THE QUANTUM PHYSICS OF SOLIDS 



719 



weight, show that for manganese the Fermi energy outweighs the ex- 

 change energy so that manganese is not ferromagnetic at all . In Fig. 3 1 

 we represent the state of affairs predicted for chromium; the exchange 



+ SPIN 



- SPIN 



+ SPIN 



UNWAGNETIZED STABLE STATE MAGNETIZED UNSTABLE STATE 



NUMDER OF QUANTUM STATES AND ELECTRONS PER UNIT ENERGY 



Fig. 31 — The absence of ferromagnetism for chromium. 



energy is over-balanced by the Fermi energy and for this metal the 

 unmagnetized arrangement has the least energy and is the stable state. 

 A very instructive curve can be drawn to illustrate the criterion for 

 the occurrence of ferromagnetism. It is shown in Fig. 32. The 

 vertical scale is the energy of the unmagnetized state, Eu, minus the 

 energy of the magnetized state, E^^. When Eu - E^ is positive, the 

 magnetized state has the lower energy and will be the stable state, 



-I 



< UJ 

 2 I 



MANGANESE 



RADIUS OF 3d ORBIT 



Fig. 32 — Criterion for the occurrence of ferromagnetism. 



