Ferromagnetic Lattice Research Articles

Anomalous dual valley Hall effect in the two-dimensional ferromagnetic honeycomb lattice

Anomalous dual valley Hall effect in the two-dimensional ferromagnetic honeycomb lattice

Valley modulation and topological phase transition in Staggered Kagome Ferromagnets

Abstract Owing to its charge-free property, magnon is highly promising to achieve dissipationless transport without Joule heating and thus potentially applicable to energy-efficient devices. Here, we investigate valley magnons and associated valley modulations in a kagome ferromagnetic lattice, with the staggered exchange interaction and Dzyaloshinskii-Moriya interaction. The staggered exchange interaction breaks the spatial inversion symmetry, leading to a valley magnon Hall effect. With nonzero Dzyaloshinskii-Moriya interaction in staggered kagome lattcie, the magnon Hall effect can be observed from only one valley. Moreover, reversing the Dzyaloshinskii-Moriya interaction (D→-D) and exchange of J 1 and J 2 (J 1 ↔ J 2) can also regulate the position of the unequal valleys. With increasing Dzyaloshinskii-Moriya interaction, a series of topological phase transitions appear when two bands come to touch and split at valleys. The valley Hall effect and topological phase transitions observed in kagome magnon lattices can be realized in the thin film of the insulating ferromagnet, such as Lu2V2O7, and will extend the basis for magnonics applications in the future.

Electrical Control of the Valley-Layer Hall Effect in Ferromagnetic Bilayer Lattices.

The layertronics based on the layer degree of freedom are of essential significance for the construction and application of new-generation electronic devices. Although the Hall layer effect has been realized theoretically and experimentally, it is mainly based on topological and antiferromagnetic lattices. On the basis of the low-energy effective k·p model, the mechanism of the controllable valley-layer Hall effect (V-LHE) in a bilayer ferromagnetic lattice through interlayer sliding has been proposed. Due to the broken time-reversal and inversion symmetries, the V-LHE based on the valley, layer degree of freedom, ferromagnetism, and ferroelectricity can be predicted. In addition, valley and layer indexes can be controlled by magnetization orientation and slipping, respectively. The mechanism can be demonstrated in the real bilayer CrSI lattice through first-principles calculations. Moreover, V-LHE can be effectively tuned by the perpendicular external electric field in configurations without out-of-plane polarization. These findings provide a new platform for the research of valleytronics and layertronics.

Intrinsic second-order magnon thermal Hall effect

In this paper, we study the intrinsic contribution of nonlinear magnon thermal Hall Effect. We derive the intrinsic second-order thermal Hall conductivity of magnon by the thermal scalar potential method and the thermal vector potential method. We find that the intrinsic second-order magnon thermal Hall conductivity is related to the thermal Berry-connection polarizability. We apply our theory to the monolayer ferromagnetic Hexagonal lattice, and we find that the second-order magnon thermal Hall conductivity can be controlled by changing Dzyaloshinskii–Moriya strength and applying strain.

Engineering Layertronics in Two-Dimensional Ferromagnetic Multiferroic Lattice.

Layertronics, rooted in the layer Hall effect (LHE), is an emerging fundamental phenomenon in condensed matter physics and spintronics. So far, several theoretical and experimental proposals have been made to realize LHE, but all are based on antiferromagnetic systems. Here, using symmetry and tight-binding model analysis, we propose a general mechanism for engineering layertronics in a two-dimensional ferromagnetic multiferroic lattice. The physics is related to the band geometric properties and multiferroicity, which results in the coupling between Berry curvature and layer degree of freedom, thereby generating the LHE. Using first-principles calculations, we further demonstrate this mechanism in bilayer (BL) TcIrGe2S6. Due to the intrinsic inversion and time-reversal symmetry breakings, BL TcIrGe2S6 exhibits multiferroicity with large Berry curvatures at both the center and corners of the Brillouin zone. These Berry curvatures couple with the layer physics, forming the LHE in BL TcIrGe2S6. Our work opens a new direction for research on layertronics.

Effect of a flat band on a multiband two-dimensional Lieb lattice with intra- and interband interactions

In this study, we explore the effect of a single flat band in the electronic properties of a ferromagnetic two-dimensional Lieb lattice using the multiband Hubbard model with polarized carriers, spin-up and spin-down. We employ the self-consistent dynamical mean field theory and a Green functions cumulant expansion around the atomic limit to obtain the correlated densities of states while varying the intra- and interband interactions. Our findings demonstrate a renormalization of the correlated density of states in both the spin-up and spin-down carriers as we varied the intra- and interband interactions. We conclude that the presence of a flat band enables the system to maintain a metal state with itinerant ferromagnetism in the spin-up carrier.

