29.10: Summary
- Page ID
- 32854
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This TLP has covered the basic points of ferromagnetism:
- In a magnetic atom there are two contributions to the magnetic dipole moment; firstly the spin of the electrons themselves and secondly that of electrons orbiting the nucleus.
- Ferromagnetism occurs in materials where all the magnetic dipole moments align parallel below the Curie temperature.
- Ferromagnetic ordering was explained by Weiss via a hypothetical average field which acts to cause the parallel alignment. However, the microscopic explanation for this can be found by looking at the Pauli Exclusion Principle; it is energetically more favourable for electrons be placed in different orbitals as this reduces the Coulomb repulsion energy and allows for the alignment of the electron spins.
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The magnitude of the magnetisation is dependent on temperature and modelled by the Curie-Weiss law:
- The formation of domains is driven by the minimisation of energy, with the main driving force often being that of the magnetostatic energy.
- Magnetic hysteresis is seen, due to the defects found in crystals, as these hinder the movement of domain walls.
- Hard magnets have a large coercive field, whereas soft magnets are easily demagnetised and so has a small coercive field.
- Both magnetocrystalline anisotropy and shape anisotropy give directions in a material along which it is easier to magnetise a sample.
Going further
Books and Papers
- Magnetic Materials : Fundamentals and Device Applications by N.A. Spaldin, Cambridge University Press (2003)
A good overall explanation of ferromagnetism which also covers other types of magnetism and some applications. - The Feynman Lectures on Physics by R.P. Feynman, R.B. Leighton and M. Sands, Addison-Wesley Publishing Company (1970)
Provides a complete explanation of magnetism including the mathematics and qualitative explanations. - P.A.M. Dirac, The quantum theory of the electron, Proc. R. Soc. London A 117 610-612 (1928)
- P.A.M. Dirac, The quantum theory of the electron Part II, Proc. R. Soc. London A 118 351-361 (1928)
These are the original papers by Dirac in which the spin of the electron was derived.
Websites
- Get Perpendicular: Hitachi Global Storage Technologies
This website gives a fun summary of one of the latest developments in magnetic memory.