The first use of linear magnetic birefringence (optical Cotton-Mouton effect) to observe a magnetic resonance is reported. This allows us to make the first direct observation of resonant motion of a ferromagnetic vortex. This vortex is present in an easy-plane garnet film at the intersection of two 90° Neel walls. Agreement between the resonant frequencies and our theory confirms a previously proposed equation of vortex motion. PACS numbers: 76.90. + d, 75.40.Dy, 78.20.Ls We present here the first conclusive evidence for a Magnus-type force acting on a simple, topologically quantized vortex in a ferromagnetic medium. The existence of such forces which act orthogonally to the velocity of quantized superfluid and superconducting vortices is well known. A similar force, based on the classical Landau-Lifshitz equation that describes ferromagnetic-spin precessions, is expected to act on vortices occurring in a ferromagnet. 1 It illustrates a general law stating that the effective force component orthogonal to the velocity V of a micromagnetic structure (soliton) MO? -V/) is proportional to the product of V and the spherical angle mapped by the structure's distribution in M space. 2 This force is dominant whenever pseudoinertial effects can be neglected. 3 Recent unpublished work provides evidence of a resonance provisionally attributed to the motion of a magnetic vortex present within a Bloch line in a 180° Neel wall found in a garnet film of 0.8 /xm thickness. 4 This configuration was complicated by the absence of a well-defined restoring force for the wall due to the presence of permeable closure domains at its ends. However, these results did give some support to the equation of vortex motion employed in a statistical theory of two-dimensional ferromagnetism. 1 We have now investigated the dynamics of a magnetic vortex which forms at the intersection of two 90° Neel walls separating well defined in-plane domains stabilized by a "Swiss cross" geometry ( Fig. 1). In this geometry, fixing the four-ends of the walls to the inner corners defines the restoring force. Moreover, the walls do not touch closure domains. Thus the present configuration is suitable for a conclusive comparison of experiment with theory. Figure 2(a) shows a magneto-optic photomicrograph of two static 90° Neel walls intersecting at right angles. The bright or dark contrast of the walls is obtained by means of the Cotton-Mouton effect, a linear birefringence, Arc = n\\ -n L , for the two eigenmodes of linearly polarized light, parallel and perpendicular to the magnetization. (The circular birefringence or Faraday effect is absent because the in-plane magnetization is orthogonal to the normally incident laser illumination.) Intensity contrast between regions of different orientations of M^ becomes visible when an optical compensator and an analyzer are suitably adjusted. (We utilize an adjustable Ehringhaus compensator with its axes fixed at 45° with respect to the crossed polarizer and analyzer axes.) For incident ^-polarized light E=*E y y, t...