Critical Current Oscillations in the Intrinsic Hybrid Vortex State of SmFeAs(O,F)

In layered superconductors the order parameter may be modulated within the unit cell, leading to nontrivial modifications of the vortex core if the interlayer coherence length ${\xi }_c(T)$ is comparable to the interlayer spacing. In the iron pnictide SmFeAs(O,F) ($T_c\approx 50\mathrm{K}$) this occurs below a crossover temperature $T^{\star }\approx 41\mathrm{K}$, which separates two regimes of vortices: anisotropic Abrikosov-like at high and Josephson-like at low temperatures. Yet in the transition region around $T^{\star }$, hybrid vortices between these two characteristics appear. Only in this region around $T^{\star }$ and for magnetic fields well aligned with the FeAs layers, we observe oscillations of the $c$-axis critical current $j_c(H)$ periodic in $1/\sqrt{H}$ due to a delicate balance of intervortex forces and interaction with the layered potential. $j_c(H)$ shows pronounced maxima when a hexagonal vortex lattice is commensurate with the underlying crystal structure. The narrow temperature window in which oscillations are observed suggests a significant suppression of the order parameter between the superconducting layers in SmFeAs(O,F), despite its low coherence length anisotropy (${\gamma }_{\xi }\approx 3–5$).

Figure 1

(a) $C$-axis critical current $j_c(H)$ at $T^{\star }=41\mathrm{K}$ for well-aligned in-plane fields, extracted from $I–V$ curves using a fixed voltage criterion. Pronounced oscillations appear on top of a decreasing background as the field is ramped up. Inset: SmFeAs(O,F) single crystal carved by a FIB into a shape suitable for vortex channel flow between the layers. The active part (purple) is a $3\mu \mathrm{m}$ long slab along the $c$ axis ($3\times 1\mu {\mathrm{m}}^2$ in cross section). The overlaid sketch illustrates the experimental situation of in-plane vortices driven by transverse currents to slide between the FeAs layers. (b) Oscillatory component $\mathrm{\Delta }{j}_c(H)$ after subtracting a power law background. The oscillations first appear around 4 T, and their amplitude grows in field.

Figure 2

(a) Sketch of the hexagonal in-plane hybrid-vortex lattice configuration (red circles indicate core centers) in a matching situation, i.e., with a lattice height $h$ being an integer multiple $n$ of the unit cell spacing $d$. The maxima in $j_c$ are observed when the period of the vortex lattice is commensurate with the underlying lattice. (b) $\mathrm{\Delta }{j}_c$ oscillations and peak indices $n$ as a function of $1/\sqrt{H}$. At large $n$, i.e., low vortex densities, the peak positions are well described by Eq. (2) (blue dashed line), while the triangular peaks at high fields appear at slightly lower fields.

Figure 3

Oscillatory component of the critical current $j_c(H)$ after background subtraction. In SmFeAs(O,F) (left), the oscillations exist only in a narrow region around $T^{\star }$. This is in contrast to other layered superconductors, in which $j_c$ oscillations are observed over a wider temperature range. An example of such a behavior is provided by $({\mathrm{V}}_2{\mathrm{Sr}}_4{\mathrm{O}}_6){\mathrm{Fe}}_2{\mathrm{As}}_2$ (right). The longer $c$-axis spacing leads to a stronger Josephson behavior when compared to SmFeAs(O,F), which induces oscillations periodic in field instead of $1/\sqrt{(}H)$.

Figure 4

Order parameter modulus $|\psi {|}^2$ in a situation of slightly suppressed OP in the SmO layer following Eq. (4). (left panel) Large Abrikosov vortex at high T spans several unit cells. (middle) Hybrid vortex at $T^{\star }$ gains condensation energy by centering the core in the SmO layer of suppressed OP, yet there still is a significant suppression of the OP in the adjacent FeAs layers leading to $c$-direction mobility. (right) Below $T^{\star }$, the vortex is completely confined between two FeAs layers. The suppression of the superfluid density limits the local critical current perpendicular to the layers, leading to an elongation of the core along the $a$ direction.