Ferromagnetic Case Research Articles

Surfaces of axion insulators

Axion insulators are magnetic topological insulators in which the non-trivial $\mathbb{Z}_2$ index is protected by inversion symmetry instead of time-reversal symmetry. The naturally gapped surfaces of axion insulators give rise to a half-quantized surface anomalous Hall conductivity (AHC), but the sign of the surface AHC cannot be determined from topological arguments. In this paper, we consider topological phenomena at the surface of an axion insulator. To be explicit, we construct a minimal tight-binding model on the pyrochlore lattice and investigate the all-in-all-out (AIAO) and ferromagnetic (FM) spin configurations. We also implement a recently proposed approach for calculating the surface AHC directly, which allows us to explore how the interplay between surface termination and magnetic ordering determines the sign of the half-quantized surface AHC. In the case of AIAO ordering, we show that it is possible to construct a topological state with no protected metallic states on boundaries of any dimension (surfaces, hinges, or corners), although chiral hinge modes do occur for many surface configurations. In the FM case, rotation of the magnetization by an external field offers a promising means of control of chiral hinge modes, which can also appear on surface steps or where bulk domain walls emerge at the surface.

Analysis of the impact of changes in the stator magnetic circuit on static properties of the electromagnetic linear motor model

In this paper, the static characteristics as a function of changes in geometric dimensions of the stator magnetic circuit of the linear stepper actuator with permanent magnets is presented. The stator is built from a series of cylindrical coils encapsulated with ferromagnetic case. The runner is made of permanent magnet rings connected with ferromagnetic spacers. The electromagnetic interac-tion between the stator and the runner for the sequential supply of coils was analyzed. The electro-magnetic force as a function of the geometry of the coils and the ferromagnetic housing for the con-stant graduation of the runner was determined. The maximum, minimum, and average values of the electromagnetic force as a function of the geometric independent variable were determined. The ratio of the mean force to the maximum, and mechanical work calculated as the integral of the force on the path of the runner was adopted as the evaluation criteria. A comparison between the maximum, average and relative values of forces as a function of the geometric dimensions of the stator was made. Keywords: modelling and simulation, linear actuator, finite element method, field calculations, cogging force, magnetic force.

Response and phase transition of a Kitaev spin liquid in a local magnetic field

We study the response of the Kitaev spin liquid (KSL) to a local magnetic field perpendicular to the Kitaev honeycomb lattice. The local magnetic field induces a dynamical excitation of a flux pair in the spin liquid and the system can be described by a generally particle-hole asymmetric interacting resonant level model. The dynamical excitation of the flux pair closes the flux gap in the spectrum of the spin correlation function locally for the gapless KSL even from the perturbative response to a weak magnetic field. Beyond the perturbative regime, the p-h asymmetry competes with the magnetic field and results in a rich phase diagram. Moreover, the magnetic field breaks the gauge equivalence of the ferromagnetic and anti-ferromagnetic Kitaev couplings of the ground state and leads to very different behaviors for the two cases. The anti-ferromagnetic case experiences a first order phase transition to the polarized state during magnetization whereas the ferromagnetic case does not. This study can be generalized to the Kitaev model in a uniform magnetic field and may help understand issues in recent experiments on KSL candidates.

First-principles study of electronic structure, transport, and optical properties of EuCd2As2

Recent experimental measurements on the layered triangular-lattice antiferromagnet ${\mathrm{EuCd}}_{2}{\mathrm{As}}_{2}$ have revealed an interesting interplay among magnetism, charge transport, and optical properties. To explore the nature of the interaction among these degrees of freedom, the electronic structure, magnetic properties, electrical transport, and optical properties of ${\mathrm{EuCd}}_{2}{\mathrm{As}}_{2}$ are investigated using density functional theory and Boltzmann transport theory under various approximations such as the generalized gradient approximation (GGA), GGA+$U$, and GGA+$U$+spin orbit (SO). A semimetallic electronic structure with compensating electron and hole pockets is observed. Among the various magnetic states studied, A-type antiferromagnetic (A-AFM) and ferromagnetic (FM) states emerge as having competing total energies even though A-AFM is found to be energetically favored. Further, our GGA+$U$+SO calculations reveal the presence of a magnetic anisotropy which drives the spin moments to align along the crystallographic $b$ direction. We observe from our transport calculations that in the case of A-AFM, the anisotropy between out-of-plane and in-plane resistivities $({\ensuremath{\rho}}_{zz}/{\ensuremath{\rho}}_{xx})$ is much higher than that in the FM case, and it increases as temperature goes down, exactly what has been observed experimentally for this system. The huge difference between the resistivities of A-AFM and FM states at lower temperatures is indicative of the presence of negative magnetoresistance in the system as seen in the experimental measurements. In-plane optical reflectivity reveals that intraband contributions play a major role in reproducing the experimental features in the low-frequency regime.