Exchange regime of the spin waves in two-dimensional honeycomb-like ferromagnetic lattices

Exchange regime of the spin waves in two-dimensional honeycomb-like ferromagnetic lattices

Designing Layered 2D Skyrmion Lattices in Moiré Magnetic Heterostructures

AbstractSkyrmions are promising for the next generation of spintronic and magnonic devices, but their zero‐field stability and controlled nucleation through chiral interactions remain challenging. In this theoretical study, the potential of moiré magnetic heterostructures to generate ordered skyrmion lattices from the stacking‐dependent magnetism in 2D magnets is explored. Heterostructures formed by twisting ultrathin CrBr3 films on top of CrI3 substrates are considered, assuming a moderate interfacial Dzyaloshinskii–Moriya interaction. At large moiré periodicity and appropriate substrate thickness, a moiré skyrmion lattice emerges in the interfacial CrBr3 layer due to the weaker exchange interactions in CrBr3 compared to CrI3. This lattice is then projected to the remaining layers of the CrBr3 film via chiral interlayer exchange fields. By varying the pristine stacking configurations within the ultrathin CrBr3 film, layered ferromagnetic and antiferromagnetic skyrmion lattices without the need for a permanent magnetic field are realized. These findings suggest the possibility of creating ordered skyrmion lattices in moiré magnetic heterostructures, enabling further exploration of their fundamental properties and technological relevance.

Intrinsic Localized Modes in a Two-Dimensional Checkerboard Ferromagnetic Lattice

Intrinsic Localized Modes in a Two-Dimensional Checkerboard Ferromagnetic Lattice

Spin waves in two-dimensional placoid-like ferromagnetic lattices

The topology of placoid scales is explored as a model of a two-dimensional ferromagnetic lattice. We start from Heisenberg’s Hamiltonian, adopting in low temperature regime and performing the study of free modes of the magnetic excitations. The Holstein–Primakoff approximation was employed, restricting our attention to the bilinear terms in the quantized second operators. The dispersion relation was obtained and the properties of the magnetic modes were studied in terms of the physical fit parameter J2, which reveals the energy dynamics for different regions of the Brillouin Zone. A comparison was made with the energy maps from the square and triangular lattices in order to verify the equivalence of the effects from the placoid geometry. We concluded that this topology imprints a significant energy growing in the regime of low wave vectors with more effective rates than those observed in the triangular lattice, a fact that can be explained by the presence of 4 sites in the unit cell.

Spin–valley splitting and spontaneous valley polarization in antiferromagnetic Mn2P2X3Y3 monolayers

In the current stage, valley-contrasting physics is mainly rooted in nonmagnetic and/or ferromagnetic hexagonal lattices and is rarely used to observe the simultaneous spin and valley polarization in antiferromagnetic materials. In this work, we propose a general scheme that can be achieved easily in experiments to break the PT joint symmetry of antiferromagnetic structures, that is, introducing an out-of-plane potential gradient to realize spin–valley splitting and spontaneous valley polarization. In combination of the model analysis and first-principles calculations, we translate the concept into Mn2P2X3Y3 monolayers and clarify the valley-related physics. It is obvious that our finding significantly extends the scope of valleytronics in both theory and experiments.

A versatile model with three-dimensional triangular lattice for unconventional transport and various topological effects.

The finite Berry curvature in topological materials can induce many subtle phenomena, such as the anomalous Hall effect (AHE), spin Hall effect (SHE), anomalous Nernst effect (ANE), non-linear Hall effect (NLHE) and bulk photovoltaic effects. To explore these novel physics as well as their connection and coupling, a precise and effective model should be developed. Here, we propose such a versatile model-a 3D triangular lattice with alternating hopping parameters, which can yield various topological phases, including kagome bands, triply degenerate fermions, double Weyl semimetals and so on. We reveal that this special lattice can present unconventional transport due to its unique topological surface states and the aforementioned topological phenomena, such as AHE, ANE, NLHE and the topological photocurrent effect. In addition, we also provide a number of material candidates that have been synthesized experimentally with this lattice, and discuss two materials, including a non-magnetic triangular system for SHE, NLHE and the shift current, and a ferromagnetic triangular lattice for AHE and ANE. Our work provides an excellent platform, including both the model and materials, for the study of Berry-curvature-related physics.

