J. Phys. Chem. C 2010, 114, 12487–12489
12487
Unexpected Magnetic Moments in Ultrafine Diamagnetic Systems Lin He* Department of Physics, Beijing Normal UniVersity, Beijing 100875, P. R. China ReceiVed: May 3, 2010; ReVised Manuscript ReceiVed: May 28, 2010
On the basis of recent experimental results reported in the literature (Science 2010, 327, 843.), we introduce a model in which the up and down spins within ultrafine diamagnetic system are spatially separated. The net magnetic moments within these systems arise from the imbalance between the spatial spin density distributions. This mechanism is distinct from that of the two well-known paradigms for magnetism, i.e., the localized ferromagnetism and the itinerant ferromagnetism. The influences of diameter and protective agents on the magnetic moments of these systems are also quantitatively taken into account in the proposed model. Our finding opens a new route toward room temperature ferromagnetic semiconductors without doping magnetic ions. The appearance of magnetic moments in otherwise diamagnetic materials has recently been reported for a number of nanoscale systems.1-11 Among physicists, it was long held that magnetic moments could only be seen in materials containing magnetic ions; therefore, these reports came as a big surprise. How do nonmagnetic atoms develop magnetism in diamagnetic materials as the dimensions of diamagnetic materials are reduced? Each electron of an atom occupies one quantum state defined by n (principal quantum number), l (orbital angular momentum quantum number), m (magnetic quantum number), and s (spin angular momentum). It is generally accepted that ferromagnetic materials require atoms having partially filled shells of d or f electrons. For a fully filled shell, half of the electrons have positive (up) spin, while the remaining half of the electrons have negative (down) spin so that the resultant spin is zero, and the corresponding material reveals diamagnetism (Figure 1a). However, an imbalance between the up and down spins is expected to emerge in ultrafine diamagnetic systems. Indeed, to stabilize the core of ultrafine diamagnetic particles, charges will transfer from surface atoms to the inner ones.12,13 For a nanoparticle with a few to less than a hundred of atoms, the moments of a particle can be viewed as consisting of a core macro-moment and a surface macro-moment according to the first principles calculations.13-15 Additionally, the magnetization of the core tends to oppose the magnetization of the surface. These results indicate that only the electrons with down spins (or only the electrons with up spins) of surface atoms transfer to the inner core of a diamagnetic nanoparticle. Recently, similar a spatial spin density distribution has been directly observed in ultrafine ferromagnetic Co nanostructures by spin-polarized scanning tunneling microscopy (SP-STM).16 Figure 1b shows a schematic spin structure of an ultrafine diamagnetic particle. The number of negative spins NV and positive spins Nv are proportional to the number of atoms within the particle (also the volume of the particle). We can write the number of negative spins as NV ) aVD3 and the number of positive spins as Nv ) avD3, where aV and av are constants, and D is the diameter of the particle. In bulk phase, * To whom correspondence should be addressed. E-mail: helin@ bnu.edu.cn.
Figure 1. Schematic drawing of the up and down spins in bulk (a) and ultrafine diamagnetic (b) systems.
