Ferromagnetic correlations in Yb$_2$Ti$_2$O$_7$ as revealed by small angle neutron scattering techniques

We report low temperature SANS measurements on frustrated S$_\text{eff}$=1/2 XY pyrochlore magnet Yb$_2$Ti$_2$O$_7$[1]. The ground state of this material has been proposed as a realization of a quantum spin ice; however, the low temperature phase behaviour has been complicated by sample dependencies believed to be related to weak ``stuffing" [2]. Our SANS study focuses on the low Q structure of elastic ``rods'' of magnetic scattering which extend from Q=0 along the 111 direction. Using a single crystal sample, we characterize the low Q ($<$0.2\AA$^{-1}$) temperature dependence of this structured diffuse scattering intensity to T=30mK, passing through the enigmatic heat capacity anomaly near Tc=200mK. The temperature dependence of this diffuse scattering near Q=0 is largely consistent with that measured previously near 111 [3]. [1] K.A. Ross et al., Phys. Rev. X 1, 021002 (2011) [2] K.A. Ross et al., Phys. Rev. B 86, 174424 (2012) [3] K.A. Ross et al., Phys. Rev. B 84, 174442 (2011)