Electronic manipulation of magnon topology by chirality injection from boundaries

Magnon bands are known to exhibit nontrivial topology in ordered magnets under suitable conditions, engendering topological phases referred to as magnonic topological insulators. Conventional methods to drive a magnonic topological phase transition are bulk magnetic or thermal operations such as changing the direction of an external magnetic field or varying the temperature of the system, which are undesired in device applications of magnon topology. In this work, we lift the limitation of the magnon topology control on the bulk nonelectronic manipulation by proposing a scheme to manipulate magnonic topological phases by electronic boundary operations of spin chirality injection. More specifically, we consider a ferromagnetic honeycomb lattice and show that a finite spin chirality injected from the boundary of the system via the spin Hall effects introduces a tunable sublattice-symmetry-breaking mass term to the bosonic counterpart of the Haldane model for the Chern insulators and thereby allows us to electronically manipulate the bulk topology of magnons from the boundary. The ``shoulder'' in the thermal Hall conductivity profile is proposed as an experimental probe of the chirality-induced topological phase transition. The scheme for the boundary manipulation of the magnon topology is shown to work for a honeycomb antiferromagnet as well. We envisage that the interfacial chirality injection may offer a nonintrusive electronic means to tune the static and the dynamical bulk properties of general magnetic systems.

Breakdown of the scaling relation of anomalous Hall effect in Kondo lattice ferromagnet USbTe

The interaction between strong correlation and Berry curvature is an open territory of in the field of quantum materials. Here we report large anomalous Hall conductivity in a Kondo lattice ferromagnet USbTe which is dominated by intrinsic Berry curvature at low temperatures. However, the Berry curvature induced anomalous Hall effect does not follow the scaling relation derived from Fermi liquid theory. The onset of the Berry curvature contribution coincides with the Kondo coherent temperature. Combined with ARPES measurement and DMFT calculations, this strongly indicates that Berry curvature is hosted by the flat bands induced by Kondo hybridization at the Fermi level. Our results demonstrate that the Kondo coherence of the flat bands has a dramatic influence on the low temperature physical properties associated with the Berry curvature, calling for new theories of scaling relations of anomalous Hall effect to account for the interaction between strong correlation and Berry curvature.

Localized Surface Magnon Modes in Cubic Ferromagnetic Lattices

A theoretical formalism for calculating the bulk and surface spin modes in Heisenberg semi-infinite lattices is presented on a ferromagnetic cubic network of spins, coupled via nearest and next-nearest neighbors exchange interactions. The magnetic surface can be considered as semi-infinite slabs at the end of the bulk structures. The breakdown of translation symmetry, in the normal direction of the surface, gives rise to localized spin wave modes in its neighborhood. The localized magnon spectrum is derived as elements of a Landauer-type scattering matrix, in the three cubic lattices sc, bcc and fcc. The magnon properties are simulated and determined numerically for each cubic lattice by using the matching technique. The observed fluctuations in the numerical results demonstrate the interference magnon effects between scattered spinwaves and the localized magnon states, generated by the surface region with characteristic Fano resonances. In cubic leads, the localized surface spin states are sensitive to the local magnetic coupling and the incident direction in the surface boundary. In this contribution, the normalized energy of spinwaves arising from the absence of translation symmetry is analyzed for each cubic system as a function of the exchange integral parameters. This addresses the dependence of the surface magnon on the different possibilities of the of the exchange parameters variation from softening to hardening in the neighborhood of the surface region.

Exact results for the orbital angular momentum of magnons on honeycomb lattices

We obtain exact results for the orbital angular momentum (OAM) of magnons at the high symmetry points of ferromagnetic (FM) and antiferromagnetic (AF) honeycomb lattices in the presence of Dzyallonshinskii–Moriya (DM) interactions. For the FM honeycomb lattice in the absence of DM interactions, the values of the OAM at the corners of the Brillouin zone (BZ) (, ) are alternately for both magnon bands. The presence of DM interactions dramatically changes those values by breaking the degeneracy of the two magnon bands. The OAM values are alternately and 0 for the lower magnon band and and 0 for the upper magnon band. For the AF honeycomb lattice, the values of the OAM at the corners of the BZ are on one of the degenerate magnon bands and on the other, where κ measures the anisotropy and the result is independent of the DM interaction.

