Resistivity, magnetization and microscopic $^{75}$As nuclear magnetic resonance (NMR) measurements in the antiferromagnetically ordered state of the iron-based superconductor parent material CaFe$_2$As$_2$ exhibit anomalous features that are consiste
nt with the collective freezing of domain walls. Below $T^*approx 10$ K, the resistivity exhibits a peak and downturn, the bulk magnetization exhibits a sharp increase, and $^{75}$As NMR measurements reveal the presence of slow fluctuations of the hyperfine field. These features in both the charge and spin response are strongly field dependent, are fully suppressed by $H^*approx 15$ T, and suggest the presence of filamentary superconductivity nucleated at the antiphase domain walls in this material.
Magnetization and torque measurements were performed on CeCoIn$_5$ single crystals to study the mixed-state thermodynamics. These measurements allow the determination of both paramagnetic and vortex responses in the mixed-state magnetization. The par
amagnetic magnetization is suppressed in the mixed state with the spin susceptibility increasing with increasing magnetic field. The dependence of spin susceptibility on magnetic field is due to the fact that heavy electrons contribute both to superconductivity and paramagnetism and a large Zeeman effect exists in this system. No anomaly in the vortex response was found within the investigated temperature and field range.
In-plane torque measurements were performed on heavy fermion CeCoIn$_5$ single crystals in the temperature $T$ range 1.8 K $leq T leq 10$ K and applied magnetic field $H$ up to 14 T. The normal-state torque is given by $tau_n propto H^4(1+T/T_K)^{-1}
sin 4phi$. The reversible part of the mixed-state torque, obtained after subtracting the corresponding normal state torque, shows also a four-fold symmetry. In addition, sharp peaks are present in the irreversible torque at angles of $pi/$4, 3$pi$/4, 5$pi$/4, 7$pi$/4, etc. Both the four-fold symmetry in the reversible torque and the sharp peaks in the irreversible torque of the mixed state imply $d_{xy}$ symmetry of the superconducting order parameter. The field and temperature dependences of the reversible mixed-state torque provide further evidence for $d_{xy}$ wave symmetry. The four-fold symmetry in the normal state has a different origin since it has different field and temperature dependences than the one in the mixed state. The possible reasons of the normal state four-fold symmetry are discussed.
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 st
ate. In addition, the mixed-state magnetizations for both $Hparallel c$ and $Hparallel ab$ 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.
