Langmuir 2000, 16, 11-14
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Magnetic Properties of an Individual Fe-Cu-B Nanoparticle† N. Duxin and M. P. Pileni* SRSI, URA CNRS 1662, BP 52, 4 place Jussieu, 75005 Paris, France and CEA-DSM-DRECAM SCM, CEA Saclay, 91191 Gif sur Yvette, France
W. Wernsdorfer* and B. Barbara* LLN-CNRS, BP166, 38042 Grenoble Cedex 9, France
A. Benoit CRTBT-CNRS, BP166, 38042 Grenoble Cedex 9, France
D. Mailly L2M-CNRS, 196 Avenue H. Ravera, 92220 Bagneux, France Received August 10, 1998. In Final Form: November 23, 1998 Superparamagnetic elongated Fe-Cu-B alloys were prepared in aqueous solution via sodium borohydride reduction of copper and iron dodecyl sulfate, Cu(DS)2 and Fe(DS)2. The magnetization reversal of an individual Fe-Cu-B nanoparticle can be described by uniform rotation of magnetization and by thermal activation over a single-energy barrier as originally proposed by Ne´el and Brown.
1. Introduction Superparamagnetic nanoparticles exhibit a single magnetic moment aligned along one of the two easy axes of magnetization. These directions are described by two equivalent ground states separated by an energy barrier which is due to shape and crystalline anisotropy. The magnetic moment can escape to the opposite direction by thermal activation, according to the Ne´el-Brown theory1-3 or by quantum tunneling at low temperatures.4,5 Characterization and magnetic properties of an individual Fe-Cu-B nanoparticle are here presented. In a previous paper,6 we showed that a rather homogeneous alloy of immiscible Fe and Cu can be made from reverse micelles as the starting point of the chemical reaction. Recently,7 we have reported the formation of nanosized elongated Fe-Cu-B alloyed materials and a magnetic study of the collective nanoparticles. The distributions of sizes, shapes, and compositions and the dipolar interactions between the particles is difficult to take into account to understand the magnetization reversal of the superparamagnetic nanoparticles. * To whom correspondence should be addressed. † Part of the Special Issue “Clifford A. Bunton: From Reaction Mechanisms to Association Colloids; Crucial Contributions to Physical Organic Chemistry”. (1) Ne´el, L. Ann. Geophys. 1949, 5, 99. Brown, W. F. Phys. Rev. 1963, 130, 1677. (2) Jones, D. H.; Srivastava, K. K. P. J. Magn. Magn. Mater. 1989, 78, 320; Rev. B 1994, 49, 3926. (3) Garg, A. Phys. Rev. B 1995, 51, 15592. (4) Ha¨nggi, P.; Talkner, P.; Borkovec, M. Rev. Mod. Phys. 1990, 62, 251. (5) Stamp, P. C. E.; Chudnovsky, E. M.; Barbara, B. Int J. Mod. Phys. B 1992, 6, 1335. (6) Duxin, N.; Brun, N.; Bonville, P.; Colliex, C.; Pileni, M. P. J. Phys. Chem. B 1997, 101, 8907. (7) Duxin, N.; Brun, N.; Colliex, C. Pileni, M. P. Langmuir, 1998, 14 (8), 1984.
