Dzyaloshinskii-Moriya Coupling Research Articles

Non-equilibrium magnetic interactions in strongly correlated systems

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name twist exchange, which formally resembles Dzyaloshinskii–Moriya coupling, but is not due to spin–orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well.

Chirality selection in the vortex state of magnetic nanodisks with a screw dislocation

Structural defects in magnetic crystalline materials may locally change magnetic properties and can significantly influence the behavior of magnetic nanostructures. E.g., surface-induced Dzyaloshinskii-Moriya in- teractions can strongly a ect vortex structures in magnetic nanodisks causing a chirality selection. Near lattice defects, the spin-orbit interactions induce local antisymmetric Dzyaloshinskii-Moriya exchange and cause eec- tive anisotropies, which can result in spin canting. Broken inversion symmetry near a defect leads to locally chiral exchange. We present a phenomenological approach for dislocation-induced Dzyaloshinskii-Moriya couplings. As an example we investigate eects of a screw dislocation at the center of a magnetic nanodisk with a vortex state. By numerical calculations on vortex profiles we analyze equilibrium parameters of the vortex as functions of applied magnetic field and the material and geometrical parameters. It is proposed that magnetic nanodisks with defects provide a suitable experimental setting to study induced chirality by spin-orbit eects.

Ab initio study on magnetism and pressure-induced transitions in cubic MnGe

State of the art density functional theory (DFT) calculations within the generalized gradient approximation (GGA) are reported for the (metastable) cubic MnGe with chiral B20 structure under applied pressure. It is found that the ambient pressure metallic (nominally) ferromagnetic high spin state (2 μB/ f.u.) in MnGe undergoes a transition into a low spin state (1 μB/ f.u.). From the calculations, the pressure at this first-order transition is about 18 GPa. The low moment state is halfmetallic, i.e., a small band-gap opens in the density of states for the majority spin electrons at the Fermi edge. Calculations for decreasing lattice parameter show that a fully metallic ferromagnetic low spin state should be recovered, before at still higher pressures the magnetic moment collapses and a non-spin polarized state arises. For the zero, low and high spin states, the equation of state has been determined. As the non-centrosymmetric crystal structure enables chiral Dzyaloshinskii-Moriya couplings, the magnetic order in MnGe is long-period modulated. The theoretical results suggest that half-metallic transport properties could be observed on the background of chiral complex spin-structures in MnGe under presssure or in strained thin films.

Order in a spatially anisotropic triangular antiferromagnet

The phase diagram of the spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice of weakly coupled chains, a model relevant to Cs2CuCl4, is investigated using a renormalization group analysis, which includes marginal couplings important for connecting to numerical studies of this model. In particular, the relative stability of incommensurate spiral spin-density order and collinear antiferromagnetic order is studied. While incommensurate spiral order is found to exist over most of the phase diagram in the presence of a Dzyaloshinskii-Moriya (DM) interaction, at small interchain and extremely weak DM couplings, collinear antiferromagnetic order can survive. Our results imply that Cs2CuCl4 is well within the part of the phase diagram where spiral order is stable. The implications of the renormalization group analysis for numerical studies, many of which have found spin-liquidlike behavior, are discussed.

Destruction of valence-bond order in aS=12sawtooth chain with a Dzyaloshinskii-Moriya term

A small value of the spin gap in quantum antiferromagnets with strong frustration makes them susceptible to nominally small deviations from the ideal Heisenberg model. One such perturbation, the anisotropic Dzyaloshinskii-Moriya (DM) interaction, is an important perturbation for the $S=1/2$ kagome antiferromagnet, one of the current candidates for a quantum-disordered ground state. We study the influence of the DM term in a related one-dimensional system, the sawtooth chain, which has valence-bond order in its ground state. Through a combination of analytical and numerical methods, we show that a relatively weak DM coupling, $0.115J$, is sufficient to destroy the valence-bond order, close the spin gap, and turn the system into a Luttinger liquid with algebraic spin correlations. A similar mechanism may be at work in the kagome antiferromagnet.

