Theory of Strain-Induced Magnetic Order and Splitting of $T_c$ and $T_{\mathrm{TRSB}}$ in Sr${}_2$RuO${}_4$

Abstract

The internal structure of the superconducting state in Sr${}_2$RuO${}_4$ remains elusive at present, and exhibits evidence for time-reversal symmetry breaking. Recent muon spin relaxation measurements under uniaxial strain have revealed an increasing splitting between the superconducting critical temperature $T_c$ and the onset of time-reversal symmetry breaking $T_{\mathrm{TRSB}}$ with applied strain [Grinenko et al., arXiv:2001.08152]. In addition, static magnetic order is induced by the uniaxial strain beyond $\sim$1 GPa, indicating that unstrained Sr${}_2$RuO${}_4$ is close to a magnetic quantum critical point. Here, we perform a theoretical study of the magnetic susceptibility and the associated pairing structure as a function of uniaxial strain. It is found that the recent muon relaxation data can be qualitatively explained from the perspective of spin-fluctuation mediated pairing and the associated strain-dependence of accidentally degenerate pair states in unstrained Sr${}_2$RuO${}_4$. In addition, while unstrained Sr${}_2$RuO${}_4$ features mainly $(2\pi /3,2\pi /3)$ magnetic fluctuations, uniaxial strain promotes $(\pi ,\pm \pi /2)$ magnetism.

8 pages, 4 figures

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• Unsplit superconducting and time reversal symmetry breaking transitions in Sr${}_2$RuO${}_4$ under hydrostatic pressure and disorder
• Superconducting state of Sr${}_2$RuO${}_4$ in the presence of longer-range Coulomb interactions
• Heat capacity double transitions in time-reversal symmetry broken superconductors
• Intrinsic nature of spontaneous magnetic fields in superconductors with time-reversal symmetry breaking
• Leading superconducting instabilities in three-dimensional models for Sr2RuO4
• Strain-induced time reversal breaking and half quantum vortices near a putative superconducting tetra-critical point in Sr${}_2$RuO${}_4$
• Constraints on the superconducting state of Sr${}_2$RuO${}_4$ from elastocaloric measurements
• Neutron scattering studies on spin fluctuations in Sr${}_2$RuO${}_4$
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• Hidden anomalous Hall effect in Sr${}_2$RuO${}_4$ with chiral superconductivity dominated by the Ru $d_{xy}$ orbital
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• Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4
• Suppressed fluctuations as the origin of the static magnetic order in strained Sr${}_2$RuO${}_4$
• Electronic structure correspondence of singlet-triplet scale separation in strained Sr2RuO4
• Tunable topological states hosted by unconventional superconductors with adatoms
• Effects of orbital selective dynamical correlation on the spin susceptibility and superconducting symmetries in Sr${}_2$RuO${}_4$
• Tunable electronic and magnetic phases in layered ruthenates: SrRuO3-SrTiO3 heterostructure upon strain
• Magic angle of Sr${}_2$RuO${}_4$: Optimizing correlation-driven superconductivity
• Superconducting gap symmetry from Bogoliubov quasiparticle interference analysis on {Sr}${}_2${RuO}${}_4$
• Nonlocal electrodynamics and the penetration depth of superconducting Sr${}_2$RuO${}_4$
• Shear Modulus Anomaly of Unconventional Superconductor in a Symmetry Breaking Field
• Competing spin-fluctuations in Sr${}_2$RuO${}_4$ and their tuning through epitaxial strain
• Influence of Fermi Surface Geometry and Van Hove Singularities on the Optical Response of Sr${}_2$RuO${}_4$