The plastic response of magnetoelastic amorphous solids

We address the cross-effects between mechanical strains and magnetic fields on the plastic response of magnetoelastic amorphous solids. It is well known that plasticity in nonmagnetic amorphous solids under external strain γ is dominated by the codimension-1 saddle-node bifurcation in which an eigenvalue of the Hessian matrix vanishes at γP like √ γP − γ. This squareroot singularity determines much of the statistical physics of elasto-plasticity, and in particular that of the stress-strain curves under athermal-quasistatic conditions. In this letter we discuss the much richer physics that can be expected in magnetic amorphous solids. Firstly, magnetic amorphous solids exhibit codimension-2 plastic instabilities, when an external strain and an external magnetic field are applied simultaneously. Secondly, the phase diagrams promise a rich array of new effects that have been barely studied; this opens up a novel and extremely rich research program for magnetoplastic materials. Copyright c © EPLA, 2012 Introduction. – The well-known magnetostriction effect where switching on a magnetic field changes the volume of a sample of magnetoelastic solid and the Villari effect in which mechanical strain changes the magnetization are just two examples of the rich variety of cross-effects that exist in magnetoelastic materials when both an external mechanical strains and a magnetic field are employed. Surprisingly, the fundamental physics of plasticity has been studied much more extensively in the context of pure mechanical strains in non-magnetic amorphous solids, with many experiments and numerical simulations becoming available in recent decades. A much richer physics of plasticity can, however, be expected in magnetoelastic amorphous materials like metallic glasses, and the aim of this letter is to commence a research program in this direction. The fundamental physics of plastic instabilities in nonmagnetic amorphous solids has been uncovered in recent years in the context of athermal, quasistatic mechanical (AQS) strain. While many experiments are done at finitetemperature and finite-strain rates, AQS studies afford a unique laboratory for exposing the clean fundamental physics of plastic instabilities. In particular bifurcation theory, sometime known as catastrophe theory, provides (a)E-mail: [email protected] a powerful framework for the discussion of the singular behavior of such instabilities. For purely mechanical strains irreversible plastic events occur in AQS conditions when an eigenvalue of the Hessian matrix H hits zero. In d dimensions the Hessian matrix is defined as Hij ≡ ∂U ∂ri∂rj , Nd×Nd symmetric matrix, (1) where U({ri(γ)}, γ) is the total potential energy of a solid containing N particles whose coordinates depend on the external strain γ, i.e., {r1(γ) . . . rN (γ)}. The systems that we consider are metallic glasses that consist of mixtures of metallic and non-metallic atoms. Such mixtures are expected to exhibit strong coupling between mechanical and magnetic effects. In our model we consider the atoms as point particles interacting via potentials that are detailed below. The generic plastic event [1,2] is a codimension-1 saddle-node bifurcation which occurs at some value of γ = γP of the external strain where the lowest eigenvalue of the Hessian matrix (excluding Goldstone modes when they exist) hits zero like √ γP − γ. The saddle-node bifurcation has been shown to be universal for a large variety of amorphous solids from simple binary glasses with pair potentials to metallic glasses with manybody interaction potentials [3]. Among other interesting phenomena this square-root singularity determines the