aV equals av resulting in zero net spin polarization (Figure 1a). In a nanoparticle with the diameter below a critical value D0, an imbalance between the up and down spins occurs near the surface, i.e., aV * av. The spin correlation of the Fermi hole effect near the surface region of nanoparticles has been discussed as the origin of the imbalance.3,4,17,18 However, there is no clear theoretical prediction on the relationship of the Fermi wavenumber and the electron-hole pairs within a nanoparticle. The numerical critical diameter according to the Fermi hole effect is given by 2π/kF, where kF is the Fermi wavenumber. The number of positive spins becomes Nv ) avD3 - SvD2 due to the influence of the surface. The term SvD2 reflects the influence of the broken translation symmetry of surface atoms on the positive spin. Then, the net magnetic moments of the bare nanoparticle is M ) | Nv - NV | ) aD3 + SvD2, where a ) (aV - av). Above D0, the imbalance between the up and down spins of the nanoparticle is assumed to decrease exponentially with increasing diameter. Additionally, the ultrafine nanoparticles are generally stabilized by protective agents such as polyallylamine hydrochloride (PAAHC), polyvinyl pyrolidone (PVP), and dodecane thiol (DT). These agents influence the d electrons of the nanoparticles19,20 and consequently tune the magnetic properties of the nanoparticles. The effect of agents on the magnetic moments of each particle is assumed to be proportional to the number of surface atoms and can be determined by SaD2, where Sa is a constant that depends on the interaction between the nanoparticle and the protective agent. Then the magnetic moments of each particle can be estimated according to the following equation:
10.1021/jp104031y 2010 American Chemical Society Published on Web 07/01/2010
12488
J. Phys. Chem. C, Vol. 114, No. 29, 2010
M(D) )
{
He
|aD3 - (Sa - Sv)D2 |
D e D0 |(aD3 + SvD2)exp(D0 - D) - SaD2 | D > D0 (1)
The existence of intrinsic magnetic moments of Au nanoparticles has been confirmed by several groups using various experimental methods.2-5,7,8,21-24 By using the DT as the protective agent, the diameter of Au nanoparticles can be controlled from 1.5 to 10 nm with narrow size distribution.4,22 Therefore, the size dependent magnetic moments of Au nanoparticles in DT provide a model system to demonstrate the proposed model. Figure 2 shows the magnetic moments of each Au particle (right axis) as a function of the diameter.4,22,25 The solid curve (left axis) is the computed result of eq 1 with D0 ) 3.3 nm, a ) 0.14 µB/nm3 (µB is the Bohr magneton), Sv ) 0.26 µB/nm2, and Sa ) 0.36 µB/nm2. Obviously, eq 1 can give a quantitative description of the experimental results. The numerical spin-correlation length from the surface for Au is given by π/kF ) 1.5 nm,18 which is quantitatively consistent with the critical radius D0/2 ) 1.65 nm obtained by eq 1. The induced magnetic moments of each Au surface atom bound to DT can be estimated as 0.0083 µB by considering Sa ) 0.36 µB/nm2. Although Au particles with large diameter and bulk Au also have magnetic moments induced by agents at the surface according to eq 1, the surface atoms represent a negligible fraction of the total; therefore, the magnetic moments are insignificant, and the intrinsic diamagnetic signal of Au will cover up the magnetic moments. In the case of 1.4 nm thiolderivatized Au nanoparticles, Au-SR, the magnetic moment of each particle determined at 5 K is about 3 µB.2 This agrees with the computed value 3.2 µB of eq 1 by considering the value of ≈0.07 µB/Au atom bound to sulfur obtained through the X-ray absorption near-edge structure (XANES) measurements on thiol-capped Au nanoparticles.20 For a Au nanoparticle containing 25 gold atoms stabilized by 18 thiolate ligands (abbreviated as Au25(SR)18), each particle has a 1 µB magnetic moment.7 This also agrees with the calculated value 1.02 µB of eq 1 assuming that each thiolate ligand contributes 0.07 µB20 to the net magnetic moments of the particle. An important aspect of the present model is that it takes into account the contribution on magnetic moments from bare nanoparticles as well as from protective agents. Table 1 lists the induced magnetic moments of each Au surface atom bound to various agents. These data are estimated by eq 1 with the available magnetic data reported in the literature. It indicates that different capping systems have distinct influ-
Figure 2. Diameter dependent magnetic moments of each particle of monodisperse Au nanoparticles. The magnetic moments (right axis) are calculated by using the saturation magnetization published in refs 4 (O) and 22 and 25 (∆).The solid curve (left axis) is the computed result of eq 1 with D0 ) 3.3 nm, a ) 0.14 µB/nm3, Sv ) 0.26 µB/nm2, and Sa ) 0.36 µB/nm2.
