The present status of theoretical and experimental investigations of solitary excitations in one-dimensional magnetic systems is reviewed. A survey of exact solutions to the nonlinear equations of motion for pertinent classical chain systems (sine-Gordon chain and ferromagnetic Heisenberg chains with various anisotropies) is given. Particular emphasis is devoted to the role of solitons in the thermodynamics of such systems. Models corresponding to real quasi-one-dimensional magnets are broadly discussed to demonstrate the properties of their solitary excitations. The experimental significance of such nonlinear excitations in the static and dynamic quantities of such systems is discussed in detail. The models and model substances are the easy-plane ferromagnet (model substances CsNiF3 and (C6H11NH3)CuBr3), the easy-plane antiferromagnet (CH3)4NMnCl3) and the S = ½ Ising chain with transverse interactions (CsCoCl3). The quantum aspects of solitary excitations are treated in some theoretical detail....

Solitary excitations in one-dimensional magnets

The critical behaviour of an integrable model of a spin- 1/2 chain with nearest-neighbour XXZ interaction and a competing three-spin interaction involving nearest and next-nearest neighbours is studied. The phase diagram at zero temperature is obtained. Methods from conformal field theory are used to compute the asymptotics of the spin-spin correlation functions.

Integrable spin-1/2 XXZ Heisenberg chain with competing interactions

We present a numerical study of the magnetization process of frustrated quantum spin-$S$ chains with $S=1,3∕2,2$ as well as the classical limit. Using the exact diagonalization and density-matrix renormalization techniques, we provide evidence that a plateau at one third of the saturation magnetization exists in the magnetization curve of frustrated spin-$S$ chains with $Sg1∕2$. Similar to the case of $S=1∕2$, this plateau state breaks the translational symmetry of the Hamiltonian and realizes an up-up-down pattern in the spin component parallel to the external field. Our study further shows that this plateau exists both in the cases of an isotropic exchange and in the easy-axis regime for spin-$S=1$, $3∕2$, and 2, but is absent in classical frustrated spin chains with isotropic interactions. We discuss the magnetic phase diagram of frustrated spin-1 and spin-$3∕2$ chains as well as other emergent features of the magnetization process such as kink singularities, jumps, and even-odd effects. A quantitative comparison of the one-third plateau in the easy-axis regime between spin-1 and spin-$3∕2$ chains on the one hand and the classical frustrated chain on the other hand indicates that the critical frustration and the phase boundaries of this state rapidly approach the classical result as the spin $S$ increases.

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Universal emergence of the one-third plateau in the magnetization process of frustrated quantum spin chains

We study the energy per particle of a one-dimensional ferromagnetic/antiferromagnetic frustrated spin chain with nearest and next-to-nearest interactions close to the helimagnet/ferromagnet transition point as the number of particles diverges. We rigorously prove the emergence of chiral ground states, and we compute, by performing the $$\Gamma $$
 -limits of proper renormalizations and scalings, the energy for a chirality transition.

Frustrated Ferromagnetic Spin Chains: A Variational Approach to Chirality Transitions

Motivated by a novel cyclic compound $Fe_{10}Gd_{10}$ with record ground state spin in which the arrangement of magnetic ions with $s=\frac{5}{2}$ and $s=\frac{7}{2}$ corresponds to a saw-tooth chain we investigate the thermodynamics of the delta-chain with competing ferro- and antiferromagnetic interactions. We study both classical and quantum versions of the model. The classical model is exactly solved and quantum effects are studied using full diagonalization and a finite temperature Lanczos technique for finite delta-chains as well as modified spin wave theory. It is shown that the main features of the magnetic susceptibility of the quantum spin delta chain are correctly described by the classical spin model, while quantum effects significantly change the low-temperature behavior of the specific heat. The relation of the obtained results to the $Fe_{10}Gd_{10}$ system is discussed.

Thermodynamics of a delta chain with ferromagnetic and antiferromagnetic interactions

Exact results for the thermodynamic quantities of the one-dimensional classical Heisenberg model with nearest- and next-nearest-neighbor exchange interactions are obtained by means of the numerical transfer matrix method. For a wide range of exchange constants, the system exhibits helical short-range order on which we focus our attention. We find that the Fourier-transformed spin correlation function shows a maximum with asymmetric shape at the characteristic wave-number ±qm (≠0, ±π). The correlation length defined as the inverse of the width atq=qm obeys a simple scaling law and shows a power-law singularity at zero temperature. Results for the heat capacity and the susceptibility are also presented and discussed in connection with the helical short-range order.

H. J. Mikeska

Papers

Thermodynamic properties of the classical Heisenberg chain with nearest- and next-nearest-neighbor interactions