  We study non-equilibrium transport through a single-orbital Anderson model in
a magnetic field with spin-dependent hopping amplitudes. In the cotunneling
regime it is described by an effective spin-1/2 dot with a
Dzyaloshinsky--Moriya--Kondo (DMK) interaction between the spin on the dot and
the electron spins in the leads. Using a real-time renormalization group
technique we show that at low temperatures (i) the DMK interaction is strongly
renormalized, (ii) the renormalized magnetic field acquires a linear voltage
dependence, and (iii) the differential conductance exhibits a voltage asymmetry
which is strongly enhanced by logarithmic corrections. We propose transport
measurements in which these signatures can be observed.
