Zeeman, hyperfine, and magnetic dipolar effects on the EPR spectrum of a cubic copper tetramer

The Zeeman interaction for an isolated multiplet of a cubic Cu2+ tetramer, characterized by the total spin quantum number S, is shown to be essentially isotropic, with g=(g∥+2g⊥)/3, where g∥ and g⊥ are single Cu2+ ion components. Matrix elements are given for the off-diagonal part of the Zeeman interaction within the three S=1 multiplets. The hyperfine structure for each isotope in a [100] direction is shown to be a 13 line structure. The intracluster magnetic dipole–dipole (MDD) interaction has nonzero matrix elements within the three S=1 multiplets, which are degenerate for an isotropic exchange interaction with equal coupling constants. With the MDD interaction treated as a perturbation of the Zeeman interaction, it is found that the single line at g=2.10, expected on the basis of the Zeeman interaction alone, is split into four lines separated from the former line by ±h0 and ±2h0, where h0≂480 G. The MDD coupling constant, calculated assuming point dipoles, is an order of magnitude too small to explain the zero-field splitting of the S=2 multiplet measured by EPR in Cu4OCl6(TPPO)4.