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Significance of shape anisotropy for nano-particles
Over the last decade a growing interest in the field of fundamental and applied research has been stimulated by the new category of materials shaped by nanostructures. A great deal of physical and chemical techniques such as colloidal solutions (Bréchignac et al. 2008) has been proven extremely effective for controlling not only the size but also the shape of developed nanoparticles. Shape anisotropy, sometimes also referred to as magnetic dipolar anisotropy (Bland, 2002), is mediated by dipolar long-range interaction where its contribution is dependent on the shape of a given sample (Bland, 2002). Magnetic dipole-dipole interactions exhibit an important and well known feature that, regardless of their weakness with respect to exchange coupling, plays a vital role in magnetic systems. The long-range characteristic is used to determine the ground state, excitation spectrum, and breaking of a bulk sample in several magnetic domains, in such magnetic system (Politi & Pini, 1998). The distinctiveness of such dipolar interaction in three dimensions in expounded by the fact that the shape anisotropy is always present (Politi & Pini, 1998) which is independent of the size of the sample. Shape of hysteresis loops is strongly affected by magnetic anisotropy which also controls the coercivity and remanence (Liu at el, 2008). Consequently, taking infinite sample is meaningless without specifying the limiting shape of the sample (Politi & Pini, 1998).
The shape anisotropy due to such magnetic dipole-dipole interactions allows an in-plane magnetization without constituting any discriminatory direction within the film. It is mainly for these reasons that shape anisotropy becomes significant in thin films and often forms in-plane alignment of moments (Bland, 2002) (Politi & Pini, 1998) and as shape anisotropy is exploited in the design of most magnetic materials of commercial importance, therefore shape anisotropy is of considerable practical significance (Bréchignac et al. 2008) (He & Chen, 2007) (Chang et al, 2006).
The following section elaborates on a few examples discussing the significance of Shape anisotropy:
One of the latest researches reported by Liu at el. (2008) reveals the dominance of shape anisotropy, in Superconducting Quantum Interference Device (SQUID) measurements, which is demonstrated by the weak temperature dependence of the enhanced coercive field along the wire axis. The dominance of shape anisotropy has been validated by using the temperature dependence of the hysteresis response. Temperature has been indicated to have little effect on the coercivity as compared to the bulk material. This is shown in fig.1, where the coercivity almost remains constant as the temperature increases from 1.8K to room temperature and implies that the shape anisotropy prevails over the magnetization fluctuation. Furthermore, the existence of distinct dipoles of opposite polarity at the wire-ends is also observed besides a spatial magnetization modulation along the wire with a period of 700nm. Liu at el. (2008) has shown that such modulation is instigated from the dominant shape anisotropy along the wire-axis and the competition between the magneto-crystalline polarizations along the easy-axis.
Fig.1. Hysteresis responses of Co nanowire at different temperatures illustrating the dominance of shape anisotropy and weak temperature dependence of coercivity (Liu at el. 2008)
In an other research reported by He & Chen (2007), it has been found that for soft magnetic materials, such as fcc Ni, fcc Co and bcc Fe, the intrinsic magneto-crystalline anisotropy does not significantly contribute to the total anisotropy. It is the shape anisotropy that consequently becomes significant to affect the magnetization reversal process in nanoscaled magnetic materials. He & Chen (2007) also believe that enhanced shape anisotropy is one of the most important reasons for the enhanced coercivity in nanoparticles. He & Chen (2007) proposed the following extended equation in the Néel-Brown (N-B) analysis framework for the temperature variation effect of shape anisotropy on the coercivity Hc (T) of aligned Stoner-Wohlfarth nanoparticles such as such as fcc Ni, fcc Co and bcc Fe
Where the factor m(t) accounts for the temperature-dependent effect of the shape anisotropy which is particularly important for nanoparticles of soft ferromagnetic materials. He & Chen (2007) have found that for the estimation of the blocking temperature or the blocking energy barrier, the factor m2(t) for Ni at T = 300 K becomes 0.86 which indicates that the shape anisotropy effect has become increasingly significant to estimate the blocking temperature. He & Chen (2007) have also shown that the correction on Hc (T) attributed to the effect of temperature dependent shape anisotropy greatly depends on the reduced spontaneous magnetization m(t) and becomes increasingly significant as the particle volume size increases. Fig.2. shows Hc (T) of aligned Stoner-Wohlfarth fcc Ni nanoparticles with the reduced volumes, Vred = 0.02, 0.04, 0.1, 0.4, and 1. The symbols are for the data calculated by taking into account the effect of temperature dependent shape anisotropy calculated according to the above equation. The solid curves are for the fittings of these points using this equation.
