Modeling the spin-Peierls transition of spin-$1/2$ chains with correlated states: $J_1-J_2$ model, CuGeO${}_3$ and TTF-CuS${}_4$C${}_4$(CF${}_3$)${}_4$

Abstract

The spin-Peierls transition at $T_{SP}$ of spin-$1/2$ chains with isotropic exchange interactions has previously been modeled as correlated for $T>T_{SP}$ and mean field for $T<T_{SP}$. We use correlated states throughout in the $J_1-J_2$ model with antiferromagnetic exchange $J_1$ and $J_2=\hat{I}\pm J_1$ between first and second neighbors, respectively, and variable frustration $0\le \hat{I}\pm \le 0.50$. The thermodynamic limit is reached at high $T$ by exact diagonalization of short chains and at low $T$ by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter $T_{SP}$ yields both the stiffness and the lattice dimerization $\hat{I}´(T)$. The relation between $T_{SP}$ and $\hat{I}”(\hat{I}´,\hat{I}\pm )$, the $T=0$ gap induced by dimerization, depends strongly on $\hat{I}\pm$ and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-CuS${}_4$C${}_4$(CF${}_3$)${}_4$ crystals ($J_1=79$ K, $\hat{I}\pm =0$, $T_{SP}=12$ K) and CuGeO${}_3$ crystals ($J_1=160$ K, $\hat{I}\pm =0.35$, $T_{SP}=14$ K). The same parameters describe the specific heat anomaly of CuGeO${}_3$ and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that $\hat{I}´(0)$ limits the range of spin correlations at $T=0$ while $T>0$ limits the range at $\hat{I}´=0$.

9 pages, 10 figures