It is the purpose of this paper to show that the magnetization reversal of a single ferromagnetic nanoparticle can be described by thermal activation over a single-energy barrier as originally proposed by Ne´el and Brown. Simple particle measurement using the microSQUID technique5 confirms the result obtained on cobalt nanoparticles synthesized by arc discharge, with dimensions between 10 and 30 nm.8 2. Experimental Section Sodium dodecyl sulfate, CH3(CH2)11SO3Na (SDS), was bought from Fluka while copper chloride (CuCl2), iron chloride (FeCl2), and sodium borohydride (NaBH4) were obtained from Prolabo and Sigma, respectively. They were used without further purification. Singly distilled water was passed through a Millipore “MilliQ” system cartridge until its resistivity reached 18 MΩ‚cm. Copper and iron dodecyl sulfate, Fe(DS)2 and Cu(DS)2, were prepared as in ref 99: an aqueous solution of 0.2 M sodium dodecyl sulfate is mixed with 0.3 M of either ferrous or copper chloride. The solution is kept at 2 °C, and the precipitate which appears is washed several times with a 0.1 M iron or copper chloride solution and recrystallized in distilled water. Iron and copper dodecyl sulfate, Fe(DS)2 and Cu(DS)2, form micellar aggregates of mixed surfactant with a critical micellar concentration, cmc, determined from conductivities of 1.2 × 10-3 and 1.39 × 10-3 M, respectively. The cmc of the mixed surfactant used for the synthesis (30% Fe(DS)2 and 70% Cu(DS)2) is 1.34 × 10-3 M. These values are in good agreement with that in ref 9. Because the Fe(DS)2 and Cu(DS)2 cmc are very close, to a first approximation, formation of mixed micelles is assumed. The shape and size of Fe(DS)2 and Cu(DS)2 micellar solutions were (8) Wernsdorfer, W.; Bonet Orozco, E.; Hasselbach, K.; Benoit, A.; Barbara, B.; Demoncy, N.; Loiseau, A.; Boivin, D.; Pascard, H.; Mailly, D. Phys. Rev. Lett., 78, 1997, 1791. (9) Moroi, Y.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1974, 46, 111.
10.1021/la9810049 CCC: $19.00 © 2000 American Chemical Society Published on Web 07/22/1999
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determined by small angle X-ray scattering and by light scattering.10 They are prolate ellipsoidal micelles with a hydrodynamic radius of 2.7 nm. A Stoe Stadi P goniometer with a Siemens Kristalloflex X-ray generator using a cobalt anticathode driven by a personal computer through the Daco-PM interface was used. A JEOL electron microscope (JEOL 100 CX 2) was used.
3. Synthesis of Fe-Cu-B Elongated Particles In our previous paper we described and characterized the synthesis of an elongated Fe-Cu-B alloy.7 The material was produced under the same conditions, as described in ref 7, through reduction of mixed micelles of 1.05 × 10-3 M Cu(DS)2 and 4.5 × 10-4 M Fe(DS)2 with 3 × 10-3 M sodium borohydride, NaBH4, as the reducing agent. To prevent oxidation, the synthesis is performed in a glovebox in a nitrogen atmosphere. Immediately after the NaBH4 addition, the solution turns black with formation of dispersed elongated nanoparticles.7 The distance between two planes, determined at high resolution, is 2 Å and is in good agreement with the distance between the [111] planes in the fcc copper bulk phase. The fcc structure is confirmed by X-ray diffraction (XRD). Neither an oxide phase nor a body core centered (bcc) structure due to an R-Fe phase is detected. The estimated average composition of the material from EDS measurements in various regions of the carbon grid is 14% iron and 86% copper atoms. The comparison between the percentage of iron and copper atoms determined by EDS and that used to make the material (30% Fe and 70% Cu) indicates that part of Fe(DS)2 is not reduced by NaBH4. This is confirmed by Mo¨ssbauer spectroscopy at 4.2 K. From this latter technique are obtained two components that can be resolved: first, a broad, six-line pattern with a mean hyperfine field value of 209 kOe of relative intensity 75%; second, a quadrupolar doublet with δ ) 1.45 mm/s and ∆ ) 2 mm/s attributed to Fe2+. The relative intensity of this component is 25%. These data indicate the formation of Fe-Cu alloys. However, the EDS technique gives an average value for the composition. To obtain information at the nanoscopic scale, electron energy loss spectroscopy, EELS, measurements were made. Several sequences of spectra in the line-spectrum mode were acquired across several particles and indicate the simultaneous presence of iron and copper in the particles. However, the Fe/(Fe + Cu) ratios show that the particles contain more iron at the surface. Other measurements on these particles confirm this result and show that the iron and copper concentrations range from 2% to 35% and 98% to 65% respectively. From the data described in our previous paper7 we concluded that an Fe-Cu alloy, where the iron atoms replace copper atoms in its fcc matrix, is formed. However, the number of iron per copper atoms is not constant. An iron gradient from the core to the surface takes place. This disorder of iron atoms in a fcc copper structure and the absence of an R-Fe phase is supported by the broad Mo¨ssbauer six-line spectra and by X-ray diffraction patterns. The presence of interstitial boron in the material is expected as shown in ref 6. 