Non-local symmetries of first-order equations

It is shown how one can transform scalar first-order ordinarydifferential equations which admit non-local symmetries of theexponential type to integrable equations admitting canonicalexponential non-local symmetries. As examples we invoke theAbel equation of the second kind, the Riccati equation and naturalgeneralizations of these. Moreover, our method describes howa double reduction of order for a second-order ordinary differentialequation which admits a two-dimensional Lie algebra of generatorsof point symmetries can be affected if the second-order equationis first reduced in order once by a symmetry which does notspan an ideal of the two-dimensional Lie algebra.     

Magnon excitation by spin injection in thin Fe/Cr/Fe films

The technique of Brillouin light scattering is used to observe strong excitation of magnons in antiferromagnetically coupled trilayers of Fe/Cr/Fe at room temperature. The magnons are driven out of equilibrium by a microwave current applied in the trilayer through point contacts. The magnitude of the scattering intensity is investigated as a function of the magnon wave number and applied magnetic field. Confirming recent theoretical predictions, the observations provide strong evidence of electronic spin injection in the rf driving field.