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At the present time there are a lot of MFM probes of various types [1].
The proper choice of a probe for studying a specific microstructure is
sometimes an independent and complicated problem and is determined by a
researcher experience. To simplify the problem, one needs to have
techniques that allow to quantify magnetic characteristics of probes,
the major of which are the magnetic moment per unit volume of a film
(magnetization) and magnetic coating coercivity.
To characterize
probes, many methods were proposed from analysis of their interaction
with a hard disk or magnetic tape surface [2], including measurements of magnetic heads field [3] to even exotic technique connected with studying the magnetotactical bacteria [4].
However, the simplest from the standpoint of interpretation is the
technique of the interaction detection between the tip and the magnetic
field of a current-carrying microconductor. The magnetic field of such
systems can be calculated with a high accuracy using methods of
conventional magnetostatics even in an analytic form in most cases.
In [5]
it was proposed to use a straight current carrying strip line for this
purpose. The scanning was performed across the strip in the presence of
external magnetic field. Determined was the coercitive field (along and
across the tip) for the following coatings  ,  (150A, 400A),  ,  . Also, the authors of [5] succeeded in estimating an effective magnetic moment. However, in [6]
the role of the electrostatic interaction with a conductor was revealed
and a method of electrostatic and magnetic interaction separation was
proposed. Though in [5]
the electrostatic interaction was not taken into account, the sample
was prepared very thoroughly. In particular, a thin layer of gold
several tens of angstrom thick was deposited over a dielectric layer.
The golden coating was connected to the ground potential that
apparently minimized the electrostatic interaction of a probe with a
current-carrying conductor.
Further development of magnetic probe calibration techniques led to the use of a current  -ring magnetic field. In [7]
the rings of diameter 1-5 micron and strip width of 200 nm manufactured
by submicron lithography were first used for the magnetic tip
calibration. However, the qualitative analysis of the experiment was
not quite correct, in particular because the authors used the model of
a point dipole assuming that it was situated precisely at the tip end.
As is shown in [8],
such assumption results, after accurate data processing, in
unreasonable magnitudes of effective monopole and dipole. A more
accurate experiment [8]
permitted to determine the magnitude of magnetic dipole and its
location inside the sample. It was shown experimentally that the
effective dipole should be located approximately in the center of an
area whose vertical dimension depends on characteristic attenuation
length of magnetic field. This length is proportional to the ring
radius. In this case, the cantilever magnetic moment becomes dependent
on the radius of the ring used in experiment. A theoretical calculation
by integration over the interaction region under the assumption that
the magnetic moment of the film unit volume is equal to macroscopic
saturation magnetization of the coating material, gives a reasonable
agreement with measurement results.
Thus, the effective
moment of the tip with magnetic coating depends on what kind of
magnetic structure is studied. Therefore, for such tips it is
reasonable to measure and tabulate not the magnetic moment of the tip
but the magnetic moment per unit area of a coating film. On the other
hand, determination of the total magnetic moment for tips with
localized magnetic moment [9-12] is quite reasonable and in this case its location is determined unambiguously.
To measure the hysteresis loop of tips magnetic coatings, in [13]
it is proposed to place the whole cantilever in a magnetic field with
changing gradient (external coil produces field of 0.2 Oe) and
frequency close to the cantilever resonant frequency. Measuring the
amplitude of oscillations, the force magnitude was estimated and the
magnetic moment was determined in relative units. Varying the external
field by permanent magnet (up to 280 Oe), the authors measured the
hysteresis loop for such coatings as  ,  , .
In chapter 2.7.4 and 2.7.5
the technique of determination of point dipole and monopole effective
value is described in detail. However, as it is pointed out before, the
quantitative characteristic of point dipole (monopole) and its location
in a probe depend much on the attenuation length of a studied sample
magnetic field. Therefore, in order to unambiguously calibrate the
magnetic probe it is necessary to measure the magnetization of the
probe ferromagnetic hard magnetic material.
For this purpose, a special Flash model
was developed which calculates theoretically the change in amplitude,
phase and frequency of a probe oscillation or the static deflection of
a probe during the second pass across a sample surface in the standard
AC MFM mode. In this model the current-carrying rectangular conductor
acts as the sample for study. The spatial distribution of magnetic
field produced by the current in a rectangular strip is obtained in chapters 2.7.9.
Utilizing a general case of the model of a hard magnetic probe interaction with a sample magnetic field (see chapter 2.7.3),
a theoretical analysis of the current-carrying strip magnetic field
interaction with probes of various types: cylindrical, spherical,
conical, and diamagnetic conical with ferromagnetic coating is
performed (see chapter 2.7.9 and Appendices
for it). The models allow to study the effect of variation of sample
geometry, probe parameters (dimensions, magnetization, stiffness,
resonant frequency, quality factor), measurement mode parameters within
permissible limits. The calculation of the amplitude, phase and
frequency change is performed in accordance with formulas (18), (16),
(11) of chapter 2.3.4.
Thus, substituting
the experimental data of the strip line magnetic field MFM measurements
in AC mode into this Flash model, it is possible to compare them with
theoretical ones at various probe and sample parameters. Hence, using
this model, one can determine unknown parameters of the probe
(magnetization, in particular) by varying model parameters until
experimental and theoretical data fit well. Moreover, a set of optimal
parameters can be selected that provides the maximum change of detected
signals from given samples.
Summary.
- A review of magnetic probes calibration methods and accompanying problems is presented.
- The most widespread and simple
enough technique of a probe magnetic characteristics determination is
its calibration in the magnetic field of a current-carrying
microconductor.
- Presented are the theoretical
aspects of a Flash model which allow to calculate the measured in a
standard AC MFM mode parameters depending on the sample parameters
(strip line/-ring).
- By means of the developed Flash
model one can determine unknown probe parameters appearing in an
experiment and choose an optimal set of a system theoretical parameters
that provides the maximum change in detected signals.
References.
- P. Grutter, H.J. Mamin, D. Rugar, in Scanning Tunneling Microscopy
II, edited by R. Wiesendanger and H.-J. Guntherodt (Springer, Berlin,
1992) pp. 151-207.
- D. Rugar, H.J. Mamin, P. Guethner et al, J. Appl. Phys. 68, 1169 (1990).
- S. Khizroev, W. Jayasekara, J. Bain et al, IEEE Trans. Magn. 34, 2030 (1998).
- R.B. Proksch, T.E. Shaffer, B.M. Moskowitz, Appl. Phys. Lett. 66, 2582 (1995).
- K.L. Babcock, V.B. Elings, J. Shi et al, Appl. Phys. Lett. 69, 705 (1996).
- T. Alvarez, S.V. Kalinin, D.A. Bonnell, Appl. Phys. Lett. 78, 1005 (2001).
- L. Kong, S.Y. Chou, Appl. Phys. Lett. 70, 2043 (1997).
- J. Lohau, S. Kirsch, A. Carl et al, J. Appl. Phys. 86, 3410 (1999).
- M.R. Koblischka, U. Hartmann, T. Sulzbach, Thin Solid Films 428, 93 (2003).
- T. Arie, H. Nishijima, S, Akita et al, J. Vac. Sci. Technol. B 18, 104 (2000).
- T. Arie, N. Yoshida, S. Akita et al, J. Phys. D 34, L34 (2001).
- N. Yoshida, T. Arie, S. Akita, Y. Nakayama, Physica B: Cond. Matt. 323, 149 (2002).
- J. Lohau, S. Kirsch, A. Carl et al, J. Appl. Phys. 86, 3410 (1999).
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