Effects of the Dzyaloshinskii-Moriya interaction on spin waves in domain walls

We propose novel ways of manipulating spin wave propagation useful for data processing and storage within the field of magnonics. We analyse the effects of the Dzyaloshinskii-Moriya interaction (DMI) on magnetic structures using an analytical formalism. The DMI is the antisymmetric form of the exchange interaction and becomes relevant in magnetic structures where surface phenomena are important as in thin ferromagnetic films. The antisymmetric nature of the DMI modifies the magnetic ground state stabilising chiral structures. In particular, the DMI favours one kind of domain wall, Néel wall, over the common Bloch-type wall. In this thesis, we focus on taking advantage of the new features found in the small fluctuations, or spin waves, around a DMI driven-Néel type wall in order to propose new magnonic devices. Studies about the influence of the DMI on spin waves in uniformly magnetised films show that the dispersion can be non-reciprocal, i.e. the frequency is not symmetric with respect to the wave vector, Ω(k) /= Ω(−k). In domain walls, we observe that the non-reciprocity phenomenon arises for propagation parallel to the plane of the wall. In this direction, the domain wall acts as a confining potential and provides a way of channelling the spin waves even in curved geometries. The non-reciprocity increases the spin wave group velocity to a range useful for information technologies. For propagation perpendicular to the wall plane we find that spin waves are reflected due to the DMI. We consider a periodic array of Néel walls and calculate the band structure in which frequency gaps appear. The reflection phenomenon in the periodic array is the basis of a tunable frequency filter device Examining the symmetries of the magnetic Lagrangian, we find that energy and linear momentum are conserved. We analyse how energy conservation explains the non-reciprocal dispersion and how linear momentum conservation is achieved by spin waves transferring linear momentum to the domain wall and moving it. Following similar symmetry considerations, we calculate the continuity equation for the total angular momentum of the system. We find that the total angular momentum of the system consists of an orbital and a spin contribution. We demonstrate that an angular momentum transfer from the orbital part, associated with the DMI, to the spin part, given by the magnetic moments, needs to occur for the total angular momentum to be conserved. We propose that this mechanism leads to spin wave-driven domain wall motion