Determination of the hyperfine electron-nuclear level scheme in HoCo₂Zn₂₀

We determined the electron–nuclear level scheme in the paramagnetic state of the holmium-based cubic compound HoCo₂Zn₂₀ using macroscopic thermodynamic probes alone. From magnetization and specific heat measurements, together with detailed analyses, we obtained the crystalline electric field (CEF) parameters, the magnetic exchange constant, and the hyperfine coupling constant between the 4f magnetic moment and the ¹⁶⁵Ho nuclear spin. These refined parameters reveal that the Γ₅ CEF ground state is split by the hyperfine coupling, and that the sextet formed through coupling between the effective S = 1 spin of the f electrons and the I = 7/2 spin of the ¹⁶⁵Ho nucleus constitutes the paramagnetic ground state. Remarkably, the splitting energy width exceeds 1 K at zero magnetic field, underscoring the importance of electron–nuclear spin coupling in strongly correlated electron systems.