Realization of quantum dipoles in triangular lattice crystal ${\mathrm{Ba}}_3\mathrm{Yb}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_3$

We investigate the thermodynamic properties of the ytterbium-based triangular lattice compound ${\mathrm{Ba}}_3\mathrm{Yb}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_3$. The results demonstrate the absence of any long-range ordering down to 56 mK. Analysis of the magnetization, susceptibility, and specific heat measurements suggests that ${\mathrm{Ba}}_3\mathrm{Yb}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_3$ may realize an $S=\frac{1}{2}$ quantum dipole lattice, in which the dominant interaction is the long-range dipole-dipole coupling on the geometrically frustrated triangular lattice, and exchange interactions are subdominant or negligible.

Figure 1

(a) Temperature-dependent magnetic susceptibilities (${\chi }_{ab}$ and ${\chi }_c$) obtained for the ${\mathrm{Ba}}_3\mathrm{Yb}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_3$ crystal are shown. Directional magnetic anisotropy is more pronounced below 2 K, as shown in the inset. (b) Inverse magnetic susceptibility results and the Curie-Weiss fittings (solid red lines) obtained for the high-temperature regime are shown.

Figure 2

Isothermal magnetization data collected at different temperatures are plotted with lines fitted to a pure Van Vleck contribution and the Brillouin function of single-ion Zeeman energy, along the (a) crystallographic $c$ direction and (b) $ab$ plane of ${\mathrm{Ba}}_3\mathrm{Yb}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_3$.

Figure 3

(a) The heat capacity results obtained for single-crystalline ${\mathrm{Ba}}_3\mathrm{Yb}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_3$ and powder ${\mathrm{Ba}}_3\mathrm{Lu}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_3$ samples are shown. The inset shows the heat capacity data (blue) and fit based on Eq. (2) (red) as a function of $1/T^2$ at an intermediate temperature range $0.5\text{K}\lesssim T\lesssim 4\text{K}$. (b) Heat capacity data plotted for various magnetic fields with fits (red solid lines) calculated for the magnetic Schottky contribution $C_{\text{Sch}}(T,H)$—see Eq. (4). The inset shows the energy gap $\mathrm{\Delta }\left(H\right)$ (left vertical axis) and $n$ representing the number of free spins per f.u. (right vertical axis) as a function of applied magnetic fields. (c) Magnetic heat capacity $C_{\text{mag}}$ (left $Y$ axis, open symbols) of ${\mathrm{Ba}}_3\mathrm{Yb}{\left(\mathrm{B}{\mathrm{O}}_3\right)}_3$ carried out under different magnetic fields are shown vs the logarithmic temperature axis. The changes in magnetic entropy [$\mathrm{\Delta }{S}_{\text{mag}}=S\left(\mathrm{K}\right)-S\left(\text{56}\text{mK}\right)$, right vertical axis, solid symbols] are plotted with linear temperature shown on the top axis.