Static magnetic moments revealed by muon spin relaxation and thermodynamic measurements in the quantum spin ice ${\text{Yb}}_2{\text{Ti}}_2{\text{O}}_7$

We present muon spin relaxation ($\mu$SR) and specific-heat versus temperature $C\left(T\right)$ measurements on polycrystalline and single-crystal samples of the pyrochlore magnet ${\text{Yb}}_2{\text{Ti}}_2{\text{O}}_7$. $C\left(T\right)$ exhibits a sharp peak at a $T_C$ of 0.21 and 0.26 K for the single-crystal and polycrystalline samples, respectively. For both samples, the magnetic entropy released between 50 mK and 30 K amounts to $Rln2$ per Yb. At temperatures below $T_C$ we observe a steep drop in the asymmetry of the zero-field $\mu$SR time spectra at short time scales, as well as a decoupling of the muon spins from the internal field in longitudinal magnetic fields of $\le 0.25$ T for both the polycrystalline and single-crystal samples. These muon data are indicative of static magnetic moments. Our results are consistent with the onset of long-range magnetic order in both forms of ${\text{Yb}}_2{\text{Ti}}_2{\text{O}}_7$.

Figure 1

(a) Specific heat versus temperature $C\left(T\right)$ for our single crystal [3] (closed symbols) and powder (open symbols) samples of ${\text{Yb}}_2{\text{Ti}}_2{\text{O}}_7$ on a semilogarithmic scale. The lines are a guide to the eye. Data from Ross et al. [10], Yaouanc et al. [11], D'Ortenzio et al. [13], and Blöte et al. [7] are also shown for comparison. (b) Left-hand $y$ axis: magnetic entropy versus temperature $S\left(T\right)$. The phonon contribution, estimated from $C\left(T\right)$ data for nonmagnetic ${\text{Y}}_2{\text{Ti}}_2{\text{O}}_7$ and corrected for the difference in the atomic mass of Y and Yb [17], and a nuclear Schottky contribution [7], have been subtracted from the data. Right-hand $y$ axis: the flipping ratio of the neutron spins at the (111) Bragg peak as a function of temperature for the single-crystal sample of ${\text{Yb}}_2{\text{Ti}}_2{\text{O}}_7$ used in this work (see Ref. [3]). The vertical black and red dashed lines indicate the temperature of the specific heat peak for the crystal and powder, respectively.

Figure 2

ZF $\mu$SR asymmetry time spectra for (a) the powder and (b) the single-crystal samples of ${\text{Yb}}_2{\text{Ti}}_2{\text{O}}_7$ between 0.05 and 4 K.

Figure 3

Temperature dependence of the normalized ZF $\mu$SR asymmetry, $A_2(t=0,T)/A_2(t=0,T=0.6\mathrm{K})$, and the depolarization rate, ${\lambda }_2$, of the slowly depolarizing component for (a) powder and (b) single-crystal samples of ${\text{Yb}}_2{\text{Ti}}_2{\text{O}}_7$.

Figure 4

LF $\mu$SR asymmetry time spectra for polycrystalline ${\text{Yb}}_2{\text{Ti}}_2{\text{O}}_7$ at (a) 0.1 and (b) 0.7 K and single-crystal ${\text{Yb}}_2{\text{Ti}}_2{\text{O}}_7$ at (c) 0.075 and (d) 0.7 K.