Isotropic Heisenberg Exchange Interaction Research Articles

The magnetic susceptibility of Mn<sub>3</sub>Sn single crystal is enhanced under GPa-level uniaxial stress

At room temperature, controlling the spin of noncollinear antiferromagnetic Mn<sub>3</sub>Sn presents a challenge. In this study, we modulate the magnetic structure by subjecting Mn<sub>3</sub>Sn single crystals to GPa-level uniaxial stress using a high-pressure binding deformation approach. Initially, the single crystal is sliced into regular cuboids, then embedded in a stainless steel sleeve, and finally, uniaxial stress is applied along the [01<span style="text-decoration:overline">2</span>0] and [01<span style="text-decoration:overline">1</span>0] directions of the Mn<sub>3</sub>Sn single crystal. Under high stress, the single crystal undergoes plastic deformation. Our observations reveal lattice distortion in the deformed single crystal, with the lattice parameter gradually decreasing as the stress level increases. In addition, the magnetic susceptibility of Mn<sub>3</sub>Sn under GPa uniaxial stress (<i>χ</i>) is different from that under MPa uniaxial stress, and its value is no longer fixed but increases with the increase of stress. When 1.12 GPa stress is applied in [01<span style="text-decoration:overline">2</span>0] direction, <i>χ</i> reaches 0.0203 <i>μ</i><sub>B</sub> f.u.<sup>-1</sup>T<sup>-1</sup>, which is 1.42 times that of the undeformed sample. In the case of stress applied along the [01<span style="text-decoration:overline">1</span>0] direction, <i>χ </i>≈ 0.0332 <i>μ</i><sub>B</sub> f.u.<sup>-1</sup>T<sup>-1</sup> when the stress is 1.11 GPa. This result is also 2.66 times greater than the reported results. We further calculate the trimerization parameter (<i>ξ</i>), isotropic Heisenberg exchange interaction (<i>J</i>), and anisotropic energy (<i>δ</i>) of the system under different stresses. Our results show that <i>ξ</i> gradually increases, <i>J</i> gradually decreases, and <i>δ</i> gradually increases with the increase of stress. These results show that the GPa uniaxial stress introduces anisotropic strain energy into the single crystal, breaking the symmetry of the in-plane hexagon of the kagome lattice, which causes the bond length of the two equilateral triangles composed of Mn atoms to change. Thus, the exchange coupling between Mn atoms in the system is affected, the anisotropy of the system is enhanced, and the antiferromagnetic coupling of the system is enhanced. Therefore, the system <i>χ </i>is no longer a constant value and gradually increases with the increase of stress. This discovery will provide new ideas for anti-ferromagnetic spin regulation.

Spin-based quantum Otto engines and majorization

The concept of majorisation is explored as a tool to characterize the performance of a quantum Otto engine in the quasi-static regime. For a working substance in the form of a spin of arbitrary magnitude, majorisation yields a necessary and sufficient condition for the operation of the Otto engine, provided the canonical distribution of the working medium at the hot reservoir is majorised by its canonical distribution at the cold reservoir. For the case of a spin-1/2 interacting with an arbitrary spin via isotropic Heisenberg exchange interaction, we derive sufficient criteria for positive work extraction using the majorisation relation. Finally, local thermodynamics of spins as well as an upper bound on the quantum Otto efficiency is analyzed using the majorisation relation.

Quantum Heat Engines with Complex Working Media, Complete Otto Cycles and Heuristics.

Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.

Orbitally-resolved ferromagnetism of monolayer CrI3

Few-layer CrI3 is the most known example among two-dimensional (2D) ferromagnets, which have attracted growing interest in recent years. Despite considerable efforts and progress in understanding the properties of 2D magnets both from theory and experiment, the mechanism behind the formation of in-plane magnetic ordering in chromium halides is still under debate. Here, we propose a microscopic orbitally-resolved description of ferromagnetism in monolayer CrI3. Starting from first-principles calculations, we construct a low-energy model for the isotropic Heisenberg exchange interactions. We find that there are two competing contributions to the long-range magnetic ordering in CrI3: (i) Antiferromagnetic Anderson’s superexchange between half-filled t2g orbitals of Cr atoms; and (ii) Ferromagnetic exchange governed by the Kugel–Khomskii mechanism, involving the transitions between half-filled t2g and empty eg orbitals. Using numerical calculations, we estimate the exchange interactions in momentum-space, which allows us to restore the spin-wave spectrum, as well as estimate the Curie temperature. Contrary to the nearest-neighbor effective models, our calculations suggest the presence of sharp resonances in the spin-wave spectrum at 5–7 meV, depending on the vertical bias voltage. Our estimation of the Curie temperature in monolayer CrI3 yields 55–65 K, which is in good agreement with experimental data.

