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We report the detection of slice-selective electron spin resonance with an external magnetic field gradient comparable to local interatomic gradients, using the techniques of magnetic resonance force microscopy. An applied microwave field modulated the spin-gradient force between a paramagnetic DPPH sample and a micrometer-scale ferromagnetic tip on a force microscope cantilever. A sensitivity equivalent to 184 polarized electron moments in a one-Hertz detection bandwidth was attained. We mapped the tip magnetic field with a resonant slice thickness of order one nanometer, thereby demonstrating magnetic resonance on length scales comparable to molecular dimensions.

In magnetic resonance force microscopy (MRFM) experiments, magnetic forces couple to the motion of microscale cantilever beams. Extension of MRFM to the detection of single electrons will require both unprecedented force sensitivity and motional stability of the cantilever. We describe the principles and performance of optimal cantilever motion control. The method accounts for inherent noise processes and practical application of control forces. We show that active feedback control improves cantilever motional stability, enabling instrument designs of much higher sensitivity and faster imaging than passive designs. Experimental results of implemented cantilever control systems are presented in Part II.

Parametric coupling has been demonstrated between mechanical vibration modes in a magnet-tipped microcantilever. An external magnetic field, coupled to the magnetic tip, pumps the effective spring constant at a frequency which is either the sum or the difference of the mode resonance frequencies. The presence of the pump field can be detected by driving one mode and observing the parametrically pumped excitation of the other mode, even though the pump frequency is off-resonance with respect to both mechanical modes. In a room temperature experimental realization, the magnetic flux coupling the pump field to the tip was approximately one flux quantum and the dominant noise source was the thermal vibration of the cantilever. Parametric mode coupling is a useful new design option in magnetic resonance force microscopy, whereby modulation is advantageously performed off-resonance to avoid parasitic excitations caused by stray couplings. Parametric coupling also provides a low-noise technique for amplifying mechanical oscillations. The reported experiment completes the set of all possible force microscope interaction Hamiltonians up to third order in time-dependent fields.

We describe a fiber-optic interferometer that employs wavelength changes to achieve maximum sensitivity. Wavelength changes are induced by adjusting the operating temperature of the laser, eliminating the need for an actuator to vary the spacing between the sensing fiber and the object to be monitored. The instrument and techniques described are suitable for cryogenic, high vacuum applications such as magnetic resonance force microscopy, where space is limited and micromanipulation can be challenging. The noise floor of 1.6×10−3 nm/Hz is adequate for monitoring subangstrom displacement of force microscope cantilevers.