Supplementary material for An upper bound for the magnetic force gradient in graphite

Cobalt-coated PPP-MFMR NanoSensors cantilevers were used in dynamic mode. The stiffness and resonance frequency of the cantilevers used for the experiments reported in figs. 1 and 2 in the letter were k= 1.5 N/m, f0= 69 kHz and k= 1.2 N/m and f0= 59 kHz respectively (k was determined using Sader’s method [1]). The magnetic probes used in our experiments have been characterized by scanning the magnetic field over a reference sample (a magnetic hard drive) as shown in figs. SM1a-b. The hysteresis loop can be obtained from this 3D mode images [2] (a more detailed explanation can be found in ref. [3]). Fig SM1c shows a typical hysteresis loop obtained in that way for one of the magnetic tips used in our experiments. Notice that after saturating the sample in opposite directions, the MFM contrast is completely reversed (see Fig SM1 d-g).