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Magnetic Interactions in Fe Nanoparticle Arrays D. Farrella, S. Yamamuroa, Yumi Ijirib, and S. A. Majeticha a Dept. of Physics, Carnegie Mellon University Pittsburgh, PA 15213, U.S.A. b Dept. Of Physics, Oberlin College Oberlin, OH 44074

ABSTRACT The preparation of monodisperse Fe nanoparticles and self-assembly into hcp and fcc or fcc-like arrays is described. Here dipolar interactions dominate for the interparticle spacings studied (1.4-3.4 nm). Comparison of the low temperature magnetic properties of multilayer arrays with those of dilute suspensions of the same particles show increased coercivity and slower magnetic relaxation in the arrays. Mean field calculations of magnetic interaction fields suggest the type of ordered structures formed.

INTRODUCTION Here we describe how dipolar interactions between nanoparticles affect the structure and the magnetic properties of self-assembled arrays. Compared with other selfassembling nanoparticle systems, magnetic nanoparticles possess additional magnetostatic forces due to dipolar interactions. The dipolar field Bdip surrounding a monodomain particle is anisotropic, Bdip =

µ0  3(µ • r)r µ  − 3,  5 4π  r r 

(1)

and so are the dipolar forces. Here µo is the permeability of free space, µ is the dipole moment, and r is the distance from the center of the dipole. When magnetic nanoparticles have a stable magnetic moment and magnetostatic forces dominate over the dispersion forces, the particles prefer to form chains. This problem can be circumvented if the magnetic interactions are weaker than the other forces driving self-assembly, which occurs when the particles are superparamagnetic. While arrays rather than chains are formed, it is unclear whether the magnetic interactions have more subtle morphological effects due to dipolar interactions during self-assembly. Dipolar interactions affect the magnetic properties of nanoparticles even under high dilution [1, 2]. It is therefore expected that at high concentration, as in a closepacked array, that there will be significant differences in the behavior. What differentiates these arrays from nanocrystalline magnets is the lack of exchange interactions. Between atoms the exchange strength J between atoms is given by J = J0exp[-R/Lex].

Y9.1.1

(2)

Here Jo is a constant, R is the separation, and Lex is the exchange length. Lex = (Aex/K)1/2, where A is the exchange stiffness and K is the magnetocrystalline anisotropy. For bulk Fe, Lex is on the order of 15 nm. Between particles the exchange strength depends on the interparticle separation s and a barrier height ∆ε: Jinterparticle ~ (1/s2)exp[-(const.)(∆ε)1/2].

(3)

[3] The estimated exchange field Hex between islands in Reference 17 is 50-100 Oe. The nanoparticles of Figure 2 had a 3.6 nm closest spacing between particles. Here Hex < 10-3 Oe, but the dipolar field estimated by including up to fifth nearest neighbors is ~ 800 Oe. For an edge-to-edge interparticle spacing of 3.6 nm, typical of oleic acid-coated nanoparticles in self-assembled arrays, this exchange fiel