Artificial magnetic granularity effects on patterned epitaxial $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$ thin films

An artificial “multigranular” YBCO thin film has been prepared by patterning a network of gridlines, emulating the current-restricting behavior of grain boundaries. This model system allowed us to investigate the magnetic effects of granularity and current percolation problem, having control on the geometry, number of grains, and ratio of inter-to-intragrain critical-current density reduction, $J_c^{\mathrm{GB}}∕J_c^{\mathrm{G}}$. The dc magnetization cycle at $5\mathrm{K}$ showed a peak shift to a positive applied magnetic field value, typically ascribed to granularity. ac measurements performed up to very high driving ac magnetic fields show that ac losses are dominated by dissipation over the whole grain boundary network, whereas the contribution of individual grains cannot be resolved. A high-resolution $(<5\mu \mathrm{m})$ Hall-probe imaging system has been used to visualize the evolution of the magnetization distribution with a cycled applied magnetic field (at 4.2 and $77\mathrm{K}$), and deduce maps of the intragranular and intergranular currents by solving the inverse problem. Quantitative information about the $J_c^{\mathrm{GB}}$ and $J_c^{\mathrm{G}}$ magnetic field dependence and the spatial distribution of $J_c^{\mathrm{G}}$ are presented and discussed.

Figure 1

(Color online) Micrograph of the artificial $21\times 21$ multigranular sample. The grain size is $200\times 200\mu {\mathrm{m}}^2$. The small holes defining the GBs are $30\mu \mathrm{m}$ size, spaced by $10\mu \mathrm{m}$ $(J_c^{\mathrm{GB}}∕J_c^{\mathrm{G}}=0.25)$.

Figure 2

SQUID determined magnetization cycles normalized by the peak magnetization value $M∕M_{\text{peak}}^{\mathrm{sat}}$ vs applied magnetic field at $5\mathrm{K}$, before (bold) and after (open) patterning the granular structure. Cycles measured for different values of the maximum applied magnetic field ${\mu }_0{H}_m$: (◇) $60\mathrm{mT}$, (▵) $80\mathrm{mT}$, (◻) $110\mathrm{mT}$, and (엯) $140\mathrm{mT}$. The inset shows the saturation of the remanent magnetization for ${\mu }_0{H}_m>80\mathrm{mT}$.

Figure 3

(Color online) (a) Temperature dependence of the real ${\chi }^{\prime }$ and imaginary ${\chi }^{″}$ components of the ac susceptibility (SI units) for ${\mu }_0{H}_{\mathrm{ac}}=0.01$, 0.05, 0.1, 0.5, 1.0, and $1.5\mathrm{mT}$ at $f=1111\mathrm{Hz}$; (b) ac magnetic field dependence of the real ${\chi }^{\prime }$ and imaginary ${\chi }^{″}$ components of the ac susceptibility for $f=90$, 270, 810, and $2430\mathrm{Hz}$ at $77\mathrm{K}$.

Figure 4

Temperature dependence of the intergranular (bold) and intragranular (open) critical-current densities determined from SQUID dc magnetometry (squares), $T$ sweep ac susceptibility (circles), and $H_a$ sweep ac susceptibility at $77\mathrm{K}$ (star). The $J_c^{\mathrm{G}}\left(T\right)$ dependence (dashed line) is estimated as $J_c^{\mathrm{G}}\left(T\right)∕f$, where the GB transparency $f=0.25$ is settled by the photolithography dimensions and is therefore temperature independent.

Figure 5

(Color online) Magnetization in the remanence simulated by the program TRAZACORRIENTES® for the $21\times 21$ granular sample with a critical-current density reduction at each GB of 0.25.

Figure 6

(Color online) (a) $B_z$ map in the remanence after a fc process of a region close to the sample border (indicated by the dotted line), measured with a resolution of $10\mu \mathrm{m}$; (b) detail of the magnetic structure at one of the artificially patterned “GBs,” measured with resolution $2.5\mu \mathrm{m}$. Cross sections along the GB (top figure) and transversal to the GB (right figure) are shown.

Figure 7

(Color online) $B_z$ Hall-probe image of approximately $\frac{1}{4}$ of the sample surface, at an applied magnetic field ${\mu }_{0}H=43.5\mathrm{mT}$ on the initial magnetization curve, at $4.2\mathrm{K}$ (ZFC). Also shown, $B_z$ profile along (a) a line of grains, (b) an artificial GB, and (c) a column of grains close to the sample border.

Figure 8

Integrated “magnetization” $\left[B_z\text{−}{\mu }_{0}H\right]$ vs applied magnetic field ${\mu }_{0}H$ cycle determined from Hall-probe magnetometry at $4.2\mathrm{K}$.

Figure 9

(a) “Reconstructed” $\left[B_z\text{−}{\mu }_{0}H\right]$ map at ${\mu }_{0}H=25\mathrm{mT}$ on the return branch of the hysteresis cycle, $T=4.2\mathrm{K}$ (ZFC). Also shown, $\left[B_z\text{−}{\mu }_{0}H\right]$ profile along a row of grains (top figure) and along a column of grains (right figure), indicated by black arrow lines; (b) calculated $J_{\mathrm{x}}(x,y)$ component of the critical-current density. The white arrow indicates the column of grains used for the $J_c^{\mathrm{G}}\left(d\right)$ determination. Right figure: $J_{\mathrm{cy}}\left(y\right)$ profile across the sample center (black arrow) from which $J_c^{\mathrm{GB}}$ is determined; (c) calculated $J_{\mathrm{y}}(x,y)$ critical-current density component. Top figure: $J_{\mathrm{cy}}\left(x\right)$ profile along a line of grains.

Figure 10

Magnetic field dependence of $J_c^{\mathrm{GB}}\left(H\right)$ (엯) and $J_c^{\mathrm{G}}\left(H\right)$ (●) at $4.2\mathrm{K}$. The intragranular $J_c^{\mathrm{G}}$ has been determined for a particular grain (2,5) indicated in Fig. 9b.

Figure 11

(Color online) Determination of the position dependent intragranular $J_c^{\mathrm{G}}(x,y)$ at ${\mu }_{0}H=25\mathrm{mT}$ for six grains [their position within the sample is indicated in Fig. 9c]. Top figure: $J_x$ profile across a single grain from which $J_c^{\mathrm{G}}$ is determined as the value at the maximum. The $J_c^{\mathrm{G}}$ value at each grain is given in $\mathrm{A}∕{\mathrm{m}}^2$.

Figure 12

Dependence of the intragranular critical-current density with the position of the grain respect to the sample border, $J_c^{\mathrm{G}}\left(d\right)$, as sketched in the inset.