Lattice relaxations in disordered Fe-based materials in the paramagnetic state from first principles

In this work we propose a method for the structural relaxation of magnetic materials in the paramagnetic regime, in an adiabatic fast-magnetism approximation within the disordered local moment (DLM) picture in the framework of density functional theory (DFT). The method is straight forward to implement using any $ab$ $initio$ code that allows for structural relaxations. We illustrate the importance of considering the disordered magnetic state during lattice relaxations by calculating formation energies and geometries for an Fe vacancy and C insterstitial atom in bcc Fe as well as bcc Fe$_{1-x}$Cr$_x$ random alloys in the paramagnetic state. In the vacancy case, the nearest neighbors to the vacancy relax towards the vacancy of 0.16 {\AA} (-5% of the ideal bcc nearest neighbor distance), which is twice as large as the relaxation in the ferromagnetic case. The vacancy formation energy calculated in the DLM state on these positions is 1.60 eV, which corresponds to a reduction of about 0.1 eV compared to the formation energy calculated using DLM but on ferromagnetic-relaxed positions. The carbon interstitial formation energy is found to be 0.41 eV when the DLM relaxed positions are used, as compared to 0.59 eV when the FM-relaxed positions are employed. For bcc Fe$_{0.5}$Cr$_{0.5}$ alloys, the mixing enthalpy is reduced by 5 meV/atom, or about 10%, when the DLM state relaxation is considered, as compared to positions relaxed in the ferromagnetic state.

Successive Majorana topological transitions driven by a magnetic field in the Kitaev model

We study quantum phase transitions in the honeycomb Kitaev model under a magnetic field, focusing on the topological nature of Majorana fermion excitations. We find a gapless phase between the low-field gapless quantum spin liquid and the high-field gapped forced-ferromagnetic state for the antiferromagnetic Kitaev model in the [001] field by using the Majorana mean-field theory, in conjunction with the exact diagonalization and the spin-wave theory supporting the validity of this approach. The transition between the two gapless phases is driven by a topological change of the Majorana spectrum --- line node formation interconnecting two Majorana cones. The peculiar change of the Majorana band topology is rationalized by a sign change of the effective Kitaev coupling by the magnetic field, which does not occur in the ferromagnetic Kitaev case. Upon tilting the magnetic field away from [001], the two gapless phases become gapped and topologically nontrivial, characterized by nonzero Chern numbers with different signs. The sign change of the Chern number leads to a reversal of the thermal edge current in the half-quantized thermal Hall effect.

Phase diagrams and multistep condensations of spin-1 bosonic gases in optical lattices

Motivated by recent experimental processes, we systemically investigate strongly correlated spin-1 ultracold bosons trapped in a three-dimensional optical lattice in the presence of an external magnetic field. Based on a recently developed bosonic dynamical mean-field theory (BDMFT), we map out complete phase diagrams of the system for both antiferromagnetic and ferromagnetic interactions, where various phases are found as a result of the interplay of spin-dependent interaction and quadratic Zeeman energy. For antiferromagnetic interactions, the system demonstrates competing magnetic orders, including nematic, spin-singlet and ferromagnetic insulating phase, depending on longitudinal magnetization, whereas, for ferromagnetic case, a ferromagnetic-to-nematic-insulating phase transition is observed for small quadratic Zeeman energy, and the insulating phase demonstrates the nematic order for large Zeeman energy. Interestingly, at low magnetic field and finite temperature, we find an abnormal multi-step condensation of the strongly correlated superfluid, i.e. the critical condensing temperature of the mF = −1 component with antiferromagnetic interactions demonstrates an increase with longitudinal magnetization, while, for ferromagnetic case, the Zeeman component mF = 0 demonstrates a local minimum for the critical condensing temperature, in contrast to weakly interacting cases.

