Paramagnetic electron-nuclear spin entanglement in HoCo 2 Zn 20

We investigated electron-nuclear spin entanglement in the paramagnetic ground state of the Ho-based cubic compound HoCo 2 Zn 20 . From analyses of magnetization and specific heat data, we determined the cubic crystalline electric field (CEF) parameters, the magnetic exchange constant, and the hyperfine coupling constant between the 4 f magnetic moment and the Ho 165 nuclear spin. Our results show that the Γ 5 CEF ground state is split by the hyperfine coupling, with an energy width of 1.3 K at 0 T, and that the true paramagnetic ground state is a quasisextet arising primarily from entanglement between the f -electron effective spin S = 1 and the Ho 165 nuclear spin I = 7 / 2 . We further demonstrate that, depending on the CEF parameters, the paramagnetic ground state can switch to an electron-nuclear coupled dectet. These findings underscore the importance of accurately identifying the electron-nuclear level scheme for understanding the low-temperature properties of rare-earth compounds containing spin-active nuclei.