order magnetic transition in [Yb$_2$Ti$_2$O$_7$]{}**]{}

Samples and demagnetizing factors
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As stated in the main text, the reported magnetization and a.c. susceptiblity were measured on the same samples as Ref. : two powder samples, from the same synthesis, and a single crystal. The details of the single crystal growth are given in Ref. .

The shape of these samples is irregular thus preventing an accurate correction for demagnetizing effects. Using the formula provided for parallelepipeds [@Aharoni98], the demagnetizing factors $N$ could be nevertheless estimated:\
i) for the single crystal, $N$ is within the range \[2.7; 3.5\] and \[5.3; 4.7\] (cgs units) for measurements along the \[100\] and \[110\] directions respectively.\
ii) the compacted powder has an elongated shape, giving $N \approx 2$ (cgs units).\
iii) for the crushed powder, the estimation is much harder, but $N$ should be larger.

Magnetization vs Temperature below 4.2 K
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![$M/H$ vs $T$ for the single crystal ($H$ // \[100\]) and for the two powder samples. The applied field was 5 Oe below 1 K and 100 Oe above (where the magnetization $M$ is linear in $H$ for such fields). Inset: $H/M$ vs $T$ for the single crystal. The line is a fit to 