Lecture handout including QS - Department of Materials Science ...

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BH40 Course B: Materials for Devices BH40 Small particles: A domain structure won’t form in a small particle, or grain, if domain wall energy > stray field energy. The domain structure of a polycrystalline material depends upon grain size: grains may be too small to support a domain boundary ⇒ form uniformly magnetised, single domain grains. Ferromagnetic Hysteresis In the presence of an applied field, domains with magnetisation antiparallel to the field DO NOT spontaneously flip. It is energetically cheaper for the magnetisation to switch by moving domain walls. Plotting Magnetisation, M as a function of Applied Field, H: Extrapolation of the curve from M sat back to the axis defines the Spontaneous M a b c d dipole rotation growth of favourably Magnetisation (the net magnetisation oriented domains within a uniformly magnetised microscopic volume, in zero field) irreversible wall motion reversible wall motion H H H H H a b c d *Domains in unmagnetised sample cancel out ⇒ zero net magnetisation, M *Moments are aligned along easy axes *Wall motion and M are reversible *Favourably oriented domains grow by wall motion *M increases sharply *Wall motion is irreversible (due to pinning by imperfections) *Whole sample is aligned as a single magnetic domain (along easy axis, not along external field direction) *Moment is pulled away from easy axis, into line with external field *Saturation magnetisation M sat produced by rotation of moments to lie along H
BH41 Course B: Materials for Devices BH41 Cycling the field back and forth produces hysteresis: Residual magnetisation remaining at zero applied field (H = 0) is the remanent Reduce applied field ⇒ moment relaxes back to easy crystallographic axis, but then the domain remains stable as field is reduced further magnetisation, M r magnetisation M sat Continued field reversal ⇒ domains grow in the opposite direction M = 0 (multi-domain umagnetised state) at the coercive field, H C . applied field Further field reversal ⇒ saturation in the opposite direction M sat • area within the loop ∝ energy dissipated during one cycle, i.e. 2 × energy needed to switch M • imperfections (grain boundaries, impurities, vacancies, etc.) pin domain walls, ⇒ increase H C
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Lecture handout including QS - Department of Materials Science ...

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