Skyrmion dynamics in single-hole Néel ordered doped two-dimensional antiferromagnets with arbitrary spin

We develop an effective theory to study the skyrmion dynamics in the presence of a hole (removed spins from the lattice) in Néel ordered two-dimensional antiferromagnets with arbitrary spin value S. The general equation of motion for the “mass center” of this structure is obtained. The frequency of small amplitude oscillations of pinned skyrmions around the defect center is calculated. It is proportional to the hole size and inversely proportional to the square of the skyrmion size.     

Theoretical estimates for proton-NMR spin–lattice relaxation rates of heterometallic spin rings

Heterometallic molecular chromium wheels are fascinating new magnetic materials. We reexamine the available experimental susceptibility data on MCr₇ wheels in terms of a simple isotropic Heisenberg Hamiltonian for M=Fe, Ni, Cu, and Zn and find in that FeCr₇ needs to be described with an iron–chromium exchange that is different from all other cases. In a second step we model the behavior of the proton spin lattice relaxation rate as a function of applied magnetic field for low temperatures as it is measured in nuclear magnetic resonance (NMR) experiments. It appears that CuCr₇ and NiCr₇ show an unexpectedly reduced relaxation rate at certain level crossings.     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

Ground-state long-range order in quasi-one-dimensional Heisenberg quantum antiferromagnets: high-order coupled-cluster calculations

We investigate the ground-state magnetic long-range order of quasi-one-dimensional quantum Heisenberg antiferromagnets for spin quantum numbers s = 1/2 and s = 1. We use the coupled cluster method to calculate the sublattice magnetization and its dependence on the inter-chain coupling J_⊥. We find that for the unfrustrated spin-1/2 system, an infinitesimal inter-chain coupling is sufficient to stabilize magnetic long-range order, in agreement with results obtained by other methods. For s = 1, we find that a finite inter-chain coupling is necessary to stabilize magnetic long-range order. Furthermore, we consider a quasi one-dimensional spin-1/2 system, where a frustrating next-nearest neighbor in-chain coupling is included. We find that for stronger frustration as well, a finite inter-chain coupling is necessary to have magnetic long-range order in the ground state, and that the strength of the inter-chain coupling necessary to establish magnetic long-range order is related to the size of the spin gap of the isolated chain.     

Modified spin-wave theory for the S = 1 frustrated antiferromagnetic Heisenberg chain

We study the one-dimensional isotropic spin-1 Heisenberg magnet with antiferromagnetic nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions by using the modified spin wave theory (MSWT). The ground state energy and the singlet-triplet energy gap are obtained for several values of j, defined as the ratio of the nnn interaction constant to the nn one. We also compare two different ways of implementing the MSWT currently found in the literature, and show that, despite the remarkable differences between the equations to be solved in each procedure, the results given by both are equivalent, except for the predicted value of the j_max, the maximum value of j accessible in each treatment. Here, we suggest that j_max is related to the disorder point of the first kind. Our results show that the ground state and the gap energies increase with j, for j ≤j_max, in accordance to previous numerical results.     

Magnetization studied on spin alignments in organic molecule-based ferrimagnetics

A physics picture of spin alignments in molecule-based ferrimagnets is presented from studying the temperature dependence of the effective sublattice magnetic moments and the total reduced magnetization by means of Green’s function theory combined with the Jordan-Wigner transformation. The ferrimagnetic chain includes an S=1 biradical and an S=1/2 monoradical with antiferromagnetic alternating interactions, and the S=1 site in the chain is composed of two S=1/2 spins coupled by a finite ferromagnetic interaction. From the calculations of the sublattice magnetic moments, the magnetic moment of the S=1 biradical is negative, while that of the S=1/2 monoradical is positive, leading to a ferrimagnetic ground state. With the different kinds of the elementary excitations and the competition between the magnetic interactions and thermal fluctuations, the temperature dependence of the magnetization displays rich thermodynamic properties. Meanwhile, the external magnetic field dependence of the magnetization has a clear plateau at one third of the saturation magnetization, which can be compared with the possible experimental findings.     

