Spin Peierls transition of $J_1-J_2$ and extended models with ferromagnetic $J_1$.Sublattice dimerization and thermodynamics of zigzag chains in $\beta$-TeVO${}_4$

Abstract

The spin$-1/2$ chain with ferromagnetic exchange $J_1<0$ between first neighbors and antiferromagnetic $J_2>0$ between second neighbors supports two spin-Peierls (SP) instabilities depending on the frustration $\alpha =J_2/|J_1|$. Instead of chain dimerization with two spins per unit cell, $J_1-J_2$ models with $\alpha >0.65$ and linear spin-phonon coupling are unconditionally unstable to sublattice dimerization with four spins per unit cell. Unequal $J_1$ to neighbors to the right and left extends the model to gapped ($\gamma >0$) chains with conditional SP transitions at $T_{SP}$ to dimerized sublattices and a weaker specific heat $C(T)$ anomaly. The spin susceptibility $\chi (T)$ and $C(T)$ are obtained in the thermodynamic limit by a combination of exact diagonalization of small systems with $\alpha >0.65$ and density matrix renormalization group (DMRG) calculations of systems up to $N\sim 100$ spins. Both $J_1-J_2$ and $\gamma >0$ models account quantitatively for $\chi (T)$ and $C(T)$ in the paramagnetic phase of $\beta$-TeVO${}_4$ for $T>8$ K, but lower $T$ indicates a gapped chain instead of a $J_1-J_2$ model as previously thought. The same parameters and $T_{SP}=4.6$ K generate a $C(T)/T$ anomaly that reproduces the anomaly at the $4.6$ K transition of $\beta$-TeVO${}_4$, but not the weak $\chi (T)$ signature.

12 pages, 13 figures

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