Entanglement in a two-qubit Heisenberg XXZ chain with different Dzyaloshinskii-Moriya couplings and an inhomogeneous magnetic field

Ground state entanglement and thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of the different Dzyaloshinski-Moriya interaction and inhomogeneous magnetic field are investigated. By the concept of concurrence, we find that the inhomogeneity of the magnetic field may make entanglement last for a long time and the critical temperature is dependent on Jz and b. The entanglement can be increased by increasing the temperature in some cases. We also find that the x-component parameter Dx has a higher critical temperature and more entanglement for a certain condition than the z-component parameter Dz.

Influence of the Dzyaloshinskii-Moriya interaction on vortex states in magnetic nanodisks

Curling magnetic vortices with chiral rotation sense and polarity of the core magnetization can exist in magnetic circular nanostructures. Broken mirror symmetry at surfaces/interfaces of magnetic nanostructures induces chiral Dzyaloshinskii-Moriya interactions which may strongly affect the magnetic properties. Using a micromagnetic approach, we investigate the influence of these chiral interactions on the vortex states in magnetic nanodisks. We calculate numerically the shape, size, and stability of the vortices in equilibrium as functions of magnetic field and the material and geometrical parameters. As a result, under the influence of the chiral magnetic interactions vortices of opposite chirality should have different sizes. We provide detailed numerical analysis of this effect, which can be applied to measure the strength of the induced Dzyaloshinskii-Moriya coupling in magnetic thin film elements.

Theory of vortex states in magnetic nanodisks with induced Dzyaloshinskii-Moriya interactions

Broken inversion symmetry in magnetic nanostructures induces Dzyaloshinskii-Moriya couplings. In the presence of surfaces/interfaces the magnetism of magnetic nanodisks can be essentially affected by these chiral couplings. Within a micromagnetic approach we calculate the equilibrium sizes and shape of the vortices as functions of magnetic field, the material, and the geometrical parameters of nanodisks. It was found that the Dzyaloshinskii-Moriya coupling can considerably increase sizes of vortices with ``right'' chirality and suppress vortices with opposite chirality. This allows to form a bistable system of vortices with the same chirality as a basic element for storage applications.

Quantum phase transition induced by Dzyaloshinskii-Moriya interactions in the kagome antiferromagnet

We argue that the $S=1/2$ kagome antiferromagnet undergoes a quantum phase transition when the Dzyaloshinskii-Moriya coupling is increased. For $D<{D}_{c}$ the system is in a moment-free phase, and for $D>{D}_{c}$ the system develops antiferromagnetic long-range order. The quantum critical point is found to be ${D}_{c}\ensuremath{\simeq}0.1J$ using exact diagonalizations and finite-size scaling. This suggests that the kagome compound ${\text{ZnCu}}_{3}{(\text{OH})}_{6}{\text{Cl}}_{3}$ may be in a quantum critical region controlled by this fixed point.

Spin-orbit effects inNa4Ir3O8: A hyper-kagome lattice antiferromagnet

We consider spin-orbit coupling effects in ${\text{Na}}_{4}{\text{Ir}}_{3}{\text{O}}_{8}$, a material in which ${\text{Ir}}^{4+}$ spins form an hyper-kagome lattice, a three-dimensional network of corner-sharing triangles. We argue that both low-temperature thermodynamic measurements and the impurity susceptibility induced by dilute substitution of Ti for Ir are suggestive of significant spin-orbit effects. Because of uncertainties in the crystal-field parameters, we consider two limits in which the spin-orbit coupling is either weak or strong compared to the noncubic atomic splittings. A semi-microscopic calculation of the exchange Hamiltonian confirms that indeed large antisymmetric Dzyaloshinskii-Moriya (DM) and/or symmetric exchange anisotropy may be present. In the strong spin-orbit limit, the Ir-O-Ir superexchange contribution consists of unfrustrated strong symmetric exchange anisotropy, and we suggest that spin-liquid behavior is unlikely. In the weak spin-orbit limit, and for strong spin-orbit and direct Ir-Ir exchange, the Hamiltonian consists of Heisenberg and DM interactions. The DM coupling is parametrized by a three-component DM vector (which must be determined empirically). For a range of orientation of this vector, frustration is relieved and an ordered state occurs. For other orientations, even the classical ground states are very complex. We perform spin-wave and exact diagonalization calculations, which suggest the persistence of a quantum spin liquid in the latter regime. Applications to ${\text{Na}}_{4}{\text{Ir}}_{3}{\text{O}}_{8}$ and broader implications are discussed.

