MAGNETIC RESONANCEFREQUENCY SWEEPS: The first measurement in order to find a magnetic resonance response of the sample is usually to vary the centre fcentreof the
ARP pulse with RF-frequency fRFand set all other variables to estimated values. Based
on a guess of the lower and upper boundary of the tip field Bztip (typically ∼ 150 − 300
mT), fres is calculated according to fres = γ/(2π) · (B0 + Bztip). The resonance
frequency sweep8 measurement consists of a series of single measurements starting with fcentre far below and sweeping it to well above the range where fres is assumed.
Off resonance σipand σqdare approximately equal. Matching the resonance, σipraises, 8The expression resonance frequency "sweep" can be confusing since finally it is a sweep a swept
frequency. It is used for historical reasons. Within an ARP pulse, fRF(t) is varied to invert the spins,
the pulses are repeated and the signal is averaged for a time taqui. Now, the centre frequency fcentreof
whilst σqdideally stays the same as shown in fig.4.5. A possible increase of σqdmight
be due to an incorrect set phase of the lock-in amplifier and can be accordingly corrected (see paragraph Sweep Parameters Optimisation below). The several blank measurements off resonance give indication of absent artificial driving, e.g. by a possible existing electric component of ~B1. A resonance frequency sweep measurement usually takes a
bit more than one to several hours, depending on the range over which fcentreis swept,
the averaging time taquiand the interval size.
FIGURE4.5: A RAWMRFM SIGNAL– FINALLY
Magnetic resonance frequency sweep traces. Upper graph: Variance of the magnetic force (In phase 1 to 6; black and blueish to greenish curves) versus the carrier frequency alias centre frequency fcentre. The reddish flat curves (out of phase 1 to 6) reflect the
uncorrelated thermal noise. The each 6 curves correspond to different bandwidth filters. The decomposition of the raw signal this way enables the instantaneous determination of τm(section4.2.3). The smaller peaks at higher frequencies are spurious excitations
of the cantilever. Lower graph: Spin ensemble correlation time τmversus fcentre. On
resonance (165 MHz to 170 MHz) values between ∼ 100 ms to ∼ 300 ms are measured. Away from resonance the fit based on the different filters is erroneous and crazy values result.
If the sweep reveals no resonance signal a new position (primary different in x, maybe in z) is chosen and the resonance frequency sweep is repeated with the same parameters. This makes sense, since knowing empirical values for Bztip, B1, ∆fmodand
βHS9, the biggest unknown is Gzx, which is determined by the position and can easily be
too small to not find a measurable signal at all at the chosen position.
If this is still not successful, the other variable parameters are changed similar to the optimisation description below, e.g. in the following order B1, ∆fmod, βHS, and even
more positions are tested, e.g. also by spatial scans.
9β
4.3 Performing MRFM in Practise 77
SWEEP PARAMETERS OPTIMISATION: Once a resonance signal, i.e. fresfor a given
position is found, the other parameters of the ARP pulses are optimised. Therefore sweeps of one of the variables B1, ∆fmod, βHSare made, whilst the others and fcentreare
set to a fixed value.
Changing ∆fmodand βHSin a moderate range10is unproblematic and optimal settings
can easily be found. Though, varying B1changes the power of the RF-pulse and thus the
heating produced by the micro-wire. This in turn can change the position of the sample relative to the nano-magnet, which has to be considered especially if B1 is swept over a
large range. Even if the change in position is small and intentionally neglected, fL0 still
changes. It can take up to a few seconds until the changes are equalised. Therefore a waiting time after the update of ωRFand before measuring fL0 is introduced. If necessary
this is also done for variations of parameters other than B1.
If σqd shows an increase on resonance, also the phase between the driving of the
spins via the ARP pulses and the detection by the lock-in amplifier has to be optimised. With an internal function of the lock-in amplifier the best phase, yielding the highest difference between σip and σqd, can be evaluated. The settings of this function are
limited and also off resonance, where only thermal noise is present, the optimal phase is evaluated, spoiling the proper measurement of σspin-signal. Hence it is only suitable
to find the optimal phase. In any case, the actual measurement of σspin-signal has to be
remade with a fixed phase. By using a four-channel detection scheme as demonstrated by Moores et al. [18,156] the evaluation of the phase can be done with external computing software enabling more customisation and yielding more complete information of the signal.
SPATIAL SCANS: In order to find the position with the highest gradient a spatial scan over the half or the full width of the tip is made. Therefore a distinct fcentreis set and the
position is typically swept in x-direction. Changing the position alters the cantilever’s interaction with its environment and introduces a considerable delay until fL0 is again
stable. This is accounted for in a similar way to the above mentioned RF update waiting time; although here it can be up to a few minutes.
Further, also the damping due to non-contact friction can vary, which changes Qdamped
and thereby the conversion from displacement to force. Ideally, each time the new Qdampedshould have to be measured by the ring-down method, which is not done in our
case.