Exchange splitting levels

An exchange splitting of the band levels is produced for every k, which is proportional to the magnetization A = I(n+ - n ). 

Fig. 3.8 Left-hand panel The on-site atomic energy levels for up and down spin electrons due to the exchange splitting Im where / and m are the Stoner exchange integral and local moment respectively. Right-hand panel The local magnetic moment m, as a function of //2 / where / and h are the exchange and bond integrals respectively. Compare with the self-consistent LSDA solution in the upper panel of Fig. 3.6.

Formulated in another way, the metal (M)-level is suddenly pulled down from well above to well below the ligand (L) valence levels a distance larger than the exchange splitting 2H]2 as a consequence, the system cannot follow adiabatically but undergoes a diabatic (curve crossing) transition to an excited state of the ionic system. 

Fig. 3. Splitting of atomic energy levels in a scaled magnetic field. The value A = 1 corresponds to the self consistent atomic XC-field. At this value, the exchange splitting of the Ni 3d states ( 0.6 eV) is much larger than the spin-orbit splitting of these states (fti 0.2 eV). Thus, the 3d states in nickel have almost pure spin character (see also Fig. 9 below). On the contrary, the 4p states show a much smaller exchange splitting and thus remain almost pure K-states.

Fig. 5.17 Left part energy dependence of the photoelectron spectra analogously obtained to Fig. 5.16. The islands were created by heating an epitaxial cobalt film to about 1,000 K. From [55], used with permission. Right part for comparison, a fully relativistically calculated band structure for hcp(OOOl) bulk cobalt with in-plane magnetization is displayed. This calculation takes into account both spin-orbit interaction and exchange splitting on the same level of accuracy. The circles in the initial states show two regions where hybridization effects arc present. Reprinted from [28], Copyright (1998), with permission from Elsevier...

Fig. 5.19 Exchange splitting of the O 2px level of oxygen being chemisorbed on Fe/W(110) as a function of exposure. A reduction of occurs with increasing dosage. After starting of the oxidation process (>12 L) the exchange splitting vanishes within the margin of error. Reprinted from [65], Copyright (1999), with permission from Elsevier...

By increasing the sample temperature both peaks of the Tb(OOOl) surface state shift towards thereby decreasing the exchange splitting A ex- Just above Tcb (T — 223 K) the occupied part of the surface state has already approached the Fermi level very closely [U — —50 34 mV]. In contrast to earlier experiments on Gd(OOOl), this trend continues for Tb(OOOl) even above its bulk magnetic phase transition temperatures Tcb = 220 K and Tnb = 228 K. At T = 248 K the former occupied part of the surface state is energetically localized at the Fermi level [17 = 10 30 mV]. Increasing the temperature further T — 258 K and T — 271 K) the maximum in the dUdU spectra crosses Ejs. As a result the surface state which was clearly occupied at low temperature (T = 85 K) becomes partially empty above T = 250 K. 

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