The Bethe–Slater curve is a

heuristic A heuristic or heuristic technique (''problem solving'', '' mental shortcut'', ''rule of thumb'') is any approach to problem solving that employs a pragmatic method that is not fully optimized, perfected, or rationalized, but is nevertheless ...

explanation for why certain metals are

ferromagnetic Ferromagnetism is a property of certain materials (such as iron) that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagne ...

and others are

antiferromagnetic In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring Spin (physics), spins (on different sublattices) pointing in oppos ...

. It assumes a Heisenberg model of magnetism, and explains the differences in exchange energy of

transition metals In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. The lanthanide and actinid ...

as due to the ratio of the interatomic distance ''a'' to the radius ''r'' of the ''3d''

electron shell In chemistry and atomic physics, an electron shell may be thought of as an orbit that electrons follow around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by the "2 shell" (o ...

. When the magnetically important ''3d'' electrons of adjacent atoms are relatively close to each other, the exchange interaction,

J_

, is negative, but when they are further away, the exchange interaction becomes positive, before slowly dropping off. The idea of relating exchange energy to inter-atomic distance was first proposed by John C. Slater in 1930, and illustrated as a curve on a graph in a review by

Sommerfeld Arnold Johannes Wilhelm Sommerfeld (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretical p ...

and Bethe in 1933. For a pair of atoms, the exchange interaction ''w_ij'' (responsible for the energy ''E'') is calculated as:Soshin Chikazumi, Physics of Ferromagnetism, Oxford University Press, New York, 1997, p. 125,

w_= - 2 J_  S_i \cdot S_j

where:

J_

= exchange integral; ''S'' = electron spins; ''i'' and ''j'' = indices of the two atoms. The Slater curve does produce realistic results, predicting Iron, Cobalt and Nickel to be the elements with ferromagnetic ordering. The curve is of practical use as a simple way of estimating

J_

based on the average atomic separation. However, more recent evaluations with realistic calculations of the exchange interactions show significantly more complex physics when treating the interactions of different atomic orbitals in an atom separately, rather than as a single unit.

External links

Open Quantum Materials Database

References

{{DEFAULTSORT:Bethe-Slater curve Magnetic exchange interactions Ferromagnetism