$\mu \mathrm{SR}$ measurements on ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ under $\langle 110\rangle$ uniaxial stress

Muon spin rotation/relaxation ($\mu \mathrm{SR}$) and polar Kerr effect measurements provide evidence for a time-reversal symmetry breaking (TRSB) superconducting state in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. However, the absence of a cusp in the superconducting transition temperature ($T_{\mathrm{c}}$) vs stress and the absence of a resolvable specific heat anomaly at TRSB transition temperature ($T_{\mathrm{TRSB}}$) under uniaxial stress challenge a hypothesis of TRSB superconductivity. Recent $\mu \mathrm{SR}$ studies under pressure and with disorder indicate that the splitting between $T_{\mathrm{c}}$ and $T_{\mathrm{TRSB}}$ occurs only when the structural tetragonal symmetry is broken. To further test such behavior, we measured $T_{\text{c}}$ through susceptibility measurements and $T_{\text{TRSB}}$ through $\mu \mathrm{SR}$, under uniaxial stress applied along a $\langle 110\rangle$ lattice direction. We have obtained preliminary evidence for suppression of $T_{\text{TRSB}}$ below $T_{\text{c}}$, at a rate much higher than the suppression rate of $T_{\text{c}}$.

Figure 1

(a) Photographs of the holder with a mounted sample A consisting of three rectangular-shaped pieces glued into the holder side by side. (Left) The front view of the mounted sample with hematite masks used to screen the portions of the holder in the muon beam. Concentric coils behind the sample (not seen) are used for in situ measurements of $T_{\text{c}}$. (Right) The photograph of the sample from the back side with two glued strain gauges. (b) Schematics of the ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ rod cross section illustrating the orientation of the individual pieces, determined by x-ray Laue photos. The misalignment of the pieces regarding the crystallographic $c$ axis is intended to reduce the probability of a cleavage under stress. (c) Comparison of the temperature dependence of the specific heat and in situ ac susceptibility measured at zero stress. (d) The temperature dependencies of the in situ ac susceptibilities at different applied uniaxial stress. Inset shows zoom of a region close to $T_{\mathrm{c}}=1.448\pm 0.015$ K, which we take as the transition midpoint. Heat capacity and transverse-field $\mu \mathrm{SR}$ data show that the samples are fully superconducting, so we identify the extrema of the susceptibility signal as $4\pi \chi =0$ and $-1$.

Figure 2

(a)–(c) Sample A: Zero-field $\mu \mathrm{SR}$ asymmetry $A\left(t\right)$ at a temperature above $T_{\text{c}}$ and at the lowest temperature reached at 0 GPa, $-0.19$ GPa, and $-0.4$ GPa $\langle 110\rangle$ compressive stress. (d)–(f) Temperature dependence of the muon spin relaxation rate $\lambda$ (left) and magnetic susceptibility (right). The fits to $\lambda \left(T\right)$ (maroon lines) are explained in the text. Sample B: Zero-field $\mu \mathrm{SR}$ asymmetry $A\left(t\right)$ at a temperature above and below $T_{\text{c}}$ (g) zero stress and (h) $-0.75$ GPa $\langle 110\rangle$ compressive stress. (i), (j) Temperature dependence of the muon spin relaxation rate $\lambda$ (left) and in situ diamagnetic susceptibility data (right). Maroon solid lines are the fits to $\lambda \left(T\right)$ with $b$ as a common fitting parameter for panels (i), (j); dashed orange curve in panel (j) is the fit with $b$ as an individual fitting parameter. For further details, see the text.

Figure 3

(a) Comparison of the temperature dependence of the in situ ac susceptibility between samples A and B. (b), (c) Temperature dependencies of the muon spin relaxation rate at 0 GPa and $-0.40$ GPa for sample A and at 0 GPa and $-0.75$ GPa for sample B, plotted together. Note that the $-0.75$ GPa curve for sample B was shifted down for better comparison with 0 GPa data.

Figure 4

Stress dependence of the superconducting and TRSB transition temperatures extracted from the experimental data together with linear fitting curves to extract $|d{T}_{\text{c}}/d{\sigma }_{110}|$ and the upper limit for the $|d{T}_{\text{TRSB}}/d{\sigma }_{110}|$ slope.