2.7.6 Interaction between soft magnetic probe and magnet sample
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  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:
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  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 .
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  this method was used for the calculation of the permalloy domain walls distribution in the presence of the iron tip. In  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.
- 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.
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