Two-dimensional Magnetism in κ-(BEDT-TTF)2Cu[N(CN)2]Cl, a Spin-1/2 Heisenberg Antiferromagnet with Dzyaloshinskii–Moriya Interaction

The finite phase transition temperature, T-N, of quasi two-dimensional (2D) Heisenberg antiferromagnetic (AF) crystals results from in-plane anisotropy or coupling between layers. It is usually not known which is the determining factor when both are weak. We show by an electron spin resonance experiment that in the quasi 2D antiferromagnetic crystal,kappa-(BEDT-TTF)(2)Cu[N(CN)(2)] Cl, TN is determined by in-plane anisotropy while interlayer coupling plays a minor role. The compound has a large isotropic Heisenberg exchange interaction between sites with S = 1/2 spins. The Dzyaloshinskii-Moriya (DM) interaction is the main source of anisotropy, while in-plane anisotropy and the interlayer coupling are very weak. The external-field field-induced static and fluctuating AF magnetizations are independent in adjacent layers above the (zero-field) ordering temperature.

Stability of Skyrmions in discrete arrays of spins with Heisenberg and truncated RKKY-interaction and single-spin anisotropy

In two-dimensional discrete classical spin arrays subject to ferromagnetic nearest-neighbour isotropic Heisenberg exchange interaction and single-spin anisotropy D localised single excitations of Skyrmion-type are studied. Following Abanov and Pokrovsky (AP) [Ar. Abanov, V.L. Pokrovsky, Phys. Rev. 58 (1998) R8889], also RKKY interaction is simulated by including antiferromagnetic next-nearest-neighbour interaction. Their stability is tested numerically by letting their energy relax. For the isotropic case ( D=0), the narrowing of single Skyrmions with larger radius is very slow. Excitations with easy axis anisotropy shrink in size much faster than in the isotropic case, whereas excitations with easy plane anisotropy are stable. Already RKKY interaction truncated to AF next-nearest-neighbour interaction stabilises Skyrmions to distinct radius in agreement with (AP), including also D=0 beyond their treatment.

Magnetic structure and spin waves in the Kagomé jarosite compoundKFe3(SO4)2(OH)6

We present a detailed study of the magnetic structure and spin waves in the Fe jarosite compound ${\rm KFe_3(SO_4)_2(OH)_6}$ for the most general Hamiltonian involving one- and two-spin interactions which are allowed by symmetry. We compare the calculated spin-wave spectrum with the recent neutron scattering data of Matan {\it et al.} for various model Hamiltonians which include, in addition to isotropic Heisenberg exchange interactions between nearest ($J_1$) and next-nearest ($J_2$) neighbors, single ion anisotropy and Dzyaloshinskii-Moriya (DM) interactions. We concluded that DM interactions are the dominant anisotropic interaction, which not only fits all the splittings in the spin-wave spectrum but also reproduces the small canting of the spins out of the Kagom\'e plane. A brief discussion of how representation theory restricts the allowed magnetic structure is also given.

Impurity induced midgap state and magnetism in spin-Peierls systems

Effects of impurities on the spin-Peierls systems are investigated by using fermion representation of spin operators within the continuum limit approximation. We use XY model instead of the isotropic Heisenberg exchange interaction. The Bogoliubov–de Gennes-type equations are solved on the assumption that an impurity changes the spin–lattice coupling at the impurity site. It is shown that midgap bound states are formed. The lattice distortion is reduced around the impurities and its spatial dependence is expressed by a composition of parts of the soliton solution in polyacetylenes. There are a few possible impurity states depending on the total S z , which is determined by the filling of the midgap states. Uniform magnetic moments will be finite around impurities. These results are compared with the results of previous theoretical studies based on the bosonized phase Hamiltonian. Since the previous works are for the isotropic Heisenberg exchange interaction, the behavior of the magnetic moments around the impurity is different from the present case.

