• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.149-156
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• 1998

We relate the existence of rational curves with the existence of rigid bundles of any even rank on Enriques surfaces and compare with the case of K3 surfaces.

• Current Applied Physics
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• v.18 no.11
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• pp.1240-1247
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• 2018

Magnetic hysteresis in Ni nanowire arrays grown by electrodeposition inside the pores of anodic alumina templates is studied as a function of temperature in the range between 5 K and 300 K. Nanowires with different diameters, aspect ratios, inter-wire distance in the array and surface condition (smooth and rough) are synthesized. These microstructure parameters are linked to the different free magnetic energy contributions determining coercivity and the controlling magnetization reversal mechanisms. Coercivity increases with temperature in arrays of nanowires with rough surfaces and small diameters -33 nm and 65 nm- when measured without removing the alumina template and/or the Al substrate. For thicker wires -200 nm in diameter and relatively smooth surfaces- measured without the Al substrate, coercivity decreases as temperature rises. These temperature dependences of magnetic hysteresis are described in terms of an effective magnetic anisotropy $K_a$, resulting from the interplay of magnetocrystalline, magnetoelastic and shape anisotropies, together with the magnetostatic interaction energy density between nanowires in the array. The experimentally determined coercive fields are compared with results of micromagnetic calculations, performed considering the magnetization reversal mode acting in each studied array and microstructure parameters. A method is proposed to roughly estimate the value of $K_a$ experimentally, from the hysteresis loops measured at different temperatures. These measured values are in agreement with theoretical calculations. The observed temperature dependence of coercivity does not arise from an intrinsic property of pure Ni but from the nanowires surface roughness and the way the array is measured, with or without the alumina template and/or the aluminum support.