Absence of pure quadrupole ordering in SmSn${}_3$: Dipole-dipole and quadrupole-quadrupole interactions in Sm-based compounds

The intermetallic cubic compound SmSn${}_3$ is currently the only candidate for pure quadrupole ordering among existing Sm-based compounds. In this paper, we report on magnetic susceptibility and muon spin relaxation measurements on SmSn${}_3$ and demonstrate that a spontaneous local magnetic field appears in the ordered state, which undoubtedly rules out the pure quadrupole ordering. Dipole-dipole and quadrupole-quadrupole interactions in trivalent lanthanide systems are discussed on the basis of a de Gennes theory, indicating that the former tends to dominate in Sm intermetallics. This also provides a general guideline for future searches of quadrupole-related phenomena in trivalent lanthanide systems.

Figure 1

Temperature dependence of magnetic susceptibility $\chi \left(T\right)$ in SmSn${}_3$ below 14 K in a magnetic field of 0.1 T applied along the [001] direction. The inset shows the $H$-$T$ phase diagram extracted from $\chi \left(T\right)$.

Figure 2

(a) ZF-$\mu$SR spectra in SmSn${}_3$ at several temperatures between 9.4 and 15.8 K. The solid curves represent the best fits with Eq. (1). (b) LF-$\mu$SR spectra in SmSn${}_3$ at several LFs at 10.6 K in the phase II. (c) $p$ in ZF as a function of temperature. (d) ${\lambda }_1$ and ${\lambda }_2$ in ZF as functions of temperature.

Figure 3

(a) $dG$, (b) $Q$, and (c) $Q/dG$ for Ln${}^{3+}$ ions. The closed and open symbols represent Kramers and non-Kramers ions, respectively.