Surface magnetic excitation within Influence Dzyaloshinskii– Moriya term in the weakly non-collinear configuration Application to MF ₃ structure (M= Fe, Cr)

In this study, we have theoretically investigated the influence of the anisotropy field and the Dzyaloshinskii-Moriya (D-M) type coupling on bulk and surface spin excitations. Two applications of the formalism developed here have been done on the trifluorides MF 3 (M=Fe, Cr) structures which provides a good illustration of the presence of magnetic frustration due to competing interactions and the existence of non-collinear structures. In the first part the bulk and surface spin dynamics are analyzed under the influence of anisotropy field whereas in the second step the antisymmetric interaction (D-M) is considered thus enabling a detailed analysis on the influence of the Dzyaloshinskii-Moriya (D-M) term on the propagating and evanescent precessional fields occurring in the neighborhood of the bulk-surface region. The bulk-surface spin dynamics are studied using theoretical formalism based on the symmetry properties obtained from the semi-infinite system by examining the matching equations for evanescent and propagating solutions deduced from the bulk secular equation, satisfying surface boundary conditions. The calculations have been carried out considering the competing inter-sublattices nearest and intra-sublattices next nearest neighbors exchange interactions occurring in the bulk and surface. It was found that the spin wave dispersion associated with the bulk as well as with the surface ar estrongly dependent on the values of ratio of bulk-surface parameter (J S /J AB ) and the canting angle Θ. An energy gap which illustrates a new magnetic ground state for surface spin quantum configuration is evidenced. In addition, it was observed that this energy gap increases as the non-collinearity increases.