Macroscopic quantum coherence of the Neel vector in antiferromagnetic system without Kramers' degeneracy

At low temperatures the Neel vector in a small antiferromagnetic particle can possess quantum coherence between the classically degenerate minima. In some cases, the topological term in the magnetic action can lead to destructive interference between the symmetry-related trajectories for the half-integer excess spin antiferromagnetic particle. By studying a macroscopic quantum coherence problem of the Neel vector with biaxial crystal symmetry and a weak magnetic field applied along the hard axis, we find that the quenching of tunnel splitting could take place in the system without Kramers' degeneracy. Both the Wentzel-Kramers-Brillouin exponent and the pre-exponential factors are found exactly for the tunnel splitting. Results show that the tunnel splitting oscillates with the weak applied magnetic field for both the integer and half-integer excess spin antiferromagnetic particles, and vanishes at certain values of the field. All the calculations are performed based on the two sublattices model and the instanton method in spin-coherent-state path integral. Received: 24 July 1997 / Accepted: 30 September 1997     

Effect of frustration on spin-wave excitation spectra and ground-state properties of the quasi-one-dimensional antiferromagnetic chain with asymmetrical sublattices

We investigate the effect of frustration on spin-wave excitation spectra and the properties of the quasi-one-dimensional Heisenberg chain using a spin-wave-wave analysis, the exact diagonalization method and the density matrix renormalization group method. The results show that frustration can cause the softening of the acoustic excitation spectrum ω₃, as well as the hardening of the optical excitation spectrum ω₁. As a function of the frustration parameter α, the phase diagram exhibits a ferromagnetic phase, a narrow canted phase and a singlet phase. The results obtained from numerical methods show that the spin gap obviously opens and the tetramer-dimer state dominates the properties of the ground state in the singlet phase.     

Thermodynamics of the spin-S antiferromagnetic Heisenberg chain

The numerical solution of the Bethe ansatz equations of an integrableSU (2)-invariant generalization of the spin-S antiferromagnetic Heisenberg chain in zero magnetic field is presented. The thermodynamics is obtained numerically. The temperature dependence of the entropy, specific heat and susceptibility is presented forS5/2. The results are compared to those of then-channel Kondo problem with a spin-S impurity withn=2S.     

Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains

The free energy and correlation lengths of the spin-1/2XYZ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all eigenvalues. Analytic results are presented for the low-temperature asymptotics, in particular for the criticalXXZ chain in an external magnetic field. These results are compared to predictions by conformal field theory. The integral equations are solved numerically for the non-criticalXXZ chain and the related spin-1 biquadratic chain at arbitrary temperature.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Thermodynamic properties of the spin-Peierls transition in CuGeO3

We present an investigation of the spin-Peierls transition atT _SP=14.5 K in polycrystalline CuGeO₃ through specific-heat and thermal-expansion measurements. Clear second-order phase-transition anomalies are found in both properties atT _SP, although only a small entropy of S0.1 Rn2 is released at the transition. Most of the entropy is released atT _SP<T<150 K, where the temperature dependence of the magnetic contribution to the specific heat as well as the thermal expansion exhibit extrema atT ^*40 K. These are caused by one-dimensional antiferromagnetic fluctuations along the Cu chains, possibly accompanied by structural fluctuations. Using Ehrenfest's relation, a hydrostatic pressure coefficient (T _SP/_p)_p0 (0.45±0.06) K/kbar is derived.     

Beam splitter for spin waves in quantum spin network

We theoretically design and analytically study a controllable beam splitter for the spin wave propagating in a star-shaped (e.g., a Y-shaped beam) spin network. Such a solid state beam splitter can display quantum interference and quantum entanglement by the well-aimed controls of interaction on nodes. It will enable an elementary interferometric device for scalable quantum information processing based on the solid system.     

