Magnetic anisotropy

Magnetic anisotropy describes the fact that magnetic materials can have a preferred direction or preferred plane for magnetization . The measure for this is the magnetic anisotropy energy, which is defined as the work that is required to twist the magnetization of a closed system (no particle exchange ) out of the "easy direction" (the preferred direction).

The magnetic anisotropy causes the coupling of the magnetization to the crystal lattice and is z. B. responsible for the fact that a magnetic needle turns (and thus follows the orientation of the spin lattice).

to form

There are several forms of magnetic anisotropy:

• magnetocrystalline anisotropy of the coupling of magnetization and crystal lattice (described above)
• Shape anisotropy is based on the change in the shape of the body
• Magnetoelastic anisotropy is based on elastic tension
• In 1956 a new effect was discovered ( exchange bias , also unidirectional exchange anisotropy), which causes a preferred direction of magnetization in a ferromagnet due to the interaction with a neighboring antiferromagnet and has applications in read heads of hard drives based on thin ferromagnetic layers (use e.g. B. the GMR effect ).
• Interface anisotropy in magnetic thin layers .

Examples

• Shape anisotropy : In the case of a monocrystalline iron cylinder whose length is significantly greater than its radius, the magnetization preferably remains in the direction of the longitudinal axis. This is a so-called easy direction ( easy axis ). Here the anisotropy is essentially determined by the shape of the sample.

Form anistropy in thin layers: The dashed lines represent Bloch walls , the red lines the magnetic alignment of the domains.

• ferromagnetic thin layers : their magnetization does not show out of the surface, since the magnetic conductivity of air is much worse. The magnetic domains are also in equilibrium and ideally (i.e. single-crystal layer without defects) aligned in such a way that as few magnetic field lines as possible point out of the layer, see graphic.
• Crystal anisotropy (English: crystalline anisotropy ): A monocrystalline iron ball also has preferred directions of magnetization despite its isotropic shape. This is due to the internal structure.

Explanation

The occurrence of magnetic anisotropy is surprising at first glance. The exchange interaction , which is responsible for the collective order of the magnetic moments , is isotropic , just like the Heisenberg spin Hamilton operator (as a scalar product ).

However, magnetic anisotropy is a fact of experience. A thermodynamic view leads to the density of Gibbs free energy (a phenomenological approach in which symmetry considerations play a leading role) and thus to the terms that describe the anisotropy; this was first carried out by the Russian physicist Akulow (1900–1976).

The spontaneous magnetization is isotropic; H. the same size for all directions. This follows from the observation that the magnetization of a ferromagnetic single crystal in a sufficiently high field is the same for all directions. All ferromagnetic properties of a ferromagnetic are lost in all directions at the same temperature; H. the Curie point is isotropic.

Occur

However, depending on the direction, a different magnetization behavior can be measured: An iron single crystal reaches its saturation magnetization very quickly if it is magnetized along its cube edges; with magnetization along the surface diagonal, the magnetization grows more slowly.

The magnetic anisotropy can be characterized by the work of magnetization . In iron, the work of magnetization is lowest along the edges of the cube, this direction is called the easy direction . Iron has three easy and four difficult directions (along the room diagonal). In cobalt, on the other hand, one can find an easy (the hexagonal axis) and an infinite number of difficult directions.

The magnetic anisotropy energy describes the energy associated with the orientation of the magnetization. The magnitude of the magnetic anisotropy energies are several orders of magnitude below those of the exchange energy, which is responsible for the spontaneous collective order of the permanent magnetic moments. The corresponding fields for the exchange effect are 400–2000  Tesla , while those for anisotropy are around 0.01 to 10 T.

causes

Basically, magnetic anisotropy is caused by two physical interactions:

1. Dipole-dipole interaction
   • Shape anisotropy,
   • Crystal anisotropy (determined in a higher order by dipolar interactions)
2. Spin-orbit coupling
   • Crystal anisotropy,
   • Surface anisotropy.

The spin-orbit coupling plays a role in particular in magnetocrystalline anisotropy, which, because of its small size compared to the exchange interaction, for example, poses difficulties for the theoretical derivation of the anisotropy from models.

The crystal anisotropy is influenced by mechanical stresses , this effect is also called inverse magnetostriction .

Applications and meaning in practice

Research into magnetic anisotropy is of paramount importance in the development of new hard drives . Ever faster access times and in particular ever higher storage densities will lead to the superparamagnetic limit in the near future (see Moore's law ). At this limit, the individual magnetic areas become so small that they cannot keep their magnetization stable over the long term. The magnetic anisotropy can, for example, be used specifically to increase the stability of the bits (an overcoming energy, as is present in the case of anisotropy, always causes a certain stability of the system), which can influence each other with decreasing dimensions; the latter would result in an undesirable loss of information .

In this context, magnetic thin-film technology is particularly interesting .

The positive magnetoelastic anisotropy of iron is used to find near-surface residual stresses in iron materials and steel parts with the Barkhausen noise.

Web links

• Kilian Lenz Magnetic anisotropy and damping mechanisms in ultra-thin 3D ferromagnets: an FMR study , dissertation FU Berlin 2005 (PDF file; 3.98 MB)
• Peter Miltényi Microscopic origin of the exchange coupling in ferromagnetic / antiferromagnetic layers , dissertation, Aachen 2000, with an overview of magnetic anisotropies (PDF file, 4.2 MB)

Individual evidence

1. ^ WH Meiklejohn, CH Bean New Magnetic Anisotropy , Physical Review, Volume 105, 1957, pp. 904-913
2. ↑ Stöhr, Siegmann Magnetism , Springer 2006, Chapter 7.9. Examples of derivation from microscopic models are, for example, Daalderup, Kelly, Schuurmans First-principles calculation of the magnetocrystalline anisotropy energy of iron, cobalt, and nickel , Physical Review B, Volume 41, 1990, p. 11919, Abstract , the same Magnetocrystalline anisotropy and orbital moments in transition-metal compounds , Physical Review B, Volume 44, 1991, p. 12054, abstract
3. ↑ Stresstech GmbH: Possibilities for analysis with the barque noise ( memento of the original from March 28, 2016 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice.