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shell structure
ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 322 (2010) 2117–2126
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Effects of pressure on maghemite nanoparticles with a core/shell structure Y. Komorida a,n, M. Mito a, H. Deguchi a, S. Takagi a, T. Tajiri b, A. Milla´n c, N.J.O. Silva d, M.A. Laguna c, F. Palacio c a
Faculty of Engineering, Kyushu Institute of Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu 804-8550, Japan Faculty of Science, Fukuoka University, Fukuoka 814-0180, Japan c ´n, CSIC-Universidad de Zaragoza, Zaragoza 50009, Spain Instituto de Ciencia de Materiales de Arago d CICECO, Universidade de Aveiro, Aveiro 3810-193, Portugal b
a r t i c l e in fo
abstract
Article history: Received 17 April 2009 Received in revised form 29 January 2010 Available online 4 February 2010
The magnetic property and intraparticle structure of the g phase of Fe2O3 (maghemite) nanoparticles with a diameter (D) of 5.1 7 0.5 nm were investigated through AC and DC magnetic measurements and powder X-ray diffraction (XRD) measurements at pressures (P) up to 27.7 kbar. Maghemite originally exhibits ferrimagnetic ordering below 918 K, and has an inverse-spinel structure with vacancies. Maghemite nanoparticles studied here consist of a core with structural periodicity and a disordered shell without the periodicity, and core shows superparamagnetism. The DC and AC susceptibilities reveal that the anisotropy energy barrier (DE/kB) and the effective value of the core moment decrease against the initial pressure (P r 3.8 kbar), recovering at P Z 3.8 kbar. The change of DE/kB with P is qualitatively identical with that of the core moment, suggesting a down-and-up fluctuation of the number of Fe3 + ions constituting the core at the pressure threshold of about 4 kbar. This phenomenon was confirmed by the analysis of the XRD measurement using Scherrer’s formula. The core volume decreased for P r 2.5 kbar, whereas at higher pressure the core was restructured. For 2.5 r P r 10.7 kbar, the volume shrinkage of particle hardly occurs. There, DE/kB is approximately proportional to the volume associated to the ordered fraction of the nanoparticles as seen from XRD, Vcore. From this dependence it is possible to separate the core/shell contribution to DE/kB and estimate core and surface anisotropy constants. As for the structural experiments, similar experimental data have been obtained for D= 12.8 7 3.2 nm as well. & 2010 Elsevier B.V. All rights reserved.
Keywords: Pressure effect Nanoparticle Core/shell structure Maghemite Superparamagnetism
1. Introduction The study on magnetic properties of nanoparticles is one of the most active research areas in condensed matter physics from the viewpoints of both fundamental science and industrial application. When the particle size reaches the nano-meter scale, superparamagnetism appears due to single-domain formation [1,2]. The magnetically active state of this minuscule domain let one expects that it is possible to apply it to high-bit information storage devices. Physically, the effect of surface in nanoparticle is quite interesting. The structural defects in the surface can bring about complex magnetic behavior, and the influence of the defects is more remarkable than in bulk systems. On the other hand, interparticle interaction via the spins of the surface also affects the magnetic properties [3]. The understanding of these basic physical properties of magnetic nanoparticles is quite
n
Corresponding author. Tel./fax: + 81 93 884 3286. E-mail addresses: [email protected] (Y. Komorida), [email protected] (M. Mito). 0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2010.01.044
important for the development of nano-science and advanced technologies. Iron oxide nanoparticles have already been also used in several biomedical fields like magnetic resonance imaging, hyperthermiatargeted drug delivery and tissue engineering [4,5]. Among iron oxides, the g phase of Fe2O3 (maghemite) is one of the most attractive materials for industrial application because of its chemical stability. Maghemite originally exhibits ferrimagnetic ordering below 918 K [6]. The basic structure of bulk maghemite is the inverse-spinel structure with some vacant sites, and possesses cubic symmetry (P4332) with a lattice constant of a= 8.34 A˚ [7,8]. However, the recent structural study on the highpurity crystal has revealed that the ordered vacancies on the octahedral positions form the tetragonal superlattice (space group P41212) [7,8]. In the case of maghemite, the existence of these vacancies strongly influences the generation of the spontaneous magnetization. Especially in nanoparticles with many surface molecules, the effect becomes considerable, and the magnetic properties are indeed dependent on the synthesis method [9,10]. In the present study, both core and shell in maghemite nanoparticles are modified by pressurization. Here, let us briefly
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describe the ‘‘core/shell structure’’ of ferrimagnetic nanoparticles. The central part, i.e., the core, has structural periodicity, and can maintain spontaneous magnetization. The core with nano-meter size brings about superparamagnetism. In contrast, the surface region, i.e., the shell, has no structural periodicity. The core-shell model is an approximation that, however, has been successfully used to model the magnetic properties of nanoparticles [11–15]. Most of the net moment of the entire particle usually originates from the moment of the core. The surface shell is treated as a disordered layer like spin glasses [16], and is analyzed as paramagnetic or antiferromagnetic component in the data of magnetization curve [17]. The magnetic interaction between the core and the shell can appear as an exchange bias effect. In the frame of this core-shell model, the magnetic behavior of maghemite nanoparticle systems is well understood [17]. Milla´n et al. [17] have reported that the shell thickness is independent of the particle size, and is estimated to be about 1 nm, through the analysis of magnetization curve data of maghemite nanoparticles with size ranging from 2 to 15 nm. In the present study, we systematically investigate the magnetic properties of this prototype magnetic nanoparticle by applying pressure. Pressurization is expected to continuously shrink and tune the defects, and occasionally restructure the system. We have already reported the preliminary results for maghemite nanoparticles with a diameter (D) of 6.570.65 nm, and there confirmed the changes in the magnetic properties under pressure [18]. Recently, we proposed a method for estimating the anisotropy constants for both core and surface via hydrostatic pressure response on maghemite nanoparticles with D= 5.170.5 nm [19]. In this paper, we report in more detail the effects of hydrostatic pressure on both the magnetic properties and the intraparticle structure in maghemite nanoparticles with D= 5.170.5 nm, according to magnetic measurements and structural analyses. As for the structural studies, the experimental data for D= 12.873.2 nm are also presented, in order to show that the pressure response in the nano-size level is independent of the particle size.
