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J. Phys. Chem. B 1999, 103, 6876-6880
Superparamagnetic Relaxation and Magnetic Anisotropy Energy Distribution in CoFe2O4 Spinel Ferrite Nanocrystallites Adam J. Rondinone, Anna C. S. Samia, and Z. John Zhang* School of Chemistry & Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 ReceiVed: April 23, 1999; In Final Form: June 15, 1999
Superparamagnetism is a unique feature of magnetic nanoparticles. Spinel ferrite nanoparticles provide great opportunities for studying the mechanism of superparamagnetic properties. CoFe2O4 nanocrystallites have been synthesized with a microemulsion method. The neutron diffraction studies and the temperature-dependent decay of magnetization show the superparamagnetic relaxation occurring in these nanoparticles. The neutron diffraction shows a high degree of inversion with the 78% tetrahedral sites occupied by Fe3+ cations. The nanoparticles with a 12 nm diameter have a blocking temperature around 320 K. The field-cooled and zerofield-cooled magnetization measurements display a divergence below the blocking temperature. The energy barrier distribution of magnetic anisotropy is derived from the temperature-dependent decay of magnetization. The magnetic anisotropy is clearly the origin of the divergence in the field-cooled and zero-field-cooled magnetization measurements. The energy barrier distribution function is used in a computer simulation of the zero-field-cooled magnetization, and the calculated magnetization has a great consistency with experimentally measured values. These studies on the magnetic anisotropy distribution elucidate the mechanism of superparamagnetic relaxation and facilitate the design and control of superparamagnetic properties in nanoparticles.
Introduction Magnetic properties of nanoparticles are of broad interest in fundamental science such as macroscopic quantum tunneling (MQT).1,2 Understanding the magnetic properties of nanoparticles surely preludes many important applications of magnetic nanoparticles. The broad applications of magnetic nanoparticles include high-density information storage,3 ferrofluid technology,4 magnetocaloric refrigeration,5 magnetic resonance imaging (MRI) enhancement,6 and magnetically guided drug delivery.7 Superparamagnetic relaxation is one of unique properties of magnetic nanoparticles.8,9 It is directly associated with the magnetic anisotropy in the nanoparticles. In single domain ferromagnetic or ferrimagnetic particulate systems, the net magnetic moments in each particle become ordered and spontaneously magnetized when the temperature is below the Curie magnetic transition temperature of the material. The spontaneous magnetization points the ordered magnetic moments in each particle to the same preferred direction(s). Such preferred direction is known as “easy axis” for magnetization. An easy axis is usually a certain crystallographic axis determined by the coupling between electron spin and its orbital angular momentum at a crystal lattice. Such couplings at the atomic level generate the anisotropy energy known as magnetocrystalline anisotropy. The potential energy is at the minimum when the magnetization of the nanoparticle aligns with its easy axis. Using the Stoner-Wohlfarth theory, the magnetocrystalline anisotropy EA of a single-domain particle can be approximated as
EA ) KVsin2θ
(1)
where K is the magnetocrystalline anisotropy constant, V is the * To whom correspondence should be addressed.
