Abstract: In the Comment, the authors state that the separation of the relative and center of mass variables in our work is not correct. Here we point out that there is a typographical error, i.e., qi instead of -e, in two of our equations which, when corrected, makes the Comment redundant. Within the ansatzes mentioned in our paper all our results are correct, in contrast to the claims of the Comment.

Abstract: Using state-of-the-art simulation methods, we optimized the performance of nanoscale superconducting scanning probe tips for advanced spatial imaging of magnetic fields. The systematic studies of the tips’ static properties as a function of the tilted magnetic field, geometric parameters, and material parameters were carried out. The sensitivity of different superconducting quantum interference devices (SQUIDs) to the magnetic field emanating from the magnetic nanoparticle, where the location of a magnetic nanoparticle is considered below the primary loop's center, was examined as a function of the primary and secondary loop dimensions. The main objective of the research was to characterize and optimize the performance of a nano-sized SQUID-on-tip (SOT) device. Optimal SOT sensitivity was sought, for different loop sizes, arm linewidth, and lead dimensions. Moreover, we revealed that a constriction in the loop arms of the SOT can substantially improve the sensitivity of the device. Finally, the properties of the theta-SOT device were examined in the presence of in-plane and out-of-plane magnetic field components, enabling nanoscale imaging of 3D distributions of the magnetic field. Altogether, the obtained results deliver an engineering solution for the optimum performance of the SOT device in desired conditions.