General theorems on large deviations for random vectors

In the paper, we present some general theorems on large deviations of random vectors with cumulants satisfying the generalized Statulevi?ius condition. The results obtained are applicable in derivation of limit theorems in the scheme of series, including the case where the dimension of the considered random vectors is growing indefinitely.     

Single-Chain Magnet Based on Cobalt(II) Thiocyanate as XXZ Spin Chain

The cobalt(II) in [Co(NCS)₂(4-methoxypyridine)₂]_n are linked by pairs of thiocyanate anions into linear chains. In contrast to a previous structure determination, two crystallographically independent cobalt(II) centers have been found to be present. In the antiferromagnetic state, below the critical temperature (T_c=3.94 K) and critical field (H_c=290 Oe), slow relaxations of the ferromagnetic chains are observed. They originate mainly from defects in the magnetic structure, which has been elucidated by micromagnetic Monte Carlo simulations and ac measurements using pristine and defect samples. The energy barriers of the relaxations are Δ_τ1=44.9(5) K and Δ_τ2=26.0(7) K for long and short spin chains, respectively. The spin excitation energy, measured by using frequency-domain EPR spectroscopy, is 19.1 cm⁻¹ and shifts 0.1 cm⁻¹ due to the magnetic ordering. Ab initio calculations revealed easy-axis anisotropy for both Co^II centers, and also an exchange anisotropy J_xx/J_zz of 0.21. The XXZ anisotropic Heisenberg model (solved by using the density renormalization matrix group technique) was used to reconcile the specific heat, susceptibility, and EPR data.