higher temperature, but the hysteresis persists. Above 250 Oe, the hysteresis is lost. The “step" in the magnetization continues reducing in magnitude and broadening.

The results are qualitatively similar in the single crystal (see inset of figure \[fig3\]) and independent of the direction of the applied field. However, the transition in the single crystal appears to be less sensitive to magnetic field, except the bump at 180 mK which is suppressed in 10 Oe. The susceptibility remains linear and the transition is unchanged up to 30 Oe. Above 50 Oe, the transition broadens and starts to shift to higher temperature (which seems analogous to the reported behavior of the a.c. susceptibility in Yb$_2$Sn$_2$O$_7$ [@Dun13]). Above approximately 200 Oe, the hysteresis disappears (similar to the powder samples) and finally, the amplitude of the “step" decreases significantly above 500 Oe. The main conclusions from this field induced behavior are: i) the hysteresis and so the first-order character is preserved up to an applied field of $\sim$ 200 Oe. ii) the increase of the applied field broadens and shifts the magnetization step to higher temperatures, as expected for ferromagnetic transitions. Above 200 Oe, the magnetization measurements alone cannot conclude whether the “step" is 