Flux pinning in ${\text{PrFeAsO}}_{0.9}$ and ${\text{NdFeAsO}}_{0.9}{\text{F}}_{0.1}$ superconducting crystals

Local magnetic measurements are used to quantitatively characterize heterogeneity and flux line pinning in ${\text{PrFeAsO}}_{1-y}$ and NdFeAs(O,F) superconducting single crystals. In spite of spatial fluctuations of the critical current density on the macroscopic scale, it is shown that the major contribution comes from collective pinning of vortex lines by microscopic defects by the mean-free-path fluctuation mechanism. The defect density extracted from experiment corresponds to the dopant atom density, which means that dopant atoms play an important role both in vortex pinning and in quasiparticle scattering. In the studied underdoped ${\text{PrFeAsO}}_{1-y}$ and NdFeAs(O,F) crystals, there is a background of strong pinning, which we attribute to spatial variations in the dopant atom density on the scale of a few dozen to 100 nm. These variations do not go beyond 5%—we therefore do not find any evidence for coexistence of the superconducting and the antiferromagnetic phase. The critical current density in sub-tesla fields is characterized by the presence of a peak effect, the location of which in the $\left(B,T\right)$ plane is consistent with an order-disorder transition of the vortex lattice.

Figure 1

Transmission electron microscopy images of single crystalline ${\text{PrFeAsO}}_{1-y}$. (a) High-resolution bright field image revealing the undulation of the FeAs layers. (b) Bright field micrograph of a zone containing a nm-size inclusion (indicated by the white arrow). (c) Bright field image revealing contrast due to a line dislocation (indicated by the arrow).

Figure 2

(Color online) Cuts through reciprocal space of the ${\text{PrFeAsO}}_{1-y}$ compound reconstructed from synchrotron radiation x-ray diffraction on crystal 7 (the same crystal as in Ref. 28). (a) The [hk0] plane (b) the [0kl] plane; (c) the [h0l] plane.

Figure 3

(Color online) (a) DMO images of the screening of an ac field of 1 Oe by ${\text{PrFeAsO}}_{1-y}$ (bi)crystal 1 at various temperatures close to $T_c$. Screening first appears in the upper left-hand corner by the crystal (indicated by the arrow). The crystal progressively transits to the superconducting state between 38 and 32 K. (b) Local permeability, defined as the ratio $\left[I\left(\mathbf{r},T\right)-I\left(\mathbf{r},T⪡T_c\right)\right]/\left[I\left(\mathbf{r},T⪢T_c\right)-I\left(\mathbf{r},T⪡T_c\right)\right]$ of the local luminous intensities $I\left(\mathbf{r},T\right)$, in the zones 1–4 indicated in (a).

Figure 4

(Color online) (a) Direct MOI of the screening of an dc field by ${\text{PrFeAsO}}_{1-y}$ crystal 7 (the same crystal as in Ref. 28) at 7.1 K. Shown are a polarized light image of the crystal; and MOI for $H_a=300$, 500 Oe, and the trapped flux in zero field (after the application of 500 Oe). (b) Flux profiles measured from top to bottom across the central part of this crystal for increasing values of the applied magnetic field $H_a$ at a temperature of 11 K.

Figure 5

(Color online) Critical current density $j_c$ of ${\text{PrFeAsO}}_{1-y}$ crystal 7 at $H_a=300\text{Oe}$ as function of temperature. $j_c$ was determined from the slope of the local magnetic flux density measured in the different regions of the crystal indicated in the Inset. The lower drawn line is a fit to Eq. (5), with $n_d=1.5\times {10}^{27}{\text{m}}^{-3}$, the upper drawn line shows that the low temperature $j_c\left(T\right)$ in the strongly pinning regions is the same. Inset: polarized light image of the crystal and five DMO images of screening of $\Delta H_a=1\text{Oe}$ by the same crystal 7 at $T=34-30\text{K}$ (in steps of $-1\text{K}$). The regions 1 – 4 over which $j_c$ was determined are indicated by drawn squares. The scale bar represents a length of $150\mu \text{m}$.

