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arXiv:cond-mat/0009175 · Physical review. B, Condensed matter

Magnetization jump in the XXZ chain with next-nearest-neighbor exchange

Armando A. Aligia

Published Dec 11, 2000• 18 citations
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Abstract

We study the dependence of the magnetization M with magnetic field B at zero temperature in the spin-1/2 $\mathrm{XXZ}$ chain with nearest-neighbor (NN) ${J}_{1}$ and next-NN ${J}_{2}$ exchange interactions, with anisotropies ${\ensuremath{\Delta}}_{1}$ and ${\ensuremath{\Delta}}_{2},$ respectively. The region of parameters for which a jump in $M(B)$ exists is studied using numerical diagonalization, and analytical results for two magnons on a ferromagnetic background in the thermodynamic limit. We find a line in the parameter space ${(J}_{2}{/J}_{1},{\ensuremath{\Delta}}_{1}{/J}_{1},{\ensuremath{\Delta}}_{2}{/J}_{1})$ (determined by two simple equations) at which the ground state is highly degenerate. $M(B)$ has a jump near this line, and at or near the isotropic case with ferromagnetic ${J}_{1}$ and antiferromagnetic ${J}_{2},$ with $|{J}_{2}{/J}_{1}|\ensuremath{\sim}1/4.$ These results are relevant for some systems containing CuO chains with edge-sharing ${\mathrm{CuO}}_{4}$ units.

DOI
10.1103/physrevb.63.014402

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