  A two-dimensional analytical model for the description of the excitation of
nonreciprocal spin waves by spin current in spin-Hall oscillators in the
presence of the interfacial Dzyaloshinskii-Moriya interaction (i-DMI) is
developed. The theory allows one to calculate the threshold current for the
excitation of spin waves, as well as the frequencies and spatial profiles of
the excited spin wave modes. It is found, that the frequency of the excited
spin waves exhibits a quadratic red shift with the i-DMI strength. At the same
time, in the range of small and moderate values of the i-DMI constant, the
averaged wave number of the excited spin waves is almost independent of the
i-DMI, which results in a rather weak dependence on the i-DMI of the threshold
current of the spin wave excitation. The obtained analytical results are
confirmed by the results of micromagnetic simulations.