2. Experimental The two kinds of maghemite nanoparticles used in this study were prepared by a procedure mentioned elsewhere [17], in which the nanoparticles were grown within an organic polymeric matrix of polyvinylpyridine (PVP) that coats the particles and prevents aggregation. These transmission electron microscopy (TEM) images and size distributions are given in Fig. 1. The particle size analysis performed on TEM images over more than 200 particles yielded D= 5.170.5 and D= 12.873.2 nm, respectively. The samples are annealed at 200 1C (D= 5.1 nm) and 250 1C (D= 12.8 nm), respectively. The nominal values of maghemite content in the samples are estimated to be 16.4 wt% (D=5.1 nm) and 52.9 wt% (D=12.8 nm). The AC and DC magnetic measurements were performed using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design, MPMS-5S) in the temperature (T) range of 5 KrTr80 K. Pressure was attained using a piston cylinder cell (CR-PSC-KY05-1, Kyowa-Seisakusho Co., Ltd.), which can be inserted into the SQUID magnetometer [20]. The pressure cell was made of a non-magnetic Cu–Be alloy. In order to apply pressure effectively, the sample was held inside the teflon cell with the aid of a pressure-transmitting medium, Apiezon-J oil, and a small amount of metallic superconductor tin. The pressures at liquidhelium temperature were estimated based on the shift in the superconducting transition temperature of tin [21]. Synchrotron radiation powder X-ray diffraction (XRD) measurements were performed at pressures up to 33.6 kbar using a
Fig. 1. TEM images and size distributions of maghemite nanoparticles with a diameter of 5.1 (a) and 12.8 nm (b). The size distribution was investigated for sampling of more than 200 particles.
cylindrical imaging plate (IP) diffractometer (Rigaku Co.) at the Photon Factory (PF) of the Institute of Materials Structure Science, the High Energy Accelerator Research Organization (KEK) [22]. All of the measurements were carried out at room temperature. The ˚ Pressurizawavelength of the incident X-ray l was 0.6883(1) A. tion was done by the use of a diamond anvil cell (DAC) with a Be backing plate, on which diamond anvils with 0.8 mm flat tips were mounted. Between the anvils, a 0.3-mm-thick Cu–Be gasket was inserted. In the sample hole with a diameter of 0.4 mm, located in the center of the gasket, the crystalline sample and a few ruby crystals were held with the aid of a pressuretransmitting medium, fluorine oil (FC77). The pressure value was calibrated by the ruby fluorescence method [23], and the
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estimated value of pressure involves the measurement error of 70.8 kbar.
0.025 P = 0 kbar
0.24
0.02
0.2
0.015
0.16
0.01
3. Experimental results
The magnetic properties of maghemite nanoparticles with D= 5.1 nm were investigated through the following three magnetic measurements: (1) zero-field-cooled (ZFC) and field-cooled (FC, from T= 80 K and H=200 Oe) DC magnetization measurements, and (2) AC susceptibility measurement and (3) magnetization curve measurement at T= 5 K. In the AC measurement, the frequency range of the AC exciting field was 1–100 Hz, and the field amplitude was 2.0 Oe. The magnetization curve at T=5 K was measured at DC magnetic fields of up to 50 kOe and at pressures of up to 14.3 kbar. The magnetic data for (1) and (2) in Figs. 2–4 were evaluated with the unit mass of the sample (maghemite+PVP), whereas only the data for (3) in Fig. 7 were done with the unit mass of maghemite. 3.1.1. DC magnetic susceptibility Fig. 2 shows the temperature dependence of the ZFC and FC magnetization (M) under pressure for maghemite nanoparticles with D= 5.1 nm. The arrows indicate the peak positions of ZFC magnetization (Tp). The value of Tp at ambient pressure was estimated to be 12.3 70.5 K. At P= 3.8 kbar, the Tp decreased to 11.2 70.5 K. However, further pressurization brings about the increase of the Tp, following an unexpected down-and-up fluctuation. Fig. 3 shows the temperature dependence of the deviation between the FC and ZFC magnetizations shown in Fig. (2), DMFC–ZFC(T), at several pressures. The data for DMFC–ZFC(T) tell us the temperature region of thermal irreversibility. The DMFC–ZFC
MFC-ZFC (emu/g)
3.1. Magnetic properties
2119
3.8 kbar 5.2 kbar 8.2 kbar 13.9 kbar 14.3 kbar
0.005
0.12
0 20
0.08
25
30
35
40
0.04
0
0
10
20
30
40
50
T (K) Fig. 3. Temperature dependence of the deviation between the ZFC and the FC magnetizations, DMFC–ZFC, at several pressures for maghemite nanoparticles with D =5.1 nm. The inset shows an enlargement of the rectangular area.
at ambient pressure rapidly increased by decreasing temperature below 30 K. When a pressure of 3.8 kbar was applied, the overall behavior of DMFC–ZFC(T) curve shifted towards the lower temperature side. Thereafter, upon further pressurization, it shifted towards the higher temperature side. The pressure dependence of DMFC–ZFC(T) is consistent with the change in Tp. The above characteristic pressure dependencies (the down-and-up fluctuation of Tp and MFC–ZFC(T)) have already been observed in maghemite nanoparticles with D=6.5 nm [18].
0.6 3.1.2. AC magnetic susceptibility Fig. 4 shows the temperature dependence of the out-of-phase component of the AC magnetic susceptibility, w’’, for f=1 Hz (a) and 10 Hz (b). The peak position allows us to determine the temperature of magnetic freezing, the so-called ‘‘blocking temperature’’ (TB). The insets of Fig. 4 show the temperature dependence of the data around TB. The arrows represent the positions of TB under each pressure. The pressure dependencies of TB at f =1 and 10 Hz are plotted in Fig. 5, showing good consistency with the results for Tp and DMFC–ZFC(T) mentioned above. The frequency dependence of TB at each pressure was analyzed using the Arrhe´nius plot, as shown in Fig. 6. Here, the effective energy barrier, DE, between the spin-up and spin-down states can be estimated using the following equation:
0.5
M (emu/g)
0.4
0.3
0.2
P ==00kbar kbar 3.8 kbar 5.2 kbar
0.1
1 kB lnð2pf Þ þlnðt0 Þ ; ¼ DE TB
8.2 kbar 14.3 kbar
0
10
100 T (K)
Fig. 2. Temperature dependence of the zero-field-cooled (ZFC, open symbols) and field-cooled (FC cooling from T= 80 K at H = 200 Oe, solid lines) magnetization under various pressures for maghemite nanoparticles with D = 5.1 nm. The arrows indicate the peak position of the ZFC magnetization at each pressure. The base line for each data in the pressure range of 3.8–14.3 kbar was shifted at an interval of 0.05 emu/g so as to guide the eye.
ð1Þ
where kB is the Boltzmann constant, and t0 is a pre-exponential factor. The solid lines show the fitting using Eq. (1), and DE/kB was estimated from the inverse of the slope. The inset of Fig. 6 shows the pressure dependence of DE/kB, which is also qualitatively consistent with the results series for Tp, DMFC–ZFC and TB. At ambient pressure, the value of DE/kB was estimated to be 378 K. At P= 3.8 kbar, the value of DE/kB decreased to 88.7% of the initial value. At P=14.3 kbar, it increased to 111% of the initial value. Thus, quantitative analyses on the TB and DE/kB reveal that the effective energy barrier DE is reduced and thereafter enhanced.
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18
0.00038
0.0004
f = 1 Hz 10 Hz
17 0.00034
16 0.0003
0.0002 P = 0 kbar 3.8 kbar 5.2 kbar 8.2 kbar 13.9 kbar 14.3 kbar
0.0001
0
8
0
10
20
30
TB (K)
χ" (emu/g)
0.0003
10 12 14 16 18 20
15
f = 1 Hz 14
13
40 50 T (K)
60
70
80
12 0
5
10
Fig. 5. Pressure dependence of the blocking temperature (TB) at f= 1 and 10 Hz for maghemite nanoparticles with D = 5.1 nm. The solid curves are visual guides.
