pubs.acs.org/JPCL
Do 8 nm Co Nanocrystals in Long-Range-Ordered Face-Centered Cubic (fcc) Supracrystals Show Superspin Glass Behavior? Dinah Parker, Isabelle Lisiecki, and M. P. Pileni* Laboratoire LM2N, UMR CNRS 7070 Universit e P. et M. Curie, b^ at. F, B.P. 52, 4 place Jussieu, F-75231 Cedex 05, France
ABSTRACT Here, we show evidence for superspin glass behavior in long-rangeordered face-centered cubic (fcc) supracrystals of 8 nm Co nanocrystals as has been well-demonstrated for disordered 3D assemblies. The dynamic behavior shows a critical slowing down, and the characteristic relaxation time is found to diverge to a finite static glass temperature. The collective nature of the glass state is supported by the existence of a memory effect. We conclude that, in the case of magnetic nanocrystal assemblies where the individual nanocrystal anisotropy is low, superspin glass behavior is observed whatever the mesoscopic order is. SECTION
Nanoparticles and Nanostructures
I
n recent years, the dynamics of assemblies of interacting ferromagnetic nanoparticles has been a subject of extensive research. It is now well accepted that a transition from pure Neel-Brown-type superparamagnetism to superspin glass behavior takes place at low temperature in these systems.1-13 Analogous with canonical atomic spin glasses, the lack of long-range magnetic order arising from magnetic frustration leads to properties such as aging, rejuvenation, and memory effects.1-3,6-8,10,12,14 In a magnetic nanoparticle system in which the nanoparticles are small enough to have a single magnetic domain, each nanoparticle acts like a giant or “super” spin. In sufficiently concentrated systems, these superspins can interact via long-range dipolar interactions, the random nature of which leads to a highly disordered and frustrated magnetic state analogous to that in atomic spin glasses. Recent work on these superspin glasses has shown that they do indeed have many properties in common with their atomic counterparts.11,12 The superspin glass state has been evidenced in several different systems by the observation of a critical slowing down of the dynamics as the sample approaches the glass temperature, Tg,2,12 and divergent behavior of the nonlinear susceptibility.4,5 Aging, memory, and rejuvenation phenomena have also been widely observed,1,11,12 although these effects are much less pronounced than those in atomic spin glasses and are attributed to the nanoparticle size distribution. Due to their relatively high magnetic moments and high glass freezing temperatures, superspin glasses are of great interest for ongoing research. Until now, the interacting systems that have been investigated have been disordered systems, where the magnetic nanoparticles are not in a regular array. Therefore, the question that arises is, what is the influence on the superspin glass behavior when magnetic nanocrystals are long-range-ordered in a close-packed structure? From a fundamental point of
r 2010 American Chemical Society
view, it is essential to determine the role played by the structural and/or magnetic anisotropy of such 3D assemblies on the magnetic order. On the basis of the magnetic phase diagram of a granular system with an insulating matrix proposed by Kleeman et al.,13,15 it is reasonable to assume that a variation of the supracrystal anisotropy could tune the system to achieve superferromagnetic behavior. This is strongly supported by the fact that supracrystals made of polycrystalline cobalt nanocrystals16 exhibit unique collective properties17,18 with a significant narrowing of the zero-fieldcooled (ZFC) magnetization versus temperature peak and an increased coercivity (Hc) due to a decrease in the distribution of energy barriers and an increased supracrystal anisotropy arising from Co nanocrystal ordering. Note that other collective properties have been identified recently, including coherent vibrations of nanocrystals within a supracrystal.19 Here, we investigate the superspin glass behavior of 8 nm Co nanocrystals in face-centered cubic (fcc) supracrystals by ac and dc susceptibility measurements. By a slow evaporation of a colloidal solution of 8 nm cobalt nanocrystals20 coated with dodecanoic acid molecules on highly ordered pyrolytic graphite (HOPG), supracrystals are produced.22 Note that the nanocrystals used are polycrystalline with a fcc structure, and consequently, they have a relatively low magnetic anisotropy and moment.18 As shown in the scanning electron microscopy (SEM) image23 (Figure 1A), the supracrystals appear cracked. Their thickness varies from a few micrometers on the border to tens of nanometers in the central part. The corresponding grazing incidence small-angle X-ray diffraction pattern (GISAXRD)24
Received Date: February 10, 2010 Accepted Date: March 9, 2010 Published on Web Date: March 17, 2010
1139
DOI: 10.1021/jz1001874 |J. Phys. Chem. Lett. 2010, 1, 1139–1142
pubs.acs.org/JPCL
Figure 2. (a) The 1/ω (log scale) versus 1/Tpeak for a fcc supracrystal of 8 nm Co nanocrystals; (b) 1/ω versus Tg/(Tpeak - Tg) (plotted on a log-log scale) for a fcc supracrystal of 8 nm Co nanoparticles.
