by Timothy D. Stowe
What is magnetic resonance force microscopy?
How can a mechanical cantilever detect magnetic resonance ?
What is the necessary force resolution to see a single electron spin?
What limits the force resolution of our cantilevers?
How close are we to our of single spin detection?
Biotechnology has undergone tremendous growth during the past decade. In large part, this growth has been due to the sequencing of the human genome which will be completed within the next few years. While this milestone provides the future groundwork for further advances in biochemistry there are still many challenges remaining. For example, a key aspect for bring down the cost of the drug discovery is determining the 3-dimensional atomic structure of membrane proteins. Unfortunately, the atomic structure of most membrane proteins has yet to be uncovered using nmr and x-ray crystallography techniques. It has been a long standing dream in the scientific community to have a general purpose imaging technique which can image the 3-dimensional structure of a single protein at the atomic level.
Magnetic Resonance Force Microscopy, also abbreviated as MRFM, is an idea which might one day accomplish the three-dimensional atomic-scale chemically-selective imaging of the atoms making up a protein molecule. The idea of using MRFM to image protein structure was originally proposed by John Sidles. ( download the lastest MRFM review pdf paper )
The idea of MRFM is to combine the imaging principles of magnetic resonance imaging (MRI) with the atomic precision of scanning probe microscopy.
It is the goal of Dan Rugar's group at IBM Almaden and our research group at Stanford to image a single electron spin using MRFM. A typical MRFM experimental setup is shown below. The key components of our experimental MRFM system are as follows: An ultrasensitive silicon cantilever probe, a high coercively ferromagnetic probe tip, a RF microcoil for exciting spins at their Larmor resonance frequency, and a fiber-optic interferometer for detecting the tip motion.
In the presence of a magnetic field (in our case this is the magnetic field of the sharp tip) , an energy splitting is induced between a particle's up and down spin states in the sample. This energy splitting defines a unique Larmor frequency defined by:
wherew is the resonance frequency, mis the magnetic moment of a single spin, B is the magnetic field, and h is planck's constant. When the frequency of the RF microcoil matches the Larmor frequency, the spin system absorbs RF energy and undergoes magnetic resonance. Because the tip of the cantilever has a high magnetic field gradient (red dotted lines), only atoms in a narrow resonance slice (black dotted lines) can undergo magnetic resonance. While a spin is in resonance, its flipping frequency, the Rabi frequency, can be as high as several hundred megahertz range which much higher than the cantilever resonance frequency in the kilohertz range. Thus the main problem in mechanical detection is how to flip a spin at the resonance frequency of the cantilever.
How can the cantilever detect magnetic resonance ?
When the cantilever is vibrated at its natural resonance frequency the cantilever tip moves closer and further away from the spin. Because the tip has a high magnetic field gradient, the spin state can be swept in and out of resonance. This method flips the spin up and down adiabatically at a rate equal to the cantilever resonance frequency. However no flipping occurs if the the Larmor condition is not met during the cantilever's swing. The force interaction between a magnetic field gradient ( produced by the tip) and the magnetic moment in the sample causes the phase of the cantilever motion to shift slightly. Thus by measuring the shift phase of the cantilever motion, the presence of a spin can be detected. The motion of the cantilever is measure using a fiber interferometer.
The interaction force between the tip and
the spin is proportional to the spins magnetic moment and the tip's field
gradient. Unfortunately, these interaction forces are extremely small.
In fact the interaction force between a single electron spin and the magnetic
tip is predicted to be on the order of 10-18 N ( 10 attoNewtons
) , a level some hundred times smaller than forces studied previously.
Fortunately, micromachined cantilevers are idea for making such small force
measurements. By custom fabricating microcantilever probes and running
our experiment at low temperatures, we have been able to achieve 2aN force
resolution in a one Hertz Bandwidth.
The force resolution of a microcantilever probe is limited by so called thermomechanical noise. This thermomechanical noise arises from the exchange of energy inside the cantilever with energy in the surrounding environment and is caused by the quantized and random nature of this energy exchange. Thermomechanical noise is analogous to the Brownian motion of particles or the Johnson noise in a resistor. This noise can also be interpreted as arising from an equivalent force noise which acts on the cantilever. This equivalent force noise is given by
F = (4k kbT B / Qw)1/2
where k is the cantilever spring constant, kbT is the thermal energy, B is the measurement bandwidth, Q is the mechanical quality factor, and w the resonance frequency. Thus the noise-equivalent force can be reduced by reducing the cantilever spring constant, reducing the temperature, reducing the measurement bandwidth, increasing the Q, and increasing the resonance frequency. The ratio k/wcan be optimized by increasing the length of the cantilever and reducing the cantilever width and thickness. High Q can be achieved by making the cantilever out of single crystal silicon and taking measures to produce smooth chemically passivated surfaces.
While we have not yet seen a single electron spin, we believe we may be very close.
Currently cantilevers as thin as 0.25 micrometers with spring constants less than 0.1 mN/m have been shown to have Q's has high as 40,000 at low temperatures. In fact, We have been able to acheive a force resultion as small as small as 3x10-18 N per root hertz! While this should be adequate force resolution for long lived spins, we believe the spin life-time might be compromised by the close proximity of our tip to the sample. This in effect, means we must open up the bandiwdth of our measurements and suffer reduced S/N.
Thus we are still striving to further improve out force resolution. The dominate loss mechanism for these cantilevers appears to be associated with surface losses cause by disorder at the surface. We believe surface defects help couple energy from the fundamental mode to higher order phonon modes in the crystal. In order to further improve this the quality factor of these cantilevers, we are working on the creation of <111> silicon cantilevers with in-situ annealing capabilities. The new <111> orientation combined with in-situ annealing should help insure the quality of the silicon faces and hopefully improve the cantilever Q.
These cantilevers are in the process of being made at the Center for Integrated Systems (CIS) which is ideally equipped for this exploration of novel microfabrication techniques. CIS is supported by NSF as a National Nanofabrication Facility, enabling low-cost access to sophisticated instrumentation. Several novel processes are being developed including selective doped epi, backside <111> etching in an STS chamber, magnetic tips made from a single SeCo ferromagnetic crystal.