Magnetic Anisotropic Energy Gap and Strain Effect in Au Nanoparticles
- Po-Hsun Shih^{1} and
- ShengYun Wu^{1}Email author
DOI: 10.1007/s11671-009-9438-z
© to the authors 2009
Received: 1 April 2009
Accepted: 9 September 2009
Published: 22 September 2009
Abstract
We report on the observation of the size effect of thermal magnetization in Au nanoparticles. The thermal deviation of the saturation magnetization departs substantially from that predicted by the Bloch T^{3/2}-law, indicating the existence of magnetic anisotropic energy. The results may be understood using the uniaxial anisotropy Heisenberg model, in which the surface atoms give rise to polarized moments while the magnetic anisotropic energy decreases as the size of the Au nanoparticles is reduced. There is a significant maximum magnetic anisotropic energy found for the 6 nm Au nanoparticles, which is associated with the deviation of the lattice constant due to magnetocrystalline anisotropy.
Keywords
Nanoparticles Magnetic anisotropy Magnetic properties Spin wavesIntroduction
Metal nanoparticles of Pd, Au, and Cu have been extensively studied, because, due to a reduction in dimensionality, their ferromagnetic polarizations are quite different from those observed in transition metals [1–6]. The most frequent effects of the small size are lattice rearrangement, crystalline imperfections, a higher degree of localization, and narrowed valence band width. It has been reported in previous studies [2, 4] that individual Pd and Au nanoparticles may reach their ferromagnetic moment at low temperatures, and that, theoretically, there may be a slight enhancement of the 4d localization, although Pd and Au are both characterized by diamagnetism in the bulk state. Bulk Au metal also demonstrates a typical diamagnetic response of −1.42 × 10^{−6} emu/g [7], when the [Xe]4f ^{14}5d ^{10}6 s ^{1} Au configuration has a closed d shell and a single s electron. Finite-size effects play a dominant role in determining the magnetic properties. A decrease in size can lead to unusual ferromagnetic and diamagnetic properties. The origin of the ferromagnetism observed in filled 4d or 5d electron nanoparticle systems can be explained as due to giant magnetic anisotropy [8] and Fermi-hole effects [9] that influence the evolution from the surface polarization spins to the diamagnetic bulk state. In this letter, we discuss the effects of surface polarization and weak magnetic anisotropy in Au nanoparticles, which indicate the appearance of ferromagnetic spin polarization and magnetic anisotropic energy at low temperatures. Moreover, the strain induced by the lattice can be used to tune the magnetic anisotropic energy, which is obtained from the quantum spin wave theory and the anisotropic Heisenberg ferromagnetic model.
Experimental Details
The Au nanoparticles used in the present study were fabricated by the thermal evaporation method. High-purity gold ingots (99.999%) were evaporated in the range of 0.1–2 T. The Ar gas was fed at a rate of ~0.1 Å/s. To avoid contamination by magnetic impurities originating from the stainless steel plate the samples were collected by a rotating silicon substrate maintained at the temperature of liquid nitrogen. The resultant samples consisted of collections of individual Au nanoparticles in the form of dried powder. The morphology and structures of the prepared nanoparticles were then characterized using transmission electron microscopy (TEM, JEM-1400 JEOL).
Results and Discussion
Structural Analysis
Magnetization
Here L(x) = coth(x)−1/x is the Langevin function, M _{s} is the saturation magnetization, k _{B} is the Boltzmann’s constant, and χ _{D} is the diamagnetic susceptibility term. The analysis relevant to Eq. 1 is based on a model which ignores the inter-particle interactions and the contributions of the distributions of the magnetic moment due to the log-normal size distribution of the nanoparticle system [15]. It can be seen that the fitted curves (solid line in Fig. 2a) are quite consistent with the experimental data. The mechanism often invoked to explain the occurrence of surface-spin polarization effects in nonmagnetic particles [4] is that the shell of the particle is ordered as a ferromagnetic shell, while the core of each Au nanoparticle still behaves as a diamagnetic single domain. Indeed, there is a discrepancy between the data and the Langevin profile shown in the M(H) curves taken at the low field regime. One possible cause of this difference in the fit is the production of a nonmagnetic surface layer by the chemical interaction between the particle and the oxidation. In light of the results obtained in various studies [16], we believe that this difference has a different origin. An alternate explanation has been made by Berkowitz [17, 18], who attributed the reduction in the expected magnetization at low temperature to difficulty in reaching saturation, because of a large surface anisotropy.
Magnetic Anisotropic Energy Gap
Summary of the size and fitting results for Au nanoparticles
<d> (nm) | M _{s}(5 K, emu/g) | Μ _{th}(emu/g) | Δ(meV) |
---|---|---|---|
3.7(9) | 0.115 | 0.015 | 0.646 |
4.3(6) | 0.058 | 0.004 | 0.709 |
5.6(4) | 0.031 | 0.0085 | 2.391 |
6.0(3) | 0.065 | 0.0076 | 6.527 |
7.9(1) | 0.014 | 0.0032 | 1.412 |
Conclusions
An analysis of the results leads to an interesting conclusion: that nanosized transition metal Au particles exhibit both ferromagnetism and superparamagnetism, which are in contrast to the metallic diamagnetism characteristic of bulk Au. The superparamagnetic component of Au nanoparticles shows an anomalous temperature dependence that can be well explained by the modified Langevin function theory. Weak magnetic anisotropy was observed in the mean deviation magnetization. The energy of the magnetic anisotropic can be determined from the fitting of the anisotropic Heisenberg model and related with the change of strain. One possible explanation for the origin of the observed superparamagnetic component of the magnetization would be the existences of non-localized holes and charge transfer which would signify that deviation from stoichiometry would make only a small paramagnetic contribution to the magnetization [31].
Declarations
Acknowledgments
We appreciate the financial support of this research from the National Science Council of the Republic of China under grant No. NSC-97-2112-M-259-004-MY3.
Authors’ Affiliations
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