Magnetic Resonance Force Microscopy
One of the long-term goals of module 3 is to develop a 3d-imaging method with chemical analysis
on the nanometer scale. Magnetic resonance imaging is well-established in medicine to map the
density of hydrogen. However, the resolution is rather limited, where 1012 spins
are required per pixel. Magnetic Resonance Force Microscopy (MRFM) is a local probe technique
which measures local magnetization by mechanical means. Ultimately, single electron spins can
be detected as it has been shown by Rugar et al. [1]. The major challenge is to detect single
nuclear spins, which have much weaker magnetic moments. At present, a novel ultrahigh vacuum
MRFM is developed at the University of Basel (Figure 1). Samples with unpaired electrons are
polarized in a static magnetic field B, which aligns the magnetic moments
μ. A high frequency magnetic field B1 oscillates with the
Larmor frequency ω (typically at 3GHz) perpendicular to the polarization
field B. Conventional spectrometers detect the precessing spins μ
with a pick up coil by measuring the induction signal generated by the magnetic moments.
Ensembles of 1012 spins can be investigated at best, because electronic noise of
the pick-up coil limits the detection sensitivity.
MRFM makes use of the fact that a force F =
∂Btip/∂z•μ
acts on a magnetic moment in a inhomogeneous magnetic field
∂Btip/∂z ≠ 0. Field gradients of up to 2 - 3G/nm can be
generated with micrometer-sized CoSm particles (Figure 2). Consequently, the average force
acting on a Bohr magneton at 4.2 is in the attonewton range.
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Figure 1: Experimental setup of the magnetic resonance force microscope. |
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Figure 2: Ultrahigh vacuum magnetic resonance force microscope. |
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Figure 3: SEM picture of focussed ion beam modified micrometer-sized magnetic CoSm tip glued on a cantilever. |
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Figure 4: Ultrasensitive Cantilever fabricated of single crystalline silicon. The length is 450µm, a width of 4 µm and a thickness of 400nm. The spring constant is 0.00015N/m. At 4.2K a force sensitivity in the order of 4 x 10-18N/√ Hz can be reached. |
Recently, it has been shown that this force sensitivity can be achieved with single crystalline cantilevers at low temperatures [2]. The magnetic tip is manually attached at the end of the cantilever by the use of micromanipulators. By measuring the frequency shift of the cantilever in a homogenous field B0 the magnetic properties of the particle can be determined, e.g., the magnetic moment is found to be 3•10-12Am2. Magnetic moments of this order of magnitude can not be sensed with conventional magnetometers. Therefore, this particular mechanical method currently represents the most sensitive magnetometry. For magnetic resonance experiments the homogenous field B0 of a superconducting magnet is superimposed with the inhomogeneous field of the oscillating magnetic tip Btip of the cantilever and placed close to the sample surface. The condition for magnetic resonance ω(r) = |(B0 + Btip(r))| is fulfilled in a limited volume (Figure 1). In this slice, where the resonance condition is fulfilled, magnetic moments precess in the rotating frame around the effective magnetic field Beff which is parallel to B1. The magnetic tip at the end of the cantilever vibrates with an amplitude of several nm at the natural frequency ωc in close vicinity to the surface (approx. 200-500nm). The magnetic field at the location of the spin changes periodically ( B = ∂Btip/∂z x(t) ). The field modulation causes, that the z-component of the magnetic moment μ switches between different polarities, while the local magnetic field B is above or below the resonance. Due to the polarity change of the magnetic moment, the cantilever senses two opposite forces within one cantilever cycle. This position dependent interaction force changes the natural frequency ωc of the mechanical sensor, which is detected with a high precision phase locked loop, where frequency changes of the order of μHz can be detected.
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Figure 5: |
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Figure 5 illustrates the force interaction of the spins acting on the cantilever, when the microwave field B1 is turned on at t=0. The sample is γ-irradiated quartz with a spin density of unpaired electrons of 1018 spins/cm3. A force signal of 600aN was determined from frequency shifts, which corresponds to a signal of 600 electron spins at 6K. With the present detection sensitivity it is possible to investigate ensembles of 10 spins. Current experiments are directed towards single spin detection, using the i-OSCAR (interrupted OScillating Cantilever Adiabatic Reversals) protocol.
[1] |
Single spin detection by magnetic resonance force microscopy
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[2] |
Temperature dependence of the force sensitivity of silicon cantilevers
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[3] |
Rast et al., to appear in Nanotechnology (2005). |
Contact:
Simon Rast |
Ernst Meyer |
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Institute of Physics |
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