Quenched metastable vortex states in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, a leading-candidate spin-triplet superconductor and a highly anisotropic quasi-two-dimensional type II superconductor, provides a unique opportunity to study unconventional as well as conventional vortex phases. To investigate its vortex-matter phases, we studied the ac susceptibility of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ for fields parallel to the ${\mathrm{RuO}}_2$ plane by adapting two different thermal processes: In addition to the ordinary field sweep (FS) process, we employed the “each-point field-cooling” (EPFC) process, in which the superconductivity is once thermally destroyed before collecting the data. We find that the ac susceptibility signal substantially changes with the EPFC process. This result indicates that we succeed in inducing new metastable vortex states via the EPFC process. We also find a new field scale $H^{*1}$, below which the FS and EPFC processes provide the same value of the ac susceptibility. This new field scale suggests a liquidlike vortex state in the low-field region.

Figure 1

(a) Schematic of the sample mounted in an ac susceptometer coil. The sample, shown in black, is placed in one part of the pickup coil. Two different thermal processes, (b) the field sweep (FS) process and (c) the each-point field-cooling (EPFC) process, were used in this study.

Figure 2

In-plane dc field dependence of the real part of the ac susceptibility ${\chi }_{\mathrm{SC}}^{\prime }$ of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ at various temperatures for (a) $H_{\mathrm{dc}}\parallel \left[110\right]$ and (b) $H_{\mathrm{dc}}\parallel \left[100\right]$. The triangles indicate data measured in FS processes and the circles indicate EPFC processes. Each curve is shifted vertically by 0.25 for clarity. (c, d) Dependence on dc field of $\Delta {\chi }_{\mathrm{SC}}^{\prime }\equiv {\chi }_{\mathrm{SC}}^{\prime }\left(\mathrm{FS}\right)-{\chi }_{\mathrm{SC}}^{\prime \mathrm{avg}}\left(\mathrm{EPFC}\right)$. Each curve is shifted vertically by 0.2 for clarity. The arrows indicate $H^{*1},H^{*2}$, and $H^{*3}$ characterizing the field dependence of $\Delta {\chi }_{\mathrm{SC}}^{\prime }$ (see text). All panels contain data for up-field sweep (open symbols) and down-field sweep (solid symbols).

Figure 3

Stability of the EPFC branch against a small cycling of the dc field. (a) Changes of the EPFC state toward the FS state after a small dc-field cycling $\delta H_{\mathrm{dc}}$ to a state on the EPFC branch. (b) Results of FS measurements after an EPFC process at ${\mu }_0{H}_{\mathrm{dc}}=1.263$ T, revealing the detailed evolution of the EPFC branch toward the FS branch by a field cycling. The directions of the FS are indicated with arrows. The values of ${\chi }_{\mathrm{SC}}^{\prime }$ in the FS and EPFC processes at 1.265 T are indicated by dashed lines. The insets explain field and thermal treatments in these measurements.

Figure 4

Field-temperature phase diagrams of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ for the dc field along the (a) [110] and (b) [100] directions. The black squares indicate $H_{\mathrm{c}2}$. The red circles, green triangles, and blue triangles indicate $H^{*1},H^{*2}$, and $H^{*3}$, respectively, derived from the comparison between FS and EPFC branches (see text).

Figure 5

Schematic comparison of vortex-lattice configurations for isotropic and anisotropic superconductors with the same vortex density. The red spots indicate vortex cores. The expressions for intervortex distances $a_{\mathrm{iso}},a_{\mathrm{L}}$, and $a_{\mathrm{S}}$ are given in the text.