volume of the nanoparticle, and θ is the angle between the magnetization direction and the easy axis of the nanoparticle. In magnetic nanoparticles with a spherical shape, the magnetocrystalline anisotropy can be approximated as the total magnetic anisotropy.10 This anisotropy serves as the energy barrier to prevent the change of magnetization direction. When the size of ferromagnetic or ferrimagnetic nanoparticles is reduced below a threshold value, EA becomes comparable with thermal activation energy, kBT with kB as the Boltzmann constant. The anisotropy energy barrier is so small that thermal activation energy and/or an external magnetic field can easily move the magnetic moments away from the easy axis. Consequently, the collective behavior of the magnetic nanoparticles is the same as that of paramagnetic atoms. Although the magnetic order still exists in the nanoparticles, each particle behaves like a paramagnetic atom but with a giant magnetic moment. Such behavior is known as superparamagnetism. When a superparamagnetic state is achieved, the magnetic nanoparticle goes through a superparamagnetic relaxation process, in which the magnetization direction of the nanoparticle rapidly fluctuates instead of fixing along certain direction. The temperature, at which the magnetic anisotropy energy barrier of a nanoparticle is overcome by thermal activation and the nanoparticle becomes superparamagnetically relaxed, is known as the blocking temperature. The study of the mechanism of superparamagnetic relaxation in magnetic nanoparticles will facilitate the control of superparamagnetic behavior. Understanding and controlling the superparamagnetic properties of nanoparticles is vital to many important applications. For instance, in pursuing high-density information storage, the size of magnetic bits is steadily reduced. However, the superparamagnetic relaxation of the magnetization direction in the data bits has to be avoided in order to keep the digital data usable. On the other hand, superparamagnetic
10.1021/jp9912307 CCC: $18.00 © 1999 American Chemical Society Published on Web 07/28/1999
Superparamagnetic Properties of CoFe2O4 relaxation is an essential requirement for the magnetic nanoparticles used as contrast agents for MRI contrast enhancement. Spinel ferrite nanoparticles provide excellent experimental systems for studying the superparamagnetic properties.11,12 We herein report the superparamagnetic properties of CoFe2O4 spinel ferrite nanoparticles. The nanoparticles with a mean size of 12 nm are prepared with a microemulsion method. The magnetization measurement shows a blocking temperature around 320 K. Below the blocking temperature, a divergence between the zero-field-cooled (ZFC) and field-cooled (FC) magnetization appears. Although the nanoparticles display paramagnetic characteristics above this blocking temperature, neutron diffraction at 523 K shows that there still is a magnetic order in the nanoparticles. It is unambiguous that the nanoparticles are at a superparamagnetic state above 320 K. The energy barrier distribution from magnetic anisotropy is obtained by measuring the temperature dependence of magnetization decay in the nanoparticles. By combining the energy barrier distribution function and the FC magnetization data, a computer simulation is performed for the ZFC magnetization. The calculated ZFC magnetization fits excellently with experimentally measured ZFC magnetization. This analysis directly connects the divergence between the FC and ZFC magnetization to the magnetic anisotropy. It also demonstrates that the energy barrier from magnetic anisotropy is a key factor to the superparamagnetic relaxation of nanoparticles. Experimental Section Synthesis of Magnetic Nanoparticles. CoFe2O4 spinel ferrite nanoparticles were synthesized by using a microemulsion method.13,14 The reagents CoCl2‚6H2O (Fisher, 98.7% pure) and FeCl2‚4H2O (Aldrich, 99% pure) were mixed in an aqueous solution. An aqueous surfactant with 0.030 mol sodium dodecyl sulfate (SDS) was added to form a mixed micellar solution of Co(DS)2 and Fe(DS)2 with the concentration of 0.005 and 0.010 M, respectively. The mixture was then heated to 50 °C in a water bath. About 11 mol CH3NH2 in an aqueous solution (Aldrich, 40 wt %) was also heated to the same temperature and rapidly added into the surfactant mixture. The nanoparticles were precipitated. After the reaction mixture was stirred vigorously for 3 h, the nanoparticles were isolated by centrifugation. The nanoparticles were washed five times with 5% (v/v) NH3 solution. The final product was dried in air at 110 °C. Transmission Electron Microscopy. The transmission electron microscopy (TEM) studies were performed using a Hitachi HF-2000 field-emission transmission electron microscope. A magnification of 80 000 was used. The nanoparticles were dispersed on holey carbon grids for TEM observation. Neutron Diffraction. Neutron diffraction data were collected using a HB4 powder diffractometer at the High-Flux Isotope Reactor (HFIR) of Oak Ridge National Laboratory. The CoFe2O4 sample in a vanadium can was placed in a vacuum furnace with a niobium heating element for data collection at 150 °C over the 2-θ range of 11° to 135° in steps of 0.05°. The sample temperature in the furnace was calibrated using the thermal expansion of magnesium oxide. The wavelength was precisely determined to be 1.4997(1) Å based on the refinements of Si standard. The data were corrected for the variation in detector efficiencies, which were determined using a vanadium standard.15 Magnetic Measurement. Magnetic properties of the CoFe2O4
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Figure 1. X-ray diffraction pattern (Cu KR-radiation) of CoFe2O4 nanoparticles.
