  Direct tunneling in ferromagnetic junctions is compared with
impurity-assisted, surface state assisted, and inelastic contributions to a
tunneling magnetoresistance (TMR). Theoretically calculated direct tunneling in
iron group systems leads to about a 30% change in resistance, which is close to
experimentally observed values. It is shown that the larger observed values of
the TMR might be a result of tunneling involving surface polarized states. We
find that tunneling via resonant defect states in the barrier radically
decreases the TMR (down to 4% with Fe-based electrodes), and a resonant tunnel
diode structure would give a TMR of about 8%. With regards to inelastic
tunneling, magnons and phonons exhibit opposite effects: one-magnon emission
generally results in spin mixing and, consequently, reduces the TMR, whereas
phonons are shown to enhance the TMR. The inclusion of both magnons and phonons
reasonably explains an unusual bias dependence of the TMR.
  The model presented here is applied qualitatively to half-metallics with 100%
spin polarization, where one-magnon processes are suppressed and the change in
resistance in the absence of spin-mixing on impurities may be arbitrarily
large. Even in the case of imperfect magnetic configurations, the resistance
change can be a few 1000 percent. Examples of half-metallic systems are
CrO$_2$/TiO$_2$ and CrO$_2$/RuO$_2$, and an account of their peculiar band
structures is presented. The implications and relation of these systems to CMR
materials which are nearly half-metallic, are discussed.