0.0005
0.0006
0.08
0.0004
P = 0 kbar 3.8 kbar kbar 5.2 kbar kbar 8.2 kbar kbar 13.9 kbar 13.9 kbar 14.3 kbar 14.3 kbar
0.0005 0.0003
8 10 12 14 16 18 20 22 24 26 28 30
0.07
f = 10 Hz 0.0003 P = 0 kbar 3.8 kbar 5.2 kbar 8.2 kbar 13.9 kbar 14.3 kbar
0.0001
0
10
20
30
0.06
40 50 T (K)
60
70
0.05
3.1.3. Magnetization curve Fig. 7 shows the magnetization curve in unit mass of maghemite for P= 0 (a) and 14.3 (b) kbar at T= 5 K (open circles), which is sufficiently below TB. The field dependence is expressed as the summation of saturation and linear-like contributions. Thus, the magnetization curve up to 50 kOe was analyzed by the use of a modified Langevin equation with the linear term against the magnetic field, H, as follows: 1 ð2Þ þ wshell H ; M ¼ N mcore cothx x mcore H ; kB T
400
300
200
80
Fig. 4. Temperature dependence of the out-of-phase component of the AC susceptibility, w’’, at f= 1 (a) and 10 Hz (b) for maghemite nanoparticles with D = 5.1 nm. The pressure range is the same as that of Fig. 3. The inset shows an enlargement of the rectangular area. The arrows indicate the blocking temperature (TB) at each pressure. The solid curve is a visual guide.
x¼
500
ΔE/k (K)
0.0002
0
1/TB (1/K)
χ" (emu/g)
0.0004
15
P (kbar)
0.0006
ð3Þ
where N is the particle number, and mcore is the magnetic moment of the core. In the frame of the core-shell model, the first and second terms on the right side of Eq. (2) correspond to the superparamagnetic core and shell contributions, respectively. The
1
0
5
2
10 P (kbar)
3
15
4
5
6
7
ln(2πf ) Fig. 6. Arrhe´nius plots of the inverse blocking temperature (1/TB) as a function of the frequency at various pressures for maghemite nanoparticles with D =5.1 nm. The solid line expresses Eq. (1) at each pressure. The inset shows the pressure dependence of the energy barrier (DE/kB), which is obtained from the slope of the Arrhe´nius plot. The solid curve is a visual guide.
shell contribution is modeled with high field susceptibility per one particle wshell, and the paramagnetic or antiferromagnetic behavior appears as the linear field dependence. The data analyses using Eqs. (2) and (3) did not fit the data with sufficient accuracy especially at low magnetic field. Thus we considered that the distribution of the magnetic moment of the core based on the size distribution (see Fig. 1 (a)) [24,25]. In low magnetic field, the size distribution of the shell is not so important because of the field dependence, whereas that of the core gives significant influence on magnetization development. Here, the experimental data were reproduced with the following equation, Z 1 ð4Þ f ðmcore Þdmcore þ wshell H ; M¼N mcore coth x x
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Fraction (%)
6 4 2 0
0
2 8 10 12 14 6 4 mcore (x10-18 emu/particle)
0
2 8 10 12 14 6 4 mcore (x10-18 emu/particle)
Fraction (%)
6
4
2
0
Fig. 7. Magnetization curve for magnetic fields up to 50 kOe of maghemite nanoparticles with D =5.1 nm at T= 5 K for P= 0 and 14.3 kbar. The value of M is evaluated with the unit mass of maghemite. The open circles represent the experimental data. The solid curve (a) represents the modified Langevin function Eqs. (4) and (5). The solid curve (b) shows the core contribution, which corresponds to the first term of the right side of Eq. (4), while a solid line (c) shows the shell contribution, which corresponds to the second term. The inset shows the distribution of the magnetic moment of the core (mcore), determined by the lognormal fit (solid red curve).
where, f(mcore) denotes a lognormal distribution function of mcore ( ) 1 ðln mcore =mm Þ2 : ð5Þ f ðmcore Þ ¼ pffiffiffiffiffiffi exp 2s2 2psmcore Here, mm is the medium value of the magnetic moment of the core, and s is the standard deviation of the distribution of log (mcore). The insets of Fig. 7 show the distribution of mcore with a lognormal type of distribution symmetry, used in analyzing the data for P= 0 and 14.3 kbar. In order to simplify the analysis procedure, the distribution of Eq. (5) was reproduced in the actual analysis with a discrete distribution divided into 60 parts. The solid line (b) expresses the first term of Eq. (4), while the solid line (c) expresses the second. The solid curve (a) shows the fitting data using the modified Langevin function Eqs. (4) and (5). For fitting parameters such as N= 5.68 1018 particles/g-Fe2O3, wshell =2.96 10-22 emu/particle (g-Fe2O3), mm =2.91 10 18 emu/ particle (g-Fe2O3) and s =0.60, we see a good agreement between the experimental data at ambient pressure and the modified Langevin function Eqs. (4) and (5). Bulk maghemite has the magnetic moment of 17.36 mB per unit cell [26]. Based on this reference value, the present value of (g-Fe2O3) (= 3.14 102 mB/particle 2.91 10 18 emu/particle (g-Fe2O3)) corresponds to the moment of maghemite nanoparticles with the diameter of the core, Dcore = 2.7 nm. This suggests the
Fig. 8. Pressure dependencies of the medium value of the magnetic moment of the core (mm) and the magnetic susceptibility of the shell contribution (wshell) for maghemite nanoparticles with D = 5.1 nm.
existence of a shell with thickness of 1.2 nm for the particle size of D=5.1 nm. The present analytic result is consistent with the previous report by Milla´n et al. [17]. Herein the values of mm and wshell obtained by fitting the magnetization curve are shown in Fig. 8. In the analysis of the data under pressure, the value of N was fixed, and s hardly changed. When pressure was applied, mm decreased temporarily at the initial pressure, and reached a minimum at around 4 kbar. At P44 kbar, mm continued to increase with pressure in a linear fashion. The pressure dependence of wshell showed a behavior contrary to that of mm. The change of wshell per a particle surely reflects a change in the number of Fe3 + ions constituting the shell, and there is the change of up-and-down. Namely, the spatial region of the core is temporarily shrunk at PoPC ( 4 kbar), whereas at P4PC, the core region is re-stabilized due to restructuring. This suggests that the nanoparticle structure is quite sensitive to external stress. In order to obtain direct information on the intraparticle structural changes, we performed the XRD experiments under pressure at room temperature. 3.2. X-ray diffraction (XRD) measurements Synchrotron radiation powder X-ray diffraction (XRD) measurements of maghemite nanoparticles with D=5.1 nm were performed at pressures of up to 27.7 kbar. So as to confirm that the pressure response obtained for D= 5.1 nm is also unique for D410 nm, the data for D=12.8 nm are also presented. Fig. 9 shows the XRD patterns of maghemite nanoparticles with D= 5.1 and 12.8 nm. These diffraction patterns are consistent with the Rietveld simulation based on the space group P4332 with a= 8.34 A˚ (labeled with (a)). It reveals that vacancy sites are not ordered in the present magnetic nanoparticles. The intensities of these patterns were not perfectly reproduced by the Rietveld simulation especially around 2y = 161, owing to the broadening effects of the nano-scale size. The Rietveld simulation could not be an effective analytic approach, even if the effective backgrounds (b) and (c) are assumed. Fig. 10 shows the XRD patterns for P= 0 (a), 2.5 (b), 8.5 (c) and 14.8 kbar (d) as representative data for maghemite nanoparticles with D= 5.1 nm. In the experimental data shown in Fig. 10, the
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Fig. 9. X-ray diffraction (XRD) patterns of maghemite nanoparticles with D = 5.1 and 12.8 nm at room temperature and ambient pressure. The open circles and squares represent the experimental data for D =5.1 and 12.8 nm, respectively. The dotted curve (a) is the result of a simulation based on the bulk structure. The dotted curves (b) and (c) represent the assumed background data resulting from the fluorine oil and diamond anvils for D =5.1 and 12.8 nm, respectively.
contribution of the background, including the diamond anvils and FC77 (see Fig. 9), was subtracted. At first, the data for 2y =12–181 at P =0 kbar (a) are reproduced by the summation of seven diffraction peaks with Lorentzian shape, based on P4332. The diffraction pattern around 2y = 161 was well fitted with the summation of three Lorentzians with the plane indices (3 1 0), (3 1 1) and (2 2 2). Given these situation, using both the diffraction peak angle on the dominant diffraction peak (3 1 1) and the full-width at halfmaximum (FWHM) of the diffraction peak, the lattice constant (a) of the cubic lattice and the particle size of the core, Dcore, were estimated. The Dcore was calculated from the values of the FWHM and the diffraction peak angle using the Scherrer’s formula, as follows: Dcore ¼
0:9l ; bcosy
ð6Þ
where b is the FWHM of the diffraction peak expressed in radians, and y is the diffraction peak angle. At ambient pressure, Dcore was estimated to be 3.8 nm. Then, the thickness of the shell was calculated to be about 0.65 nm for D= 5.1 nm. Dcore =3.8 nm from the XRD measurement is slightly larger than Dcore = 2.7 nm estimated by the magnetic measurement. The above two estimated values are derived from independent physical measurements, nevertheless they are not so far each other. We think that the deviation is explained with that the entire core with the structural periodicity may not have the perfect magnetic order. Fig. 11 shows the pressure dependencies of the diameter of the core Dcore estimated from the XRD measurement and the lattice constant (a) of the cubic lattice for the maghemite nanoparticles with D=5.1 nm. The Dcore estimated from XRD measurement reached a minimum at around 2.5 kbar, and the qualitative behavior was consistent with those of the magnetic data such as MFC–ZFC(T), Tp, TB, DE and mm. As for the lattice constant of the cubic lattice, the lattice shrinkage tended to saturate in the pressure region of 2.5–10.7 kbar. At pressures above 10.7 kbar, the lattice shrinkage restarted. This
Fig. 10. XRD patterns of maghemite nanoparticles with D = 5.1 nm at room temperature for P = 0 (a), 2.5 (b), 8.5 (c) and 14.8 kbar (d). The open squares represent the experimental data. The data for 2y = 12–181 at P = 0 kbar (a) could be reproduced by the summation of seven diffraction peaks with Lorentzian shape, based on P4332. The diffraction pattern around 2y = 161 was fitted using the sum of three Lorentzians (red solid curve). The diffraction peaks of (3 1 0) and (2 2 2) are reproduced by the green solid curves, while that of (3 1 1) is reproduced by the blue solid curve. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
successive shrinkage for P410.7 kbar surely corresponds to the restructuring of the particle. After the 27.7 kbar pressure was released, the diffraction pattern almost recovered to that of the initial state, and, within the considered pressure region, the elasticity of maghemite nanoparticle remained intact. Fig. 12 shows the pressure dependencies of the volume of the entire nanoparticle and that of the core. In the shell region, the unit cell cannot be defined, because the shell region does not have the structural periodicity. Here, we suppose that the shrinkage ratio of the shell should be equal to that of the core under pressure, since the intrinsic composition is uniform over the entire particle. Under pressure, the particle volume, Vparticle, was calculated based on the following assumption: the initial particle
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Fig. 11. Pressure dependencies of the diameter of the core, Dcore, and the lattice constant a of the cubic lattice for maghemite nanoparticles with D =5.1 nm.
Fig. 13. XRD patterns of maghemite nanoparticles with D = 12.8 nm at room temperature for P =0 (a), 3.3 (b), 12.3 (c) and 33.6 kbar (d). The open squares represent the experimental data. The data for 2y = 12–181 at P = 0 kbar (a) could be reproduced by the summation of seven diffraction peaks with Lorentzian shape, based on P4332. The diffraction pattern around 2y = 161 was fitted by using the sum of three Lorentzians (red solid curve). The diffraction peaks of (3 1 0) and (2 2 2) are reproduced by the green solid curves, while that of (3 1 1) is reproduced by the blue solid curve. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. Pressure dependencies of the volume of the entire nanoparticle, Vparticle, and that of the core, Vcore, for maghemite nanoparticles with D =5.1 nm.
diameter, D, is 5.1 nm, and the shrinkage ratio of the entire nanoparticle is the same as that of the unit cell in the core under pressure. The core volume Vcore was calculated using the diameter of the core, Dcore. The residual volume after subtracting the core volume from the particle volume at each pressure corresponded to the volume of the shell, Vshell ( =Vparticle Vcore). Vcore reached a minimum at 2.5 kbar, and thereafter increased with increasing pressure. At P= 2.5 kbar, Vcore was reduced to almost half of the initial volume, and the decrease ratio was much larger than that of Vparticle. This suggests that the ratio of the core region against the particle temporarily became quite small under pressure. For D=12.8 nm, the data corresponding to Figs. 10–12 for D= 5.1 nm are presented in Figs. 13–15, respectively. The essential pressure response was similar to that for D= 5.1 nm. Fig. 16 shows the ratios of Vcore, and Vshell, to Vparticle, under pressure for both
Fig. 14. Pressure dependencies of the diameter of the core, Dcore, and the lattice constant a of the cubic lattice for maghemite nanoparticles with D= 12.8 nm.
D=5.1 and 12.8 nm. Indeed, these ratios, Vcore/Vparticle and Vshell/ Vparticle, are the same as the ratios of the number of Fe3 + ions constituting the core and shell to that constituting the entire particle. In particular for D=5.1 nm, the number of Fe3 + ions
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constituting the core, Ncore, was reduced to a half of the initial value at 2.5 kbar, and increased at pressures above 2.5 kbar. Finally, Ncore at P= 27.7 kbar exceeded the initial value in the case of D= 5.1 nm. These results indicate that the core is eroded by the shell under small stress, and the region without structural periodicity is enlarged. However, the larger stress saturates the particle shrinkage, and thereafter the core region is restructured and stabilized. Our series of magnetic measurement results are well explained by the change in Ncore, estimated through XRD measurements. In the maghemite nanoparticles with D= 25 nm, a Raman spectroscopic study has been already done in the pressure range up to 57.5 GPa [27], and it has been reported that the g phase transforms to the a phase at P= 13.5 GPa. The stability of g-phase seen in the present experiment is consistent with the above Raman spectroscopy.
