A phenomenological theory of vortex motion, where the mixed state is regarded as a continuum, has been proposed by two of the authors in a short previous letter. Its outlines are recalled in this paper with further comments and arguments; in particular the basic equations and their implications are discussed at some length. This theory leads to a model of pinning, from which we argue that critical currents I" in soft type-II samples of standard bulk homogeneity, should be governed essentially by surface defects. I, is interpreted as a physically well-defined part of the total transport current I, which is flowing over a small depth close to the surface. Thus, on the scale of an ordinary sample, this part of the transport current is superficial, the remaining part I -I, being uniformly distributed over the cross section. Coherently, an analysis of the dissipation in such samples predicts that the part VI, of the total Joule effect VI must arise as surface heat sources, while the Joule effect V(I -I, ), usually associated with the steady viscous flow of vortices, is uniformly distributed in the bulk. As a proof, we present a method, using second-sound acoustics, to detect and separate surface and volume heat sources. Experimental results give clear evidence of a surface Joule effect, and support the validity of our model of surface pinning in soft materials.

In its simplest form the magnetoelastic buckling instability refers to the sudden bending transition of an elastic rod experiencing a uniform induction field applied at a normal angle with respect to its long axis. This fundamental physics phenomenon was initially documented in 1968, and, surprisingly, despite many refinements, a gap has always remained between the observations and the theoretical expectations. Here, we first renew the theory with a simple model based on the assumption that the magnetization follows the rod axis as soon as it bends. We demonstrate that the magnetoelastic buckling corresponds to a classical Landau secondorder transition. Our model yields a solution for the critical field as well as the shape of the deformed rods which we compare with experiments on flexible ferromagnetic nickel rods at the centimeter scale. We also report this instability at the micrometer scale with specially designed rods made of nanoparticles. We characterized our samples by determining all of the relevant parameters (radius, length, Young modulus, magnetic susceptibility) and, using these values, we found that the theory fits extremely well the experimental results for both systems without any adjustable parameter. The superparamagnetic feature of the microrods also highlights the fact that ferromagnetic systems break the symmetry before the buckling. We propose a magnetic "stick-slip" model to explain this peculiar feature, which was visible in past reports but never detailed. magnetoelasticity | buckling | nanoparticles | instability | magnetic I n the past decade there has been an emerging field of research on new magnetic and elastic soft materials whose shape can be remotely controlled by application of an external magnetic field (1-3). Indeed, at many scales and in various domains, magnetic filaments (4, 5), gels (6), and so on (7) show great promise in numerous domains of application (8). With the progress in the design of these materials, their magnetic susceptibility increases, and brings them closer to the behavior of the more conventional magnetic alloys. Thus, they can benefit a more ancient domain of research that described their magnetoelastic properties. Magnetoelasticity generally describes various phenomena that couple magnetization and mechanical deformation of solid-state objects (9). Excluding magnetostriction, the domain splits into two categories depending on whether the system is driven by free macroscopic currents or only by bound currents. In this latter case, the system may be studied only for its equilibrium configuration, or for its dynamic behavior (10). The complexity of the solution of the magnetic field in the general case justifies that a comprehensive description of the phenomenon is restricted to some trivial geometries such as rods of large aspect ratios (11). The main contribution to the field was made in 1968 with an elegant work (12) that paved the way both for experiments and theory but whose measures showed a critical field twice lower than expected. Further studies (1...