Spontaneous vortex phases in superconductor-ferromagnet Pb-Co nanocomposite films

We report measurements which indicate the appearance of spontaneous vortices in lead superconducting films with embedded magnetic nanoparticles and a temperature-induced phase transition between different vortex phases. Unlike common vortices in superconductors, the vortex phase appears in the absence of applied magnetic field. The vortices nucleate exclusively due to the stray field of the magnetic nanoparticles, which serve the dual role of providing the internal field and simultaneously acting as pinning centers. Transport measurements reveal dynamical phase transitions that depend on temperature $\left(T\right)$ and applied field $\left(H\right)$ and support the obtained $H\text{−}T$ phase diagram.

Figure 1

(Color online) (a) TEM image of the Co nanoclusters. (b) Hysteresis loop for a sample with 5% Co volume fraction at 8 K. The inset shows the virgin magnetization curve taken in small external magnetic fields.

Figure 2

(a) Resistivity $\left(\rho \right)$ versus temperature $\left(T\right)$ for an as-prepared film of lead containing about $3.7\text{vol}\%$ cobalt nanoparticles at zero applied magnetic field, (b) normalized resistivity $\left(\rho /{\rho }_{\text{normal}}\right)$ versus temperature $\left(T\right)$ for a reference sample of as-prepared and annealed (at 300 K) pure lead prepared by the same method, and (c) $\rho$ versus $T$ for the same sample in (a) but annealed at 300 K. $T_G$ is the temperature that characterizes the transition to a zero-resistance state. $T^{\ast }$ is the temperature that indicates the kink in the resistivity. The current used in all measurements was $I=0.1\text{mA}$.

Figure 3

(Color online) (a) Isotherms of voltage $\left(V\right)$ versus current $\left(I\right)$ in a log-log scale with no magnetic field applied and $T$ are 2.26, 2.35, 2.44, 2.53, 2.6, 2.72, 2.8, 2.9, 3.0, 3.1, 3.2, 3.4, 3.6, 3.8, 4.0, and 4.2 K from right to left. (b) Low-voltage region of the same isotherms of $V\text{−}I$. (c) Scaling analysis for the same data presented in (a) from $T$ varying from 2.44 to 3.8 K. The exponent $s$ is given by $s=\nu \left(z-2+D\right)$. In the curves different colors indicate different temperatures. (d) Effect of positive and negative magnetic fields (varying from $-0.01$ to 0.01 T) in the $V\text{−}I$ curves at 2.9 K. For details, see main text.

Figure 4

(Color online) $H\text{−}T$ phase diagram of the hybrid system containing Co nanoparticles. SVS represents the spontaneous vortex solid. It is separated by critical line $T_G$ from a strongly PVL. The boundary to the unpinned VL is $T^{\ast }$, the characteristic temperature of the kink feature seen in Fig. 2. The last critical curve is the main superconducting transition at $T_c$ to the N state. Inset: resistivity $\left(\rho \right)$ versus temperature $\left(T\right)$ for various applied magnetic fields from 0 to 0.3 T (right to left).