Jill C. Bonner

Susceptibility calculations for alternating antiferromagnetic chains

Earlier work of Duffy and Barr consisting of exact calculations on alternating antiferromagnetic Heisenberg spin‐1/2 chains is extended to longer chains of up to 12 spins, and subsequent extrapolations of thermodynamic properties, particularly the susceptibility, are extended to the weak alternation region close to the uniform limit. This is the region of interest in connection with the recent experimental discovery of spin‐Peierls systems. The extrapolated susceptibility curves are compared with corresponding curves calculated from the model of Bulaevskii, which has been used extensively in approximate theoretical treatments of a variety of phenomena. Qualitative agreement is observed in the uniform limit and persists for all degrees of alternation, but quantitative differences of about 10% are present over the whole range, including the isolated dimer limit. Potential application of the new susceptibility calculations to experiment is discussed.

The Spin-Peierls Transition

In a spin-Peierls transition, a spin-lattice system consisting of one-dimensional antiferromagnetic linear chains in a 3-D lattice progressively dimerizes and thereby becomes nonmagnetic at T = 0. Like the usual Peierls transition, this is a soft-mode transition associated with a “fermi-surface-driven” instability (in a pseudo-fermion representation). We discuss the character of the transition and make predictions concerning the dynamic structure factor.

Renormalization group and other calculations for the one‐dimensional spin‐1/2 dimerized Heisenberg antiferromagnet

A zero‐temperature renormalization group (RG) approach is applied to the one‐dimensional, spin‐1/2 antiferromagnetic Heisenberg dimerized (alternating) chain. Specifically, the ground state energy and lowest‐lying spectral excitations are examined. The calculation indicates the existence of a gap in the spectrum of the dimerized chain which vanishes only in the limit of a uniform spin chain, in contrast to a recent Green’s function approach. The RG results are in reasonable agreement with numerical extrapolations on the exact eigenvalue spectrum of finite chains of up to 12 spins. Both methods are compared with several other approximate treatments of the Heisenberg system, and tested by comparison with exact results for the spin‐1/2 XY dimerized chain.

Generalized Heisenberg quantum spin chains (invited)

Since the Heisenberg spin chain can be considered the simplest realistic model of magnetism, surprise and some degree of controversy have resulted from recent work of Haldane. The prediction is that quantum spin chains with half‐integer spin should all display T=0 phase behavior equivalent to that of the Bethe Ansatz integrable (solvable) spin‐1/2 quantum chain. More remarkably, the class of integer spin chains is predicted to show very different phase behavior. In particular, a gap should be present in the spectrum of a Heisenberg antiferromagnetic chain. This remarkable feature is counterintuitive in terms of accepted wisdom in magnetism (spin‐wave theory, spin‐Peierls theory) and critical phenomena. Consequently the vertification of the prediction is of great interest. A considerable amount of numerical work has been done, involving finite‐chain, finite‐size scaling, variational, Monte Carlo and other calculations, which will be reviewed here. The present consensus is that the weight of numerical evide...

Quantum Spin Chains

Serious scientific interest in one-dimensional (1-D) physics arose in the early 1960’s. This interest was stimulated by exact as well as accurate numerical solutions to a variety of quantum spin chain problems [1]. The potential relevance of such solutions to real experimental systems was first demonstrated by Griffiths [2] in conjunction with workers at the Kamerlingh Onnes Laboratorium, Leiden. Theory and experiment were shown to be in excellent agreement for a naturally quasi-1-D Heisenberg spin 1/2 antiferromagnet, copper tetrammine sulphate [Cu(NH3)4SO4·H2O]. Further stimulus to the new field of quasi-1-D magnetism was provided by an annotated collection of reprinted papers on a variety of 1-D model systems, including lattice gases, dynamical disordered crystal lattices, many-fermion gases (electron gases) as well as magnets. The collection appeared in book form, and remains today an important introduction to 1-D theory [3].

HIGH MAGNETIC-FIELD BEHAVIOR OF MEM-(TCNQ)2

Abstract The charge-transfer complex MEM(TCNQ)2 is a spin-Peierls system with a non-magnetic, singlet ground state at T=0. We report high-field magnetization data which provide some evidence for a new magnetic spin-Peierls phase at fields above 190 kOe. The experimental results are compared to those for TTFCuBDT.

One-Dimensional Model Systems: Theoretical Survey

In the early 1960’s one-dimensional model systems were regarded as amusing toys with the advantage of being far more easily solvable than their ’’real’’ three-dimensional counterparts. Now essentially 1-D (quasi-1-D) magnets can be ’’tailor-made’’ in the laboratory. Even more popular is the field of organic conductors like TTF⋅TCNQ, which are naturally quasi-1-D. Currently solitons and related solutions of non-linear, dispersive 1-D differential equations are ubiquitous in physics, including the area of 1-D magnetism. These developments are discussed in the Introduction. The rest of this paper is concerned with model Hamiltonians, model comparisons, critical singularities in 1-D (quasi-1-D) systems, accuracy of numerical techniques in comparison with exact solutions, brief accounts of dilute and disordered 1-D systems, and 1-D spin dynamics. Finally, a comment is made on a variety of interesting isomorphisms between 1-D magnets and phenomena in several other areas of physics, for example 2-D ferroelectric...

Thermal and magnetic study of exchange in the quasi‐1‐D molecular compound, TTF⋅PtS4C4(CF3)4

Single crystal magnetic susceptibility results from 2.5 K to 270 K and specific heat results from 3 K to 16 K are reported for TTF⋅PtS4C4(CF3)4, (TTF=tetrathiafulvalene). The combined results are analyzed using a simple model which ignores differences between the two types of S=1/2 spin carriers and involves a system of ferromagnetic chains treated ’’exactly’’, with interchain antiferromagnetic interaction evaluated in a mean field approximation. Above an apparent ordering transition at 8 K, the susceptibility is well described by the model irrespective of whether the ferromagnetic exchange is Heisenberg, Ising or intermediate to these. The magnetic contribution to the specific heat is obtained using earlier results for the isostructural Au compound. Comparison with specific heat calculations for the Heisenberg, Ising and intermediate cases successfully narrows the ambiguity to an intermediate anisotropic exchange close to the Heisenberg limit.

Spin-peierls phase diagrams: Observations and models

Abstract We discuss systems displaying the spin-Peierls transition, a unique magnetoelastic phase transition which has been the subject of considerable experimental and theoretical attention recently. The first high magnetic field experiments, involving neutron scattering and magnetization measurements, have been performed. Analysis is made with reference to theoretical models.

Comparison of spin anisotropy and exchange alternation

Quasi‐1‐D magnetic systems with on the one hand an Ising‐Heisenberg type spin anisotropy and on the other hand an alternating (dimerized) character have many interesting features in common and a few interesting differences in their phase behavior and general magnetic properties. This report reviews results rather scattered in the literature in addition to presenting new results. These rather complex quantum models present a theoretical challenge. It is also hoped that this work will be helpful to magnetochemists interested in identifying the underlying magnetic character of their systems, and to experimentalists in general.