The initial permeability of polycrystalline MnZn ferrites: The influence of domain and microstructure

Abstract

The validity of nonmagnetic grain-boundary (NMGB) models for the initial permeability of polycrystalline ferrites is examined. The domain size in a series of wet-chemically prepared polycrystalline MnZn ferrites, in the demagnetized state, has been determined by neutron depolarization. A transition in the intragranular domain structure from mono- to two domain is observed at grain size D≊4 μm. An expression for this transition has been derived for a dense magnetic material. The grain size dependence of the initial permeability of the ferrites studied, particularly for monodomain grains, is consistent with the NMGB model. The grain-boundary width and composition have been determined with a nanoprobe (1.5 nm resolution). Composition variations extend ≊10 nm into the grain. The findings suggest that, although the NMGB model considers ‘‘nonmagnetic’’ grain boundaries, in practice the grain boundary may be hard magnetic.

Domain structure in polycrystalline MnZn ferrite imaged by magnetic force microscopy

“…14 This can be done either by using a reduced effective value for the saturation magnetization M s , 12 or by introducing an ͑isotropic͒ initial permeability. 4 The latter yields a reduction of the demagnetization energy by a factor 2 3 i . Applying the permeability correction to the upper and lower limits for the critical grain size derived by Brown 9 yields D cr,lower ϭ3.6ͱ…”

“…In the bulk ferrite discussed here, the grains are neither spherical not isolated and especially the soft-magnetic environment of the grain should be taken into account. 4,14 This yields correlations between the magnetization direction in neighboring grains such that the condition div MϷ0 between such grains is met ͑for instance, in the case when four neighboring grains form a diamond-like magnetization structure͒. In a first approximation for the calculation of D cr , one can study the effect of the soft-magnetic environment by ͑artificially͒ lowering the magnetostatic energy of the grain.…”

“…For instance, it was shown by neutron depolarization ͑ND͒ studies that a critical grain size D cr exists, below which the grains are mono-domain. 3,4 For the MnZn ferrites to be discussed here, D cr is about 4 m. Recently, it was found from magnetic susceptibility measurements that the energy dissipation at MHz frequencies is substantially lower in samples with grain size DϽD cr , which was attributed to the absence of domain walls in these small grains. 5,8 Still, a number of questions persists.…”

“…For instance, theoretical estimates for D cr of an isolated grain [9][10][11][12] yield values which are orders of magnitude lower than experimentally found. 4,10 Even when taking into account that the grain is embedded in a soft magnetic environment, the upper limit for the estimates of D cr barely reaches the experimental value. 5,12 Moreover, the change in energy dissipation as function of grain size can be surprisingly sharp, taking place in less than 0.1 m. 5 Given the distribution of grain sizes inherent to ceramic materials, the expectation would be a more gradual change in the region where grains with single domains and two domains should coexist.…”

“…1,2 Since this property is related to domain wall motion, several studies have been performed lately on the domain structure of poly-crystalline MnZn and NiZn ferrites, and its relation to the average grain size. [3][4][5] The latter parameter can be controlled by the sinter temperature in the preparation process and allows tuning of the grain size with small size distributions from below 1 m to above 10 m while maintaining a constant composition. 6,7 Due to the low magneto-crystalline anisotropy of certain MnZnferrite compositions, the domain wall size can be very large, of the order of 1 m, so that the grain size can be varied from below to above the domain wall size.…”