Static Analysis of the Tubular Electromagnetic Linear Actuator with Permanents Magnets

Abstract In this paper a results of a static analysis of the tubular linear electromagnetic actuator is presented. The linear actuator consist of two parts: a cylindrical unmovable coils surrounded by a soft ferromagnetic case, and a runner made from sequence of permanent magnet with a soft ferro-magnetic gasket. In the first part of the paper the analytical method was performed for preliminary analysis. In the second part of the paper the more detailed analysis was depicted with using finite element method (FEM). The magnetic circuit shape and impact of selected dimensions on static characteristics is presented. Then the axial and radial electromagnetic force as a function of the runner dimensions were analysed.

Magnon-induced superconductivity in a topological insulator coupled to ferromagnetic and antiferromagnetic insulators

We study the effective interactions between Dirac fermions on the surface of a three-dimensional topological insulator due to the proximity coupling to the magnetic fluctuations in a ferromagnetic or antiferromagnetic insulator. Our results show that the magnetic fluctuations can mediate attractive interactions between Dirac fermions of both Amperean and BCS type. In the ferromagnetic case, we find pairing between fermions with parallel momenta, so-called Amperean pairing, whenever the effective Lagrangian for the magnetic fluctuations does not contain a quadratic term. The pairing interaction also increases with increasing Fermi momentum, and is in agreement with previous studies in the limit of high chemical potential. If a quadratic term is present, the pairing is instead of BCS type above a certain chemical potential. In the antiferromagnetic case, BCS pairing occurs when the ferromagnetic coupling between magnons on the same sublattice exceeds the antiferromagnetic coupling between magnons on different sublattices. Outside this region in parameter space, we again find that Amperean pairing is realized.

Magnetic Anisotropy by Rashba Spin–Orbit Coupling in Antiferromagnetic Thin Films

Magnetic anisotropy in an antiferromagnet (AFM) with inversion symmetry breaking (ISB) is investigated. The magnetic anisotropy energy (MAE) resulting from the Rashba spin-orbit and s-d type exchange interactions is determined for two different models of AFMs. The global ISB model, representing the effect of a surface, an interface, or a gating electric field, results in an easy-plane magnetic anisotropy. In contrast, for a local ISB model, i.e., for a noncentrosymmetric AFM, perpendicular magnetic anisotropy (PMA) arises. Both results differ from the ferromagnetic case, in which the result for PMA depends on the band structure and dimensionality. These MAE contributions play a key role in determining the direction of the Neel order parameter in antiferromagnetic nanostructures, and reflect the possibility of electrical-field control of the Neel vector.

Investigation of phase diagrams for cylindrical Ising nanotube using cellular automata

Recent developments in the field of applied nanoscience and nanotechnology have heightened the need for categorizing various characteristics of nanostructures. In this regard, this paper establishes a novel method to investigate magnetic properties (phase diagram and spontaneous magnetization) of a cylindrical Ising nanotube. Using a two-layer Ising model and the core-shell concept, the interactions within nanotube has been modelled. In the model, both ferromagnetic and antiferromagnetic cases have been considered. Furthermore, the effect of nanotube's length on the critical temperature is investigated. The model has been simulated using cellular automata approach and phase diagrams were constructed for different values of inter- and intra-layer couplings. For the antiferromagnetic case, the possibility of existence of compensation point is observed.

Monte Carlo Study of Magnetic Properties of Mixed Spins in a Fullerene X30Y30-Like Structure

In this work, inspiring form of the fullerene-C60 structures, we study the mixed $$ X_{30} Y_{30} $$ fullerene-like structure and investigate its magnetic properties. In a such a structure, the carbons are assumed to be replaced by magnetic atoms having spin moments σ = 1/2 and S = 1. Firstly, we elaborate the ground-state phase diagrams in different physical parameter planes. In a second stage, we investigate the exchange coupling interaction effects in the absence or presence of both external magnetic and crystal fields. Using the Monte Carlo method, we carried out a study of the system magnetic properties and the thermal behavior of such a system for the ferromagnetic case. It is found that the critical temperature increases when increasing the coupling exchange interactions. On the other hand, the coercive magnetic field increases also when increasing the coupling exchange interactions. However, this physical parameter decreases when increasing the reduced temperature.

