In condensed matter physics, the Slater–Pauling rule states that adding an element to a metal alloy will reduce the alloy's saturation magnetization by an amount proportional to the number of valence electrons outside of the added element's d shell.[1] Conversely, elements with a partially filled d shell will increase the magnetic moment by an amount proportional to number of missing electrons. Investigated by the physicists John C. Slater[2] and Linus Pauling[3] in the 1930s, the rule is a useful approximation for the magnetic properties of many transition metals.
The use of the rule depends on carefully defining what it means for an electron to lie outside of the d shell. The electrons outside a d shell are the electrons which have higher energy than the electrons within the d shell. The Madelung rule (incorrectly) suggests that the s shell is filled before the d shell. For example, it predicts Zinc has a configuration of [Ar] 4s2 3d10. However, Zinc's 4s electrons actually have more energy than the 3d electrons, putting them outside the d shell. Ordered in terms of energy, the electron configuration of Zinc is [Ar] 3d10 4s2. (see: the n+ℓ energy ordering rule)
Element | Magnetic valence | Predicted moment per atom | ||
---|---|---|---|---|
[Kr] 4d10 5s2 5p2 | -4 | -4 \muB | ||
[Ne] 3s2 3p1 | -3 | -3 \muB | ||
[Ar] 3d10 4s2 | -2 | -2 \muB | ||
[Ar] 3d10 4s1 | -1 | -1 \muB | ||
[Kr] 4d10 | 0 | 0 \muB | ||
Cobalt | [Ar] 3d7 4s2 | +1 | +1 \muB | |
[Ar] 3d6 4s2 | +2 | +2 \muB | ||
[Ar] 3d5 4s2 | +3 | +3 \muB |
The basic rule given above makes several approximations. One simplification is rounding to the nearest integer. Because we are describing the number of electrons in a band using an average value, the s and d shells can be filled to non-integer numbers of electrons, allowing the Slater–Pauling rule to give more accurate predictions. While the Slater–Pauling rule has many exceptions, it is often a useful as an approximation to more accurate, but more complicated physical models.
Building on further theoretical developments done by physicists such as Jacques Friedel,[4] a more widely applicable version of the rule, known as the generalized Slater–Pauling rule was developed.[5] [6]