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We present an optimization study of the spin sensitivity of nanoSQUIDs basedon resistively shunted grain boundary Josephson junctions. In addition the dcSQUIDs contain a narrow constriction onto which a small magnetic particle canbe placed (with its magnetic moment in the plane of the SQUID loop andperpendicular to the grain boundary) for efficient coupling of its straymagnetic field to the SQUID loop. The separation of the location of optimumcoupling from the junctions allows for an independent optimization of thecoupling factor $\phi_\mu$ and junction properties. We present differentmethods for calculating $\phi_\mu$ (for a magnetic nanoparticle placed 10\,nmabove the constriction) as a function of device geometry and show that thoseyield consistent results. Furthermore, by numerical simulations we obtain ageneral expression for the dependence of the SQUID inductance on geometricalparameters of our devices, which allows to estimate their impact on thespectral density of flux noise $S_\Phi$ of the SQUIDs in the thermal whitenoise regime. Our analysis of the dependence of $S_\Phi$ and $\phi_\mu$ on thegeometric parameters of the SQUID layout yields a spin sensitivity$S_\mu^{1/2}=S_\Phi^{1/2}/\phi_\mu$ of a few $\mu_{\rm{B}}/\rm{Hz^{1/2}}$($\mu_B$ is the Bohr magneton) for optimized parameters, respectingtechnological constraints. However, by comparison with experimentally realizeddevices we find significantly larger values for the measured white flux noise,as compared to our theoretical predictions. Still, a spin sensitivity on theorder of $10\,\mu_{\rm B}/\rm{Hz^{1/2}}$ for optimized devices seems to berealistic.

Optimizing the spin sensitivity of grain boundary junction nanoSQUIDs -- towards detection of small spin systems with single-spin resolution