Zero-field time correlation functions of four classical Heisenberg spins on a ring

A model relevant for the study of certain molecular magnets is the ring of N=4 classical spins with equal near-neighbor isotropic Heisenberg exchange interactions. Assuming classical Heisenberg spin dynamics, we solve explicitly for the time evolution of each of the spins. Exact triple integral representations are derived for the auto, near-neighbor, and next-nearest-neighbor time correlation functions for any temperature. At infinite temperature, the correlation functions are reduced to quadrature. We then evaluate the Fourier transforms of these functions in closed form, which are double integrals. At low temperatures, the Fourier transform functions explicitly demonstrate the presence of magnons. Our exact results for the infinite temperature correlation functions in the long-time asymptotic limit differ qualitatively from those obtained assuming diffusive spin dynamics. Whether such explicitly non-hydrodynamic behavior would be maintained for large-N rings is discussed.

Monte Carlo study of fractional (1 1 1) monolayers of EuTe

The magnetic properties depending on the temperature and magnetic field of few (1 1 1) monolayers of antiferromagnetic EuTe are analyzed by means of Monte Carlo simulations. We apply a classical Heisenberg as well as a XY model Hamiltonian with ferromagnetic nearest neighbor ( J 1=0.06 K) and antiferromagnetic next-nearest-neighbor ( J 2=−0.16 K) exchange constants. Furthermore, dipolar interaction is included which links the spin space to real space and therefore introduces the easy plane anisotropy. Structures consisting of incomplete sets of monolayers, e.g. two perfect monolayers and a finite island as the third monolayer, are investigated. We analyze the atomic spin patterns and compare these results with total magnetization and neutron diffraction experiments. It is emphasized that EuTe in the reduced dimensional limit of few odd numbers of monolayers exhibits a field-induced uniaxial anisotropy, even in the frame of isotropic Heisenberg exchange interaction. A concomitant field-parallel ferrimagnetic order is sustained up to a field H ap.

Magnetism and spin dynamics in the cluster compound[Cr4S(O2CCH3)8(H2O)4](NO3)2⋅H2O

The magnetism and spin dynamics of [Cr{sub 4}S(O{sub 2}CCH{sub 3}){sub 8}(H{sub 2}O){sub 4}](NO{sub 3}){sub 2}{center_dot}H{sub 2}O have been investigated by magnetic susceptibility and proton NMR measurements and by theoretical calculations. The proton-spin lattice relaxation rate 1/T{sub 1}, as a function of the temperature T and external magnetic field B, provides a very useful probe of the dynamical behavior of the four Cr{sup +3} (spins s=(3/2)) paramagnetic ions which are ferromagnetically coupled via isotropic Heisenberg exchange interaction. From our derived formulas for the two-ion time correlation functions, we find that 1/T{sub 1} may be expressed as a function of the single scaling variable {mu}{sub B}B/(k{sub B}T), where {mu}{sub B} is the Bohr magneton and k{sub B} is Boltzmann's constant, for the regime of our measurements. Our experimental data are in good agreement with this prediction and our derived form of the scaling function. (c) 2000 The American Physical Society.

Exact solutions for simple spin clusters with isotropic Heisenberg exchange interactions

On passe en revue les configurations de spins pour lesquelles l'Hamiltonien d'echange de Heisenberg peut etre diagonalise exactement par des techniques simples de recouplage des moments cinetiques. Cette methode, deja utilisee pour des configurations de n≤4 spins, est systematiquement developpee jusqu'a 9 spins. On montre qu'elle peut egalement s'appliquer a des ions ayant des facteurs g isotropes differents. On donne une expression simplifiee de la susceptibilite magnetique dont on discute la precision

