Local exchange splitting

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.

Density functional calculations using the nonrelativistic local exchange-only functional, splittings in atomic units (Hartrees)... 

Fig. 3.12 Tunneling spectra measured at T = 117 K for local coverages loc = 1, 2, 3, and >4 ML ( island ). For local coverages of 2 and 3 ML the surface state exists but the exchange splitting is reduced. The spectrum of island B in Fig. 3.11a is shifted by about 25 meV, possibly due to a stacking fault which will be discussed below. From [33], copyright 1998, rejnoduced with permission liom World Scientific Publishing Co. Pte. Ltd...

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. 

Although for wide band metallic materials the valence band XPS spectra probably provide a fairly direct picture of the occupied band structure, where the valence electrons are localized the correlation with the final hole state must be considered. This is apparent for 4/compounds and also quite nicely for FeFa . The situation for other transition metal compounds with possibly wider d bands and greater covalent mixing is less clearcut, but a similar effect is observed in the exchange splitting of core levels in magnetic ions . 

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