Effects of bond-randomness and Dzyaloshinskii-Moriya interactions on the specific heat at low temperatures of a spherical kagom\'{e} cluster in {W$_{72}$V$_{30}$}

Abstract

For the spin-1/2 spherical kagom\'{e} cluster, as well as for the 2D kagom\'{e} lattice, many low-energy singlet excitations have been expected to exist in the energy region below the spin gap, which has been actually confirmed by Kihara $et \ al.$ in their specific heat measurements up to 10K in {W$_{72}$V$_{30}$}, for which the exchange interaction was estimated as $J=115$K. However, the experimental result of the specific heat can not be reproduced by the theoretical result in the Heisenberg model. Although the theoretical result has a peak around 2 K, the experimental one does not. To elucidate this difference, we incorporate Dzyaloshinskii-Moriya (DM) interactions and bond-randomness into the model Hamiltonian for {W$_{72}$V$_{30}$} and calculate density of states, entropy, and specific heat at low temperatures by using the Lanczos method. We find that DM interactions do not significantly affect the energy distribution of about ten singlet states above the ground state, which are involved in the peak structure of the specific heat around 2K, while even 10% bond-randomness disperses this distribution to collapse the 2K peak. Kihara $et \ al.$ also reported experimental specific heats under magnetic fields up to 15T $(=0.17J)$, and found that the specific heats show almost no magnetic-field dependence, which strongly suggests that the bond randomness is much stronger than the magnetic fields. For example, our calculated specific heats with 50% randomness reproduce the experimental ones up to about 5K.