Fig. 15. Pressure dependencies of the volume of the entire nanoparticle, Vparticle, and that of the core, Vcore, for maghemite nanoparticles with D =12.8 nm.
4. Discussion In principle, changes in magnetic properties observed with the application of pressure may be attributed to interparticle and/or intraparticle effects. In the case of interparticle effects, dipolar interactions are more plausible than exchange ones, since the nanoparticles are coated with polymer. In a regular array of identical dipoles, the transition temperature associated to dipolar interactions is given by [3] Td ¼
a0 m0 m2 4pkB d3
ð7Þ
with a0 being of the order of 1–10, m0 is the magnetic permeability of vacuum, m is the magnetic moment, and herein corresponds to mm. d is the distance between neighboring dipoles. This expression has also been used to estimate the ordering temperature in systems of randomly distributed particles, where m and d are average values [3]. For the nanocomposite with D= 5.1 nm, considering a0 =10, d =13.8 nm (estimated from D and from the maghemite mass concentration) and mm (see Fig. 8), Td = 0.5 K at ambient pressure, which means that dipolar interactions do not play an important role in the present discussion, even considering that at the highest pressure the total volume shrinks to half. If the random field of the dipole–dipole interaction induces a glassy behavior, one can ascertain the sign based on the non-linear AC susceptibility. In the present study, at all pressures, no non-linear response was detected in the AC susceptibility measurement for D=5.1 and 12.8 nm. In this view we should focus our attention on only intraparticle effects. In ferromagnetic nanoparticles, the energy barrier is expressed as proportional to volume (V) considering an effective anisotropy constant (Keff) as DE =KeffV. This expression is also used in ferrimagnetic nanoparticles. As mentioned above, the change of Vparticle reflects intrinsic shrinkage, while Vcore does both shrinkage and change of the number of Fe3 + ions constituting the core. For 2.5rPr10.7 kbar, the shrinkage of Vparticle is small, and the change of the numbers of Fe3 + ions constituting core and shell appears dominantly. Thus, for 2.5rPr10.7 kbar, combining information of DE/kB (P) (from Fig. 6) with information of Vparticle (P) and Vcore (P) as Fig. 17(a), we find out that DE/kB is approximately proportional to Vcore (P). Then, in the core-shell model, surface anisotropy (KS) is sometimes relevant, being expressed as an extra term, such as [19]
DE ¼ Kcore Vcore þ Ks S:
ð8Þ
Fig. 16. Pressure dependence of the ratios of the core volume, Vcore, and the shell volume, Vshell, to the volume of the entire particle, Vparticle, for D =5.1 (a) and 12.8 nm (b). These ratios are the same as the ratios of Fe3 + ions constituting the core and the shell to the number of Fe3 + ions constituting the entire particle.
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resonance measurement (K1 = 2.5 105 erg/cm3) [28], and that found in maghemite nanoparticles (K1 = 3.6–6 106 erg/cm3) [29]. At the same time, DE/kB extrapolates to 246 710 K at Vcore = 0, corresponding to the energy barrier associated to the shell. Considering D(P)= 5.0 nm for 2.5rPr10.7 kbar according to Fig. 12, one can determine KS = 4.2 10 2 erg/cm2. This value is of the order of that previously found for maghemite nanoparticles (KS = 6 10 2 erg/cm2) and Fe2.93O4 nanoparticles (KS = 2.9 10 2 erg/cm2) [30,31], and about one order of magnitude lower than that found in Co nanoparticles by magnetic measurement (KS =2–3 10 1 erg/cm2) [32]. A similar analysis is made by plotting mm as a function of Vcore and Vparticle (Fig. 17 (b)). As in the case of DE/kB, for 2.5rPr10.7 kbar, mm is approximately proportional to Vcore. On the other hand, considering DE/kB and mm obtained at different pressures (Fig. 17 (c)), one finds that they are quite proportional over the entire pressure region, showing that they have a similar dependence on P. In other words, the change of DE/kB and mm with P has most probably the same physical origin related to the change of the number of Fe3 + ions constituting the core against P. As explained in Section 3, Tp, TB, DE, mm, and Vcore exhibited similar pressure dependence. First, mm is connected with Vcore as shown in Fig. 17 (b). Second, DE is expressed as a function of Vcore as Eq. (8). Finally, Tp is intrinsically the same as TB, and they are connected with DE. Thus, all physical quantities listed above are connected each other, suggesting that a down-and-up fluctuation of the number of Fe3 + ions constituting the core.
5. Conclusion
Fig. 17. (a) Anisotropy energy barrier DE/kB as a function of Vcore and Vparticle for maghemite nanoparticles with D = 5.1 nm. Solid line represents the best linear fitting against DE/kB vs Vcore and dotted line its extrapolation for Vcore = 0 for 2.5 rP r 10.7 kbar. (b) The medium value of the core magnetic moment mm as a function of Vcore and Vparticle for maghemite nanoparticles with D = 5.1 nm. Solid line represents the best linear fitting against mm vs Vcore for 2.5 rP r 10.7 kbar. (c) DE/kB as a function of mm for maghemite nanoparticles with D =5.1 nm. Solid line represents the best linear fitting.
Here, Kcore is the effective anisotropy constant per unit volume of the core, and S is the surface area of the particle. From the slope of the curve for 2.5rP r10.7 kbar and Kcore = 7.7 105 erg/cm3. This value is between that found for the magnetocrystalline anisotropy (K1) of single-domain particle of maghemite by ferromagnetic
The effects of pressure on the g phase of Fe2O3 (maghemite) nanoparticles with a diameter of 5.1 and 12.8 nm were studied through magnetic measurements and powder X-ray diffraction (XRD) measurements. An experimental data series revealed that the anisotropy energy barrier DE/kB and the effective value of the magnetic moment of the core decrease against the initial pressure (P r3.8 kbar), recovering at P Z3.8 kbar. This was interpreted as a pressure-induced down-and-up fluctuation of the number of Fe3 + ions constituting the core. These experimental findings indicate that the core/shell structure of nanoparticles with vacancy site is unstable against external stress, and under high pressure, the core can be restructured. For 2.5rPr10.7 kbar, DE/kB is approximately proportional to the volume associated to the ordered fraction of the nanoparticles as seen from XRD, Vcore. From this dependence it is possible to separate the core/shell contribution to DE/kB and estimate core and surface anisotropy constants, with the core one being of the order of magnetocrystaline anisotropy of maghemite. In this view, applying pressure constitutes an elegant way of changing the core/shell ratio in an identical system in order to separate core from surface anisotropy.
