Re-examination of the relaxation dynamics of [TbPc₂][NBu₄]

Slow magnetic relaxation in monometallic single-molecule magnets containing Kramers ions in the lanthanide series are reasonably well understood. However, less work has been performed on the non-Kramers ions of the series, especially in the presence of hyperfine coupling between nuclear and electronic spins. Here we perform a thorough characterisation of the relaxation properties of [TbPc₂][NBu₄], in zero and non-zero magnetic fields. In zero magnetic field and high temperatures, we find the Orbach relaxation barrier U_eff = 611(6) K, significantly larger than the original report, but consistent with the original NMR data. Below 20 K and 400 Oe, we find that either a phonon-assisted quantum tunnelling process or a field-dependent Raman process dominates the relaxation dynamics, with transitions occurring between hyperfine split states between the electronic ground J = 6 multiplet and the I = 3/2 nuclear spin. This process is robust on the application of a small magnetic field, however, between 100 and 200 Oe, avoided level crossings enhance the tunnelling efficiency, leading to an unusual increase in the relaxation rate. Ab-initio calculation of the phonon modes of the molecular crystal and spin-phonon coupling allow us to calculate the magnetic relaxation rates from first-principles, which show good qualitative agreement with experimental data.