ac susceptibility investigation of vortex dynamics in nearly optimally doped $R$FeAsO${}_{1-x}$F${}_x$ superconductors ($R$ = La, Ce, Sm)

Ac susceptibility and static magnetization measurements were performed in the nearly optimally doped LaFeAsO${}_{0.9}$F${}_{0.1}$ and CeFeAsO${}_{0.92}$F${}_{0.08}$ superconductors, complementing earlier results on SmFeAsO${}_{0.8}$F${}_{0.2}$ [Phys. Rev. B 83, 174514 (2011)]. The magnetic field-temperature phase diagram of the mixed superconducting state is drawn for the three materials, displaying a sizable reduction of the liquid phase upon increasing $T_c$ in the range of applied fields ($H⩽5$ T). This result indicates that SmFeAsO${}_{0.8}$F${}_{0.2}$ is the most interesting compound among the investigated ones in view of possible applications. The field-dependence of the intragrain depinning energy $U_0$ exhibits a common trend for all the samples with a typical crossover field value (2500 Oe $\lesssim H_{\mathrm{cr}}\lesssim 5000$ Oe) separating regions where single and collective depinning processes are at work.

Figure 1

$M_{\mathrm{dc}}/H$ vs. $T$ curves (volume units) in FC conditions at $H=5$ Oe. The estimated $T_c\left(0\right)$ values are indicated in correspondence of the diamagnetic onsets.

Figure 2

Left:${\chi }_{\mathrm{ac}}$ vs. $T$ raw data for CeFeAsO${}_{0.92}$F${}_{0.08}$ ($H_{\mathrm{ac}}=1.5$ Oe and ${\nu }_m=478$ Hz) at different $H$ values. The imaginary and the real components are shown in the upper and lower panels, respectively (volume units). Right: zoom of the onset region of the curves already reported in the left panels relative to ${\chi }_{\mathrm{ac}}^{\prime \prime }$ and to the first derivative of ${\chi }_{\mathrm{ac}}^{\prime }$ with respect to $T$ (upper and lower panels, respectively. See text for further details).

Figure 3

Phase diagrams for the FLs in the investigated samples. Data for SmFeAsO${}_{0.8}$F${}_{0.2}$ have already been reported in Ref. 11. Open symbols track the irreversibility line as deduced from data taken at ${\nu }_m=37$ Hz (dashed-dotted lines are guides for the eye). Full symbols track ${\langle H_{c2}\left(T\right)\rangle }_{\mathrm{pwd}}$ (continuous lines are linear fits).

Figure 4

Representation of the irreversibility lines relative to the investigated samples [already reported in the phase diagrams (see Fig. 3)], where $H_{\mathrm{irr}}\left(T\right)$ has been normalized with respect to the relative value of ${\langle H_{c2}\left(0\right)\rangle }_{\mathrm{pwd}}$. Continuous lines are best fits according to Eq. (5).

Figure 5

Main panel: $H$ dependence of the depinning energy barriers ${\langle U_0\left(H\right)\rangle }_{\mathrm{pwd}}$ in the three investigated samples. Data relative to SmFeAsO${}_{0.8}$F${}_{0.2}$ have already been reported in a previous work.[11] Continuous lines are best-fits to data according to a simple $1/H$ dependence. Inset: logarithmic ${\nu }_m$ dependence of $1/T_p$ in CeFeAsO${}_{0.92}$F${}_{0.08}$ ($H_{\mathrm{ac}}=1.5$ Oe while ${\mu }_{0}H=1.5$ T). The continuous line is a best-fit function according to Eq. (6).

Figure 6

Graphical representation of the collapse of experimental data represented in Fig. 5 after a proper normalization according to the value of $1/{\lambda }_{\mathrm{ab}}^2\left(0\right)$ estimated at 250 Oe. The continuous line is a guide to the eye.

Figure 7

Graphical representation of the quantity between curly brackets in Eq. (B9). The dashed lines are guides for the eye and they can be used to extrapolate the intercept values back to $H=0$ Oe.