spinel ferrite nanoparticles were studied by using a Quantum Design MPMS-5S SQUID magnetometer with a magnetic field up to 5 T. Results and Discussion X-ray powder diffraction shows that the nanoparticles are CoFe2O4 spinel ferrites. No impurity peak is observed in the X-ray diffraction pattern (Figure 1). The diffraction peaks are clearly broadened, which can be the result of lattice strain and/ or the reduced particle size. The full width at half of maximum (fwhm) peak intensity from five peaks in the diffraction has been plotted verses the Bragg diffraction angle following the Williamson-Hall method.16 The result shows an absence of strain in the crystal lattice. Therefore, the peak broadening is purely due to the reduced particle size. The peak width in the diffraction pattern can be used to calculate the mean particle size with the use of Scherrer’s equation. The CoFe2O4 nanoparticles have a size of 12 nm. This particle size is consistent with the direct observation from transmission electron microscopy (TEM) studies. Figure 2 displays the CoFe2O4 nanoparticles with fairly uniform size. The consistency of particle size between X-ray diffraction and TEM observation indicates that the CoFe2O4 nanoparticles are single crystal nanocrystallites. Because of the purpose of this study, there is no further attempt for narrowing the particle size distribution. The chemical composition analysis by using an inductively coupled plasma (ICP) technique shows the ratio of Co to Fe as 1 to 2 in these nanoparticles. The temperature-dependent decay of magnetization is shown in Figure 3. For measuring this magnetization decay, the CoFe2O4 nanoparticles are cooled from room temperature to 5 K under a magnetic field of 100 G. Before the magnetization is measured, the applied magnetic field is turned off. The remanent magnetization is then measured as temperature rises. Clearly, the magnetization decreases as a function of the temperature. When the temperature reaches about 320 K, all of the remanent magnetization approaches zero and the sample becomes demagnetized even though the temperature is still much below the Curie temperature of CoFe2O4. The Curie temperature for CoFe2O4 is about 790 K.17 Figure 4 shows the neutron diffraction pattern of the CoFe2O4 nanoparticles at 523 K. Results from the Rietveld refinement using the GSAS program clearly display a magnetic structure in these nanoparticles. The magnetic moments in the nanoparticles are aligned following an antiferromagnetic order, which is consistent with the ferrimagnetic nature of spinel ferrites.18 Cation distribution between the tetrahedral and octahedral sites shows an inversion degree of 72% for Fe at tetrahedral sites.
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Figure 4. Neutron diffraction patterns of CoFe2O4 nanoparticles at 523 K. The “goodness of fit”, χ2, is 1.39. Below the pattern, the first row of sticks marks the peaks from the magnetic scattering of CoFe2O4 nanoparticles. The second row of sticks corresponds to the peaks from the nuclear scattering. The excluded region near 2θ ) 38°, eliminating the 110 diffraction peak of the Nb heating element of the furnace.
Figure 2. Transmission electron micrograph of CoFe2O4 nanoparticles with a mean size of about 12 nm.
Figure 5. Temperature dependence of the magnetization for zero-fieldcooled (ZFC) and field-cooled (FC) 12 nm CoFe2O4 nanoparticles under a magnetic field of 100 G.
Figure 3. Temperature dependence of magnetization decay for 12 nm CoFe2O4 nanoparticles cooled under a magnetic field of 100 G.