4. Treatment of Individual Magnetic Data In order to study the magnetization reversal of a single Fe-Cu-B nanoparticle, we built planar Nb microbridgeDC-SQUID (of 1-2 µm diameter) on which we placed a ferromagnetic particle. The SQUID detected the flux (10) Lisiecki, I.; Dias, O.; Pileni, M. P. To be submitted
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through its loop produced by the sample’s magnetization. The method consists of measuring the critical current of the SQUID loop. As the critical current is a periodic function of the flux going through the SQUID loop, one can easily deduce the flux change in the SQUID loop.11 The achieved sensitivity of these SQUIDs is about 10-4Φ0/ Hz1/2 (Φ0 ) h/2e ) 2 × 10-15 Wb). For hysteresis loop measurements, the external field is applied in the plane of the SQUID; thus the SQUID is only sensitive to the flux induced by the stray field of the sample’s magnetization. Due to the close proximity between sample and SQUID, a very efficient and direct flux coupling is observed. This permits detection of magnetization reversals corresponding to 104 µB (10-16 emu), i.e., 109 times better than a commercial SQUID magnetometer. This experimental setup allows measurements of hysteresis loops in magnetic fields of up to 2 T and temperatures below 6 K, with a time resolution of 100 µs. In order to place an Fe-Cu-B nanoparticle on the SQUID detector, a drop of colloidal solution is deposited on a chip of about a 100 SQUIDs. When a particle falls on or near a microbridge, the coupling between the SQUID and the particle is strong enough to detect the magnetization reversal. The position of the nanoparticles is detected by scanning electron microscopy (SEM). The influence of the temperature on the magnetization reversal of a single nanoparticle was first studied by Ne´el and later by Brown.1-3 In this model, a single domain particle with uniform magnetization has two equivalent ground states of opposite magnetization separated by an energy barrier due to uniaxial anisotropy, and the system escapes from one state to the other by thermal activation with a single relaxation time. This theory is widely used in magnetism, particularly in order to describe the time dependence of magnetization of collections of particles,12 thin films, and bulk materials.13 Further descriptions of magnetization reversal of a single nanoparticle predicted quantum tunneling reversal at low temperatures.5,14 Even for a nanoparticle at zero field, the energy barrier between the two states of opposite magnetization is much too high to observe a spontaneous magnetization reversal. However, the barrier can be lowered by applying a magnetic field in the opposite direction of the particle’s magnetization. When the applied field is close to the switching field at zero temperature, Hsw0, thermal fluctuations are sufficient to drive the system to overcome the barrier. A simple analytical approximation for the field dependence of the energy barrier E(H) is
E(H) ) E0(1 - H/Hsw0)R
(1)
where E0, H, and Hsw are the energy barrier extrapolated at zero field, the applied field, and the switching field, respectively. The exponent R is in general equal to 1.5.15,16 The probability that the magnetization has not switched (11) Chapelier, C.; El Khatib, M.; Perrier, P.; Benoit, A.; Mailly, D. In SQUID 91, Superconducting Devices and Their Applications; Koch, H., Lubbig, H. Eds.; Springer-Verlag: Berlin, 1991; p 286. (12) Studies of Magnetic Properties of Fine Particles, Dormann, J. K., Fiorani, D., Eds.; Elsevier Science Publishers: New York, 1992. (13) Bertram, H. N.; Zhu, J.-G. In Solid State Physics; Ehrenreich, H., Turnbull, D. Eds.; Academic: New York, 1992; Vol. 46. (14) Thomas, L.; Lionti, F.; Ballou, R.; Gatteschi, D.; Sessoli, R.; Barbara, B. Nature 1996, 383, 145. (15) Victora, R. H. Phys. Rev. Lett. 1989, 63, 457. (16) Using the Stoner-Wohlfarth analytical expressions of the energy E(H), we can numerically show that R is near 1.5 and increases up to a value of 2 if the applied field forms an angle smaller than a few degrees with the easy axis (Wernsdorfer, W. Thesis, Grenoble-France, 1996).