Series expansion analysis of a tetrahedral cluster spin chain

Using analytical series expansion by continuous unitary transformations we study the magnetic properties of a frustrated tetrahedral spin- chain. Starting from the limit of isolated tetrahedra we analyze the evolution of the ground state energy and the elementary triplet dispersion as a function of the inter-tetrahedral coupling. The quantum phase diagram is evaluated and is shown to incorporate a singlet product, a dimer, and a Haldane phase. Comparison of our results with those from several other techniques, such as density matrix renormalization group, exact diagonalization, bond-operator theory and other numerical series expansion are provided and convincing agreement is found.     

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.     

Solitary excitations in antiferromagnet CsFeBr3

With employing the Dyson-Maleev transformation and the coherent-state ansatz, two partial different motion equations are obtained from Hamiltonian of antiferromagnet CsFeBr₃. By using the method of multiple scales and the long-wavelength approximation, these equations are changed into a nonlinear Schrödinger equation. By applying inverse-scattering transformation, solution of the equation is obtained, solitary excitations in antiferromagnet CsFeBr₃ are also investigated.     

Spin current in quantum XXZ spin chain

The spin current in the one-dimensional quantum XXZ spin chain is studied based on the exact solutions. It is found that the spin voltage controlled by the unparallel boundary magnetic fields can induce the pure longitudinal spin current in the system. By using Wiener–Hopf and generalized algebraic Bethe ansatz methods, the analytic expressions for the spin current and the spin conductance are obtained. The spin current is proportional to the inverse of the length of the spin chain. The magnitude of spin current can be manipulated by the strength and the twist angle of two boundary magnetic fields. The exact analysis also shows that there exist an Ohm law or London equation type relation between the spin current and the spin conductance.     

Quantum anisotropic Heisenberg triangular antiferromagnet: application to CsCuCl3

Triangular anisotropic Heisenberg antiferromagnet shares with the triangular planar antiferromagnet the rich phenomenology found in presence of an external magnetic field. The physical interest in the triangular Heisenberg model is obvious because the planar model has not the quantum analogous one and, more seriously, it does not allow out-of-plane fluctuations so that it provides a very rough representation of actual magnetic insulators. Indeed, we show that magnetic resonance data on CsCuCl₃ are satisfactorily understood on the basis of the properties of the quantum triangular Heisenberg antiferromagnet with easy-plane exchange anisotropy.     

Unified quantum mechanical picture for confined spinons in dimerized and frustrated spin chains

A quantum mechanical picture is presented to describe the behavior of confined spinons in a variety of S =1/2 chains. The confinement is due to dimerization and frustration and it manifests itself as a nonlinear potential , centered at chain ends () or produced by modulation kinks (b > 1). The calculation extends to weak or zero frustration some previous ideas valid for spinons in strongly frustrated spin chains. The local magnetization patterns of the confined spinons are calculated. A (minimum) enhancement of the local moments of about 11/3 over a single S =1/2 is found. Estimates for excitation energies and binding lengths are obtained. Received: 8 May 1998 / Revised and Accepted: 12 August 1998     

Quantum communication through anisotropic Heisenberg XY spin chains

We study quantum communication through an anisotropic Heisenberg XY chain in a transverse magnetic field. We find that for some time t and anisotropy parameter γ, one can transfer a state with a relatively high fidelity. In the strong-field regime, the anisotropy does not significantly affect the fidelity while in the weak-field regime the affect is quite pronounced. The most interesting case is the intermediate regime where the oscillation of the fidelity with time is low and the high-fidelity peaks are relatively broad. This would, in principle, allow for quantum communication in realistic circumstances. Moreover, we calculate the purity, or tangle, as a measure of the entanglement between one spin and all the other spins in the chain and find that the stronger the anisotropy and exchange interaction, the more entanglement will be generated for a given time.