is then equal to the inverse of the demagnetizing factor $N$. For the four measurements performed (two powder samples and two orientations of a single crystal), the measured $M/H$ value (which can be considered as the susceptibility in such small fields) is roughly equal to the estimated value of $1/N$ [@SupMat]. This result shows that a spontaneous magnetization exists in [Yb$_2$Ti$_2$O$_7$]{} below the specific heat anomaly, thus implying the existence of an ordered ferromagnetic component in the system. It also suggests that the specific heat anomaly is associated with a magnetic transition. Analysis of the $M$ vs $H$ curves at low field gives an estimation of the ordered moment between 0.35 and 0.8 $\mu_B$/Yb, with a main component along the \[100\] direction, which implies that a fraction of the moment is still fluctuating in the ordered phase [@SupMat]. The obtained orientation might indicate that the magnetic structure is similar to the one determined in the related compound Yb$_2$Sn$_2$O$_7$ [@Yaouanc13].

![(color online) $M/H$ vs $T$ for the single crystal in an applied fied $H=5$ Oe parallel to the \[100\] axis at the proximity of the transition. The temperature was swept in steps of 5 mK and 100 extractions were made at 