On the magnetostatics of chains of magnetic nanoparticles

A novel approach is presented for the computation of the magnetostatic energy of straight and bent chains of identical, uniformly magnetized particles of arbitrary shape. The formalism relies on the concept of the magnetometric tensor field, and allows for closed form expressions for the magnetostatic energy, demagnetization factor, Young's modulus, and bending modulus of chains in terms of the shape amplitude of the particles. Analytical solutions are presented for straight chains of spheres, cubes, and cylinders, and for bent chains of spheres. Numerical results include chains of octahedra, tetrahedra, cuboctahedra, and bi-cones. The axial demagnetization factor for the bi-cone shape is derived in analytical form. An approximate energy expression, using the full shape-dependent interaction formalism for short separation distances, and the standard dipolar interaction expression for larger distances, is introduced.

► We have derived analytical expressions for several of these quantities for chains of spheres, cubes, and cylinders.
► We have applied the formalism to more complex shapes, including tetrahedra, octahedra, cuboctahedra, and bi-cones.
► For the bi-cone, we have derived an analytical expression for the axial demagnetization factor.