Normal state magnetic susceptibility measurements in underdoped YBa$_2$Cu$_3$O$_{7-\delta}$

Motivated by the observation of staggered magnetic moments by Fauqu\'e\textit{ et al.} [Phys. Rev. Letters 96, 197001 (2006)] using neutron diffraction in underdoped YBa$_2$Cu$_3$O$_{7-\delta}$, we have measured the magnetization of fourteen underdoped YBa$_2$Cu$_3$O$_{7-\delta}$ samples under 1 T from $T_C$ to 400 K. The oxygen contents are ranging from 6.43 to 7.00, and the critical temperatures $T_C$ from about 30 K to 91 K. We present here high resolution susceptibility data corresponding to a sensitivity of $10^{-8}$ $\mu_B$ per Cu atom. We separate the different contributions to the magnetization. We find: i) a small ferromagnetic contribution, visible at all temperatures within our range of measurement and consistent with a few ppm of $Fe_30_4$, ii) A ``1/T'' paramagnetic contribution attributed to a few percent of free Cu ions, iii) The contribution of the ``pseudogap'' which gives a susceptibility increasing with temperature excepted in the optimally doped samples where the susceptibility is flat as expected for Pauli paramagnetism. We discuss the physical implications of this contribution in light of experiments from Fauqu\'e \textit{et al}.