MODE-COUPLING APPROACH TO THE SPIN DYNAMICS OF EUROPIUM COMPOUNDS

The results of a numerical solution of the mode-coupling equations for EuO and EuS taking into account the microscopical properties of the compounds are presented. Good agreement with the available neutron scattering data is found and predictions for further experiments on EuS are given. The results of high resolution neutron scattering experiments on insulating ferromagnetic Europium compounds EuO and EuS appeared in literature in recent years [I-41. The particular attention devoted to such compounds, is due to the fact that already in the earlier neutron scattering comprehensive investigation on E n 0 and EuS [I] it was shown that the magnetic behaviour of these systems is very well described by a simple isotropic Heisenberg exchange interaction. The availability of experimental data at and above the ordering temperature Tc has encouraged a renewal of theoretical studies on critical and paramagnetic spin fluctuations in Heisenberg ferromagnets. The most successful theories appear to be those ones based on Renormalization Group (RG) or on the mode-coupling approximation. RG techniques constitute a well established method to study the static and dynamic critical properties of a system; they allow to evaluate critical exponents as well as universal functions which characterize the critical behaviour. Very recently an attempt has been made to extend RG calculations to temperatures above Tc [5], but some problems persist to make possible a quantitative comparison with experimental data. The mode coupling approximation, in spite of its heuristic character, has revealed very useful in many problems of condensed matter physics [6]. For pure Heisenberg magnets, for example, it gives for the critical dynamical scaling ex,ponent z the value z = 171, in a agreement with 2 the experiments. Moreover it has been shown very recently [8] that by taking into account the dipolar macroscopic interaction, the mode-coupling theory can be able to interpret the unexpected simple exponential decay obtained in neutron spin-echo experiment on EuO at T = Tc and very small wave vector [4], which remained until now inexplicable. However the mode-coupling theory appears also suitable to investigate the dynamical behaviour of ferromagnetic systems in all the paramagnetic region and throughout the Brillouin Zone. In this paper we present the results of a numerical solution of the modecoupling equations for EuO and EuS taking into account the microscopical features of these compounds. This allows to show some distinctive characters which distinguish EuS from EuO that cannot be accounted by previous approximate solutions, which were limited to simple cubic nearest neighbours interaction [7] or confined to the continuum limit [6]. Europium compounds can be described by a Heisenberg exchange hamiltonian: I for an FCC lattice of magnetic ions with S = -. The 2 experiments [I] have shown that the interaction is restricted to nearest neighbours (J1) and next nearest neighbours (Jz ) . For EuO: J1 = 1.22' K , J2 = 0.25' K and a = 5.12 A; for EuS: J1 = 0.48' K , J2 = -0.24' K and a = 5.95 A, a being the lattice constant. The final result given by the mode-coupling theory is the following integr~differential equation: for the relaxation function Fq ( t ) , whose Fourier Transform is related to the measured scattering function S (q, w ) by the relation: W (q' W, = 1 exp (-v/KBT) .x (4) F, ( w ) . (3) Not with standing formal differences in the various derivations, behind equation (2) is the following fundamental approximation: correlation and relaxation functions among more than two spin operators have been decoupled. Equation (2) is only one of the forms in which this equation is obtained, however all such forms are equivalent if we use for the static susceptibility that one given by the spherical model: Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888720 C8 1572 JOURNAL DE PHYSIQUE This susceptibility turns out to be compatible with the dynamical equation (2). The temperature dependent parameter X appearing in equation (4) can be evaluated by using the sum rule: (I/N) C T X ~ = s(S + 1) /3.

Magnetization and magnetic excitations in HoAl2

The magnetization of HoAl2 single crystals parallel and perpendicular to the applied field for three crystallographic directions has been measured between 4.2 and 300 K in fields up to 8 T. Further the spin wave excitations were investigated by inelastic neutron scattering at 5.2 K along , and directions in reciprocal space. The results are interpreted consistently in terms of a cubic crystal field using a simple molecular field to calculate the magnetization and an isotropic Heisenberg exchange interaction to obtain the magnetic excitations.

Crystal-field excitations in ferromagnetic NdAl 2

By means of neutron inealastic scattering we measured the dispersion of magnetic excitations in ferromagnetic NdAl 2 at 4.2 K for wave-vectors along the 〈001〉 direction. 3 acoustic and 3 optic branches and partly a fourth optic branch have been resolved. The experiments are well described in terms of a cubic crystal field and an isotropic Heisenberg exchange interaction.

Dispersion relations for magnetic excitons in NdAl2

The magnetic excitation spectrum in NdAl2 has been measured by means of inelastic neutron scattering at 5.3K for momentum transfer in the (110) direction. Several excitation branches are observed and discussed in terms of a hamiltonian including an isotropic Heisenberg exchange interaction and a cubic crystalline electric field. The spectrum is interpreted as comprising of six excitation modes four of which are transverse spin-wave-like excitations (two acoustic and two optical). The remaining two excitations are longitudinal in character (acoustic and optical). The authors obtain values for both the exchange interaction and the crystal-field parameters.