Evidence of low-energy singlet excited states in the spin- 12 polyhedral clusters {Mo72V30

Abstract

Magnetization, specific heat, and electron spin resonance (ESR) measurements are carried out to clarify the low-energy excitations for the S = 1/2 polyhedral clusters {Mo72V30} and {W72V30}. The clusters provide unique model systems of Kagomé network on a quasi-sphere. The linear field variation of magnetization at low temperatures indicates that the ground state is singlet for both clusters. The temperature and the magnetic field dependence of specific heat shows a distinct difference between two clusters with differing structural symmetries. In {W72V30} with Ih symmetry, the existence of the several tens of low-energy singlet excited states below the lowest triplet excited state is revealed. The specific heat of the slightly distorted {Mo72V30} with D5h symmetry leads to a drastic decrease of the singlet contribution, which is consistent with the partial lifting of the frustration and the decrease of degenerated low-energy states. The singlet excitation existence is confirmed further by the temperature dependence of the ESR spectra. Comprehensive experimental studies have demonstrated unique low-energy excitations of the spherical Kagomé networks and their sensitivity to the cluster symmetry.

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

“…( 1) was estimated to be ∆ s = 0.048J ∼ 1 4 ∆ t [22], and thus, the 10 % bond-randomness is enough to disperse the distribution of states over an energy range ∼ ∆ s , which is plausible to give an impact on the specific heat at very low temperatures. Due to reducing the size of bondrandomness from 30 % [28] to 10 %, the experimental magnetization [28][29][30] can not be reproduced by only adding 10 % bond-randomness, but we expect adding both 10 % bond-randomness and 10 % DM interactions to resolve this problem. Now, with these perturbations added, we write our total Hamiltonian as…”

“…where −0.1J ≤ α i,j ≤ 0.1J, D = 0.1J, θ = 0.5π, g = 1.95, and J = 115 K, and H denotes the magnetic field. The orientations of magnetic clusters in polycrystalline samples of {W 72 V 30 } used in the magnetization measurements [28][29][30], where discrete and well-separated magnetic spherical kagomé clusters are embedded in a nonmagnetic environment, are distributed randomly and are expected to be unaffected by the magnetic field direction. Therefore, we set the direction of the magnetic field H in Eq.…”

“…Subsequently, in 2019, Kihara et al, experimentally measured the specific heat at low temperatures of {W 72 V 30 } and revealed the existence of many low-energy nonmagnetic singlet states below the first excited triplet state [30]. As expected from the above mentioned experiments, which suggests the existence of the DM interaction or bond-randomness, their experimental result on the specific heat also extremely differs from theoretical results for the Heisenberg model [21,22].…”

“…An icosidodecahedron is composed of corner-sharing triangles [see Fig. 1(a)] and realized in {W 72 V 30 } [27][28][29][30]. The main part of the Hamiltonian for {W 72 V 30 } is presented as…”

“…Thus, it was unclear whether the agreement was consistent even at very low temperatures below 0.1J ≃ 10 K. Also, Schnack, Kunisada, and Fukumoto calculated the magnetization process and the specific heat [21,22], which were expected to be observed experimentally in {W 72 V 30 }. * e-mail:yfuku@rs.tus.ac.jp However, contrary to the theoretical prediction, later experiments show that although the theoretical magnetization curve has staircase structure the experimental one increases linearly with magnetic field and that theoretical susceptibility vanishes faster than measured susceptibility as the temperature drops to low [28][29][30]. Schnack et al, suggested that the discrepancies were attributed to the distribution of nearest-neighbor exchange couplings, which was called bond-randomness, where the width of the variance in exchange interactions was estimated to be 30 % of the average value J [28].…”