Magnetic Anisotropic Energy Gap and Strain Effect in Au Nanoparticles
- Po-Hsun Shih^{1} and
- ShengYun Wu^{1}Email author
- 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 waves
Introduction
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
References
- Teranishi T, Kiyokawa I, Miyake M: Adv. Mater.. 1998, 10: 596. COI number [1:CAS:528:DyaK1cXjsl2nurc%3D] COI number [1:CAS:528:DyaK1cXjsl2nurc%3D] 10.1002/(SICI)1521-4095(199805)10:8<596::AID-ADMA596>3.0.CO;2-YView ArticleGoogle Scholar
- Hori H, Teranishi T, Nakae Y, Seino Y, Miyake M, Yamada S: Phys. Lett. A. 1999, 263: 406. COI number [1:CAS:528:DC%2BD3cXnvFer]; Bibcode number [1999PhLA..263..406H] COI number [1:CAS:528:DC%2BD3cXnvFer]; Bibcode number [1999PhLA..263..406H] 10.1016/S0375-9601(99)00742-2View ArticleGoogle Scholar
- Li W-H, Wu SY, Yang CC, Lai SK, Lee KC, Huang HL, Yang HD: Phys. Rev. Lett.. 2002, 89: 135504. Bibcode number [2002PhRvL..89m5504L] Bibcode number [2002PhRvL..89m5504L] 10.1103/PhysRevLett.89.135504View ArticleGoogle Scholar
- Yamamoto Y, Miura T, Suzuki M, Kawamura N, Miyagawa H, Nakamura T, Kobayashi K, Teranishi T, Hori H: Phys. Rev. Lett.. 2004, 93: 116801. COI number [1:STN:280:DC%2BD2cvotVGitQ%3D%3D]; Bibcode number [2004PhRvL..93k6801Y] COI number [1:STN:280:DC%2BD2cvotVGitQ%3D%3D]; Bibcode number [2004PhRvL..93k6801Y] 10.1103/PhysRevLett.93.116801View ArticleGoogle Scholar
- Hori H, Yamamoto Y, Iwamoto T, Miura T, Teranishi T, Miyake M: Phys. Rev. B. 2004, 69: 174411. Bibcode number [2004PhRvB..69q4411H] Bibcode number [2004PhRvB..69q4411H] 10.1103/PhysRevB.69.174411View ArticleGoogle Scholar
- Crespo P, Litrán R, Rojas TC, Multigner M, de la Fuente JM, Sánchez-López JC, García MA, Hernando A, Penadés S, Fernández A: Phys. Rev. Lett.. 2004, 93: 087204. COI number [1:STN:280:DC%2BD2cvotVKqsw%3D%3D]; Bibcode number [2004PhRvL..93h7204C] COI number [1:STN:280:DC%2BD2cvotVKqsw%3D%3D]; Bibcode number [2004PhRvL..93h7204C] 10.1103/PhysRevLett.93.087204View ArticleGoogle Scholar
- Shih JW: Phys. Rev.. 1931, 38: 2051. COI number [1:CAS:528:DyaA38XhtV2kuw%3D%3D]; Bibcode number [1931PhRv...38.2051S] COI number [1:CAS:528:DyaA38XhtV2kuw%3D%3D]; Bibcode number [1931PhRv...38.2051S] 10.1103/PhysRev.38.2051View ArticleGoogle Scholar
- Hernando A, Crespo P, García MA: Phys. Rev. Lett.. 2006, 96: 057206. COI number [1:STN:280:DC%2BD287gtF2mtQ%3D%3D]; Bibcode number [2006PhRvL..96e7206H] COI number [1:STN:280:DC%2BD287gtF2mtQ%3D%3D]; Bibcode number [2006PhRvL..96e7206H] 10.1103/PhysRevLett.96.057206View ArticleGoogle Scholar
