Enhancement of critical current density and vortex activation energy in proton-irradiated Co-doped ${\mathbf{BaFe}}_{\mathbf{2}}{\mathbf{As}}_{\mathbf{2}}$

The effect of proton irradiation in $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Co}}_{0.07}\right)}_2{\mathrm{As}}_2$ single crystals is reported. We analyze temperature dependence of the current density and normalized flux relaxation rate in the framework of the collective-creep model. The glassy exponent and barrier height for flux creep are directly determined by Maley's method. Our model functions for barrier height and critical current density in the absence of flux creep are explained by the superposition of $\delta T_c$ and $\delta l$ pinnings. We also approach true critical current density by means of the generalized inversion scheme, and the obtained result is in reasonable agreement with our model function. The proton-irradiation effect on temperature dependence of the current density and normalized relaxation rate can be summarized as doubling of the barrier height at the beginning of flux creep.

Figure 1

Field dependence of $J_s$ in (a) pristine and (b) ${\mathrm{H}}^{+}$-irradiated $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Co}}_{0.07}\right)}_2{\mathrm{As}}_2$ at several temperatures. The dotted line on $•$ (2 K) shows power-law decay of (a) $H^{-0.5}$ and (b) $H^{-0.3}$, respectively. The vertical line indicates the field where we discuss the vortex dynamics $H=5\mathrm{kOe}$.

Figure 2

Inverse current-density dependence of effective pinning energy $U^{*}$ in (a) pristine and (b) ${\mathrm{H}}^{+}$-irradiated $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Co}}_{0.07}\right)}_2{\mathrm{As}}_2$. Inset: Temperature dependence of normalized relaxation rate $S$. The solid line indicates fitting by Eq. (1).

Figure 3

Current-density dependence of $U$ in (a) pristine and (b) ${\mathrm{H}}^{+}$-irradiated $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Co}}_{0.07}\right)}_2{\mathrm{As}}_2$ constructed by the extended Maley's method. The solid line indicates power-law fitting in the large $J$ region.

Figure 4

Temperature dependence of $J_s$ determined from the magnetic hysteresis loop ($•$), model function of $J_c$ before and after creep with the parameters in Table (solid line), $\delta T_c$ and $\delta l$ pinning (dashed line), and $J_c$ reconstructed by GIS (+) in (a) pristine and (b) ${\mathrm{H}}^{+}$-irradiated $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.93}{\mathrm{Co}}_{0.07}\right)}_2{\mathrm{As}}_2$.