Dopant Diameter Dependence of $J_{\textrm{c}}(B)$ in Doped YBCO Films

In YBCO films doped with artificial pinning centers, such as BaZrO
₃
nanorods or BaCeO
₃
nanodots, the critical current density, J
_c
(B || c), is usually described with the form J
_c
~ B
^-α
even though the shape of the J
_c
(B)-curve does not really allow this. In the field region just above the low field plateau, the shape of the Jc(B)-curve (in log-log scale) is rounded and not straight as in undoped films. The exponent α is found to decrease from 0.5 to around 0.2 in BaZrO
₃
doped films and to 0.4 in BaCeO
₃
doped films. The incompatibility with the curved data and the linear fit has lead to publication of α-parameters which are not comparable to each other due to different fitting limits. In this paper we show that it is better to use the Dew-Hughes pinning force F
_p
(B) = F
_p0
(B/B
_irr
)
^p
(1 - B/B
_irr
)
^q
to describe the field dependence, where α ≈ 1 - p. We also show that the p and the roundness of the curve depend on the diameter of the pinning centers, but not, e.g., temperature or dopant concentration. This is shown from measurements of differently doped thin YBCO films and from large scale Ginzburg-Landau simulations. The result should have been expected since the diameters of the dopants are roughly the same size as the coherence length and it has been shown earlier that pinning centers much smaller than the coherence length lead to α = 0.5 and those much larger lead to α = 1.