Experimental realization of a quantum breathing pyrochlore antiferromagnet

The synthesis and characterization of a Yb-based material ${\mathrm{Ba}}_3{\mathrm{Yb}}_2{\mathrm{Zn}}_5{\mathrm{O}}_{11}$ are reported. This material is identified as a model system of a pseudospin-1/2 quantum antiferromagnet on “breathing” pyrochlore lattice characterized by an alternating array of small and large Yb tetrahedra. Despite dominant antiferromagnetic interactions $J\sim 7$ K, a large amount of magnetic entropy (25%) remains at 0.38 K, indicating that each small Yb tetrahedron forms a unique doubly degenerate singlet state. These results are well described by the Heisenberg pseudospin-1/2 single tetrahedron model.

Figure 1

(a) Crystal structure of ${\mathrm{Ba}}_3{A}_2{\mathrm{Zn}}_5{\mathrm{O}}_{11}$ ($A=\text{Lu}$ and Yb). $A_4{\mathrm{O}}_{16}$ cluster and ${\mathrm{Zn}}_{10}{\mathrm{O}}_{20}$ supertetrahedron are depicted. (b) Breathing pyrochlore lattice formed by $A^{3+}$ ions. Inter- and intratetrahedron distances are given for $A={\mathrm{Yb}}^{3+}$. (c) X-ray diffraction pattern (black circles) of ${\mathrm{Ba}}_3{\mathrm{Yb}}_2{\mathrm{Zn}}_5{\mathrm{O}}_{11}$ in the presence of a silicon standard at room temperature. The red line corresponds to the best fit from the Rietveld refinement based on the structural model of the Lu analog [22]. Upper and lower vertical marks denote the Bragg peak positions for ${\mathrm{Ba}}_3{\mathrm{Yb}}_2{\mathrm{Zn}}_5{\mathrm{O}}_{11}$ and the silicon standard, respectively. The bottom line represents the difference between experimental and calculated intensities. Inset: Local environment of ${\mathrm{Yb}}^{3+}$ and associated geometrical parameters. The crystalline electric field formed by six surrounding ${\mathrm{O}}^{2-}$ ions exhibits a cubiclike symmetry with a small trigonal distortion along the $\langle 111\rangle$ direction.

Figure 2

(a) Temperature dependence of the inverse magnetic susceptibility $1/\chi \left(T\right)$ measured at a field of 0.1 T for $T<30$ K and 1 T for $T>30$ K. The red line is the calculated curve based on the cubic CEF. The corresponding CEF scheme is illustrated. (b) $\chi \left(T\right)$ below $T=30$ K. The red line shows the fit of the single tetrahedral Heisenberg model (see text).

Figure 3

Magnetic field dependence of the magnetization at selected temperatures. Open black squares (6.0 K), red circles (4.2 K), and blue triangles (1.8 K) represent experimental data. Solid lines correspond to values calculated using Eq. (3) with a set of parameters obtained from the fitting of $\chi \left(T\right)$.

Figure 4

(a) Temperature dependence of the magnetic specific heat $C_{\mathrm{M}}$ (open circles) after subtracting the lattice contribution $C_{\mathrm{L}}$ (dashed line) from the measured specific heat $C_P$ (closed circles). The red solid line is a fit of Eq. (5), which yields $J=-7.1$ K. (b) Corresponding magnetic entropy expressed as a variation from $T=0.38$ K, $\Delta S_{\mathrm{M}}=S_{\mathrm{M}}\left(T\right)-S_{\mathrm{M}}\left(0.38\mathrm{K}\right)$. The solid line is calculated using Eq. (5) with $J=-7.1$ K. Dashed lines represent the entropy for a two-level system $R\ln \left(2\right)$ and a single tetrahedron model $(3/4)R\ln \left(2\right)$. The difference between the two corresponds to the remaining entropy due to the singlet degeneracy.