Thermal entanglement in molecular spin rings

The thermal entanglement in the triangular molecular spin ring with Dzyaloshinskii--Moriya interaction is studied. The concurrences of arbitrary two spins of the triangular molecular spin ring for various cases are evaluated. The tendency of the concurrence with Dzyaloshinskii--Moriya interaction and temperature is analysed and discussed. We note that the concurrence arrives at its maximum in the regime with the large Dzyaloshinskii--Moriya interaction and low temperature, and gradually decreases to zero with the increase of temperature. The concurrence has different features for the ferromagnetic and antiferromagnetic cases. For completeness, we also numerically calculate the concurrence of spin rings with N>3 spins and analyse their behaviours.