Magnetism and Electrons — Question 6

Question 6

Paired electrons remove spin moment while unpaired electrons set saturation

A model ion has five degenerate orbitals filled by seven electrons: place one parallel-spin electron in each orbital before pairing. Each pair is a spin singlet; orbital moments are quenched. Take g=2 and neglect interactions between ions.

1. Count paired and unpaired electrons and find the maximum z moment per ion.

2. For ion number density n, find the saturation magnetization and the fraction of this saturation when the mean moment per ion is 0.6muB.

Question 6 - Solution

Paired electrons remove spin moment while unpaired electrons set saturation

(a) Method and calculation

$$7=2(2)+3\Rightarrow\boxed{2\text{ pairs and }3\text{ unpaired electrons}}.$$$$\mu_{z,\max}=g\mu_B(3/2)=\boxed{3\mu_B}.$$

(b) Interpretation and further calculation

$$\boxed{M_s=3n\mu_B}.$$$$\boxed{M/M_s=(0.6n\mu_B)/(3n\mu_B)=0.20}.$$

Physical check

This is a specified high-spin, spin-only model; the saturation projection is not the quantum vector magnitude.