- Harbola MK, Sahni V: Phys. Rev. B. 1988, 37: 745. Bibcode number [1988PhRvB..37..745H] Bibcode number [1988PhRvB..37..745H] 10.1103/PhysRevB.37.745View ArticleGoogle Scholar
- Garitaonandia JS, Insausti M, Goikolea E, Suzuki M, Cashino JD, Kawamura N, Ohsawa H, de Muro IG, Suzuki K, Plazaola F, Rojo T: Nano Lett.. 2008, 8: 661. COI number [1:CAS:528:DC%2BD1cXptl2jsg%3D%3D]; Bibcode number [2008NanoL...8..661G] COI number [1:CAS:528:DC%2BD1cXptl2jsg%3D%3D]; Bibcode number [2008NanoL...8..661G] 10.1021/nl073129gView ArticleGoogle Scholar
- Chen J, Jin G, Ma Y-Q: J. Phys. Condens. Matter. 2007, 19: 236225. Bibcode number [2007JPCM...19w6225C] Bibcode number [2007JPCM...19w6225C] 10.1088/0953-8984/19/23/236225View ArticleGoogle Scholar
- Xu C, Li ZY, Hui PM: J. Appl. Phys.. 2001, 89: 3403. COI number [1:CAS:528:DC%2BD3MXhsFGgtLs%3D]; Bibcode number [2001JAP....89.3403X] COI number [1:CAS:528:DC%2BD3MXhsFGgtLs%3D]; Bibcode number [2001JAP....89.3403X] 10.1063/1.1348326View ArticleGoogle Scholar
- Bean CP, Livingston JD: J. Appl. Phys.. 1959, 30: S120. Bibcode number [1959JAP....30S.120B] Bibcode number [1959JAP....30S.120B] 10.1063/1.2185850View ArticleGoogle Scholar
- Kittel C: Introduction to solid state physics. Wiley, New York; 1996.Google Scholar
- Chantrell RW, Popplewell J, Charles SW: IEEE Trans. Magn.. 1978, MAG-14: 975. COI number [1:CAS:528:DyaE1cXlvFSjt7c%3D]; Bibcode number [1978ITM....14..975C] COI number [1:CAS:528:DyaE1cXlvFSjt7c%3D]; Bibcode number [1978ITM....14..975C] 10.1109/TMAG.1978.1059918View ArticleGoogle Scholar
- Popplewell J, Charles SW: IEEE Trans. Magn.. 1981, MAG-17: 2923. COI number [1:CAS:528:DyaL38XitV2gsbs%3D]; Bibcode number [1981ITM....17.2923P] COI number [1:CAS:528:DyaL38XitV2gsbs%3D]; Bibcode number [1981ITM....17.2923P] 10.1109/TMAG.1981.1061670View ArticleGoogle Scholar
- Du YW, Lu HX, Wang YQ, Wang TX: J. Magn. Magn. Mater.. 1983, 31: 896. Bibcode number [1983JMMM...31..896D] Bibcode number [1983JMMM...31..896D] 10.1016/0304-8853(83)90729-1View ArticleGoogle Scholar
- Berkowitz AE, Lahut JA, Jacobs IS, Levinson LM, Forester DW: Phys. Rev. Lett.. 1975, 34: 594. COI number [1:CAS:528:DyaE2MXhsVyku70%3D]; Bibcode number [1975PhRvL..34..594B] COI number [1:CAS:528:DyaE2MXhsVyku70%3D]; Bibcode number [1975PhRvL..34..594B] 10.1103/PhysRevLett.34.594View ArticleGoogle Scholar
- Mandal K, Mitra S, Kumar PA: Europhys. Lett.. 2006, 75: 618. COI number [1:CAS:528:DC%2BD28XhtVWgs7jK]; Bibcode number [2006EL.....75..618M] COI number [1:CAS:528:DC%2BD28XhtVWgs7jK]; Bibcode number [2006EL.....75..618M] 10.1209/epl/i2006-10148-yView ArticleGoogle Scholar
