Theory of strain-induced magnetic order and splitting of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>T</mml:mi><mml:mi>TRSB</mml:mi></mml:msub></mml:math> in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Sr</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi>Ru</mml:mi><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>

Abstract

The internal structure of the superconducting state in ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ 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 $\ensuremath{\sim}1$ GPa, indicating that unstrained ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ 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 ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$. In addition, while unstrained ${\mathrm{Sr}}_{2}\mathrm{Ru}{\mathrm{O}}_{4}$ features mainly $(2\ensuremath{\pi}/3,2\ensuremath{\pi}/3)$ magnetic fluctuations, uniaxial strain promotes $(\ensuremath{\pi},\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ magnetic order.

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