Quantum thermodynamics with local control.

We investigate the limitations that emerge in thermodynamic tasks as a result of having local control only over the components of a thermal machine. These limitations are particularly relevant for devices composed of interacting many-body systems. Specifically, we study protocols of work extraction that employ a many-body system as a working medium whose evolution can be driven by tuning the on-site Hamiltonian terms. This provides a restricted set of thermodynamic operations, giving rise to alternative bounds for the performance of engines. Our findings show that those limitations in control render it, in general, impossible to reach Carnot efficiency; in its extreme ramification it can even forbid to reach a finite efficiency or finite work per particle. We focus on the one-dimensional Ising model in the thermodynamic limit as a case study. We show that in the limit of strong interactions the ferromagnetic case becomes useless for work extraction, while the antiferromagnetic case improves its performance with the strength of the couplings, reaching Carnot in the limit of arbitrary strong interactions. Our results provide a promising connection between the study of quantum control and thermodynamics and introduce a more realistic set of physical operations well suited to capture current experimental scenarios.

Spin-resolved inelastic electron scattering by spin waves in noncollinear magnets

Topological non-collinear magnetic phases of matter are at the heart of many proposals for future information nanotechnology, with novel device concepts based on ultra-thin films and nanowires. Their operation requires understanding and control of the underlying dynamics, including excitations such as spin-waves. So far, no experimental technique has attempted to probe large wave-vector spin-waves in non-collinear low-dimensional systems. In this work, we explain how inelastic electron scattering, being suitable for investigations of surfaces and thin films, can detect the collective spin-excitation spectra of non-collinear magnets. To reveal the particularities of spin-waves in such non-collinear samples, we propose the usage of spin-polarized electron-energy-loss spectroscopy augmented with a spin-analyzer. With the spin-analyzer detecting the polarization of the scattered electrons, four spin-dependent scattering channels are defined, which allow to filter and select specific spin-wave modes. We take as examples a topological non-trivial skyrmion lattice, a spin-spiral phase and the conventional ferromagnet. Then we demonstrate that, counter-intuitively and in contrast to the ferromagnetic case, even non spin-flip processes can generate spin-waves in non-collinear substrates. The measured dispersion and lifetime of the excitation modes permit to fingerprint the magnetic nature of the substrate.

Dirac Magnons in Honeycomb Ferromagnets

The discovery of the Dirac electron dispersion in graphene led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching, the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of the Van der Waals-bonded stacks of honeycomb layers, e.g chromium trihalides CrX3 (X = F, Cl, Br and I), that display two spin wave modes with energy dispersion similar to that for the electrons in graphene. At the single particle level, these materials resemble their fermionic counterparts. However, how different particle statistics and interactions affect the stability of Dirac cones has yet to be determined. To address the role of interacting Dirac magnons, we expand the theory of ferromagnets beyond the standard Dyson theory to a case of non-Bravais honeycomb layers. We demonstrate that magnon-magnon interactions lead to a significant momentum-dependent renormalization of the bare band structure in addition to strongly momentum-dependent magnon lifetimes. We show that our theory qualitatively accounts for hitherto unexplained anomalies in a nearly half century old magnetic neutron scattering data for CrBr3. We also show that honeycomb ferromagnets display dispersive surface and edge states, unlike their electronic analogs.

Spin‐1 Bose Hubbard Model with Nearest Neighbour Extended Interaction

AbstractA spinor () Bose gas is studied in presence of a density‐density interaction through a mean field approach and a perturbation theory for either sign of the spin dependent interaction, namely the antiferromagnetic (AF) and the ferromagnetic cases. In the AF case, the charge density wave (CDW) phase appears to be sandwiched between the Mott insulating (MI) and the supersolid phases for small values of the extended interaction strength. But the CDW phase completely occupies the MI lobe when the extended interaction strength is larger than a certain critical value related to the width of the MI lobes and hence opens up the possibilities of spin singlet and nematic CDW insulating phases. In the ferromagnetic case, the phase diagram shows similar features as that of the AF case and are in complete agreement with a spin‐0 Bose gas. The perturbation expansion calculations nicely corroborate the mean field phase results in both these cases. Further, we extend our calculations in presence of a harmonic confinement and obtained the momentum distribution profile that is related to the absorption spectra in order to distinguish between different phases.

