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In chapter 2.7.3
we described the general model of a hard magnetic probe interaction
with a magnetic field of a sample and neglected the fact that a tip and
a sample can mutually affect their magnetic characteristics. This
influence should, in fact, be taken into account when constructing
theoretical models of a hard magnetic tip interaction with the sample
magnetic field. An assumption that the sample magnetization is not
affected by the tip magnetic field is a good approximation for hard
magnetic samples and is not valid for the soft ones, for example, for  (permalloy) [1-3].
In [4]
it is shown that the tip magnetic field affects the magnetic properties
of the sample and vice-versa in case when magnetic field of one exceeds
the magnetic anisotropy field of the other:
 or  |
(1) |
where  and  – magnetic fields of tip and sample and, respectively,  ,  – magnetic anisotropy fields. Near the tip and sample surface the magnetic field can be taken equal to  , where 
– a material magnetization, and can exceed much the magnetic anisotropy
field of a soft magnetic material like iron or permalloy. To avoid this
effect it is necessary to increase the tip-sample separation [5] that results in sufficient lateral resolution deterioration.
In [2,3]
the theories were developed that take into account the magnetization
vector rotation under the external magnetic field. These theories
predict the appearance of an additional attraction force between a tip
and a sample because magnetic moments in a sample tend to align with
the tip magnetic field and vice-versa. This effect was observed in
permalloy [5].
Perhaps, the most
successful way of the tip-sample interaction description is the
determination of a system minimum energy. The method is a sample
decomposition into infinitesimal cells and a subsequent calculation of
the minimum energy of magnetic states taking into consideration the
exchange interaction, anisotropy energy and magnetostatics. In [6] this method was used for the calculation of the permalloy domain walls distribution in the presence of the iron tip. In [7]
the energies of the tip magnetic states equilibrium and the resultant
force acting on it in the magnetic field was calculated by integration
of the Landau-Lifshits-Hilbert equation.
Summary.
- In case when magnetic field of a sample
exceeds the magnetic anisotropy field of a tip and vice-versa, they can
mutually affect the magnetic characteristics of each other.
- Presented is a brief review of
quantification methods of a soft magnetic tip interaction with a sample
magnetic field and, accordingly, a soft magnetic sample interaction
with a tip magnetic field.
References.
- T. Goodenhenrich, U. Hartmann, M. Anders, C. Heiden: J. Microscopy 152, 527 (1988).
- J.J. Saenz, N. Garcia, J.C. Slonczewski; Appl. Phys. Lett. 53, 1449 (1988).
- D.W. Abraham, F.A. McDonald: Appl. Phys. Lett. 56, 1181 (1990).
- U. Hartamnn: J. Appl. Phys. 64, 1561 (1988).
- H.J. Mamin, D. Rugar, J.E. Stern, R.E. Fontana, Jr., P. Kasiraj: Appl. Phys. Lett. 55 318 (1989).
- M.R. Scheinfein et al. J. Appl. Phys. 67, 5932 (1990).
- M. Mansuripur: IEEE Trans. Magn. 25, 3467 (1989).
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