ac susceptibility measurements are needed to provide insight into the characteristic relaxation times present in the system. Figure 1C and D shows the in-phase (χ0 ) and out-of-phase (χ00 ) components of the ac susceptibility versus temperature of a fcc Co supracrystal, measured for ac frequencies ranging from 0.08 to 8 Hz.25 Note that this range of frequencies spanning 2 orders of magnitude is suitable to analyze relaxation processes in our samples.27,28 The χ00 data is unfortunately rather noisy as the signal is very small due to the low mass of the sample and the limited amplitude of the ac measurement field. Both the χ0 and χ00 curves show a clear frequency dependence where the maximum, Tpeak, decreases in temperature with decreasing frequency, f. Tpeak represents the temperature at which the relaxation time of the system, τ, is equal to the observation time, t, which is related to the measurement frequency by t = 1/ω, where ω = 2πf. Frequency dependence in an ac measurement is observed both in superparamagnetic and superspin glass materials. In order to differentiate between these two types of behavior, one can analyze quantitatively the change in Tpeak with measurement frequency and hence extract a value for τ. As the imaginary component is not of sufficient quality, we use here the real component of the ac susceptibility, which is recognized as a standard procedure13,27,28 to analyze relaxation processes. The value of Tpeak for each measurement frequency was taken as the maximum in the χ0 curves shown in Figure 1C. The error in each value is estimated to be (0.5 K and is taken into account when estimating the total error in the extracted values of τ and the critical exponent (Figure 2). For a superparamagnet, where dipolar interactions between the magnetic moments are negligible, the frequency dependence should follow an Arrhenius law τ = τ0 expEa/kBT (related to the N eel-Brown model), where τ0 is the angular inverse attempt frequency, Ea is the anisotropy energy, and kB is the Boltzmann constant. By plotting log10 τ versus 1/Tpeak (Figure 2a) and fitting the data to the Arrhenius law, the value of τ0 can be extracted, and in this case, we find τ0 = 10-31 s. This unphysically small value indicates that the magnetic response is not best described by simple energy barrier blocking and thermal activation, that is, the flipping rate of
Figure 1. (a) SEM image of a supracrystal comprised of 8 nm Co nanocrystals (thick region). (b) Corresponding SAXRD pattern. (c) In-phase and (d) out-of-phase part of the ac susceptibility versus temperature, measured at frequencies between 0.08 and 8 Hz in an ac driving field of 1.7 Oe.
(Figure 1B) shows several reflections characteristic of longrange order of the nanocrystals in a fcc suprastructure growing in the [111] direction.16 The (111) reflection is very narrow and nearly resolution-limited (0.0045 nm-1), indicating longrange out-of-plane order. This gives us the minimum value for the coherence length, 140 nm. From the (111) reflection, we deduce a stacking periodicity equal to 9 nm. This value D(2/3)1/2 leads to a coated diameter, D, of 11 nm including the metal core diameter and a coating contribution and gives us an interparticle gap of 3 nm. Due to the interdigitation of the alkyl chains, these long-range self-organizations are highly stable over several weeks, and neither oxidation nor coalescence of the Co nanocrystals is observed.17 The field-cooled (FC) and ZFC dc magnetization versus temperature curves25 have been obtained for the supracrystals. The ZFC magnetization increases with increasing temperature up to a maximum, Tmax, above which the behavior is superparamagnetic. The blocking temperature, Tmax, is significantly larger (130 K) than that observed for a dilute system of Co nanocrystals (∼90 K) of similar size26 due to the strong magnetic dipolar interactions between the nanocrystals in the supracrystal. The FC magnetization curve is nearly temperature-independent below Tmax, which is a first indication of strong dipolar interactions between blocked moments of single nanocrystals which lead to superspin glass behavior.10-12,14,18 Note that in weakly interacting systems with superparamagnetic behavior, the FC magnetization curve increases with decreasing temperature.26 In order to further investigate the possibility of superspin glass behavior,
r 2010 American Chemical Society
1140
DOI: 10.1021/jz1001874 |J. Phys. Chem. Lett. 2010, 1, 1139–1142
pubs.acs.org/JPCL
