. The Bell System technical journal . 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 theunmagnetized arrangement has the least energy and is the stable very instructive curve can be drawn to illustrate the criterion forthe occurrence of ferromagnetism. It is shown in Fig. 32. Thevertical scale is the energy of the unmagnetized state, Eu, minus theenergy of the magnetized state, E^^. When Eu - E^ is positive, thema
. The Bell System technical journal . 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 theunmagnetized arrangement has the least energy and is the stable very instructive curve can be drawn to illustrate the criterion forthe occurrence of ferromagnetism. It is shown in Fig. 32. Thevertical scale is the energy of the unmagnetized state, Eu, minus theenergy of the magnetized state, E^^. When Eu - E^ is positive, themagnetized state has the lower energy and will be the stable state, -I < UJ2 I MANGANESE. RADIUS OF 3d ORBIT Fig. 32—Criterion for the occurrence of ferromagnetism. 720 BELL SYSTEM TECHNICAL JOURNAL and when Eu — Ej^ is negative, the reverse is true. Hence a positivevalue for Ev — Ej^ is a necessary and sufficient condition for ferro-magnetism. The variable on the horizontal scale is ra (the distance be-tween nearest neighboring atoms in the crystal) divided by Td (the aver-age radius for the ^d wave function). Small values of rajra meancrowding together of the atoms, large values of the Fermi energy, andno ferromagnetism. Certain values of rajrd, such as are found for iron,cobalt, and nickel, favor ferromagnetism. Very large values of Valrdmean widely separated atoms and low Fermi energy and, conse-quently, ferromagnetism; however, for very widely separated atoms,the energy of interaction between them is small and so is the energy ofmagnetization. The curve shown in Fig. 32 is only qualitative. Thetheory that the curve should have this form was first worked out byBe
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