Neutron scattering study of crystalline electric field level schemes and magnetic structures of caged compounds Nd$\textit{Tr}{2}$Zn${20}$ ($\textit{Tr}$ = Co, Rh, Ir)

Rare-earth caged compounds $R\textit{Tr}_{2}X_{20}$ ($R$: rare-earth, $\textit{Tr}$: transition metal, $X$ = Al, Zn, and Cd) crystallizing in the cubic CeCr$_{2}$Al$_{20}$-type structure [1] have been extensively studied due to the manifestation of correlated electronic phenomena. Because the $R$ ion is in the nearly spherical environment formed by 16 $X$ atoms, relatively weak crystalline electric field (CEF) and enhanced hybridization with conduction electrons are expected. In the present work, we focus on the 4$f^{3}$ configuration systems Nd$\textit{Tr}_{2}$Zn$_{20}$ ($\textit{Tr}$ = Co, Rh, Ir) [2,3]. The magnetic specific heat $C_{\rm{m}}$ exhibits a Schottky-type peak at around 15 K, which is reproduced by a CEF level scheme with a $\Gamma_{6}$ doublet ground state and a $\Gamma_{8}$ quartet lying at around 40 K. This scheme, however, does not explain the softening of the transvers elastic modulus $C_{44}$ below 40 K [4]. These compounds undergo antiferromagnetic (AFM) transitions at $T_{\rm{N}}$ = 0.53, 0.94, and 0.65 K for $\textit{Tr}$ = Co, Rh, and Ir, respectively. The magnetic entropy $S_{\rm{m}}$ at $T_{\rm{N}}$ is nearly 50$\%$ of $R$ln2 expected for the $\Gamma_{6}$ doublet ground state. The full recovery to $R$ln2 is achieved on heating to 5 K. The reduced $S_{\rm{m}}$ implies the existence of magnetic fluctuations in the paramagnetic state.
To determine the CEF level schemes and magnetic structures, we performed inelastic neutron scattering (INS) and neutron diffraction experiments of powdered samples of Nd$\textit{Tr}_{2}$Zn$_{20}$ ($\textit{Tr}$ = Co, Rh, Ir). INS spectra were measured with a chopper spectrometer MARI at ISIS, RAL. The figure shows the INS spectra for $\textit{Tr}$ = Co with initial neutron energy of $E_{\rm{i}}$ = 11.8 meV at $T$ = 5, 30, and 80 K. Two excitation peaks were observed at 3.7 and 7.2 meV (small arrows). The peak intensity decreases with increasing temperature, which is reproduced by a CEF level scheme of $\Gamma_{6}$ (0) $-$ $\Gamma_{8}^{(1)}$ (44 K) $-$ $\Gamma_{8}^{(1)}$ (84 K). Interestingly, an additional excitation except for the CEF ones was observed at around 7.5 meV as shown with the small arrows. Because the excitation is $Q$-dependent and the energy is close to that of the CEF excitation, the intensity is probably enhanced by the CEF and phonon coupling.
Powder neutron diffraction experiments were carried out with a diffractometer G4-1 at Orph$\rm{\acute{e}}$e reactor of Laboratoire L$\rm{\acute{e}}$on Brillouin. For $\textit{Tr}$ = Co, Rh, and Ir, superlattice reflections were observed for $T$ $<$ $T_{\rm{N}}$, indicating the AFM orders. The magnetic reflections for $\textit{Tr}$ = Rh characterized by the propagation vector (1/2, 1/2, 1/2) suggest the magnetic moments are aligned as $\uparrow\uparrow\downarrow\downarrow$ along the [111] direction. The relationship between the magnetic structure and the release of $S_{\rm{m}}$ in the paramagnetic state will be discussed.

[1] T. Nasch, W. Jeitschko, and U. C. Rodewald, Z. Naturforsch. B $\textbf{52}$, 1023 (1997).

[2] R. Yamamoto, T. Onimaru, R. J. Yamada, Y. Yamane, Y. Shimura, K. Umeo, and T. Takabatake, J. Phys. Soc. Jpn. $\textbf{88}$, 044703 (2019).

[3] Y. Yamane, R. J. Yamada, T. Onimaru, K. Uenishi, K. Wakiya, K. T. Matsumoto, K. Umeo, and T. Takabatake, J. Phys. Soc. Jpn. $\textbf{86}$, 054708 (2017).

[4] T. Umeno, I. Ishii, S. Kumano, D. Suzuki, R. Yamamoto, T. Onimaru, and T. Suzuki, JPS Conf. Proc. $\textbf{30}$, 011162 (2020).