Multiple superconducting transitions in the ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7$ region of ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7{\text{-Sr}}_2\text{Ru}{\text{O}}_4$ eutectic crystals

We report the superconducting properties of ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7{\text{-Sr}}_2{\text{RuO}}_4$ eutectic crystals, which consist of the spin-triplet superconductor ${\text{Sr}}_2{\text{RuO}}_4$ with a monolayer stacking of ${\text{RuO}}_2$ planes and the metamagnetic normal metal ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7$ with a bilayer stacking. Although ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7$ so far has not been reported to exhibit superconductivity, our ac susceptibility measurements revealed multiple superconducting transitions that occur in the ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7$ region of the eutectic crystals. The diamagnetic shielding essentially reached the full fraction at low ac fields parallel to the $c$ axis. However, both the shielding fraction and the onset temperature are easily suppressed by ac fields larger than 0.1 mT rms and no anomaly was observed in the specific heat. Moreover, the critical field curves of these transitions have a positive curvature near zero fields, which is different from the upper critical field curve of the bulk ${\text{Sr}}_2{\text{RuO}}_4$. These facts suggest that the superconductivity observed in the ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7$ region is not a bulk property. To explain these experimental results, we propose the scenario that stacking ${\text{RuO}}_2$ planes, which are the building blocks of superconducting ${\text{Sr}}_2{\text{RuO}}_4$, are contained in the ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7$ region as stacking faults.

Figure 1

(Color online) Temperature dependence of the real part of the ac susceptibility at ${\mu }_0{H}_{\text{ac}}=0.58\mathrm{\mu }\text{T}$ rms and ${\mu }_0{H}_{\text{dc}}=0\text{T}$: (a) for sample 1 (${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7{\text{-Sr}}_2{\text{RuO}}_4$ eutectic); (b) for sample 1b (i.e., the ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7$ region cut from sample 1). The insets are PLOM images of the samples.

Figure 2

(Color online) Temperature dependence of the ac susceptibility of ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7{\text{-Sr}}_2{\text{RuO}}_4$ eutectic crystals in various ac magnetic fields ($H_{\text{ac}}\parallel c$, ${\mathrm{\mu }}_0{H}_{\text{dc}}=0\text{T}$). (a) and (b) represent the real and imaginary parts of ${\chi }_{\text{ac}}$ of sample 1, respectively. (c) and (d) represent those of sample 2. The insets are PLOM images of the samples. The numbers labeling the curves give the applied ac field amplitude ${\mu }_0{H}_{\text{ac}}$ in $\mu \text{T}$ rms.

Figure 3

(Color online) Temperature dependence of the (a) real and (b) imaginary parts of ${\chi }_{\text{ac}}$ of sample 1b in different dc fields.

Figure 4

(Color online) The dc field dependence of the real part of ${\chi }_{\text{ac}}$ of sample 1b. The inset gives an enlarged view near onset. In order to take the residual fields into account in our equipment, which are estimated to be approximately 1 mT, we determined zero field as a field at which ${\chi }^{\prime }$ becomes minimum.

Figure 5

(Color online) $H\text{−}T$ phase diagram of sample 1b for $H_{\text{ac}}\parallel H_{\text{dc}}\parallel c$ determined from the ac susceptibility measurements. The circles and triangles represent the critical fields of transitions $\mathrm{B}$ and $\mathrm{C}$, respectively. The open symbols are obtained from the field sweep data and the closed symbols are from the temperature sweep data. $H_{\mathrm{c}2}$ of bulk ${\text{Sr}}_2{\text{RuO}}_4$ from specific-heat data (Ref. 14, closed squares) and from ac susceptibility measurements (Ref. 15, open squares) are also plotted. The insets show the low-field region below 3 mT. The solid lines represent fits of the data close to $T_0^{\ast }\equiv T^{\ast }\left(H_{\text{dc}}=0\right)$ by using the function $\alpha {\left(1-T/T_0^{\ast }\right)}^n$. The dashed lines present results of linear fittings to the data between 0 K and $0.7T_0^{\ast }$.

Figure 6

(Color online) $H\text{−}T$ phase diagram of sample 1b for $H_{\text{ac}}\parallel H_{\text{dc}}\parallel ab$. The circle and triangular symbols represent the critical fields of transitions $\mathrm{B}$ and $\mathrm{C}$ determined by the ac susceptibility measurements, respectively. The upper critical fields $H_{\mathrm{c}2}$ of bulk ${\text{Sr}}_2{\text{RuO}}_4$ are obtained from the ac susceptibility measurements (Ref. 15, squares). The solid lines are guides to the eye.

Figure 7

(Color online) Temperature dependence of the electronic specific heat divided by temperature $c_{\mathrm{e}}/T$ of sample 1b. The inset represents $c_p/T$ plotted against $T^2$. The arrows mark $T_{\mathrm{B}}^{\ast }$ and $T_{\mathrm{C}}^{\ast }$ of this sample at zero field.

Figure 8

(Color online) X-ray diffraction pattern for the $ab$ plane of sample 1b. Note that the vertical axis is in a logarithmic scale.

Figure 9

(Color online) Scenarios for the superconductivity observed in the ${\text{Sr}}_3{\text{Ru}}_2{\text{O}}_7$ region of eutectic crystals are depicted. The superconducting regions are probably distributed along the $ab$ planes because the shielding currents mainly flow within the $ab$ planes. Such a layered arrangement is not taken into account in our simple model calculations.

Figure 10

(Color online) [(a) and (b)] Experimental and [(c)–(f)] calculated results of ${\chi }_{\text{ac}}\left(T\right)$ at various ac magnetic fields in ${\mu }_0{H}_{\text{dc}}=0\text{T}$. The numbers labeling the curves indicate the applied ac field amplitude ${\mu }_0{H}_{\text{ac}}$ in $\mu \text{T}$ rms.