- El-Hilo M, Chantrell RW, O’Grady K: J. Appl. Phys.. 1998, 84: 5114. COI number [1:CAS:528:DyaK1cXms1Cisr8%3D]; Bibcode number [1998JAP....84.5114E] COI number [1:CAS:528:DyaK1cXms1Cisr8%3D]; Bibcode number [1998JAP....84.5114E] 10.1063/1.368761View ArticleGoogle Scholar
- Wiekhorst F, Shevchenko E, Weller H, Kötzler J: Phys. Rev. B. 2003, 67: 224416. Bibcode number [2003PhRvB..67v4416W] Bibcode number [2003PhRvB..67v4416W] 10.1103/PhysRevB.67.224416View ArticleGoogle Scholar
- Hoon SR, Lambrick DB: J. Phys. Confer. Ser.. 2005, 17: 1. Bibcode number [2005JPhCS..17....1H] Bibcode number [2005JPhCS..17....1H] 10.1088/1742-6596/17/1/001View ArticleGoogle Scholar
- Silva NJO, Amaral VS, Carlos LD: Phys. Rev. B. 2005, 71: 184408. Bibcode number [2005PhRvB..71r4408S] Bibcode number [2005PhRvB..71r4408S] 10.1103/PhysRevB.71.184408View ArticleGoogle Scholar
- Dyson FJ: Phys. Rev.. 1956, 102: 1217. Bibcode number [1956PhRv..102.1217D] Bibcode number [1956PhRv..102.1217D] 10.1103/PhysRev.102.1217View ArticleGoogle Scholar
- Katsura S: Phys. Rev.. 1962, 127: 1508. Bibcode number [1962PhRv..127.1508K] Bibcode number [1962PhRv..127.1508K] 10.1103/PhysRev.127.1508View ArticleGoogle Scholar
- Hendriksen PV, Linderoth S, LindgÅrd P-A: Phys. Rev. B. 1993, 48: 7259. COI number [1:CAS:528:DyaK3sXmvVCmurg%3D]; Bibcode number [1993PhRvB..48.7259H] COI number [1:CAS:528:DyaK3sXmvVCmurg%3D]; Bibcode number [1993PhRvB..48.7259H] 10.1103/PhysRevB.48.7259View ArticleGoogle Scholar
- Hendriksen PV, Linderoth S, LindgÅrd P-A: J. Phys. Condens. Matter. 1993, 5: 5675. COI number [1:CAS:528:DyaK3sXms1Wjtbc%3D]; Bibcode number [1993JPCM....5.5675H] COI number [1:CAS:528:DyaK3sXms1Wjtbc%3D]; Bibcode number [1993JPCM....5.5675H] 10.1088/0953-8984/5/31/029View ArticleGoogle Scholar
- Plischke M, Bergersen B: Equilibrium statistical physics. World Scientific, Singapore; 1994:393.Google Scholar
- Taylor PL: A Quantum approach to the solid state. Prentice Hall, New Jersey; 1970.Google Scholar
- Yin LF, Wei DH, Lei N, Zhou LH, Tian CS, Dong GS, Jin XF, Guo LP, Jia QJ, Wu RQ: Phys. Rev. Lett.. 2006, 97: 067203. COI number [1:STN:280:DC%2BD28rpsVantw%3D%3D]; Bibcode number [2006PhRvL..97f7203Y] COI number [1:STN:280:DC%2BD28rpsVantw%3D%3D]; Bibcode number [2006PhRvL..97f7203Y] 10.1103/PhysRevLett.97.067203View ArticleGoogle Scholar
- Stevens DK, Cleland JW, Crawford JH, Schweinler HC: Phys. Rev.. 1955, 100: 1084. COI number [1:CAS:528:DyaG28XhvVGntQ%3D%3D]; Bibcode number [1955PhRv..100.1084S] COI number [1:CAS:528:DyaG28XhvVGntQ%3D%3D]; Bibcode number [1955PhRv..100.1084S] 10.1103/PhysRev.100.1084View ArticleGoogle Scholar