Thickness-induced crossover from strong to weak collective pinning in exfoliated ${\mathrm{FeTe}}_{0.6}{\mathrm{Se}}_{0.4}$ thin films at 1 T

We studied flux pinning in exfoliated ${\mathrm{FeTe}}_{0.6}{\mathrm{Se}}_{0.4}$ thin-film devices with a thickness $d$ from 30 to 150 nm by measuring the critical current density $J_{\mathrm{c}}$. In bulk ${\mathrm{FeTe}}_{0.6}{\mathrm{Se}}_{0.4}$, the flux pinning has been discussed in the framework of weak collective pinning, while there is little knowledge on the pinning mechanism in the thin-film region. From the thickness $d$ dependence of $J_{\mathrm{c}}$ at a fixed magnetic field of 1 T, we found that the strong pinning is dominant below $d\approx 70$ nm, while the weak collective pinning becomes more important above $d\approx 100$ nm. This crossover thickness can be explained by the theoretical model proposed by van der Beek et al. [Phys. Rev. B 66, 024523 (2002)].

Figure 1

(a) Temperature dependence of magnetic susceptibilities of as-grown bulk FTS (square) and annealed bulk FTS (circle) under the magnetic field (${\mu }_0{H}_{\parallel c}$) of 1 mT. The closed and open symbols indicate data obtained with field cooling (FC) and ZFC, respectively. The vertical axis is normalized by the data for ZFC at $T=5$ K for each sample. (b) Optical microscope image of our typical device. The white scale bar corresponds to 10 $\mu \mathrm{m}$.

Figure 2

(a) Temperature $T$ dependence of $\rho$ of FTS thin-film devices. The inset shows the close-up near $T_{\mathrm{c}}$. We define two $T_{\mathrm{c}}$, i.e., $T_{\mathrm{c}}^{\mathrm{zero}}$ and $T_{\mathrm{c}}^{\mathrm{on}}$, as detailed in the main text. (b) Thickness $d$ dependence of $T_{\mathrm{c}}^{\mathrm{zero}}$ and $T_{\mathrm{c}}^{\mathrm{on}}$. We also plot $T_{\mathrm{c}}^{\mathrm{bulk}}$ of annealed bulk FTS crystal for reference.

Figure 3

(a) Current-voltage properties for $d=95$ nm thick device under the out-of-plane magnetic field ${\mu }_0{H}_{\parallel c}=1\mathrm{T}$ at various temperatures. (b) Temperature dependence of $J_{\mathrm{c}}\left(T\right)$ for $d=95$ nm thick device under the out-of-plane magnetic field ${\mu }_0{H}_{\parallel c}=1\mathrm{T}$. The green dotted line is the best fit with Eqs. (2, 3, 4), while the red and blue dashed lines are the contributions from $\delta T_{\mathrm{c}}$ and $\delta l$ pinnings, respectively.

Figure 4

(a) $J_{\mathrm{c}}$ of $d=95$ nm thick device measured at $T=3$ K as a function of ${\mu }_{0}H$ along the $ab$ plane (black circle) and the $c$ axis (red circle). (b) $J_{\mathrm{c}}$ of $d=95$ nm thick device measured at $T=3$ K and ${\mu }_{0}H=1$ T as a function of angle $\theta$ from the $c$ axis (green circle). We show the definitions of $\theta$ and ${\mu }_{0}H$ in the inset. The magnetic field applied along the $ab$ plane corresponds to $\theta ={90}^{\circ }$.

Figure 5

(a) Temperature dependence of $J_{\mathrm{c}}\left(T\right)$ at ${\mu }_0{H}_{\parallel c}=0$ T (black circles) and 1 T (red triangles) for $d=30$ and 110 nm. The green dotted line is the best fit for $d=30$ nm at ${\mu }_0{H}_{\parallel c}=0$ T using Eqs. (2, 3, 4). (b) Thickness dependence of $J_{\mathrm{c}0}$ for ${\mu }_0{H}_{\parallel c}=0$ T (black circles) and 1 T (red triangles). For comparison, we also plot $J_{\mathrm{c}}$ at ${\mu }_0{H}_{\parallel c}=1$ T for bulk FTS in Ref. [7] (red square). The solid line is the best fit with Eq. (1) for $J_{\mathrm{c}0}$ below $d=50$ nm.

Figure 6

(a) Thickness dependence of ${\eta }^{\delta l}$ (blue circles) and ${\eta }^{\delta T_{\mathrm{c}}}$ (red circles) for annealed FTS samples. We also plot ${\eta }^{\delta l}$ (blue triangles) and ${\eta }^{\delta T_{\mathrm{c}}}$ (red triangles) for as-grown FTS samples. For comparison, we also plot $\eta$ for bulk FTS in Ref. [7] (square). (b) Temperature dependence of $J_{\mathrm{c}}\left(T\right)$ for $d=105$ nm thick as-grown device under the out-of-plane magnetic field ${\mu }_0{H}_{\parallel c}=1\mathrm{T}$. The green dotted line is the best fit with Eqs. (2, 3, 4), while the red and blue dashed lines are the contributions from $\delta T_{\mathrm{c}}$ and $\delta l$ pinnings, respectively.