ences on the electronic and magnetic properties of Au nanoparticles.26-29 For gold nanoparticles stabilized by thiolate ligands, each surface atom contributes 0.069 µB to the net magnetic moments of the particle estimated by eq 1. This agrees well with the value 0.07 µB/Au atom bound to sulfur obtained through XANES.20 Additionally, exhaustive analysis of the extended X-ray absorption fine structure (EXAFS) data reveals that thiol-capped Au nanoparticles stabilized by maltose (abbreviated as Au-SRmaltose) have weaker Au-S bonds in comparison to Au-SR,29 which qualitatively agrees with the computed results listed in Table 1. The dependencies of magnetic moments per particle for bare Au nanoparticles and Au nanoparticles stabilized by various protective agents on the diameter are presented in Figure 3. The induced magnetic moments by the protective agents of each Au surface atom increase with the direction of the arrow. Our results indicate that the magnetic properties of Au nanoparticles depend strongly on the type of protective agents. Some protective agents can almost quench the magnetism of the system, which agrees well with the experimental results.2 The agreement between experimental results and theoretical assumptions demonstrates that the present model quantitatively explains the magnetic moments observed in ultrafine Au nanoparticles as well as the striking difference between magnetic moments in Au nanoparticles stabilized by various protective agents. Though we only compared the proposed model with the experimental results of ultrafine Au particles, we should stress that the proposed model may be applicable to other ultrafine diamagnetic systems. For a nanostructure with antiferromagnetic coupling spins, it is expected to reveal two interesting behaviors, i.e., the exchange bias HE in the field-cooled hysteresis
TABLE 1: Induced Permanent Magnetic Moments of Each Au Surface Atom Bound to Various Protective Agents Estimated by Eq 1 with Available Experimental Results Reported in the Literature protective agents dodecane thiol (DT)4,22 thiolate phenylethyl (SR)2,7 polyallylamine hydrochloride (PAAHC)3 tetraoctylammonium bromide (SH)2 SRmaltose21 SRlactose21 oleylamine23 polyethylene (PE)24 a
diameter (nm) surface atomsa
magnetic moments magnetic moments per per particle (µB) calculated Sa(µB/nm2) surface atomb (µB)
c
c
c
1.42 0.87 1.9 1.4 1.8 2.0 6.7 3.5
562 187 142 56 128 174 2073 510
32 17 0.4 0 0.18 0.17 7.3 3
Calculated number of atoms located at the surface of a pure gold cluster. various protective agents. c The result is shown in the Figure 2.
b
0.36 1.96
0.0083 0.069
0.63(0.41) 0.45 0.45(0.57) 0.49(0.58) 0.18 0.38(0.87)
0.016(0.010) 0.015 0.012(or 0.014) 0.011(or 0.013) 0.0039 0.009(0.021)
Induced magnetic moments of each surface atom bound to
Unexpected Magnetic Moments
J. Phys. Chem. C, Vol. 114, No. 29, 2010 12489 References and Notes
Figure 3. Diameter dependent magnetic moments of each particle of bare Au nanoparticles and Au nanoparticles stabilized by various protective agents. The induced magnetic moments by the protective agents of each Au surface atom increase with the direction of the arrow.