Fig.2. Hc (T) of aligned Stoner-Wohlfarth nanoparticles with the reduced volumes for fcc Ni (He & Chen, 2007)
Chang et al (2006) used Magnetization induced Second Harmonic Generation (MSHG) technique in order to explore the nonlinear magneto-optical and magnetic anisotropy properties, and the crystal and magnetic symmetry of nanoparticles of cobalt and cobalt oxide cobalt particle of size within the range of 10nm to 30nm at room temperature. The cobalt nanoparticle thin film’s magnetization reversal process requires the rotation of the magnetization in the surface plane but does not involve the surface normal plane. The cobalt nanoparticle thin film has been shown to have a low external magnetic field in response to a large nonlinear Kerr rotation response. The increase of coercivity field Hc (T) in the cobalt oxide nanoparticle thin film has been attributed to anti-ferromagnetic cobalt oxide shell and the strong interaction in the boundary between the ferromagnetic cobalt cores. It has been found by Chang et al (2006) that the magnetic anisotropy is due to the shape anisotropy of cobalt nanoparticle thin film and their interaction.
Lu et al (1997) have demonstrated the control of magnetic response by using the shape anisotropy and have discussed the electrode layers magnetic coupling. It has been shown by Lu et al (1997) that the shape anisotropy is useful in controlling the response properties of magnetic tunnel junctions by varying the junction shape as represented in fig.3. The figure demonstrates the shape anisotropy of the top electrode in the used devices is more important than the intrinsic anisotropy induced during film deposition.
Fig.3. Junction resistance versus magnetic field of two series of devices on the chip (Lu et al, 1997)
Bland, J. (2002) “A Mössbauer Spectroscopy and Magnetometry Study of Magnetic Multilayers and Oxides”,PhD Thesis, Department of Physics, University of Liverpool
Bréchignac, C., Houdy, P., Lahmani, M. (2008) “Nanomaterials and Nanochemistry: Colloidal Methods and Shape Anisotropy”, 1st edition, Springer, New York
Chang, Y. M., Hsu, Y. J., Liu, T. M., Chu, H. W., Chuo, Y. J., Lin, J. G., Chen, C. H. (2006) “Magnetization-induced second-harmonic generation of cobalt and cobalt oxide nanoparticles”, Ultrafast Phenomena in Semiconductors and Nanostructure Materials, Proceedings of the SPIE, Vol. 6118, pp. 262-272
He, L. and Chen, C. (2007) “Effect of temperature-dependent shape anisotropy on coercivity for aligned Stoner-Wohlfarth soft ferromagnets”, Physical Review, Series B, Vol. 75; Number 18, pp. 184424
Liu, Z., Chang, P., Chang, C., Galaktionov, E., Bergmann, G., and Lu, J. (2008) “Shape Anisotropy and Magnetization Modulation in Hexagonal Cobalt Nanowires”, Advanced Functional Materials, Vol. 18, pp. 1573-1578.
Lu, Y., Altman, R. A., Marley, A., Rishton, S. A., Trouilloud, P. L., Xiao, G., Gallagher, W. J., Parkin, S. P. (1997) “Shape-anisotropy-controlled magnetoresistive response in magnetic tunnel junctions”, Applied Physics Letters, Vol. 70, Issue 19, pp.2610-2612.
Politi, P., Pini, M. G. (1998) “Shape anisotropy and magnetic domain structures in striped monolayers”, The European Physical Journal, Series B, Vol. 2, Issue 4, pp. 475-481.
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