Manipulation of time reversal symmetry breaking superconductivity in Sr${}_2$RuO${}_4$ by uniaxial pressure

Unconventional superconductivity continues to be one of the most striking chapters in condensed matter physics, by posing challenges to our theoretical understanding of its origin. During the last three decades a large number of unconventional superconductors with exotic properties have been found arising great interest, such as the heavy fermion systems, high T${}_c$ cuprates as well as the Iron based superconductors etc. Sr${}_2$RuO${}_4$, the material I have studied, can be considered as an exemplary case in this regard. In spite of more than two decades of comprehensive research, Sr${}_2$RuO${}_4$ remains one of the most compelling superconductors till date. Various experimental results give evidence that the superconductivity of Sr${}_2$RuO${}_4$ is chiral: including measurements of the Kerr effect, sound velocities, critical currents across junctions, and muon spin relaxation (μSR), the experimental technique at the heart of this dissertation. Recent NMR Knight shift measurements suggests that the pairing is most likely spin-singlet, and in the tetragonal lattice of Sr${}_2$RuO${}_4$, the combination of singlet pairing and chirality compels consideration of an seemingly unlikely order parameter: d${}_{xz}$ ± id${}_{yz}$. It is unlikely because it comes along with a horizontal line node at k${}_z$ = 0, whereas Sr${}_2$RuO${}_4$ has a very low c-axis conductivity. And that makes the question whether or not the superconductivity of Sr${}_2$RuO${}_4$ is chiral, of great importance. This calls for an unique scenario in regard to our understanding of unconventional superconductivity, as the presence of chirality in Sr${}_2$RuO${}_4$ might imply a new form of pairing, which is yet to be firmly determined. Chiral superconductors break time reversal symmetry by definition, and in general time-reversal-symmetry breaking (TRSB) superconductivity indicates complex two component order parameters. Probing Sr${}_2$RuO${}_4$ under uniaxial pressure offers the possibility to lift the degeneracy between such components. However, despite strenuous efforts, a splitting of the superconducting and TRSB transitions under uniaxial pressure has not been observed so far. In this thesis, I report muon spin relaxation measurements on Sr${}_2$RuO${}_4$ samples, placed under uniaxial stress. The relatively large sample size suitable for μSR demanded for a customized uniaxial pressure cell in order to perform our experiments. It has been a technically challenging task to have a fully fledged uniaxial pressure cell with stringent requirements, that is suitable for time restricted facility experiments like μSR. The technical advancement has been documented thoroughly in this thesis. Using the dedicated uniaxial pressure cell, we observed the much awaited stress induced splitting between the onset temperatures of superconductivity and time reversal symmetry breaking, consistent with the qualitative expectations for a chiral order parameter in Sr${}_2$RuO${}_4$. In addition to that, we report the appearance of a bulk magnetic order in Sr${}_2$RuO${}_4$ under higher uniaxial stress for the first time, above the critical pressure at which a Lifshitz transition is known to occur. The signal in the state appearing at high stress qualitatively differs from that in the TRSB state in unstressed Sr${}_2$RuO${}_4$, which provides evidence that the enhanced muon spin relaxation at lower stresses is not a consequence of conventional magnetism. As a whole, our results strongly support the idea of two-component superconducting order parameter in Sr${}_2$RuO${}_4$, that breaks time-reversal symmetry.