the magnetic moment of a given nanocrystal is no longer dependent solely on its own anisotropy energy but is also influenced by interparticle interaction, analogous to a spin glass. Therefore, it is likely that the temperature independence of the FC magnetization curve below Tpeak arises from spin glass-like behavior. In such spin glass systems, the dynamic behavior displays a critical slowing down, and hence, the characteristic relaxation time diverges to a finite static glass temperature Tg, according to a critical power law τ = τ*(Tpeak/Tg - 1)-zν, where τ* is the relaxation time of an individual nanocrystal moment and zν is a critical exponent. In order to constrain the analysis, Tg is taken as the maximum in the dc ZFC magnetization curve (Figure 2b), and the best fit of the data yields τ* = 10-9(3 s and zν = 12 ( 2 (see Figure 2). The value of τ* fits quite well with values found for spin glasses, and zν, although slightly high, is compatible within error to that expected for a canonical spin glass for which zν = 10.14,29,30 These results support the existence of a phase transition from a superparamagnetic to superspin glass state in a fcc Co supracrystal. Let us now consider the aging and memory effects related to the nonequilibrium dynamics in spin glass and superspin glass materials,1-3,6-8,10,12,14 which can be demonstrated by a simple dc magnetization experiment. The experiments described below were performed on supracrystals composed of cobalt nanocrystals characterized by an average size of 7.1((0.5) nm, smaller than those comprising the supracrystals used for the dc magnetization and ac susceptibility measurements described above, which had a diameter of 8((0.5) nm. This change in diameter is due to the fluctuations obtained from one synthesis to another. Independent of the Co nanocrystal diameter, they self-assemble in fcc supracrystals with the same characteristic interparticle distance (3 nm). This decrease in the Co nanocrystal diameter will result in a slight decrease in the interparticle dipolar interactions; however, we do not expect this to influence the overall behavior of the assembly. First, a reference ZFC magnetization curve is obtained by cooling the sample from room temperature to 3 K. A 20 Oe field is then applied, and the magnetization is measured as the temperature increases. In the second step, the same procedure is performed, except that a stop is made in the cooling process at Ts =70 K (corresponding to 0.7 Tg) for a waiting time of tw= 104 s. Figure 3 shows that a deviation from the reference ZFC curve is observed at Ts, which is known as a “memory dip”, so-called as the system has “remembered” the spontaneous relaxation toward a zero magnetization value (aging) that occurred when the system was left unperturbed at constant temperature Ts. This memory dip is seen more clearly in the difference plot (inset, Figure 3). These aging and memory phenomena are well-known for atomic spin glasses14 and have also been observed in superspin glass systems where the effect (as in the present case) is less pronounced than in an atomic spin glass.12 These ac and dc susceptibility investigations provide strong evidence for superspin glass behavior in Co supracrystals, analogous to the disordered and frustrated magnetic state observed in canonical spin glass materials. From these data, it is concluded that fcc supracrystals made of 8 nm fcc polycrystalline Co nanocrystals exhibit
r 2010 American Chemical Society
Figure 3. ZFC magnetization curves of a fcc supracrystal of 7.1 nm Co nanocrystals measured after uninterrupted cooling from room temperature (reference) and after cooling with a 104 s stop at 70 K. Inset: difference between the “stop” and reference curves.
superspin glass behavior, similar to the disordered aggregates of magnetic nanoparticles as observed previously. The relatively high supracrystal anisotropy is not sufficient to tune the system to achieve superferromagnetic properties. To investigate the possibility of accessing superferromagnetic properties, other experiments are anticipated using nanocrystal assemblies with higher individual nanocrystal anisotropy, as is observed in single-domain hcp cobalt nanocrystals.18
SUPPORTING INFORMATION AVAILABLE A first figure showing TEM images of 8 nm cobalt nanocrystals ordered in a compact hexagonal network and the corresponding size distribution. A second figure showing the field-cooled and zero-field-cooled dc magnetization versus temperature of an 8 nm Co nanocrystal supracrystal, measured in an applied field of 20 Oe. This material is available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION Corresponding Author: *To whom correspondence should be addressed.
ACKNOWLEDGMENT The research leading to these results has
received funding from the “Agence Nationale de la Recherche” in the framework of the Project DANMA ANR-05-NANO-007-02 and from the European Community's Seventh Framework Program NMP4-SL2009-213382. Many thanks are given to Dr. Eric Vincent and Dr. Pierre Bonville of DRECAM/SPEC, CEA Saclay, for the use of their SQUID magnetometer. We also warmly thank Dr. Pierre-Antoine Albouy of LPS, Orsay University, for the structural characterization.
