  Torque and magnetization measurements in magnetic fields $H$ up to 14 T were
performed on CeCoIn$_5$ single crystals. The amplitude of the paramagnetic
torque shows an $H^{2.3}$ dependence in the mixed state and an $H^{2}$
dependence in the normal state. In addition, the mixed-state magnetizations for
both $H\parallel c$ and $H\parallel ab$ axes show anomalous behavior after the
subtraction of the corresponding paramagnetic contributions as linear
extrapolations of the normal-state magnetization. These experimental results
point towards a nonlinear paramagnetic magnetization in the mixed state of
CeCoIn$_5$, which is a result of the fact that both orbital and Pauli limiting
effects dominate in the mixed state.