Acknowledgments This work in Japan was supported by the CREST project of the Japan Science and Technology Agency (JST) and a Grant-in-Aid for Young Scientists (B) (19750118) from the MEXT of Japan. The work in Zaragoza has been supported by the research grants MAT2007-61621 and CSD2007-00010 from the Ministry of Education. The Aveiro-Zaragoza collaboration has been supported by the Integrated Spanish-Portuguese Action PT2009-0131. N. J. O. Silva acknowledges CSIC for an I3P contract and FCT for a Ciencia
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2008 contract. The authors are grateful to Angel Larrea for his help with EM observations. References [1] C.M. Sorensen, in: Kenneth J. Klabunde (Ed.), Nanoscale Materials in Chemistry, Wiley Interscience, New York, 2001. [2] J.L. Dormann, D. Fiorani (Eds.), Magnetic Properties of Fine Particles, NorthHolland, Amsterdam, 1992. [3] M.F. Hansen, S. Mørup, J. Mag. Mag. Mater. 184 (1998) 262. [4] D.K. Kim, Y. Zhang, W. Voit, K.V. Rao, J. Kehr, B. Bjelke, M. Muhammed, Scripta Mater. 44 (2001) 1713. [5] Q.A. Pankhurst, J. Connolly, S.K. Jones, J. Dobson, J. Phys. D: Appl. Phys. 36 (2003) R167. [6] O. Ozdemir, S.K. Banerjee, Geophys. Res. Lett. 11 (1984) 161. [7] A.N. Shmakov, G.N. Kryukova, S.V. Tsybulya, A.L. Chuvilin, L.P. Solovyeva, J. Appl. Cryst. 28 (1995) 141. [8] Z. Somogyva´ri, E. Sva´b, G. Me´sza´ros, K. Krezhov, I. Nedkov, I. Sajo, F. Boure´e, Appl. Phys. A 74 (2002) S1077 [Suppl.]. [9] M.P. Morales, S. Veintemillas-Verdaguer, M.I. Montero, C.J. Serna, A. Roig, Ll. Cassas, B. Martinez, F. Sandiumenge, Chem. Mater. 11 (1999) 3058. [10] S. Veintemillas-Verdaguer, O. Bomati-Miguel, M.P. Morales, Scripta Mater. 47 (2002) 589. [11] J.M.D. Coey, Phys. Rev. Lett. 27 (1971) 1140. [12] P.V. Hendriksen, F. Bødker, S. Linderoth, S. Wells, S. Mørup, J. Phys.: Condens. Matter 6 (1994) 3081. [13] P.V. Hendriksen, S. Linderoth, C.A. Oxborrow, S. Mørup, J. Phys.: Condens. Matter 6 (1994) 3091. [14] S. Linderoth, P.V. Hendriksen, F. Bødker, S. Wells, K. Davies, S.W. Charles, S. Mørup, J. Appl. Phys. 75 (1994) 6583.
[15] D. Lin, A.C. Nunes, C.F. Majkrzak, A.E. Berkowitz, J. Mag. Mag. Mater. 145 (1995) 343. [16] B. Martı´nez, X. Obradors, Ll. Balcells, A. Rouanet, C. Monty, Phys. Rev. Lett. 80 (1998) 181. [17] A. Milla´n, A. Urtizberea, N.J.O. Silva, F. Palacio, V.S. Amaral, E. Snoeck, V. Serin, J. Mag. Mag. Mater. 312 (2007) L5. [18] Y. Komorida, M. Mito, H. Deguchi, S. Takagi, A. Milla´n, F. Palacio, J. Mag. Mag. Mater 310 (2007) e800. [19] Y. Komorida, M. Mito, H. Deguchi, S. Takagi, A. Milla´n, N.J.O. Silva, F. Palacio, Appl. Phys. Lett. 94 (2009) 202503. [20] M. Mito, J. Phys., Soc. Jpn. Suppl. A 76 (2007) 182. [21] L.D. Jennings, C.A. Swenson, Phys. Rev. 112 (1958) 31. [22] A. Fujiwara, K. Ishii, T. Watanuki, H. Suematsu, H. Nakao, K. Ohwada, Y. Fujii, Y. Murakami, T. Mori, H. Kawada, T. Kikegara, O. Shimomura, T. Matsubara, H. Hanabusa, S. Daicho, S. Kitamura, C. Katayama, J. Appl. Crystallogr. 33 (2000) 1241. [23] G.J. Piermarini, S. Block, J.D. Barnett, R.A. Forman, J. Appl. Phys. 46 (1975) 2774. [24] E.F. Ferrari, F.C.S. da Silva, M. Knobel, Phys. Rev. B 56 (1997) 6086. [25] N.J.O. Silva, V.S. Amaral, L.D. Carlos, Phys. Rev. B 71 (2005) 184408. [26] P. Weiss, R. Forrer, Ann. Phys. 12 (1929) 279. [27] Z. Wang, S.K. Saxena, Solid State Commun. 123 (2002) 195. [28] E.P. Valstyn, J.P. Hanton, A.H. Morrish, Phys. Rev. 128 (1962) 2078. ˜ o, C.J. Serna, J. Appl. Phys. [29] B. Martı´nez, A. Roig, E. Molins, T. Gonza´lez-Carren 83 (1998) 3256. [30] E. Tronc, A. Ezzir, R. Cherkaoui, C. Chane´ac, M. Nogue s, H. Kachkachi, D. Fiorani, A.M. Testa, J.M. Grene che, J.P. Jolivet, J. Mag. Mag. Mater. 221 (2000) 63. [31] N. Pe´rez, P. Guardia, A.G. Roca, M.P. Morales, C.J. Serna, O. Iglesias, F. Bartolome´, L.M. Garcı´a, X. Batlle, A. Labarta, Nanotechnology 19 (2008) 475704. [32] F. Luis, J.M. Torres, L.M. Garcı´a, J. Bartolome´, J. Stankiewicz, F. Petroff, F. Fettar, J.-L. Maurice, A. Vaure s, Phys. Rev. B 65 (2002) 094409.
