Neutron spectroscopic study of crystalline electric field excitations in stoichiometric and lightly stuffed ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$

Time-of-flight neutron spectroscopy has been used to determine the crystalline electric field (CEF) Hamiltonian, eigenvalues and eigenvectors appropriate to the $J=7/2 {\mathrm{Yb}}^{3+}$ ion in the candidate quantum spin ice pyrochlore magnet ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. The precise ground state (GS) of this exotic, geometrically frustrated magnet is known to be sensitive to weak disorder associated with the growth of single crystals from the melt. Such materials display weak “stuffing,” wherein a small proportion, $\approx 2\%$, of the nonmagnetic ${\mathrm{Ti}}^{4+}$ sites are occupied by excess ${\mathrm{Yb}}^{3+}$. We have carried out neutron spectroscopic measurements on a stoichiometric powder sample of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, as well as a crushed single crystal with weak stuffing and an approximate composition of ${\mathrm{Yb}}_{2+x}{\mathrm{Ti}}_{2-x}{\mathrm{O}}_{7+y}$ with $x=0.046$. All samples display three CEF transitions out of the GS, and the GS doublet itself is identified as primarily composed of $m_J=\pm 1/2$, as expected. However, stuffing at low temperatures in ${\mathrm{Yb}}_{2+x}{\mathrm{Ti}}_{2-x}{\mathrm{O}}_{7+y}$ induces a similar finite CEF lifetime as is induced in stoichiometric ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ by elevated temperature. We conclude that an extended strain field exists about each local “stuffed” site, which produces a distribution of random CEF environments in the lightly stuffed ${\mathrm{Yb}}_{2+x}{\mathrm{Ti}}_{2-x}{\mathrm{O}}_{7+y}$, in addition to producing a small fraction of Yb ions in defective environments with grossly different CEF eigenvalues and eigenvectors.

Figure 1

The stuffed pyrochlore structure of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. The pyrochlore lattice consists of interpenetrating networks of corner-sharing tetrahedra which are generated independently by the ${\mathrm{Yb}}^{3+}$ (magnetic) and ${\mathrm{Ti}}^{4+}$ (nonmagnetic) cations. The pyrochlore lattice is said to be stuffed, wherein ${\mathrm{Yb}}^{3+}$ ions, which are normally found on the 16d site (also called A site), also occupy the ${\mathrm{Ti}}^{4+}$ 16c site (B site).

Figure 2

A comparison between the A-site and B-site oxygen environment in the pyrochlore structure of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. The left panel of the figure shows the scalenohedron environment generated by the oxygen ions at the A site where the ${\mathrm{Yb}}^{3+}$ resides. The symmetry of this structure is similar to that at the B site (right panel) where the ${\mathrm{Ti}}^{4+}$ ions are located.

Figure 3

Inelastic neutron scattering spectra $S\left(\right|Q|,\hslash \omega )$ obtained for the stoichiometric powder and the stuffed powder samples at $T=5$ K are shown in (a) and (b), respectively, with the corresponding $T=5$ K empty can subtracted from each data set. The three horizontal arrows in blue, gray, and red highlight the three crystal field excitations which are found at 76.7, 81.8, and 116.2 meV, respectively.

Figure 4

$\left|Q\right|$ integrated cut for the stoichiometric powder at $T=5$ K. A $\left|Q\right|$ integrated cut ($\left|Q\right|=[4.5,5.25]$ Å${}^{-1}$) obtained from the INS spectra in Fig. 3 for the stoichiometric powder at $T=5$ K is shown. The arrows indicate the corresponding positions of the CEFs. The inset outlines the corresponding CEF transitions from the GS doublet.

Figure 5

Energy cuts of the $\left|Q\right|=[4.5,5.25]$ Å${}^{-1}$ integrated inelastic scattering for the stoichiometric powder sample as a function of temperature. Energy cuts were taken with an appropriate background subtraction and all energy cuts for temperature above $T=5$ K has been vertically translated for clarity.

Figure 6

Energy width and shift of the CEF transitions as a function of temperature. The intrinsic energy width of the CEF transitions as extracted using Eq. (5). The intrinsic energy width corresponding to the stuffed powder is higher at both 5 and 300 K in comparison to the stoichiometric sample. The green dots shows the mean square displacement (MSD) of the ${\mathrm{Yb}}^{3+}$ taken from Ref. [21] and scaled in such a way that the MSDs and the energy widths of the CEF excitations in the stoichiometric powder have the same value at $T=100$ K. The inset shows the shift in energy of the CEF transitions as a function of temperature, relative to that at $T=5$ K.

Figure 7

A direct comparison between the INS from CEF transitions in the stuffed powder (in orange) and the stoichiometric powder (in green) ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ samples. Energy cuts taken at $T=5$ K within a range $\left|Q\right|=[4.50,5.25]$ Å${}^{-1}$ for the stuffed powder (orange) and stoichiometric powder (green) samples.

Figure 8

Magnetization of the A-site ${\mathrm{Yb}}^{3+}$ ion in presence of an O(1) oxygen vacancy. A colored sphere represents the tip of the magnetization vector centered at the ${\mathrm{Yb}}^{3+}$ ion in response to an applied external field of $H=1$ T which rotates within the plane normal to [111]. Many values of the magnetization are shown simultaneously for applied fields uniformly distributed on the unit sphere. For the same [111] component of magnetization, the center of the spheres are sufficiently close to each other, that the final impression is that of rings. The tightness of the rings around the [111] axis implies stronger Ising-like behavior of the ${\mathrm{Yb}}^{3+}$ moment, in this case with a calculated magnetic moment of $3.953 {\mu }_B$ along the local [111] direction.

Figure 9

Magnetization of the “stuffed” ${\text{Yb}}^{3+}$ ion at the B site of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Each sphere represents the tip of the magnetization vector centered at the ${\mathrm{Yb}}^{3+}$ ion in response to an applied rotating external field of $H=1$ T. Neighboring contiguous spheres form a ring pattern. The ellipsoidal shape of the ring pattern suggests Ising-like behavior of the rare earth moment along the local [111] direction, however the transverse extent of the ellipsoidal shape indicates a small precession around the Ising axis. The calculated magnetic moment is $3.25{\mu }_B$.