Magnetic Properties of an Fe-Cu-B Nanoparticle
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Figure 2. Scanning electron micrograph of Fe-Cu-B nanoparticle on the microbridge of a SQUID loop. The particle is indicated by an arrow. Figure 1. (A) Typical hysteresis loop of an Fe-Cu-B particle. (B) Hysteresis loop of a nanoparticle of about 20 nm. Dynamic measurements are performed on the jump indicated by an arrow.
after a time t is given by
P(t) ) e-t/τ
(2)
where τ (inverse of the switching rate) can be expressed by an Arrhenius law of the form
τ(T,H) ) τ0 exp(E(H)/kT)
(3)
where τ0 (inverse of the attempt frequency) depends on several parameters as, e.g., the damping and temperature.17 For simplicity, we assume that the prefactor τ0 is constant. It is often more convenient to study the magnetization reversal by ramping the applied field at a given rate and measuring the field value as soon as the particle’s magnetization switches. In this case, thermal activation leads to a distribution of the switching fields.3,18 The mean switching field Hsw is given by
( [ ( )] )
HSW ) H0 1 -
kT cT ln R-1 E0 v
1/R
(4)
where c ) kH0/(τ0RE0), ) H/Hsw, and v is the field sweeping rate. The width of the switching field distribution is given by
( ) [ ( )]
1 kT σ ) H0 R E0
1/R
ln
cT νR-1
(1-R)/R
(5)
5. Results and Discussion Figure 1A presents a hysteresis loop. It is reversible up to the switching field, the external field value where the magnetization of the particle flips in the opposite direction. This switch is in all cases faster than the time resolution of 100 µs. Dynamic measurements are performed on a nanoparticle deposited on the microbridge of the SQUID, observed by SEM (Figure 2). The corresponding hysteresis loop is displayed in Figure 1B. It shows that several particles are measured in the same loop giving several magnetization jumps; the following measurements correspond to the jump indicated by an arrow. (17) Klik, I.; Gunther, L. J. Stat. Phys. 1990, 60, 473. (18) Kurkija¨rvi, J. Phys. Rev. B 1971, 6, 832. Gunther, L.; Barbara, B. Phys. Rev. B 1994, 49, 3926.
Figure 3. Angular dependence of the switching field of an ellipsoidal Fe-Cu-B nanoparticle (20 nm in diameter) deposed on a microbridge (see Figure 2). The arrow indicates the direction of the applied field chosen for waiting time and switching field measurements. The e.a. direction indicates the in-the-SQUIDplane-projected easy axis of magnetization.
In order to study the domain structure and the reversal mode of the nanoparticle, the angular dependence of the switching field, Hsw, is measured with a magnetic field applied in the plane of the SQUID (Figure 3). The orientation of the field: Hx and Hy are in the SQUID plane so that the Hy direction of the applied field is parallel to the hard axis of magnetization. In Figure 3, the “e.a.” direction indicates the in-the-SQUID-plane-projected easy axis of magnetization. The angle θ is measured between the Hx direction and the applied in-plane field. In order to test the validity of the Ne´el-Brown theory, we study the stochastic character of the switching field by waiting time and switching field measurements. From the waiting time measurement, direct access to the switching probability is obtained. At a given temperature, the magnetic field increases to a waiting field, Hw, close to the switching field. The measurement of the elapsed time until the magnetization switches is repeated several hundred times in order to obtain a waiting time histogram. The integral of this histogram gives the not-switching probability. Figure 4 shows, at 3 K, that the probability of not-switching follows an exponential decay as expected from eq 2. Furthermore, the field and temperature dependence of τ follows eq 3. The switching fields histogram is established after several hundred cycles as described below: the applied field is ramped at a given rate and the field value is stored as soon as the sample magnetization switches. Then the field ramp is reversed and the process is repeated. The switching field histogram allows determination of the mean switching field, Hsw, and its width σ. At
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Figure 4. Probability of not-switching of magnetization as a function of the time at different applied fields at 3 K and for θ ≈ 35.5°. Full lines are fits to the data with an exponential (eq 2). (A) H ) 260.73 mT; τ ) 0.67 s (B) H ) 260.62 mT; τ ) 3.8 s. (C) H ) 260.51 mT; τ ) 30 s.