The data refinement suggests a formula for these nanoparticles as Co0.28Fe0.72(Co0.37Fe0.63)2O4 where cations in the brackets occupy the octahedral sites. The unit cell is cubic and has a lattice constant of 8.4131(7) Å. The magnetic moment is 2.42 µB at the tetrahedral lattice site and -1.60 µB at the octahedral site. The temperature-dependent magnetization of the nanoparticles is greatly different between the ZFC and FC measurements. In a ZFC measurement, the sample is cooled from room temperature to 5 K without any external magnetic field. After a magnetic field of 100 G is applied, the magnetization of the sample is measured following the rising temperature. The magnetization increases as the temperature rises from 5 K
(Figure 5). When the temperature approaches 320 K, the magnetization reaches a maximum and starts to decrease. In a FC measurement, the sample is initially cooled to 5 K under a 100 G applied magnetic field. The subsequent magnetization measurement is recorded from 5 to 400 K with the magnetic field kept at 100 G (Figure 5). The FC magnetization shows its maximum at 5 K and steadily decreases as the temperature increases. Starting around 320 K, the magnetization from the FC and ZFC measurements overlaps with each other. The experimental results from temperature-dependent decay of magnetization and neutron diffraction indicate that these CoFe2O4 nanoparticles go through superparamagnetic relaxation as the temperature increases. Under an applied magnetic field at room temperature, the magnetization direction of all magnetic moments aligns along the field direction. As temperature decreases to 5 K, the magnetization direction of the nanoparticles stays at the field direction. When the applied field is turned off at 5 K, the magnetization direction of each nanoparticle remains unaltered. Even though a local minimum of potential energy can be achieved with the alignment of the magnetization direction and the easy axis in the nanoparticle, the magnetic anisotropy as the energy barrier blocks the magnetization direction switching toward the easy axis. As the temperature
Superparamagnetic Properties of CoFe2O4
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rises, some of the nanoparticles that have low energy barriers get their energy barriers overcome by the thermal activation energy, kBT. Consequently, the magnetization direction of each thermally activated nanoparticle starts to randomly flip faster than the measuring time taken by the magnetometer. The sample magnetization reduces. As Figure 3 shows, the overall magnetization of the nanoparticles decreases with increasing temperature. The temperature, at which the thermal activation overcomes all the energy barriers, is known as the blocking temperature, TB. The overall magnetization approaches zero at the blocking temperature without an applied field, and the assembly of the nanoparticles behaves paramagnetically. Although the CoFe2O4 nanoparticles shows paramagneticlike behavior above TB with zero magnetization, the neutron diffraction studies reveal a well-defined magnetic order in the nanoparticles (Figure 4). Such results unambiguously indicate that these nanoparticles possess the superparamagnetic properties. The nanoparticles display the superparamagnetic relaxation when the energy barriers of magnetic anisotropy are overcome. As a typical superparamagnetic behavior, the ZFC and FC magnetization measurements show a great divergence (Figure 5).19 As temperature decreases in the ZFC process, the potential energy settles to a minimum by aligning the magnetization of each CoFe2O4 nanoparticle along its easy axis. Because of the random packing of the nanoparticles, the overall magnetization of the sample shows the lowest value at 5 K. The magnetization aligns with the easy axis in each nanoparticle. When the temperature rises in the measurement under an applied magnetic field, energy barriers start to get topped and superparamagnetic relaxation occurs. The magnetization direction of the nanoparticles acts the same as a typical paramagnetic sample by following with the field direction. The overall magnetization increases with increasing temperature, and the maximum magnetization is achieved at TB (ZFC plot in Figure 5). When all of the nanoparticles are at the superparamagnetic relaxation state above TB, their magnetization follows the Curie law, decreasing with increasing temperature. However, when the nanoparticles are cooled from room temperature under a magnetic field, the magnetization direction of all the nanoparticles is frozen in the field direction. The magnetization shows the maximum at 5 K in the FC process (Figure 5). After the nanoparticles are thermally activated into the superparamagnetic state, their magnetization directions certainly stay with the field direction. Above TB, all of the nanoparticles are at the same superparamagnetic relaxation state as the case in the ZFC process. As a result, the magnetization measurements give overlapping data in the ZFC and FC processes above TB. The magnetic anisotropy barrier is the key for superparamagnetic relaxation. The divergence of magnetization below TB in the ZFC and FC measurement is due to the existence of the energy barriers of magnetic anisotropy. For the temperaturedependent decay of magnetization, MTD, the number of the nanoparticles, whose energy barriers are overcome at given temperature by kBT and whose magnetization starts to flip randomly, corresponds to the decrease of magnetization at that temperature (Figure 3). Therefore, the derivative of the magnetization decay plot, f(T) represents the distribution of anisotropy energy barriers.
f(T) ) (-dMTD/dT)
(2)
Figure 6 displays the magnetic anisotropy energy barrier distribution in these 12 nm CoFe2O4 nanoparticles. As Figure 6 shows, most of the nanoparticles have overcome their energy barriers at TB, which is treated here as the temperature showing
Figure 6. Energy distribution of magnetic anisotropy in 12 nm CoFe2O4 nanoparticles.
