Pi

MW coil

Resonant slice

Cantilever

Cantilever position

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Magnetic tip

SiO2 sample \ Electron spin

Njnt cycles

Relative phase n 0

Spin z component i

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Cantilever frequency shift

Fig. 1. (A) Schematic of the MRFM apparatus. The cantilever with the attached magnetic tip is oriented vertically about 140 nm away from the surface of a sample containing a low concentration of Ecenters. A small coil placed near the sample generates microwaves at 2.96 GHz to excite electron spin resonance. At 2.96 GHz, the resonance condition for electrons is met for B0 = 106 mT. For Bext = 30 mT, the resonant slice is a paraboloidal shell that extends about 250 nm below the tip. (B) Timing diagram for the interrupted OSCAR protocol. For setups 1 and 2, the microwave (MW) power is interrupted every 88 cycles (fsig , 50 Hz) and 64 cycles (fsig , 43 Hz), respectively.

z x xpksin(2p/c0, the field experienced by a spin near the tip is modulated sinusoidally at the cantilever frequency with peak amplitude DB = Gxpk, where G = 9£0/& is the lateral gradient from the tip. For typical experimental parameters of xpk , 20 im and G , 2 x 105 T m-1, the external field experienced by spins within the resonant slice is modulated by DB = 4 mT. In the presence of the microwave field, the slow variation of the static field at the cantilever frequency causes each spin within the resonant slice to be adia-batically inverted synchronously with the cantilever motion. The back action of the spin on the cantilever in turn shifts the fundamental frequency of the cantilever by a small amount dft-

2/cGiMa pkx

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