In atomic force microscopy cantilevers are used to detect forces caused by interactions between probing tip and sample. The minimum forces which can be detected with commercial sensors are typically in the range of 10−12 N. In the future, the aim will be to construct sensors with improved sensitivities to detect forces in the range of 10−18 N. These sensors could be used for mass spectroscopy or magnetic resonance force microscopy. Achieving this goal requires smaller sensors and increased quality factor Q. In this article we describe a model to characterize the dynamics of cantilevers of each eigenmode. In contrast to previous models, the damping is treated rigorously in the calculations.

A novel sample preparation technique for deposition of small volumes from the liquid phase is described. Samples with diameters as small as 0.5 µm were created with this technique. A series of cantilever geometries was manufactured, with the aim of optimizing the Q-factor. Force sensitivities of 8 × 10 −17 N/ √ Hz were achieved at room temperature, which is a considerable improvement over commercial cantilevers. Mechanisms which determine Q-factors are discussed briefly. Quantitative understanding of MRFM is absolutely necessary. Calculations of the magnetic field and field gradients for several types of permanent magnets are presented.Magnetic resonance force microscopy (MRFM) is a novel method, has been introduced theoretically by Sidles [1-3] and experimentally by . Early experiments have shown that samples of a few nanograms in mass, corresponding to about 10 12 spins, are detectable with conventional cantilevers. Provided that cantilevers are optimized (high Q, low spring constant) and high magnetic field gradients of existing magnetic force microscopy (MFM) tips are implemented, estimations show that a resonance signal of a single spin might become detectable. At present the sample is mounted on the cantilever and relatively low magnetic field gradients are created by permanent magnets which are mounted in close vicinity to the sample. In an inhomogeneous static magnetic field B t the sample is polarized (Fig. 1). With a time-dependent RF field spin flips are induced. By modulation of the RF field and/or the static field it is possible to create a time-dependent periodic force F(t), which can be expanded into a Fourier series [5,8]. If the frequency ω of the force F(t) is the same as the frequency of the cantilever ω c , the resonance enhancement of the cantilever can be used to detect small forces. The force that acts on the cantilever is proportional to the deflection which can be measured with an interferometer or a microscope of beam-deflection type. The advantage of the mechanical detection of magnetic resonance is that the signal-to-noise ratio is larger than in classical inductive ESR. Different ways of optimizing the signal have been tried and established (cantilever design [9, 10], Fig. 1. Block diagram of the magnetic resonance force microscope three-dimensional imaging [6, 11], anharmonic modulation [8], new RF coil design [12] and RF pulses [13]).In this paper instrumental aspects of MRFM are discussed. Simulation of the magnetic field of different types of polarization magnetsA knowledge of the magnetic field B of the permanent magnet is important in estimating the distance between cantilever and sample for the resonance conditions. The field gradient ∂B/∂z is important for force calculations and for the spatial range where the sample comes into resonance [12,14]. For known geometry of the polarization magnet, the field can be calculated. The scalar potential is given byand the field is given by B(r) = −µ 0 ∇φ m (r) .Most magnetic shapes can be approximated by a spherical, cylindrical or conica...

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