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arXiv:cond-mat/0010047

Magnetization processes in quantum spin chains with regularly alternating intersite interactions

Oleg Derzhko

Published Oct 3, 2000• 0 citations
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Abstract

We consider the dependence magnetization vs. field at zero temperature for the spin-1/2 chains in which the intersite interactions regularly vary from site to site with a period p. In the limiting case when the smallest value of the intersite interactions tends to zero the chain splits into noninteracting identical fragments of p sites and the dependence magnetization vs. field can be examined rigorously. We demonstrate explicitly the appearance of plateaus in such dependence and discuss a presence of the magnetization values m predicted by the condition p(1/2-m)=integer [1]. We comment on the influence of the anisotropy in the interspin interaction on the magnetization profiles. Finally, we show how the case of nonzero smallest value of the intersite interactions can be considered.

DOI
10.48550/arxiv.cond-mat/0010047

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We consider the dependence magnetization vs. field at zero temperature for the spin-1/2 chains in which the intersite interactions regularly vary from site to site with a period p. In the limiting case when the smallest value of the intersite interactions tends to zero the chain splits into noninteracting identical fragments of p sites and the dependence magnetization vs. field can be examined rigorously. We demonstrate explicitly the appearance of plateaus in such dependence and discuss a presence of the magnetization values m predicted by the condition p(1/2-m)=integer [1]. We comment on the influence of the anisotropy in the interspin interaction on the magnetization profiles. Finally, we show how the case of nonzero smallest value of the intersite interactions can be considered.
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We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it, the magnetization at low temperatures as a function of the magnetic field, for different values of the crystal field and the width of the distributions. For the Bernoulli distribution, the number of plateaus increases, with respect to the uniform case [Litaiff et al., Solid State Commun. 147, 494 (2008)] and their presence can be linked to different ground states, when the magnetic field is varied. For the Gaussian distributions, the uniform scenario is maintained, for small widths, but the plateaus structure disappears as the width increases.
We examine the general features of the noncommutativity of the magnetization operator and Hamiltonian for small quantum spin clusters. The source of this noncommutativity can be a difference in the Land\'e ggg factors for different spins in the cluster, XYXYXY anisotropy in the exchange interaction, and the presence of the Dzyaloshinskii-Moriya term in a direction different from the direction of the magnetic field. As a result, zero-temperature magnetization curves for small spin clusters mimic those for the macroscopic systems with the band(s) of magnetic excitations, i.e., for the given eigenstate of the spin cluster the corresponding magnetic moment can be an explicit function of the external magnetic field yielding the nonconstant (nonplateau) form of the magnetization curve within the given eigenstate. In addition, the XYXYXY anisotropy makes the saturated magnetization (the eigenstate when all spins in cluster are aligned along the magnetic field) inaccessible for finite magnetic field magnitude (asymptotical saturation). We demonstrate all these features on three examples: a spin-1/2 dimer, mixed spin-(1/2,1) dimer, and a spin-1/2 ring trimer. We consider also the simplest Ising-Heisenberg chain, the Ising-XYZXYZXYZ diamond chain, with four different ggg factors. In the chain model the magnetization curve has a more complicated and nontrivial structure than that for clusters.