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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Effects of pressure on maghemite nanoparticles with a core/shell structure Y. Komorida a,n, M. Mito a, H. Deguchi a, S. Takagi a, T. Tajiri b, A. Milla´n c, N.J.O. Silva d, M.A. Laguna c, F. Palacio c a
Faculty of Engineering, Kyushu Institute of Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu 804-8550, Japan Faculty of Science, Fukuoka University, Fukuoka 814-0180, Japan c ´n, CSIC-Universidad de Zaragoza, Zaragoza 50009, Spain Instituto de Ciencia de Materiales de Arago d CICECO, Universidade de Aveiro, Aveiro 3810-193, Portugal b
a r t i c l e in fo
abstract
Article history: Received 17 April 2009 Received in revised form 29 January 2010 Available online 4 February 2010
The magnetic property and intraparticle structure of the g phase of Fe2O3 (maghemite) nanoparticles with a diameter (D) of 5.1 7 0.5 nm were investigated through AC and DC magnetic measurements and powder X-ray diffraction (XRD) measurements at pressures (P) up to 27.7 kbar. Maghemite originally exhibits ferrimagnetic ordering below 918 K, and has an inverse-spinel structure with vacancies. Maghemite nanoparticles studied here consist of a core with structural periodicity and a disordered shell without the periodicity, and core shows superparamagnetism. The DC and AC susceptibilities reveal that the anisotropy energy barrier (DE/kB) and the effective value of the core moment decrease against the initial pressure (P r 3.8 kbar), recovering at P Z 3.8 kbar. The change of DE/kB with P is qualitatively identical with that of the core moment, suggesting a down-and-up fluctuation of the number of Fe3 + ions constituting the core at the pressure threshold of about 4 kbar. This phenomenon was confirmed by the analysis of the XRD measurement using Scherrer’s formula. The core volume decreased for P r 2.5 kbar, whereas at higher pressure the core was restructured. For 2.5 r P r 10.7 kbar, the volume shrinkage of particle hardly occurs. There, DE/kB is approximately proportional to the volume associated to the ordered fraction of the nanoparticles as seen from XRD, Vcore. From this dependence it is possible to separate the core/shell contribution to DE/kB and estimate core and surface anisotropy constants. As for the structural experiments, similar experimental data have been obtained for D= 12.8 7 3.2 nm as well. & 2010 Elsevier B.V. All rights reserved.
Keywords: Pressure effect Nanoparticle Core/shell structure Maghemite Superparamagnetism
1. Introduction The study on magnetic properties of nanoparticles is one of the most active research areas in condensed matter physics from the viewpoints of both fundamental science and industrial application. When the particle size reaches the nano-meter scale, superparamagnetism appears due to single-domain formation [1,2]. The magnetically active state of this minuscule domain let one expects that it is possible to apply it to high-bit information storage devices. Physically, the effect of surface in nanoparticle is quite interesting. The structural defects in the surface can bring about complex magnetic behavior, and the influence of the defects is more remarkable than in bulk systems. On the other hand, interparticle interaction via the spins of the surface also affects the magnetic properties [3]. The understanding of these basic physical properties of magnetic nanoparticles is quite
n
Corresponding author. Tel./fax: + 81 93 884 3286. E-mail addresses: [email protected] (Y. Komorida), [email protected] (M. Mito). 0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2010.01.044
important for the development of nano-science and advanced technologies. Iron oxide nanoparticles have already been also used in several biomedical fields like magnetic resonance imaging, hyperthermiatargeted drug delivery and tissue engineering [4,5]. Among iron oxides, the g phase of Fe2O3 (maghemite) is one of the most attractive materials for industrial application because of its chemical stability. Maghemite originally exhibits ferrimagnetic ordering below 918 K [6]. The basic structure of bulk maghemite is the inverse-spinel structure with some vacant sites, and possesses cubic symmetry (P4332) with a lattice constant of a= 8.34 A˚ [7,8]. However, the recent structural study on the highpurity crystal has revealed that the ordered vacancies on the octahedral positions form the tetragonal superlattice (space group P41212) [7,8]. In the case of maghemite, the existence of these vacancies strongly influences the generation of the spontaneous magnetization. Especially in nanoparticles with many surface molecules, the effect becomes considerable, and the magnetic properties are indeed dependent on the synthesis method [9,10]. In the present study, both core and shell in maghemite nanoparticles are modified by pressurization. Here, let us briefly
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describe the ‘‘core/shell structure’’ of ferrimagnetic nanoparticles. The central part, i.e., the core, has structural periodicity, and can maintain spontaneous magnetization. The core with nano-meter size brings about superparamagnetism. In contrast, the surface region, i.e., the shell, has no structural periodicity. The core-shell model is an approximation that, however, has been successfully used to model the magnetic properties of nanoparticles [11–15]. Most of the net moment of the entire particle usually originates from the moment of the core. The surface shell is treated as a disordered layer like spin glasses [16], and is analyzed as paramagnetic or antiferromagnetic component in the data of magnetization curve [17]. The magnetic interaction between the core and the shell can appear as an exchange bias effect. In the frame of this core-shell model, the magnetic behavior of maghemite nanoparticle systems is well understood [17]. Milla´n et al. [17] have reported that the shell thickness is independent of the particle size, and is estimated to be about 1 nm, through the analysis of magnetization curve data of maghemite nanoparticles with size ranging from 2 to 15 nm. In the present study, we systematically investigate the magnetic properties of this prototype magnetic nanoparticle by applying pressure. Pressurization is expected to continuously shrink and tune the defects, and occasionally restructure the system. We have already reported the preliminary results for maghemite nanoparticles with a diameter (D) of 6.570.65 nm, and there confirmed the changes in the magnetic properties under pressure [18]. Recently, we proposed a method for estimating the anisotropy constants for both core and surface via hydrostatic pressure response on maghemite nanoparticles with D= 5.170.5 nm [19]. In this paper, we report in more detail the effects of hydrostatic pressure on both the magnetic properties and the intraparticle structure in maghemite nanoparticles with D= 5.170.5 nm, according to magnetic measurements and structural analyses. As for the structural studies, the experimental data for D= 12.873.2 nm are also presented, in order to show that the pressure response in the nano-size level is independent of the particle size.
2. Experimental The two kinds of maghemite nanoparticles used in this study were prepared by a procedure mentioned elsewhere [17], in which the nanoparticles were grown within an organic polymeric matrix of polyvinylpyridine (PVP) that coats the particles and prevents aggregation. These transmission electron microscopy (TEM) images and size distributions are given in Fig. 1. The particle size analysis performed on TEM images over more than 200 particles yielded D= 5.170.5 and D= 12.873.2 nm, respectively. The samples are annealed at 200 1C (D= 5.1 nm) and 250 1C (D= 12.8 nm), respectively. The nominal values of maghemite content in the samples are estimated to be 16.4 wt% (D=5.1 nm) and 52.9 wt% (D=12.8 nm). The AC and DC magnetic measurements were performed using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design, MPMS-5S) in the temperature (T) range of 5 KrTr80 K. Pressure was attained using a piston cylinder cell (CR-PSC-KY05-1, Kyowa-Seisakusho Co., Ltd.), which can be inserted into the SQUID magnetometer [20]. The pressure cell was made of a non-magnetic Cu–Be alloy. In order to apply pressure effectively, the sample was held inside the teflon cell with the aid of a pressure-transmitting medium, Apiezon-J oil, and a small amount of metallic superconductor tin. The pressures at liquidhelium temperature were estimated based on the shift in the superconducting transition temperature of tin [21]. Synchrotron radiation powder X-ray diffraction (XRD) measurements were performed at pressures up to 33.6 kbar using a
Fig. 1. TEM images and size distributions of maghemite nanoparticles with a diameter of 5.1 (a) and 12.8 nm (b). The size distribution was investigated for sampling of more than 200 particles.
cylindrical imaging plate (IP) diffractometer (Rigaku Co.) at the Photon Factory (PF) of the Institute of Materials Structure Science, the High Energy Accelerator Research Organization (KEK) [22]. All of the measurements were carried out at room temperature. The ˚ Pressurizawavelength of the incident X-ray l was 0.6883(1) A. tion was done by the use of a diamond anvil cell (DAC) with a Be backing plate, on which diamond anvils with 0.8 mm flat tips were mounted. Between the anvils, a 0.3-mm-thick Cu–Be gasket was inserted. In the sample hole with a diameter of 0.4 mm, located in the center of the gasket, the crystalline sample and a few ruby crystals were held with the aid of a pressuretransmitting medium, fluorine oil (FC77). The pressure value was calibrated by the ruby fluorescence method [23], and the
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0.28
estimated value of pressure involves the measurement error of 70.8 kbar.