Nonlinear electric and thermoelectric Andreev transport through a hybrid quantum dot coupled to ferromagnetic and superconducting leads

We discuss the nonlinear Andreev current of an interacting quantum dot coupled to spin-polarized and superconducting reservoirs when voltage and temperature biases are applied across the nanostructure. Due to the particle-hole symmetry introduced by the superconducting (S) lead, the subgap spin current vanishes identically. Nevertheless, the Andreev charge current depends on the degree of polarization in the ferromagnetic (F) contact since the shift of electrostatic internal potential of the conductor depends on spin orientation of the charge carrier. This spin-dependent potential shift characterizes nonlinear responses in our device. We show how the subgap current versus the bias voltage or temperature difference depends on the lead polarization in two cases, namely (i) S-dominant case, when the dot-superconductor tunneling rate ($\Gamma_R$) is much higher than the ferromagnet-dot tunnel coupling ($\Gamma_L$), and (ii) F-dominant case, when $\Gamma_L\gg \Gamma_R$. For the ferromagnetic dominant case the spin-dependent potential shows a nonmonotonic behavior as the dot level is detuned. Thus the subgap current can also exhibit interesting behaviors such as current rectification and the maximization of thermocurrents with smaller thermal biases when the lead polarization and the quantum dot level are adjusted.

On the motion of a magnetized rigid body

A method introduced by Yehia (J Phys A Math Gen 32:7565–7580, 1999 , for example) for generalizing known results of the problem of the motion of a rigid body is extended here to take magnetization by rotation (Barnett–London effect) into account. In the general case of anisotropic ferromagnets, the equations of motion are proved to be covariant under a one-parameter family of transformations which generalize the problem by inserting a parameter, with a definite physical meaning, into the dynamical equations. As an example, we generalize a particular solution of the problem of the motion of a gyrostat in a central field of attraction. It turns out that the generalized solution represents a new particular solution of the problem of the motion by inertia of a rigid body in an ideal incompressible fluid.

Critical phenomena in a mixed spin-3/2 and spin-5/2 Ising ferro-ferrimagnetic system in a longitudinal magnetic field

We apply Monte Carlo simulation techniques to study the magnetic behavior of a mixed Ising system on a square lattice, where spins SA=±3/2,±1/2 alternate with spins σB=±5/2,±3/2,±1/2 in two interpenetrating sublattices A and B, respectively. The Hamiltonian of the system contains an exchange interaction between nearest neighbors and a longitudinal magnetic field. In order to understand the differences between a mixed Ising system with competing interactions with one with cooperating ones, we study both cases, the ferrimagnetic and the ferromagnetic exchange interactions. We calculate the dependence of the total magnetization, the sublattice magnetizations, the energy, and the magnetic susceptibility, with the magnetic field, and their temperature dependence for a fixed field. We found that under the influence of the magnetic field the ferrimagnetic system presents an interesting phenomena associated with a reversal of the sublattice magnetizations at low temperatures. We found that our system has no compensation temperatures. In both, the ferri and the antiferromagnetic cases, the magnetic field smooths the transition between the ordered and the paramagnetic phase. Finally we present a phase diagram with the critical temperatures in terms of the magnetic field for the ferri and ferromagnetic cases.

Entanglement and coherence in a spin-s XXZ system under non-uniform fields

We investigate entanglement and coherence in an XXZ spin s pair immersed in a non-uniform transverse magnetic field. The ground state and thermal entanglement phase diagrams are analyzed in detail in both the ferromagnetic and antiferromagnetic cases. It is shown that a non-uniform field can control the energy levels and the entanglement of the corresponding eigenstates, making it possible to entangle the system for any value of the exchange couplings, both at zero and finite temperatures. Moreover, the limit temperature for entanglement is shown to depend only on the difference between the fields applied at each spin, leading for to a separability stripe in the field plane such that the system becomes entangled above a threshold value of . These results are demonstrated to be rigorously valid for any spin s. On the other hand, the relative entropy of coherence in the standard basis, which coincides with the ground state entanglement entropy at T = 0 for any s, becomes non-zero for any value of the fields at , decreasing uniformly for sufficiently high T. A special critical point arising at T = 0 for non-uniform fields in the ferromagnetic case is also discussed.