronic nonvolatile memory. The skyrmions can be nucleated and driven by spin-orbit torque from a current driven in a heavy metal underlayer. Along its gyrotropic path, a Magnus force can cause a skyrmion to be annihilated at the boundaries. By combining interfacial and bulk Dzyaloshinskii-Moriya interactions (DMIs), for instance by using a B20 material on top of a heavy metal layer with high spin-orbit coupling, it is possible to engineer a hybrid skyrmion th…
In the Landau levels of a two-dimensional electron system or when flat bands are present, e.g. in twisted van der Waals bilayers, strong electron-electron interaction gives rise to quantum Hall ferromagnetism with spontaneously broken symmetries in the spin and isospin sectors. Quantum Hall ferromagnets support a rich variety of low-energy collective excitations that are instrumental to understand the nature of the magnetic ground states and are also potentially useful as carriers of quantum information. Probing such collective excitations, especially their dispersion ω(k), has been experiment…
The influence of insertion of an ultra-thin NiO layer between the MgO barrier and ferromagnetic electrode in magnetic tunnel junctions has been investigated by measuring the tunneling magnetoresistance and the X-ray magnetic circular dichroism (XMCD). The magnetoresistance shows a high asymmetry with respect to bias voltage, giving rise to a negative value of -16% at 2.8 K. We attribute this to the formation of non-collinear spin structures in the NiO layer as observed by XMCD. The magnetic moments of the interface Ni atoms tilt from the easy axis due to exchange interaction and the tilting an…
We develop an effective spin theory to describe magnetic properties of the $ν=2$ Quantum Hall bilayer systems. In the absence of disorder this theory gives quantitative agreement with the results of microscopic Hartree-Fock calculations, and for finite disorder it predicts the existence of a novel spin Bose glass phase. The Bose glass is characterized by the presence of domains of canted antiferromagnetic phase with zero average antiferromagnetic order and short range mean antiferromagnetic correlations. It has infinite antiferromagnetic transverse susceptibility, finite longitudinal spin susc…
We present a microscopic study of the interlayer spacing d versus in-plane magnetic field $B_\parallel$ phase diagram for bilayer quantum Hall (QH) pseudo-ferromagnets. In addition to the interlayer charge balanced commensurate and incommensurate states analyzed previously, we address the corresponding interlayer charge unbalanced "canted" QH states. We predict a large anomaly in the bilayer capacitance at the canting transition and the formation of dipole stripe domains with periods exceeding 1 micron in the canted state.
An efficient formalism for inertial spin waves: Dzyaloshinskii-Moriya antiferromagnets as case studies
School of Physics and Electronics, Hunan University（湖南大学物理与电子学院）；College of Computer and Electrical Engineering, Hunan University of Arts and Science（湖南文理学院计算机与电气工程学院）；Institute for Theoretical Solid State Physics, RWTH Aachen University（亚琛工业大学理论固体物理研究所）
Recently, antiferromagnets have received revived interest due to their significant potential for developing next-generation ultrafast magnetic storage. Here we report dc spin pumping by the acoustic resonant mode in a canted easy-plane antiferromagnet α-Fe2O3 enabled by the Dzyaloshinskii-Moriya interaction. Systematic angle and frequency dependent measurements demonstrate that the observed spin pumping signals arise from resonance-induced spin injection and inverse spin Hall effect in α-Fe2O3/metal heterostructures, mimicking the behavior of spin pumping in conventional ferromagnet/nonmagnet …
We present a theoretical mapping to show that a ferromagnet with gain (loss) is equivalent to an antiferromagnet with an equal amount of loss (gain). Our finding indicates a novel first-order ferromagnet-antiferromagnet phase transition by tuning the gain-loss parameter. As an appealing application, we demonstrate the realization as well as the manipulation of the antiferromagnetic skyrmion, a stable topological quasiparticle not yet observed experimentally, in a chiral ferromagnetic thin film with gain. We also consider ferromagnetic bilayers with balanced gain and loss, and show that the ant…
We study the problem of controlling spin waves propagation through an antiferromagnet/ferromagnet interface via tuning material parameters. It is done by introducing the degree of sublattice noncompensation of antiferromagnet (DSNA), which is a physical characteristic of finite-thickness interfaces. The DSNA value can be varied by designing interfaces with a particular disorder or curvilinear geometry. We describe a spin-wave propagation through any designed antiferromagnet/ferromagnet interface considering a variable DSNA and appropriate boundary conditions. As a result, we calculate the phys…
