fast decrease of the $M/H$ plateau value observed in the $M$ vs $T$ curves when the field is increased (See figure 3 of the main article). This indicates that the value of the spontaneous moment is quite small.

To make quantitative comparisons, we have plotted the magnetization as a function of the internal field $H_i$, supposing, as stated previously, that the demagnetizing factors $N$ equal the values of $H/M$ in very low field.

The first conclusion is that the \[100\] direction seems to be the easy axis of magnetization, suggesting that that the moments are mainly oriented along the \[100\] direction. This result seems reasonable since it is approximately the obtained direction for the magnetic moments in Yb$_2$Sn$_2$O$_7$[@Yaouanc13].

![$M$ vs $H_i$ for the single crystal at $T=80$ mK and with $H$ applied along the \[100\] direction. $H_i$ was calculated with $N_{[100]}=3.38$ (cgs units). []{data-label="fig_Ms"}](Plot_YTO_100_MvsHi_80mK){width="7.0cm"}

So, supposing that the ferromagnetic component is parallel to the \[100\] direction, we can estimate the spontaneous moment from the low temperature curve as shown in figure \[fig\_Ms\]. Strictly speaking, the spontaneous magnetization $M_s$ corresponds to the value at which the curve leaves the zero internal field. This would lead in the present case to a 