Figure 6

(Color online) ${\text{PrFeAsO}}_{1-y}$: critical current versus temperature for two different crystals. Open and closed circles represent the upper and lower bounds of the $j_c$ of crystal 7 (Ref. 28), the closed squares represent the zero field $j_c$ of crystal 3, while the open squares depict the magnitude of the critical current in the field regime between $B^{\ast }$, above which the strong pinning contribution becomes negligible, but below the onset field of the fishtail effect, $B_{on}$. This value of $j_c$ is attributed to weak collective pinning by oxygen vacancies in the single-vortex limit; the drawn line represents a fit to Eq. (5) with $n_d=1.5\times {10}^{27}{\text{m}}^{-3}$. The dashed line is a fit to Eq. (10) summing strong and weak pinning contributions to the critical current at zero field with parameter values $n_d=1.5\times {10}^{27}{\text{m}}^{-3}$, $n_i=1\times {10}^{21}{\text{m}}^{-3}$, and $f_{p,s}=0.1{\epsilon }_0$

Figure 7

(Color online) Hysteresis loops of the self-field, defined as $H_s=B_{\perp }/{\mu }_0-H_a$, as measured with a microscopic Hall sensor in the center of ${\text{PrFeAsO}}_{1-y}$ crystal 7 at the indicated temperatures. The values of the onset field $H_{on}$ are denoted by the vertical black arrows.

Figure 8

(Color online) (a) MOI flux penetration into ${\text{NdFeAsO}}_{0.9}{\text{F}}_{0.1}$ crystal 1 at $T=9.1\text{K}$. The three frames depict the flux density distribution after the application of an applied field of 20 and 50 mT and the remanent flux after removal of the 50 mT applied field. (b) Flux density profiles measured across the central part of the crystal.

Figure 9

(Color online) Local values of the critical current density $j_c$ in the three regions of ${\text{NdFeAsO}}_{0.9}{\text{F}}_{0.1}$ crystal 1 outlined in the central panel of (a). Also shown are the values of $j_c^{SV}$ and $j_c^s\left(0\right)$ determined for both investigated crystals. The first are compared to Eq. (5) using $n_d=1.5\times {10}^{27}{\text{m}}^{-3}$ and $D_v=0.9\text{nm}$ (lower drawn line), while the latter are fit to Eq. (10) with respective parameter sets ($T_c=37\text{K}$, $n_i=6\times {10}^{21}{\text{m}}^{-3}$, and $f_{p,s}=0.1{\epsilon }_0$) and ($T_c=35\text{K}$, $n_i=2\times {10}^{22}{\text{m}}^{-3}$, and $f_{p,s}=0.1{\epsilon }_0$).

Figure 10

(Color online) ${\text{PrFeAsO}}_{1-y}$: critical current versus doping level as determined from the phase diagram of Ref. 46. Open circles indicate the critical temperature, and filled diamonds indicate the critical current density as measured in various locations in the four different crystals of Fig. 6. The dashed and drawn lines indicate the critical current density expected from weak collective pinning by oxygen vacancies [Eq. (5)] at $T=0$ and $T=5\text{K}$, respectively (here we suppose that ${\lambda }_{ab}^{-2}\propto T_c$, as in Ref. 47).

Figure 11

(Color online) (a) ${\text{PrFeAsO}}_{1-y}$: double logarithmic plot of the critical current versus magnetic field. The drawn lines show the power $B^{-5/8}$ expected from the strong pinning contribution. (b) Ibid for ${\text{NdFeAsO}}_{0.9}{\text{F}}_{0.1}$. Drawn lines show model fits to Eq. (10).

Figure 12

(Color online) $\left(B,T\right)$ vortex matter phase diagram for (1111) iron-pnictide superconductors. (Red) Circles indicate measurements on ${\text{PrFeAsO}}_{1-y}$, while (blue) squares show results on ${\text{NdFeAsO}}_{0.9}{\text{F}}_{0.1}$. Closed circles show the irreversibility field $B_{irr}\left(T\right)$ measured from the onset of a third harmonic response from ac Hall-probe magnetometry; open (blue) squares show the screening onset data of Ref. 30. Peak effect onset fields for both compounds are indicated by barred squares $\left({\text{NdFeAsO}}_{0.9}{\text{F}}_{0.1}\right)$ and open (red) circles $\left({\text{PrFeAsO}}_{1-y}\right)$. Dotted lines show the single vortex to bundle pinning crossover described by Eq. (12), while dashed-dotted lines indicate the order-disorder field described by Eq. (13).