REFERENCES (1)
(2)
(3)
1141
Jonsson, T.; Mattsson, J.; Djurberg, C.; Khan, F. A.; Nordblad, P.; Svedlindh, P. Aging in a Magnetic Particle System. P. Phys. Rev. Lett. 1995, 75, 4138–4141. Djurberg, C.; Svedlindh, P.; Nordblad, P.; Hansen, M. F.; Bodker, F.; Morup, S. Dynamics of an Interacting Particle System: Evidence of Critical Slowing Down. Phys. Rev. Lett. 1997, 79, 5154–5157. Andersson, O.; Djurberg, C.; Jonsson, T.; Svedlindh, P.; Nordblad, P. Monte Carlo Studies of the Dynamics of an
DOI: 10.1021/jz1001874 |J. Phys. Chem. Lett. 2010, 1, 1139–1142
pubs.acs.org/JPCL
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13) (14) (15)
(16)
(17)
(18)
(19)
(20)
Interacting Monodispersive Magnetic-Particle System. Phys. Rev. B 1997, 56, 13983–13988. Mamiya, H.; Nakatani, I.; Furubayashi, T. Blocking and Freezing of Magnetic Moments for Iron Nitride Fine Particle Systems. Phys. Rev. Lett. 1998, 80, 177–180. Jonsson, T.; Svedlindh, P.; Hansen, M. F. Static Scaling on an Intracting Magnetic Nanoparticle System. Phys. Rev. Lett. 1998, 81, 3976–3979. Mamiya, H.; Nakatani, I.; Furubayashi, T. Low Dynamics for Spin-Glass-Like Phase of a Ferromagnetic Fine Particle System. Phys. Rev. Lett. 1999, 82, 4332–4335. Jonsson, T.; Hansen, M. F.; Svedlindh, P.; Nordblad, P. Memory Effects in an Interacting Magnetic Nano-Particle Sample. Physica B 2000, 284, 1754–1755. Jonsson, T.; Hansen, M. F.; Nordblad, P. Nonequilibrium Dynamics in an Interacting Fe-C Nanoparticle System. Phys. Rev. B 2000, 61, 1261–1266. Sahoo, S.; Petracic, O.; Binek, Ch.; Kleemann, W.; Sousa, J. B.; Cardoso, S.; Freitas, P. P. Superspin-Glass Nature of Discontinuous Co80Fe20/Al2O3 Mulyilayers. Phys. Rev. B 2002, 65, 134406/1–134406/5. Sahoo, S.; Petracic, O.; Kleemann, W.; Stappert, S.; Dumpich, G.; Nordblad, P.; Cardoso, S.; Freitas, P. P. Cooperative Versus Superparamagnetic Behavior of Dense Magnetic Nanoparticles in Co80Fe20/Al2O3 Mulyilayers. Appl. Phys. Lett. 2003, 82, 4116–4118. Du, J.; Zhang, B.; Zheng, R. K.; Zhang, X. X. Memory Effect and Spin-Glass-Like Behavior in Co-Ag Granular Films. Phys. Rev. B 2007, 75, 014415/1–014415/7. Parker, D.; Dupuis, V.; Ladieu, F.; Bouchaud, J. P.; Dubois, E.; Perzynski, R.; Vincent, E. Spin-Glass Behavior in an Interacting γ-Fe2O3 Nanoparticle System. Phys. Rev. B 2008, 77, 104428/1–104428/9. Bedanta, S.; Kleemann, W. Superparamagnetism. J. Phys. D. 2008, 42, 013001–013027. Mydosch, J. A. Spin Glasses: An experimental introduction; Taylor & Francis: London, 1993. Kleemann, W.; Petracic, O.; Binek, Ch.; Kakazei, G. N.; Pogorelov, Yu. G.; Sousa, J. B.; Cardoso, S.; Freitas, P. P. Interacting Ferromagnetic Nanoparticles in Discontinuous Co80Fe20/Al2O3 Mulyilayers: From Superspin Glass to Reentrant Superferromagnetism. Phys. Rev. B 2001, 63, 134423/ 1–134423/5. Lisiecki, I.; Albouy, P. A.; Pileni, M. P. Face-Centered Cubic Supracrystals of Cobalt Nanocrystals. Adv. Mater. 2003, 15, 712–716. Lisiecki, I; Parker, P.; Salzemann, C.; Pileni, M. P. FaceCentered Cubic Supracrystals and Disordered Three-Dimentional Assemblies of 7.5 nm Cobalt Nanocrystals: Influence of the Mesoscopic Ordering on the Magnetic Properties. Chem. Mater. 2007, 19, 4030–4036. Parker, D.; Lisiecki, I.; Salzemann, C.; Pileni, M. P. Emergence of New Collective Properties of Cobalt Nanocrystals Ordered in fcc Supracrystals: II, Magnetic Investigation. J. Phys. Chem. C 2007, 111, 12632–12638. (a) Pileni, M. P. Self-Assembly of Inorganic Nanocrystals: Fabrication and Collective Intrinsic Properties. Acc. Chem. Res. 2007, 40, 685–693. (b) Pileni, M. P. Supracrystals of Inorganic Nanocrystals: An Open Challenge for New Physical Properties. Acc. Chem. Res. 2008, 41, 1799–1809. Cobalt nanocrystals are synthesized by chemical reduction in reverse micelles, as described in a previous paper.21 The size polydispersity is optimized by controlling the reducing agent (sodium borohydride) concentration. The Co nanocrystals
