Quantification of magnetic force microscopy using a micronscale current ring

Metal rings with inner diameters of 1 and 5 μm, fabricated using electron-beam lithography, were used to calibrate magnetic force microscopy (MFM). A MFM tip's effective magnetic charge, q, and effective magnetic moment along the tip's long axis, m_z, can be determined from the MFM signal of the ring at a different scan height and a different electric current in the ring. The magnetic moments in the directions transverse to the tip's long axis were estimated by a straight current wire. It was found that for a Si tip coated with 65 nm cobalt on one side, q is 2.8×10^-6 emu/cm, m_z is 3.8×10^-9 emu, and m_x and m_y are in the order of 10^-13 emu, which are negligible compared with m_z. Furthermore, the MFMs sensitivity to the second derivative of the magnetic field was determined from the minimum ring current for a measurable MFM signal to be 0.1 Oe/nm².