Ferromagnetic resonance on Ni nanowire arrays
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Ralph Skomski, Roger Kirby, and David J. Sellmyer Department of Physics and Astronomy, Center for Materials Research and Analysis, University of Nebraska, Lincoln, Nebraska 68588 (Received 24 January 2011; accepted 19 April 2011)
Ferromagnetic resonance investigations on Ni nanowires are reported. The angular dependence of the resonance line position is analyzed within a thermodynamic approach that includes shape anisotropy (ellipsoids of revolution), magnetocrystalline anisotropies (cubic and uniaxial), and dipole–dipole interactions. The results are supported by hysteresis loops, obtained on the same sample.
I. INTRODUCTION
The ideal magnetic nanowire is a one-dimensional system, with cylindrical shape. The Ni nanowire is spontaneously magnetized along the cylinder’s axis.1,2 Its magnetic properties are dominated by the shape anisotropy to which various contributions act as perturbations. The effect of magnetocrystalline anisotropy, triggered by the crystalline electric field or the stresses induced in Ni nanowires, has been extensively studied.2 The ratio of line intensities corresponding to [220] and [110] x-ray diffraction peaks was found3,4 to be 2.8 instead of the expected ratio for a random sample, which is about 0.2. The electrodeposited Ni nanowires are subjected to large, almost uniaxial strains.4,5 Magnetoelastic effects induce a magnetoðMEÞ crystalline anisotropy4,6,7 K1 32 kr5 32 keE, where k is the saturation magnetostriction (33 106 for bulk Ni8), e is the thermal expansion coefficient, r is the force density (per unit area), and E represents the Young modulus. The bulk modulus for Ni is ranging between 177.3 GPa9 and 330 GPa. In the case of Ni nanowires electrodeposited in polymeric membranes, the difference between the expansion coefficients of the matrix and of nanowires is larger than that in the case of nanowires deposited in alumina templates. These mechanical stresses induce a magnetocrystalline anisotropy.6,7 It was concluded4 that in the case of Ni nanowires electrodeposited in polymeric (polycarbonate) pores, the temperature dependence of the uniaxial anisotropy is related to the axial elastic strain in the nanowire and membrane. Packing the nanowires closer and closer enhances the contribution of dipole–dipole interactions.10,11 At scale lengths below 10 lm,12 the dipole–dipole interactions a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2011.146 J. Mater. Res., Vol. 26, No. 17, Sep 14, 2011
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between the nearest nanowires trigger a demagnetizing field, HD, which depends on the spacing between nanowires. Within the mean-field approximation, HD is proportional with the porosity of the template,11 which is related with the averaged spacing between nanowires.13 At high packing density, a collective behavior due to the onset of exchange interactions among nanowires was observed. The array of real nanowires presents complications related to the distribution in the size, shape, and orientation of
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