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Starting from the hamiltonian for the Heisenberg ferromagnet which comprise randomly distributed nonmagnetic ions as impurities in a Bravais lattice, we express the spin operators by means of the Dyson–Maleev transformation in terms of the Bose operators of the second quantization. Then by using methods of quantum statistical field theory, we derive the partition function and the free energy for the system. We adopt the Matsubara thermal perturbation method to a portion of the hamiltonian which describes the interaction between magnons and the stationary field of nonmagnetic ions. Upon averaging over all possible distributions of impurities, we express the free energy of the system as a function of the mean impurity concentration. Subsequently, we set up the double-time single particle Green function at temperature T in the momentum space in terms of magnon operators and derive the equation of motion for the Green function through the Heisenberg equation of motion and then solve the resulting equation. From this, we calculate the self-energy and then the spectral density function for the system. We apply the formalism to the case of the simple cubic lattice and compute the density of states, the spectral density function and the lifetime of the magnons as a function of energy for several values of the mean concentration of nonmagnetic ions in the ferromagnetic lattice. We calculate the magnon energy spectrum as a function of the average impurity concentration fraction c, which shows that for low lying states, the excitation energy increases continuously with c in the studied range 0.1≤c≤0.7. We also use the spectral density function to compute some thermodynamical quantities through the magnon occupation number. We have obtained closed form expressions for the configurationally averaged physical quantities of interest in a unified fashion as functions of the mean concentration of nonmagnetic impurities c to any order of c applicable below a critical percolation concentration cp. The quantities of interest comprise the thermodynamic potential (free energy), the spin-wave self-energy and the spectral density function from which other quantities can be derived.

Magnon valley thermal Hall effect in triangular-lattice antiferromagnets

We study the magnetic excitations of the antiferromagnetic XXZ model on two-dimensional triangular lattice. We find there is a magnon valley thermal Hall effect. As far as we know, this effect has been studied on only the ferromagnetic honeycomb lattice. We reveal that the valley thermal Hall conductivity also conforms to the universal behavior of thermal Hall conductivity proposed by Yang et al. [Phys. Rev. Lett. 124, 186602 (2020)]. We derive a low-energy effective theory near the valleys and find that although the low-energy effective dynamic matrix is non-Hermitian, the Berry curvatures are mainly determined by its Hermitian part. We show that our results are general to some extent in the Y phase of the triangular lattice. By an explicit calculation with experimental parameters, we demonstrate that ${\mathrm{Rb}}_{4}\mathrm{Mn}{({\mathrm{MoO}}_{4})}_{3}$ is a suitable material to realize the magnon valley thermal Hall effect.

Valley modulation and single-edge transport of magnons in breathing kagome ferromagnets

Owing to charge-free property, magnon is promising to achieve dissipationless transport without Joule heating. Valley degree of freedom has also been fully expressed in electronic structures, enabling information coding and manipulation via valley-based qubits. Considering the conceptual importance and application potential, it is highly desirable to couple valley to magnon excitation and realize their modulations. We demonstrate valley magnons and valley modulations in a kagome ferromagnetic lattice, with Dzyaloshinskii-Moriya and staggered exchange interactions. The staggered exchange interaction breaks spatial inversion symmetry, leading to magnon valley Hall effect. When the Dzyaloshinskii-Moriya interaction is further included, the valley degeneracy is lifted, exhibiting net anomalous Hall effect and a series of topological phase transitions. Single-edge heat transport of magnons can occur, with propagating currents along the edge and local circulating currents. These findings give full play to spin and valley degrees of freedom and add another dimension to magnonic device paradigms.

Phase diagram of the dodecahedron spin model on square lattice with diluted bonds

We study the effect of bond dilution of a dodecahedron spin model on ferromagnetic square lattice. The dodecahedron spin constitutes a discrete (polyhedral) counterpart of the continuous Heisenberg spin. Previous work found that, in the absence of dilution, the ferromagnetic dodecahedron system exhibits a finite temperature phase transition. We use Monte Carlo simulation with Wolff cluster algorithm to monitor how phase transitions are impacted by the bond dilution. We simulate the model with various bond concentrations and investigate the resulting phase diagram and critical behavior.