loop30-33 and thermal induced magnetization.34 The observations of exchange bias in ultrafine Au, Pd, and Pt nanostructures11,22 further confirm the presence of antiferromagnetic coupling between the up and down spins in these systems. Recently, the thermal induced magnetization in Sn nanoparticles was also demonstrated.35 Therefore, we contend that the spatially separated up and down spins proposed here may be a universal behavior in ultrafine systems. However, other future work is needed to see how widely applicable the proposed model is in explaining the magnetic properties of other ultrafine diamagnetic systems. The appearance of magnetic moments in ultrafine diamagnetic systems is a macroscopic quantum phenomenon, which is rather different from the ferromagnetic moments in Fe, Co, and Ni. The antiferromagnetic coupling between up and down spins in ultrafine diamagnetic systems is a direct result of the Pauli principle rather than of the exchange energy. The net magnetic moments of these systems arise from the imbalance between spatially separated up and down spins. Therefore, we can understand the experimental results that the saturation magnetization between 5 and 300 K observed in these systems is almost independent of temperature.3,9,11,21,23,24,35 Seeking room temperature ferromagnetic semiconductors is of fundamental importance in future spintronics technologies. One approach is to tailor magnetic exchange interactions between charge carriers and embedded magnetic impurity ions within the semiconductor.36-38 Recently, novel opportunities for tailoring magnetism in doped quantum dots have also been reported.39,40 The work presented here opens a new route toward room temperature ferromagnetic semiconductors without doping magnetic ions. By reducing the size of semiconductors such as Si and ZnO and using suitable protective agents, these materials should reveal magnetic moments similar to those of ultrafine Au particles. In summary, the theoretical model proposed here reveals the nature of magnetic moments in ultrafine diamagnetic systems. According to the nature of the magnetic moments in ultrafine diamagnetic systems, the magnetic state of these systems can be modulated by altering the protective agents and the diameter. The SP-STM can obtain the spatial spin density distribution of ultrafine nanoparticles16 and can give direct experimental proof of the proposed model. Acknowledgment. This work was partially supported by funds from Beijing Normal University. I thank Professor Otmar K. Foelsche for his assistance during revision of this manuscript.
(1) Venkatesan, M.; Fitzgerald, C. B.; Coey, J. M. D. Nature 2004, 263, 406. (2) Crespo, P.; Litran, R.; Rojas, T. C.; Multigner, M.; de la Fuente, J. M.; Sanchez-Lopez, J. C.; Garcia, M. A.; Hernando, A.; Penades, S. F. Phys. ReV. Lett. 2004, 93, 087204. (3) Yamamoto, Y.; Miura, T.; Suzuki, M.; Miyagawa, H.; Nakamura, T.; Kobayashi, K.; Teranishi, T.; Hori, H. Phys. ReV. Lett. 2004, 93, 116801. (4) Hori, H.; Yamamoto, Y.; Iwamoto, T.; Miura, T.; Teranishi, T.; Miyake, M. Phys. ReV. B 2004, 69, 174411. (5) Negishi, Y.; Tsunoyama, H.; Suzuki, M.; Kawamura, N.; Matsushita, M. M.; Maruyama, K.; Sugawara, T.; Yokoyama, T.; Tsukuda, T. J. Am. Chem. Soc. 2006, 128, 12034. (6) Wu, Z. K.; Gayathri, C.; Gil, R. R.; Jin, R. J. Am. Chem. Soc. 2009, 131, 6535. (7) Zhu, M. Z.; Aikens, C. M.; Hendrich, M. P.; Gupta, R.; Qian, H.; Schatz, G. C.; Jin, R. J. Am. Chem. Soc. 2009, 131, 2490. (8) Garitaonandia, J. S.; Insausti, M.; Goikolea, E.; Suzuki, M.; Cashion, J. D.; Kawamura, N.; Ohsawa, H.; Muro, I. G.; Suzuki, K.; Plazaola, F.; Rojo, T. Nano Lett 2008, 8, 661. (9) Seehra, M. S.; Dutta, P.; Neeleshwar, S.; Chen, Y. Y.; Chen, C. L.; Chou, S. W.; Chen, C. C.; Dong, C. L.; Chang, C. L. AdV. Mater. 