title: A refined theory of magnetoelastic buckling matches experiments with ferromagnetic and superparamagnetic rods.
abstract: 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 second-order 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.
authors.affiliation: Laboratoire Matière et Systèmes Complexes, UMR 7057 (CNRS), Université Denis Diderot - Sorbonne Paris Cité, 75013 Paris, France; Université Pierre et Marie Curie - Paris 6, Sorbonne Universités, 75252 Paris Cedex 05, France fabien.gerbal@upmc.fr.
authors.forename: Fabien
authors.initials: F
authors.lastname: Gerbal
authors.affiliation: Laboratoire Matière et Systèmes Complexes, UMR 7057 (CNRS), Université Denis Diderot - Sorbonne Paris Cité, 75013 Paris, France;
authors.forename: Yuan
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Laboratoire Matière et Systèmes Complexes, UMR 7057 (CNRS), Université Denis Diderot - Sorbonne Paris Cité, 75013 Paris, France; Université Pierre et Marie Curie - Paris 6, Sorbonne Universités, 75252 Paris Cedex 05, France.
authors.forename: Florian
authors.initials: F
authors.lastname: Lyonnet
authors.affiliation: Laboratoire Matière et Systèmes Complexes, UMR 7057 (CNRS), Université Denis Diderot - Sorbonne Paris Cité, 75013 Paris, France;
authors.forename: Jean-Claude
authors.initials: JC
authors.lastname: Bacri
authors.affiliation: Laboratoire Matière et Systèmes Complexes, UMR 7057 (CNRS), Université Denis Diderot - Sorbonne Paris Cité, 75013 Paris, France; Université Pierre et Marie Curie - Paris 6, Sorbonne Universités, 75252 Paris Cedex 05, France.
authors.forename: Thierry
authors.initials: T
authors.lastname: Hocquet
authors.affiliation: Laboratoire Matière et Systèmes Complexes, UMR 7057 (CNRS), Université Denis Diderot - Sorbonne Paris Cité, 75013 Paris, France;
authors.forename: Martin
authors.initials: M
authors.lastname: Devaud
keywords: buckling; instability; magnetic; magnetoelasticity; nanoparticles