We present a new nanoscale superconducting quantum interference device (SQUID) whose interference pattern can be shifted electrically in-situ. The device consists of a nanoscale fourterminal/four-junction SQUID fabricated at the apex of a sharp pipette using a self-aligned threestep deposition of Pb. In contrast to conventional two-terminal/two-junction SQUIDs that display optimal sensitivity when flux biased to about a quarter of the flux quantum, the additional terminals and junctions allow optimal sensitivity at arbitrary applied flux, thus eliminating the magnetic field "blind spots". We demonstrate spin sensitivity of 5 to 8 µ B /Hz 1/2 over a continuous field range of 0 to 0.5 T, with promising applications for nanoscale scanning magnetic imaging.KEYWORDS: superconducting quantum interference device, SQUID on tip, nanoscale magnetic imaging, current-phase relations 2 In recent years, there has been a growing effort to develop and apply nanoscale magnetic imaging tools in order to address the rapidly evolving fields of nanomagnetism and spintronics.These include magnetic force microscopy (MFM) 1,2 , magnetic resonance force microscopy (MRFM) [3][4][5] , nitrogen vacancy (NV) centers sensors [6][7][8][9] , scanning Hall probe microscopy (SHPM) 10-12 , x-ray magnetic microscopy (XRM) 13 , and micro-or nano-superconducting quantum interference device (SQUID) [14][15][16][17][18][19][20] based scanning microscopy (SSM) [21][22][23][24][25][26][27][28][29][30][31][32] . Scanning micro-and nanoscale SQUIDs are of particular interest for magnetic imaging due to their high sensitivity and large bandwidth 15,19 . The two main technological approaches to the fabrication of scanning SQUIDs are based on planar lithographic methods 21,26,[33][34][35][36] and on self-aligned SQUIDon-tip (SOT) deposition 22,24,37 .In the planar SQUID architecture, spatial resolution is limited but pickup and modulation coils can be integrated to allow operation of the SQUID at optimal flux bias conditions using a fluxlocked loop (FLL) feedback mechanism 15,18,19,21,33,38,39 . Because the magnetic field of the sample is not coupled to the SQUID loop directly, but rather through a pickup coil, integration of a modulation coil or an integrated current-carrying element 15,19,21,33,38,39 allows the total flux in the SQUID loop to be maintained at its optimal bias while the magnetic field of the sample is varied independently.SOTs, in contrast, have better spatial resolution due to their small size and close proximity to the sample, attain higher spin sensitivity, and can operate at high magnetic fields 24 . The nanoscale proximity of the SOT to the sample surface, which is its key advantage, dictates however that the flux in the SQUID loop is directly coupled to the local field of the sample and therefore cannot be modified independently. As a result, the FLL concept cannot be implemented in direct nanoscale magnetic imaging. This poses a significant drawback, since the high sensitivity of the SOT is achieved only at specific field va...