r 2010 American Chemical Society
(21)
(22)
(23) (24)
(25)
(26)
(27)
(28)
(29)
(30)
1142
are extracted from the surfactant by adding dodecanoic acid molecules and are then dispersed in hexane. In order to characterize the nanocrystals, a few drops of the solution are deposited on a transmission electron microscopy (TEM) carbon grid. Then, 8 nm cobalt nanocrystals coated with dodecanoic acid and characterized by a 9% size distribution (derived from TEM study) are produced. The entire synthesis is carried out in a N2 glovebox using deoxygenated solvents to prevent particle oxidation. Lisiecki, I.; Pileni, M. P. Synthesis of Well-Defined and Low Size Distribution Cobalt Nanocrystals: The limited Influence of Reverse Micelles. Langmuir 2003, 19, 9486–9489. The 3D fcc supracrystals are prepared by horizontally immersing a highly oriented pyrolitic graphite (HOPG) substrate (10 5 mm2) in 200 μL of a 5.5 10-7 M colloidal solution of cobalt nanocrystals dispersed in hexane. The solvent evaporation takes place at 25 °C in a nitrogen atmosphere and takes a few hours (e10 h). In order to avoid oxidation of the cobalt nanocrystals, the sample is stored under nitrogen. Scanning electron microscopy was performed with a JMS5510LV instrument. Grazing incidence small-angle X-ray scattering (GISAXS) measureaments were carried out using a rotating anode generator operated with a small-size focus (copper anode; focus size 0.2 mm 0.2 mm; 50kV, 30mA). The optics consisted of two parabolic multilayer graded mirrors in KB geometry, providing a parallel monochromatic beam. The sample was mounted on a rotating stage, and the diffraction patterns were recorded on photostimulable imaging plates. Vacuum pipes were inserted between the sample and the imaging plate to reduce air scattering. A single GISAXS measurement probed a section, several micrometers wide, from one edge to the other of the substrate. The ac and dc susceptibility measurements were carried out using a Cryogenics S600 SQUID magnetometer. For dc measurements, a small measuring field of 20 Oe was used, and magnetization curves were measured after zero-fieldcooling (ZFC) and field-cooling (FC). To probe the aging and memory effects, the ZFC magnetization measurement was made after cooling with a 104 s stop at 70 K. The ac susceptibility measurements were carried out in a zero applied dc field; the ac field amplitude was 1.7 Oe, and a range of frequencies between 0.04 and 8 Hz were used. Petit, C.; Wang, Z. L.; Pileni, M. P. Seven-Nanometer Hexagonal Close Packed Cobalt Nanocrystals for High-Temperature Magneic Applications through a Novel Annealing Process. J. Phys. Chem. B 2005, 109, 15309–15316. Nakame, S. Observation of Superspin Glass State in Magnetically Textured Ferrofluid (γ-Fe2O3). J. Appl. Phys. 2009, 105, 076318. Dormann, J. L. Thermal Variation of the Relaxation Time of the Magnetic Moment of γ-Fe2O3 Nanaoparticles with Interparticle Interactions of Various Strengths. Phys. Rev. B 1996, 53, 14291–14297. Hansen, M. F.; Jonsson, P. E.; Nordblad, P.; Svedlindh, P. Critical Dynamics of an Interacting Magnetic Nanoparticle System. J. Phys.: Condens. Matter 2002, 14, 4901–4914. J€ onsson, P.; Hansen, M. F.; Svedlindh, P.; Nordblad, P. Spin-Glass-Like Transition in a Highly Concentrated Fe-C Nanoparticle System. J. Magn. Magn. Mater. 2001, 226, 1315– 1316.
DOI: 10.1021/jz1001874 |J. Phys. Chem. Lett. 2010, 1, 1139–1142