Mutual information and swap operation in the two-qubit Heisenberg model withDzyaloshinskii–Moriya anisotropic antisymmetric interaction

Mutual information and swap operation in the two-qubit Heisenbergmodel with the Dzyaloshinskii–Moriya (DM) anisotropic antisymmetricinteraction are investigated. It is found that the mutual informationI of such a quantum channel is sensitive to the initial conditions and declines with increase intemperature. The DM interaction can lead to higher mutual information, especially for theferromagnetic case. The entanglement quality of input states cannot enhance the mutualinformation of the quantum channel. When the DM interaction is large, the mutualinformation will have the maximum value of 2 for a non-entangled input state,but it is 1 for a maximally entangled input state. It is also shown that the swapoperation can be implemented for some kinds of DM coupling. The conditionsof the DM coupling under which the swap operation is feasible are established.

Interplay between the Dzyaloshinskii–Moriya anisotropic antisymmetric interaction and the SWAP operation in a two-qubit Heisenberg model

The SWAP operation in a two-qubit Heisenberg model in the presence of Dzyaloshinskii-Moriya (DM) anisotropic antisymmetric interaction is investigated. 1t is shown that the SWAP operation can be implemented for some kinds of DM coupling and the influence of DM couplings is divided into different cases. The conditions of the DM coupling under which the SWAP operation is feasible are established. (C) 2007 Elsevier B.V. All rights reserved.

Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets

A phenomenological theory of magnetic states in noncentrosymmetric tetragonal antiferromagnets is developed, which has to include homogeneous and inhomogeneous terms (Lifshitz invariants) derived from Dzyaloshinskii-Moriya couplings. Magnetic properties of this class of antiferromagnets with low crystal symmetry are discussed in relation to the recently detected compounds ${\mathrm{Ba}}_{2}{\mathrm{CuGe}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{K}}_{2}{\mathrm{V}}_{3}{\mathrm{O}}_{8}.$ Crystallographic symmetry and magnetic ordering in these systems allow the simultaneous occurrence of chiral inhomogeneous magnetic structures and weak ferromagnetism. Incommensurate magnetic structures, chiral helices, with a rotation of the staggered magnetization accompanied by oscillations of the total magnetization, are possible. Field-induced reorientation transitions into modulated states have been studied and corresponding phase diagrams are constructed. Structures of magnetic defects (domain-walls and vortices) are discussed. In particular, vortices, i.e., localized nonsingular line defects, are stabilized by inhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosymmetric antiferromagnets.

Electron paramagnetic resonance with parallel pumping in quantum spin chains with field-induced spin gap

Recently several compounds were observed to reveal properties of a one-dimensional spin-$\frac{1}{2}$ antiferromagnetic Heisenberg chain with gapless low-lying spin excitations in an absence of an external magnetic field. However even a very weak external magnetic field yields an onset of a spin gap for those low-lying excitations. Usually this onset of a field-induced spin gap is related to the presence of a staggered Dzyaloshinskii-Moriya interaction, or to the staggered effective g factors of magnetic ions. Experiments on thermodynamic properties cannot distinguish between those two origins for the spin-gap formation. Here we propose the setup for an experiment, in which one can clearly distinguish between the staggered Dzyaloshinskii-Moriya coupling and staggered external magnetic field: an electronic paramagnetic resonance in the parallel pumping geometry. The characteristics of the system under conditions of such an experiment, i.e., the renormalization of the homogeneous and staggered magnetizations, power of the microwave magnetic field, absorbed by the system, are calculated. Several important features of the solution are discussed.

