Ferromagnetic Transition of Pyrochlore Compound Yb2Ti2O7

Abstract

R2Ti2O7 (R = Y and various rare earth elements) has pyrochlore type structure, which consists of two kinds of three-dimensional networks individually formed by the corner-sharing R4and Ti4-tetrahedra, respectively. Due to this structural characteristic, magnetic moments at the R sites are expected to be frustrated, if their nearest neighbor interaction is antiferromagnetic. For R = Tb, the value of Weiss temperature w is 19K, indicating the Tb3þ moments have antiferromagnetic nearest neighbor interaction and the system does not exhibit clear evidence for magnetic ordering. Previously, we investigated both the dynamical and static magnetic properties of Tb2Ti2O7 by means of neutron scattering on a single crystal. Based on results of measurements of the specific heat C and ac magnetic susceptibility , low temperature state of Tb2Ti2O7 was discussed in ref. 4, too. The frustration is also expected even for the system with the ferromagnetic nearest neighbor interaction, if the moments have strong uniaxial anisotropy, where each moment lies along the local principal axis corresponding to the line which connects the site with the center of gravity of the tetrahedron. (There are four principal axes along [111] and other crystallographically equivalent directions.) Such the situation can be found in R2Ti2O7 with R = Dy 5) and Ho, which are called ‘‘spin ice’’. For Yb2Ti2O7, w is equal to be 0:53K as shown in the inset of Fig. 1, indicating the nearest neighbor interaction between the Yb3þ moments is ferromagnetic. The electronic ground state of Yb3þ ion was reported to be a Kramers doublet with relatively small planar anisotropy, g? 1⁄4 4:27 and gk 1⁄4 1:70, where g? and gk are the g-values perpendicular to and along the local principal axis, respectively. Sengupta et al. reported that the system has uniaxial anisotropy, g? 1⁄4 0 and gk 1⁄4 3:4. A sharp peak of C–T curve was reported at 0.24K, indicating the existence of the phase transition. However, Hodges et al. did not observe magnetic reflection except the small angle diffuse scattring. In order to identify the specific heat anomaly at 0.24K, we have carried out neutron diffraction and other magnetic measurements on a single crystal of Yb2Ti2O7 down to 0.03K by using dilution refrigerator. Here, we report that the system exhibits ferromagnetic transition at TC 1⁄4 0:24K. We also discuss the low temperature behavior of the moments. A single crystal of Yb2Ti2O7 was grown by a floating zone (FZ) method. The magnetization M was measured by using a SQUID magnetometer. The method of the ac magnetic susceptibility is described in ref. 4. Neutron measurements were carried out by using the triple axis spectrometer HQR (T1-1) installed at the thermal guide of JRR-3 of JAERI in Tokai. The crystal was oriented with [hh0] and [00l] axes in the scattering plane. Figure 1 shows the M–H curves of Yb2Ti2O7 obtained at 5K with the magnetic fields along [001], [110] and [111], where the anisotropy of the curves is found to be relatively small. We calculated the M–H curves considering an anisotropic Kramers doublet and using a molecular field treatment of the ferromagnetic interaction with a coupling constant . By fitting the calculated curve to the data, the parameters are estimated to be 1⁄4 0:64 0:10T/ B, g? 1⁄4 3:9 0:2 and gk 1⁄4 2:6 0:4. Judging from the rather small differences among the M–H curves, the deduced anisotropy is surprisingly large, but at least much smaller than that reported in refs. 7 and 8. This can be understood as follows. Because Yb sites are divided into four sets with different local principal axes along [111] and three equivalent directions, the averaged anisotropy of the moments over these sets becomes very small, even though the anisotropy is rather large within each set of the Yb moments. The value of saturation magnetization estimated from the M–H curves is 1:8 B/Yb. The T-dependence of the real part of the ac magnetic susceptibility 0 of Yb2Ti2O7 measured with increasing T is shown in the inset of Fig. 2, where a clear anomaly has been observed in the T-dependence at 0.24K. The value of 0 at 0.24K is found to agree with the value of 1=4 N within the experimental error bar, where N is the demagnetization coefficient of the used sample. Because M=H is described as 0=ð1þ 4 0NÞ, which approaches 1=4 N as 0 ! 1, the result indicates that the system exhibits a ferromagnetic transition at TC 1⁄4 0:24K. At T 1⁄4 0:03K (<TC), neutron scattering intensity has been measured at various points Q in the (hhl) scattering plane of the reciprocal space. No reflection has been detected at Q-points except the nuclear Bragg points. The magnetic reflections are observed at several nuclear Bragg 0 2 0.0 0.5 1.0 1.5