Low-energy excitations and ground-state selection in the quantum breathing pyrochlore antiferromagnet ${\mathrm{Ba}}_3{\mathrm{Yb}}_2{\mathrm{Zn}}_5{\mathrm{O}}_{11}$

We study low-energy excitations in the quantum breathing pyrochlore antiferromagnet ${\mathrm{Ba}}_3{\mathrm{Yb}}_2{\mathrm{Zn}}_5{\mathrm{O}}_{11}$ by a combination of inelastic neutron scattering (INS) and thermodynamical property measurements. The INS spectra are quantitatively explained by spin-$\frac{1}{2}$ single-tetrahedron model having $XXZ$ anisotropy and Dzyaloshinskii-Moriya interactions. This model has a twofold degeneracy of the lowest-energy state per tetrahedron and well reproduces the magnetization curve at 0.5 K and heat capacity above 1.5 K. At lower temperatures, however, we observe a broad maximum in the heat capacity around 63 mK, demonstrating that a unique quantum ground state is selected due to extra perturbations with an energy scale smaller than the instrumental resolution of INS.

Figure 1

(a)–(d) INS spectra measured at (a) 1.5, (b) 6, (c) 12, and (d) 40 K using setup I. (e) INS spectrum measured at 1.5 K using setup II. (f) $Q$ dependence of the integrated intensity obtained from the spectrum in (e). The red solid curve is the calculation (see text).

Figure 2

(a), (b) The $\hslash \omega$ dependences of the neutron intensities at (a) 1.5 and (b) 12 K. (c) Temperature dependences of the intensities of the excitations in (a). (d) Those of the excitations additionally observed in high temperatures in (b). (e) $\hslash \omega$ dependence of the intensity at 1.5 K obtained using setup II. Throughout the panels, red and black solid curves are the calculations using the same parameters in Eqs. (3, 4, 5, 6). (f) Energy level of the $S=\frac{1}{2}$ Heisenberg spin tetrahedron model in the previous study [18] and that of the $S=\frac{1}{2}$ anisotropic spin tetrahedron in the present study.

Figure 3

(a) Heat capacity measured and reported in the previous study [18]. The red solid curve is the calculation. (b) Magnetic field dependence of magnetization at 0.5 K. The red solid curve is the calculation. (c) Solid circles indicate heat capacity. The blue dashed curve is the calculation of the empirical model where the lift of the degeneracy of the ground state is introduced as a single energy gap. The red solid curve is the calculation of the model where the empirical energy gap has distribution. (d) Entropy change estimated from (c). The calculated entropy is shifted so that the calculation has the same value of the data at 0.94 K.