Spin-1/2 Periodic Nonuniform XX Chains and the Spin-Peierls Instability

Since the discovery of the inorganic spin-Peierls compound CuGeO3 the interest in the properties of spin-Peierls systems considerably increased [1]. The models that can be examined exactly play an important role in clarifying the generic features of such systems. An example of such a model is the spin-i XX chain that was studied in several papers [2-4] (note, however, that in the non-adiabatic limit such a spin chain does not permit exact analysis [5]). The aim of the present study is to examine the influence of an additional Dzyaloshinskii–Moriya coupling on the spin-Peierls dimerization. The presence of such a term for CuGeO3 was proposed in [6, 7]. The multisublattice spin-1/2 XX chain with the Dzyaloshinskii–Moriya interaction was introduced in [8]. In our study we follow the idea of [2] and compare the total ground state energy of the dimerized and uniform chains. However, in contrast to previous works [2-4, 8] we use the continued-fraction representation for the one-fermion Green functions [9] that allows a natural extension of the calculations for more complicated lattice distortions having finite period. We consider N → ∞ spins 1/2 on a circle with the Hamiltonian

Critical properties of a spin glass with anisotropic Dzyaloshinskii - Moriya interaction

We study the classical n-vector spin glass with anisotropic quenched random Dzyaloshinskii - Moriya (DM) interaction. A random DM interaction with m independent and separated couplings defines a generalized gauge-glass model with a rotational symmetry and a broken global reflection invariance. It is shown that this model is in the same universality class as the random-gauge XY (`gauge glass') model. With an additional uniaxial anisotropy, a crossover from Ising-like to gauge-glass critical behaviour is found for a sufficiently large variance of the DM interaction. A new situation arises when there is correlation between the separated random DM couplings. We show that the critical behaviour of a spin glass with two correlated couplings of the anisotropic DM interaction is in a new universality class. The critical exponents and of this model are calculated at two-loop order near six dimensions. We also present a simplified and more rigorous field-theoretic analysis of the gauge-glass model.

Weak ferromagnetism and tricriticality in pure La2CuO4.

New data for the field dependent magnetization $M(H)$ of pure antiferromagnetic ${\mathrm{La}}_{2}$Cu${\mathrm{O}}_{4}$ are fitted by a theory which treats the interlayer coupling using mean-field theory (MFT), and includes the Dzyaloshinskii-Moriya coupling. The fits yield a novel measure of the two-dimensional (2D) staggered susceptibility ${\ensuremath{\chi}}_{2\mathrm{D}}^{\ifmmode\dagger\else\textdagger\fi{}}$, which deviates below 360 K from the 2D Heisenberg model. The fits also imply that the weak-ferromagnetic transition below the N\'eel point ${T}_{N}$ is weakly first order, with a tricritical point close to ${T}_{N}$. The MFT nicely reproduces the order parameter and the cusp in $\ensuremath{\chi}=\frac{\mathrm{dM}}{\mathrm{dH}}$.

Magnetotransport in Ni 71Mn 29 as a function of magnetic and atomic ordering

The low temperature (4.2 K) magnetic state of a Ni 71Mn 29 alloy is investigated by resistivity and magnetoresistance measurements, after cooling in field or in zero field, for different statesof atomic order. Our data are consistent with but complementary to previous NMR, magnetization and susceptibility results. They provide evidence that, besides the well-known negative magnetoresistance characteristic of spin-glasses, additional odd terms in the field are present. These new terms may be understood in terms of the unidirectional anisotropy induced by Dzyaloshinskii-Moriya couplings. For the 800°C quenched state we find also very strong irreversibility effects associated with the external applied field; this is in contrast to the perfectly reversible magnetization behaviour observed up to 12 kG.