We demonstrate a canted magnetization of biatomic zigzag Co chains grown on the 5 x 1 reconstructed Ir(001) surface using density functional theory calculations and spin-polarized scanning tunneling microscopy (SP-STM) experiments. Biatomic Co chains grow in three different structural configurations and are all in a ferromagnetic state. Two chain types possess high symmetry due to two equivalent atomic strands and an easy magnetization direction which is along one of the principal crystallographic axes. The easy magnetization axis of the zigzag Co chains is canted away from the surface normal …
Monolayer graphene at charge neutrality in a quantizing magnetic field is a quantum Hall ferromagnet. Due to the spin and valley (near) degeneracies, there is a plethora of possible ground states. Previous theoretical work, based on a stringent ultra short-range assumption on the symmetry-allowed interactions, predicts a phase diagram with distinct regions of spin-polarized, canted antiferromagnetic, inter-valley coherent, and charge density wave order. While early experiments suggested that the system was in the canted antiferromagnetic phase at a perpendicular field, recent scanning tunnelin…
A proposal to detect the purported canted antiferromagnet order for the $ν=0$ quantum Hall state of graphene based on a two-terminal spin transport setup is theoretically discussed. In the presence of a magnetic field normal to the graphene plane, a dynamic and inhomogeneous texture of the Néel vector lying within the plane should mediate (nearly dissipationless) superfluid transport of spin angular momentum polarized along the $z$ axis, which could serve as a strong support for the canted antiferromagnet scenario. Spin injection and detection can be achieved by coupling two spin-polarized edg…
Based on the construction of generalized Halperin wave functions, we predict the possible existence of a large class of broken spin symmetry states in bilayer quantum Hall structures, generalizing the recently suggested canted antiferromgnetic phase to many fractional fillings. We develop the appropriate Chern-Simons theory, and establish explicitly that the low-lying neutral excitation is a Goldstone mode and that the charged excitations are bimerons with continuously tunable (through the canted antiferromagnetic order parameter) electric charge on the individual merons.
Microwaves couple to magnetic moments in both ferromagnets and antiferromagnets. Although the magnons in ferromagnets and antiferromagnets radically differ, they can become entangled via strong coupling to the same microwave mode in a cavity. The equilibrium configuration of the magnetic moments crucially governs the coupling between the different magnons because the antiferromagnetic and ferromagnetic magnons have the opposite spins when their dispersion relations cross. We derive analytical expressions for the coupling strengths and find that the coupling between antiferromagnets and ferroma…
We simulate the switching behavior of nanoscale synthetic antiferromagnets (SAFs), inspired by recent experimental progress in spin-orbit-torque switching of crystal antiferromagnets. The SAF consists of two ferromagnetic thin films with in-plane biaxial anisotropy and interlayer exchange coupling. Staggered field-like Rashba spin-orbit torques from the opposite surfaces of the SAF induce a canted net magnetization, which triggers an orthogonal torque that drives 90$^\circ$ switching of the Néel vector. Such dynamics driven by the field-like spin-orbit torque allows for faster switching with i…
We develop a theory for spin transported by coherent Neel dynamics through an antiferromagnetic insulator coupled to a ferromagnetic insulator on one side and a current-carrying normal metal with strong spin-orbit coupling on the other. The ferromagnet is considered within the mono-domain limit and we assume its coupling to the local antiferromagnet Neel order at the ferromagnet|antiferromagnet interface through exchange coupling. Coupling between the charge current and the local Neel order at the other interface is described using spin Hall phenomenology. Spin transport through the antiferrom…
It is shown that the current-induced torques between a ferromagnetic layer and an antiferromagnetic layer with a compensated interface vanish when the ferromagnet is aligned with an axis of spin-rotation symmetry of the antiferromagnet. For properly chosen geometries this implies that the current induced torque can stabilize the out-of-plane (or hard axis) orientation of the ferromagnetic layer. This current-induced torque relies on phase coherent transport, and we calculate the robustness of this torque to phase breaking scattering. From this it is shown that the torque is not linearly depend…
