Unconventional magnetic ground state in Yb${}_2$Ti${}_2$O${}_7$

We report low-temperature specific heat and positive muon spin relaxation/rotation ($\mu$SR) measurements on both polycrystalline and single-crystal samples of the pyrochlore magnet Yb${}_2$Ti${}_2$O${}_7$. This material is believed to possess a spin Hamiltonian able to support a quantum spin ice (QSI) ground state. Yb${}_2$Ti${}_2$O${}_7$ displays sample variation in its low-temperature heat capacity and, while our two samples exhibit extremes of this variation, our $\mu$SR measurements indicate a similar disordered low-temperature state down to 16 mK in both. We report little temperature dependence to the muon spin relaxation and no evidence for ferromagnetic order, in contrast to reports by Chang et al. [Nat. Comm. 3, 992 (2012)] and Yasui et al. [J. Phys. Soc. Japan. 72, 11 (2003)]. Transverse field (TF) $\mu$SR measurements show changes in the temperature dependence of the muon Knight shift that coincide with heat capacity anomalies, which, incidentally, prove that the implanted muons are not diffusing in Yb${}_2$Ti${}_2$O${}_7$. From these results, we are led to propose that Yb${}_2$Ti${}_2$O${}_7$ enters an unconventional ground state below $T_c\sim 265$ mK. As found for all the current leading experimental candidates for a quantum spin liquid state, the precise nature of the state below $T_c$ in Yb${}_2$Ti${}_2$O${}_7$ remains unknown and, at this time, defined by what is not as opposed to what it is: lacking simple periodic long-range order or a frozen spin glass state.

Figure 1

Low-temperature specific heat measurements of Yb${}_2$Ti${}_2$O${}_7$ on a semilogarithmic scale. The red and blue curves represent samples used for this work. Our polycrystalline sample exhibits a sharp transition at $\sim$265 mK, and our single-crystal shows a broad peak at $\sim$185 mK. The black data are taken from Chang et al.'s[23] single crystal. The green points are taken from Ross et al.[21]

Figure 2

A comparison of the weak LF (less than 0.5 mT) data for polycrystalline and single-crystal Yb${}_2$Ti${}_2$O${}_7$. Asymmetry spectra [shown in (b) and (c)] were fit with a single exponential decay with a globally fixed asymmetry for all temperatures. Plot (a) shows the temperature dependence of the relaxation rate.

Figure 3

Fourier transform of $\mu$SR asymmetry spectra in a transverse field of 50 mT at $T=50$ mK. The single-crystal Yb${}_2$Ti${}_2$O${}_7$ shows four resolvable frequencies (red) and the polycrystalline Yb${}_2$Ti${}_2$O${}_7$ shows three (black). This motivates $n=4$ for the single-crystal and $n=3$ in the polycrystalline Yb${}_2$Ti${}_2$O${}_7$ for Eq. (1). The sharp signal at approximately 7 MHz for both samples reflects the precession of the muons in the Ag cryostat tails.

Figure 4

The Yb${}^{3+}$ spin susceptibility characterized by TF-$\mu$SR measurements of (a) polycrystalline and (b) single-crystal Yb${}_2$Ti${}_2$O${}_7$. For the single-crystal Yb${}_2$Ti${}_2$O${}_7$ the initial muon polarization points perpendicular to the TF $=50$ mT field which was applied parallel to $[$111$]$. There are two distinct muon signals from the polycrystalline sample, and three from the single-crystal sample. The arrows show the approximate temperature of the onset of the transition observed in the specific heat. The solid black lines represent Curie-Weiss fits, as described in the text. The insets show asymmetry spectra (black) and fit to Eq. (1) (red).