the maximum magnetization in the ZFC magnetization measurement. The blocking temperature sometimes is also defined as the temperature at which 50% of the particles overcome their energy barriers. It is clear that the blocking temperature from different definitions can differ significantly. Although there certainly are some interparticle magnetic interactions in these CoFe2O4 nanoparticles, such interactions are usually weak and the magnetization decay measurement is not affected by them.20 Hence, the energy barrier distribution function represents the intrinsic feature of the CoFe2O4 nanoparticles and directly associates with the superparamagnetic properties of the nanoparticles. In the FC process, the magnetization direction of all the nanoparticles aligns along the field direction. At each temperature, the magnetization, MFC, consists of the contribution from the total nanoparticles. However, the energy barrier has to be overcome in the ZFC process before the magnetization of the nanoparticle can switch from its easy axis to align along the field. The magnetization, MZFC, at the measuring temperature below TB reflects only the magnetization of the nanoparticles, whose energy barriers locate in the portion of the distribution function from 5 K up to the measuring temperature. Therefore, by using the total magnetization, MFC, of the sampling nanoparticles at each temperature and the normalized energy barrier distribution function, MZFC can be calculated with eq 3.
MZFC ) MFC
∫5T f(T)dT
(3)
MZFC is measured with an applied magnetic field of 100 G, and this magnetic field also contributes energy toward overcoming the energy barriers in the nanoparticles in addition to the thermal activation energy. Since MTD is obtained without any field, a minor correction of energy term contributed by the 100 G magnetic field has to be applied when f(T) is used to calculate MZFC. The calculated MZFC is shown in Figure 7. It fits excellently with the measured magnetization obtained in the ZFC process. The great consistency between the experimental data and the computer simulation clearly shows that the mechanism of the divergence below TB in the FC and ZFC magnetization can be unambiguously elucidated by the energy barrier distribution studies. The analysis of the magnetic anisotropy distribution certainly provides a quantitative characterization of superparamagnetic behavior of magnetic nanoparticles.
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Rondinone et al. superparamagnetic relaxation and facilitate the design and control of superparamagnetic properties in nanoparticles. Acknowledgment. We thank Dr. Bryan Chakoumakos of Oak Ridge National Laboratory for his help in neutron diffraction studies. A.J.R. is partially supported by a Cherry Henry Emerson Chemistry Fellowship and a Molecular Design Institute Fellowship. We gratefully acknowledge the financial support in part from DARPA/Office of Naval Research (ONR14-98-108460) and NSF (DMR-9875892). Z.J.Z. is a Beckman Young Investigator supported by the Arnold and Mabel Beckman Foundation. The neutron diffraction studies were carried out at Oak Ridge National Laboratory, which is managed by Lockheed Martin Energy Research Corp. for the U.S. Department of Energy under contract number DE-AC0596OR22464.
Figure 7. Experimentally-measured (0) and computer-simulated (s) temperature dependence of magnetization for 12 nm CoFe2O4 nanoparticles under 100 G magnetic field.
Conclusions The studies on the temperature-dependent decay of magnetization and neutron diffraction of the CoFe2O4 nanocrystallites show the superparamagnetic relaxation occurring in these nanoparticles. As a characteristic feature of superparamagnetic nanoparticles, the field-cooled and zero-field-cooled magnetization measurements show a divergence below the blocking temperature of the sample. The magnetic anisotropy is directly related to the superparamagnetic relaxation. Its distribution is derived from the temperature-dependent decay of magnetization. With the energy barrier distribution function, the ZFC magnetization can be simulated and calculated ZFC magnetization has an excellent fit with experimentally measured values. The energy barriers formed by magnetic anisotropy are clearly the origin of the divergence in FC and ZFC magnetization measurement. These studies show the key importance of magnetic anisotropy to the superparamagnetic properties of magnetic nanoparticles. Since the magnetic anisotropy originates in the magnetic couplings at atomic level, it is possible to manipulate the magnetic anisotropy in magnetic nanoparticles by controlling the chemistry at crystal lattices. Certainly, studies on the magnetic anisotropy distribution elucidate the mechanism of
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