Magnetic excitations in the ground state of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$

We report an extensive study on the zero field ground state of a powder sample of the pyrochlore ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. A sharp heat capacity anomaly that labels a low temperature phase transition in this material is observed at 280 mK. Neutron diffraction shows that a quasicollinear ferromagnetic order develops below $T_{\mathrm{c}}$ with a magnetic moment of $0.87\left(2\right){\mu }_{\mathrm{B}}$. High resolution inelastic neutron scattering measurements show, below the phase transition temperature, sharp gapped low-lying magnetic excitations coexisting with a remnant quasielastic contribution likely associated with persistent spin fluctuations. Moreover, a broad inelastic continuum of excitations at $\sim 0.6$ meV is observed from the lowest measured temperature up to at least 2.5 K. At 10 K, the continuum has vanished and a broad quasielastic conventional paramagnetic scattering takes place at the observed energy range. Finally, we show that the exchange parameters obtained within the framework of linear spin-wave theory do not accurately describe the observed zero field inelastic neutron scattering data.

Figure 1

High resolution neutron diffraction data (red) and refinement (black) for (a) 150 K and (b) 2 K. The difference between the calculated and the measured intensities is given by the blue line below each pattern.

Figure 2

The refinement ${\chi }^2$ plotted versus the stuffing level at 2 K. The minimum values of the uncertainty parameter remain below 1% stuffing. The solid black line highlights the ${\chi }^2$ when the 2.3% stuffing level is reached. The inset shows the IDP and ${\chi }^2$ versus the stuffing level calculated using FullProf. There is a clear linear correlation between the parameters. As the number of ${\mathrm{Yb}}^{3+}$ ions in the 16c site increases, the IDP value decreases, becoming negative for 2.3%.

Figure 3

(a) The flipping ratio measured at the (111) Bragg position (black). The line is a guide to the eye. The phase transition (blue) in heat capacity is also plotted for comparison. (b) Heat capacity over an extended temperature range. Note the position of the two anomalies (green arrows) at $T_{\mathrm{c}}=280$ mK and the second hump at $T\sim 2.5$ K. (c)–(e) Changes in the intensity of the (111), (222), and (400) Brillouin zone center positions around $T_{\mathrm{c}}$, measured at DNS.

Figure 4

(a) Difference between the DNS unpolarized neutron diffraction data collected at 130 and 300 mK (blue points with error bars), interpreted as pure magnetic scattering, along with the refined magnetic structure (black line). The positions of the (200) and (220) magnetic Bragg peaks, present in a splayed icelike ferromagnet and not apparent in our data, are marked in red. (b) Difference between the OSIRIS diffraction data obtained at 50 and 300 mK. The Lorentzian fit (black line) is used to estimate a minimum correlation length of 780 Å in the ground-state ferromagnetic order.

Figure 5

Inelastic neutron scattering spectra measured at OSIRIS at (a) 10 K, (b) 2.5 K, (c) 500 mK, and (d) 50 mK. The momentum transfer interval accessed at $\hslash \omega =0$ is $\left|Q\right|=[0.2,1.8]{\AA }^{-1}$.

Figure 6

Cuts along the energy axis binned in the interval $\left|Q\right|=[0.3,0.6]{\AA }^{-1}$ for (a) 10 K, (b) 2.5 K, and (c) 500 mK. The red lines show the sum of all the fit components (see main text) to the measured curves (black points with error bars). The black dashed line is the estimated contribution of the elastic incoherent scattering. The green shaded area corresponds to the fit quasielastic scattering according to Eq. (1). The inset in (a) shows the temperature evolution of the two fitting parameters ${\mathrm{\Gamma }}_Q$ and $A$ for temperatures measured above $T_{\mathrm{c}}$. The solid lines are guides to the eye.

Figure 7

Three different cuts at 50 mK for (a) $\left|Q\right|=[0.3,0.6]{\AA }^{-1}$, (b) $\left|Q\right|=[0.9,1.2]{\AA }^{-1}$, and (c) $\left|Q\right|=[1.5,1.8]{\AA }^{-1}$. Note that the (111) Bragg peak is contained in the $\left|Q\right|$ range of panel (b) and that it causes the observed broadening of the elastic line. In addition to the estimated quasielastic scattering (green), two sharp magnetic excitations (yellow and red dashed areas, respectively) at $\hslash \omega =0.10$ meV (FWHM = 25 $\mu \mathrm{eV}$) and at $\hslash \omega =0.17$ meV (FWHM = 70 $\mu \mathrm{eV}$) and estimated inelastic continuum (blue dashed area) contribute to the observed line shape.

Figure 8

(a) A broad cut corresponding to the integrated intensity over the interval $\left|Q\right|=[0.6,1.4]{\AA }^{-1}$ is shown. (b) Energy binned in the range $\hslash \omega =[0.4,0.8]$ meV displaying the $\left|Q\right|$ dependence of the continuum. The dispersion is double peaked at 0.9 and 1.4 ${\AA }^{-1}$. The red line is a guide to the eye.

Figure 9

Resolution convolved (25 $\mu \mathrm{eV}$) expected spin-wave spectra calculated using the exchange parameters determined in (a) Ref. [6] and (b) Ref. [14]. (c) Cuts along the energy axes in the same $\left|Q\right|$ ranges shown in Fig. 7, including the model of Ref. [4]. The yellow and red lines mark the position of the two sharp excitations measured in our sample.