2008, 20, 1656. (10) Meulenberg, R. W.; Lee, J. R. I.; McCall, S. K.; Hanif, K. M.; Haskel, D.; Lang, J. C.; Terminello, L. J.; Buuren, T.; van, J. Am. Chem. Soc. 2009, 131, 6888. (11) Teng, X. W.; Han, W. Q.; Ku, W.; Hucker, M. Angew. Chem., Int. Ed. 2008, 47, 2055. (12) Chang, C. M.; Chou, M. Y. Phys. ReV. Lett. 2004, 93, 133401. (13) Pereiro, M.; Baldomir, D. Phys. ReV. A 2005, 72, 045201. (14) Magyar, R. J.; Mujica, V.; Marquez, M.; Gonzalez, C. Phys. ReV. B 2007, 75, 144421. (15) Pereiro, M.; Baldomir, D.; Arias, J. E. Phys. ReV. A 2007, 75, 063204. (16) Oka, K.; Ignatiev, P. A.; Wedekind, S.; Rodary, G.; Niebergall, L.; Stepanyuk, V. S.; Sander, D.; Kirschner, J. Science 2010, 327, 843. (17) Juretschke, H. J. Phys. ReV. 1953, 92, 1140. (18) Harbola, M. K.; Sahni, V. Phys. ReV. B 1988, 37, 745. (19) Hakkinen, H.; Barnett, R. N.; Landman, U. Phys. ReV. Lett. 1999, 82, 3264. (20) Zhang, P.; Sham, T. K. Appl. Phys. Lett. 2002, 81, 736. (21) Crespo, P.; Garcia, M. A.; Pinel, E. F.; Multigner, M.; Alcantara, D.; Fuente, J. M.; Penades, S.; Hernando, A. Phys. ReV. Lett. 2006, 97, 177203. (22) Dutta, P.; Pal, S.; Seehra, M. S.; Anand, M.; Roberts, C. B. Appl. Phys. Lett. 2007, 90, 213102. (23) de la Presa, P.; Multigner, M.; de laVenta, J.; Garcia, M. A.; RuizGonzalez, M. L. J. Appl. Phys. 2006, 100, 123915. (24) Venta, J. de la; Pucci, A.; Pinel, E. F.; Garcia, M. A.; Fernandez, C. de J.; Crespo, P.; Mazzoldi, P.; Ruggeri, G.; Hernando, A. AdV. Mater. 2007, 19, 875. (25) He, L. Phys. ReV. B 2010, 81, 096401. (26) Zhang, P.; Sham, T. K. Phys. ReV. Lett. 2003, 90, 245502. (27) Walter, M.; Akola, J.; Acevedo, O. L.; Jadzinsky, P. D.; Calero, G.; Ackerson, C. J.; Whettern, R. L.; Gronbeck, H.; Hakkinen, H. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 9157. (28) Jadzinsky, P. D.; Calero, G.; Ackerson, C. J.; Bushnell, D. A.; Kornberg, R. D. Science 2007, 318, 430. (29) Lopez-Cartes, C.; Rojas, T. C.; Litran, R.; Martinez, D. M.; Fuente, J. M.; Penades, S.; Fernandez, A. J. Phys. Chem. B 2005, 109, 8761. (30) Nogues, J.; Schuller, I. K. J. Magn. Magn. Mater 1999, 192, 203. (31) Nogues, J.; Sort, J.; Langlais, V.; Skumryev, V.; Surinach, S.; Munoz, J. S.; Baro, M. D. Phys. Rep. 2005, 422, 65. (32) Berkowitz, A. E.; Takano, K. J. Magn. Magn. Mater 1999, 200, 552. (33) Gruyters, M. Phys. ReV. Lett. 2005, 95, 077204. (34) Morup, S.; Frandsen, C. Phys. ReV. Lett. 2004, 92, 217201. (35) Li, W.-H.; Wang, C.-W.; Li, C.-Y.; Hsu, C. K.; Yang, C. C.; Wu, C.-M. Phys. ReV. B 2008, 77, 094508. (36) Ohno, H. Science 1998, 281, 951. (37) Dietl, T.; Ohno, H.; Matsukura, F.; Cibert, J.; Ferrand, D. Science 2000, 287, 1019. (38) Ando, K. Nature 2006, 312, 1883. (39) Abolfath, R. M.; Hawrylak, P.; Zutic, I. Phys. ReV. Lett. 2007, 98, 207203. (40) Abolfath, R. M.; Petukhov, A. G.; Zutic, I. Phys. ReV. Lett. 2008, 101, 207202.
JP104031Y
