The low-temperature behavior of a two-level system (TLS) with spin is
investigated, where the atom tunneling between two positions possesses
a spin and interacts with the conduction electrons by an exchange int
eraction. To describe the physical properties of this TLS a generalize
d model is developed, where in addition to the usual screening and ele
ctron assisted tunneling processes exchange interaction and exchange a
ssisted interactions with the conduction electrons are introduced. The
se exchange interaction terms break the SU(2) symmetry of the original
TLS model corresponding to the conduction-electron spin. Summing up t
he leading logarithmic vertex corrections we show that if the Kondo te
mperature associated with the orbital degrees of freedom, T-K(orb), is
smaller than that associated with the exchange interaction, T-K(magn)
, then the orbital degrees of freedom of the TLS are frozen out when t
he magnetic Kondo effect takes place and only a magnetic Kondo effect
occurs. In this case the ground state of the system seems to be a Ferm
i-liquid state. In the opposite case, T-K(orb) > T-K(magn) two orbital
electron channels become dominant below T-K(orb) and a new fixed poin
t appears. The possibility of experimental realizations is also shortl
y discussed.