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YBa$_2$Cu$_3$O$_7$ 24$^\circ$ (30$^\circ$) bicrystal grain boundary junctions(GBJs), shunted with 60\,nm (20\,nm) thick Au, were fabricated by focused ionbeam milling with widths $80\,{\rm nm} \le w \le 7.8\,\mu$m. At 4.2\,K we findcritical current densities $j_c$ in the $10^5\,{\rm A/cm^2}$ range %\dkc{\#1}(without a clear dependence on $w$) and an increase in resistance timesjunction area $\rho$ with an approximate scaling $\rho\propto w^{1/2}$. For thenarrowest GBJs $j_c\rho\approx 100\,\mu$V, which is promising for therealization of sensitive nanoSQUIDs for the detection of small spin systems. Wedemonstrate that our fabrication process allows the realization of sensitivenanoscale dc SQUIDs; for a SQUID with $w\approx 100$\,nm wide GBJs we find anrms magnetic flux noise spectral density of $S_\Phi^{1/2}\approx4\,\mu\Phi_0/{\rm Hz}^{1/2}$ in the white noise limit. We also derive anexpression for the spin sensitivity $S_\mu^{1/2}$, which depends on$S_\Phi^{1/2}$, on the location and orientation of the magnetic moment of amagnetic particle to be detected by the SQUID, and on the SQUID geometry. Forthe not optimized SQUIDs presented here, we estimate$S_\mu^{1/2}=390\,\mu_B/\sqrt{\rm{Hz}}$, which could be further improved by atleast an order of magnitude.

YBa2Cu3O7 grain boundary junctions and low-noise superconducting quantum interference devices patterned by a focused ion beam down to 80 nm linewidth