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 characterization of the relaxation properties of [TbPc₂][NBu₄], in zero and nonzero 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.