Figure 5. Scaling plot of the mean switching fields Hsw for field sweeping rates between 0.01 and 85 mT/s, temperatures between 0.15 and 3 K and for θ ≈ 35.5°. Inset: Thermal dependence of the mean switching field for θ ≈ 35.5° at two different sweeping fields rates: (A) µ0 dH/dt ) 0.08 mT/s; (B) µ0 dH/dt ) 85 mT/s. The widths σ of the switching field distributions are indicated by vertical bars.
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Figure 7. Temperature dependence of the width of the switching field distribution σ for θ ≈ 35.5° and µ0 dH/dt ) 0.01120 mT. Line: prediction of Kurkija¨rvi18 for µ0 dH/dt ) 1 mT/s.
by choosing the proper values for the constants c. The model of Kurkija¨rvi predicts the width of the switching field distribution (eq 5). A good agreement between theory and measurements is found (Figure 7). We investigated this model as the function of the field sweeping direction indicated by arrows in Figure 3. An example of adjustment of the Ne´el-Brown model to the measurements of Hsw(v,T) is presented in Figure 5. For all temperatures between 0.1 and 6 K, the data of Hsw(v,T) can be aligned on the master curve being nearly a straight line. These adjustments allow us to determine all of the following parameters of the model of Kurkija¨rvi: E0 ) 1.85 × 10-18 J; the magnetization saturation, Ms ) 53 emu‚g-1; µ0Hsw0 ) 259.6 mT. These parameters being know, the model of Kurkija¨rvi predicts the width of the switching field distribution (eq 5). Again, a good agreement between theory and measurements is found (Figure 4). From the waiting time and the switching field measurements, the energy barrier E0 can be approximately converted to a thermally “activated volume” by using V ) E0/(µ0MsHsw). We found V ≈ (30 nm)3 which is larger than the value estimated by SEM. It can be attributed to the fact that the easy axis of magnetization is not parallel to the microSQUID. 6. Conclusion
Figure 6. Field sweeping rate dependence of the mean switching field for θ ≈ 35.5°. The widths σ of the switching field distributions are indicated by vertical bars. (a) T ) 0.15 K. (b) 0.5 K. (c) T ) 0.9 K (d) T ) 2 K. (e) T ) 3 K. The line is a guide for the eye.
temperatures between 0.1 and 6 K, the Hsw is measured for field sweeping rates between 0.01 and 120 mT/s. As expected for a thermally activated process, the mean switching field increases with decreasing temperatures and increasing field sweeping rate (Figure 5). Furthermore, Figure 6 shows an almost logarithmic dependence of Hsw on the field sweeping rate. The validity of eq 4 is tested by plotting the mean switching field values as a function of [T ln(cT/v1/2)]2/3. If the underlying model is sufficient, all points should collapse on one straight line
Dynamic measurements on a single Fe-Cu-B elongated nanoparticle were performed. We measured the probability for switching at a constant applied magnetic field as a function of time and temperature and evidenced that it can be described by an exponential function. The mean waiting time τ followed an Arrhenius law as proposed by Ne´el and Brown. Furthermore, the temperature (0.1-6 K) and applied field sweeping rate dependence (0.01-100 mT/s) of the mean switching field could be described by the model of Kurkija¨rvi which is based on the Ne´el-Brown theory of thermally assisted magnetization reversal over a simple potential barrier. Acknowledgment. We acknowledge A. Thiaville for very helpful discussions, C. Colliex for providing the EELS line spectrum, P. Bonville for the Mo¨ssbauer experiment, and L. Francois for technical assistance. LA9810049
