Defect interactions and canting in ferromagnets

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Abstract
The onset of spin canting due to the interaction of defect bonds has been studied by numerical calculation, continuum theory, and discrete lattice theory. This model is relevant to the problem of canting in amorphous ferromagnets. For a square lattice with a nearest-neighbor host exchange constant J, the onset of canting has been studied for the following disordering influences: a single negative bond of strength J’, a single site with two bonds J’ opposite and adjacent to one another, and two bonds J’ at arbitrary separation and relative orientation. In the case of interacting bonds it is convenient to think of the system as having dipole sources that can interact via a host ferromagnet: Indeed, both the continuum theory and the discrete lattice theory in the large separation limit give an effective interaction of two-dimensional dipolar form. When the system goes noncollinear, the nonlinear effects that occur at the impurity site are taken to provide the dominant self-limiting terms that keep the distortion small. When the effects of the periodic boundary conditions are taken into account, reasonable agreement is found between the numerical calculations and the theoretical predictions. Local mean-field theory has been employed throughout, and is used to obtain the temperature at which the relatively weak canting energy is overcome by the thermal energy, and canting disappears. These results are relevant to what we call ‘‘weak’’ defects in the magnetic alloying process: Individual impurities cannot cause canting, but the effective dipolar interaction is long range, and at a high enough impurity concentration should lead to a canted state with transverse ‘‘pseudo-’’ or ‘‘semi-’’ spin-glass order. A general discussion of experimental systems is given, in light of our results.