Frustration-Induced $\eta$ Inversion in the $S=1/2$ Bond-Alternating Spin Chain

We study the frustration-induced enhancement of the incommensurate correlation for a bond-alternating quantum spin chain in a magnetic field, which is associated with a quasi-one-dimensional organic compound ${\mathrm{F}}_{\mathrm{5}}\mathrm{P}\mathrm{N}\mathrm{N}$. We investigate the temperature dependence of the staggered susceptibilities by using the density matrix renormalization group, and then find that the incommensurate correlation becomes dominant in a certain range of the magnetic field. We also discuss the mechanism of this enhancement on the basis of the mapping to the effective $S=1/2$ $XXZ$ chain and a possibility of the field-induced incommensurate long-range order.

Figure 1

Magnetization curves obtained with the DMRG.

Figure 2

Staggered susceptibilities ${\chi }_{\parallel }$ and ${\chi }_{\perp }$ (a) for $(\alpha ,J^{\prime },H)=(0.45,0.05,1.16)$ and (b) for $(\alpha ,J^{\prime },H)=(0.45,0.15,1.19)$. The dotted (thin solid) lines show the results of power-law fitting for ${\chi }_{\perp }({\chi }_{\parallel })$.

Figure 3

Phase diagram determined by the interchain mean field approximation (a) for $(\alpha ,J^{\prime })=(0.45,0.05)$ and (b) for $(\alpha ,J^{\prime })=(0.45,0.15)$. Pluses show the critical temperature $T_{\mathrm{c}}(H)$ of ${\mathrm{F}}_{\mathrm{5}}\mathrm{P}\mathrm{N}\mathrm{N}$ with $J/k_{\mathrm{B}}=6\mathrm{K}$. The bold line in (b) indicates the ${\chi }_{\parallel }={\chi }_{\perp }$ line. Dotted lines represent the critical fields ($H_{\mathrm{c}\mathrm{1}}$ and $H_{\mathrm{c}\mathrm{2}}$), and the lower (upper) edge of the plateau $H_{\mathrm{p}\mathrm{1}}$ ($H_{\mathrm{p}\mathrm{2}}$) for the single chain.