Intertwined ordered states in NdxCe1−xCoIn5

The physics of a many-body system of strongly interacting particles defies simple extrapolation of the behavior of individual particles constructed ab-initio. Rather, interactions lead to complex phenomena and stabilize ground states with deeply intertwined degrees of freedom. As a result, novel collective phenomena emerge that are interesting from both fundamental and technological perspectives, as shown in this thesis.
Here, the complex phenomena in Nd$_x$Ce$_{1-x}$CoIn$_5$ are discussed with a focus on the interplay between superconductivity and magnetism. Two main techniques were used: neutron diffraction and ultrasound spectroscopy. It is shown that concentrations as low as 2$\%$ of local-moment Nd ions are sufficient to induce a spin density wave at zero field. The application of magnetic fields transverse to the moment direction suppresses the magnetic order at low fields, but at higher fields, a spin density wave emerges with the same magnetic structure at the Q-phase. These ground states, which have identical symmetry, show completely different interactions between superconductivity and magnetism. While superconductivity is necessary for magnetism at the Q-phase, in the low-field phase, a competing interplay between these orders is found. A detailed investigation of the low field spin density wave revealed a domain selection in the normal state. This study lead to the discovery of a new spintronic phenomenon that allows switching of antiferromagnetic domains without a Zeeman component. Our findings could also inspire studies on other materials and possibly provide a new route to control antiferromagnetic domains.
In this work, a new, flexible, digital ultrasound setup was developed. The results obtained with it show that the nature of the high-field state is deeply intertwined with the d-wave condensate. The Q-phase quantum critical field exhibits a fourfold rotational symmetry in the basal plane. The out-of-plane angular dependence of the upper critical field is characterized within a Pauli limiting model. The Q-phase critical field, however, cannot be characterized as such. Instead, our data is well described by assuming a connection with the high field state observed for $\boldsymbol{H} \parallel [0 0 1]$. Furthermore, our measurements of shear elastic modes provide evidence for vortices that are well separated along the c-axis but show an interconnection within basal plane. This interconnection could be a necessary condition for long-range ordering in the Q-phase. Although our investigations focused on the physics of CeCoIn$_5$, our results are relevant in many different research areas.