0.025 P = 0 kbar
0.24
0.02
0.2
0.015
0.16
0.01
3. Experimental results
The magnetic properties of maghemite nanoparticles with D= 5.1 nm were investigated through the following three magnetic measurements: (1) zero-field-cooled (ZFC) and field-cooled (FC, from T= 80 K and H=200 Oe) DC magnetization measurements, and (2) AC susceptibility measurement and (3) magnetization curve measurement at T= 5 K. In the AC measurement, the frequency range of the AC exciting field was 1–100 Hz, and the field amplitude was 2.0 Oe. The magnetization curve at T=5 K was measured at DC magnetic fields of up to 50 kOe and at pressures of up to 14.3 kbar. The magnetic data for (1) and (2) in Figs. 2–4 were evaluated with the unit mass of the sample (maghemite+PVP), whereas only the data for (3) in Fig. 7 were done with the unit mass of maghemite. 3.1.1. DC magnetic susceptibility Fig. 2 shows the temperature dependence of the ZFC and FC magnetization (M) under pressure for maghemite nanoparticles with D= 5.1 nm. The arrows indicate the peak positions of ZFC magnetization (Tp). The value of Tp at ambient pressure was estimated to be 12.3 70.5 K. At P= 3.8 kbar, the Tp decreased to 11.2 70.5 K. However, further pressurization brings about the increase of the Tp, following an unexpected down-and-up fluctuation. Fig. 3 shows the temperature dependence of the deviation between the FC and ZFC magnetizations shown in Fig. (2), DMFC–ZFC(T), at several pressures. The data for DMFC–ZFC(T) tell us the temperature region of thermal irreversibility. The DMFC–ZFC
MFC-ZFC (emu/g)
3.1. Magnetic properties
2119
3.8 kbar 5.2 kbar 8.2 kbar 13.9 kbar 14.3 kbar
0.005
0.12
0 20
0.08
25
30
35
40
0.04
0
0
10
20
30
40
50
T (K) Fig. 3. Temperature dependence of the deviation between the ZFC and the FC magnetizations, DMFC–ZFC, at several pressures for maghemite nanoparticles with D =5.1 nm. The inset shows an enlargement of the rectangular area.
at ambient pressure rapidly increased by decreasing temperature below 30 K. When a pressure of 3.8 kbar was applied, the overall behavior of DMFC–ZFC(T) curve shifted towards the lower temperature side. Thereafter, upon further pressurization, it shifted towards the higher temperature side. The pressure dependence of DMFC–ZFC(T) is consistent with the change in Tp. The above characteristic pressure dependencies (the down-and-up fluctuation of Tp and MFC–ZFC(T)) have already been observed in maghemite nanoparticles with D=6.5 nm [18].
0.6 3.1.2. AC magnetic susceptibility Fig. 4 shows the temperature dependence of the out-of-phase component of the AC magnetic susceptibility, w’’, for f=1 Hz (a) and 10 Hz (b). The peak position allows us to determine the temperature of magnetic freezing, the so-called ‘‘blocking temperature’’ (TB). The insets of Fig. 4 show the temperature dependence of the data around TB. The arrows represent the positions of TB under each pressure. The pressure dependencies of TB at f =1 and 10 Hz are plotted in Fig. 5, showing good consistency with the results for Tp and DMFC–ZFC(T) mentioned above. The frequency dependence of TB at each pressure was analyzed using the Arrhe´nius plot, as shown in Fig. 6. Here, the effective energy barrier, DE, between the spin-up and spin-down states can be estimated using the following equation:
0.5
M (emu/g)
0.4
0.3
0.2
P ==00kbar kbar 3.8 kbar 5.2 kbar
0.1
1 kB lnð2pf Þ þlnðt0 Þ ; ¼ DE TB
8.2 kbar 14.3 kbar
0
10
100 T (K)
Fig. 2. Temperature dependence of the zero-field-cooled (ZFC, open symbols) and field-cooled (FC cooling from T= 80 K at H = 200 Oe, solid lines) magnetization under various pressures for maghemite nanoparticles with D = 5.1 nm. The arrows indicate the peak position of the ZFC magnetization at each pressure. The base line for each data in the pressure range of 3.8–14.3 kbar was shifted at an interval of 0.05 emu/g so as to guide the eye.
ð1Þ
where kB is the Boltzmann constant, and t0 is a pre-exponential factor. The solid lines show the fitting using Eq. (1), and DE/kB was estimated from the inverse of the slope. The inset of Fig. 6 shows the pressure dependence of DE/kB, which is also qualitatively consistent with the results series for Tp, DMFC–ZFC and TB. At ambient pressure, the value of DE/kB was estimated to be 378 K. At P= 3.8 kbar, the value of DE/kB decreased to 88.7% of the initial value. At P=14.3 kbar, it increased to 111% of the initial value. Thus, quantitative analyses on the TB and DE/kB reveal that the effective energy barrier DE is reduced and thereafter enhanced.
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18
0.00038
0.0004
f = 1 Hz 10 Hz
17 0.00034
16 0.0003
0.0002 P = 0 kbar 3.8 kbar 5.2 kbar 8.2 kbar 13.9 kbar 14.3 kbar
0.0001
0
8
0
10
20
30
TB (K)
χ" (emu/g)
0.0003
10 12 14 16 18 20
15
f = 1 Hz 14
13
40 50 T (K)
60
70
80
12 0
5
10
Fig. 5. Pressure dependence of the blocking temperature (TB) at f= 1 and 10 Hz for maghemite nanoparticles with D = 5.1 nm. The solid curves are visual guides.
0.0005
0.0006
0.08
0.0004
P = 0 kbar 3.8 kbar kbar 5.2 kbar kbar 8.2 kbar kbar 13.9 kbar 13.9 kbar 14.3 kbar 14.3 kbar
0.0005 0.0003
8 10 12 14 16 18 20 22 24 26 28 30
0.07
f = 10 Hz 0.0003 P = 0 kbar 3.8 kbar 5.2 kbar 8.2 kbar 13.9 kbar 14.3 kbar
0.0001
0
10
20
30
0.06
40 50 T (K)
60
70
0.05
3.1.3. Magnetization curve Fig. 7 shows the magnetization curve in unit mass of maghemite for P= 0 (a) and 14.3 (b) kbar at T= 5 K (open circles), which is sufficiently below TB. The field dependence is expressed as the summation of saturation and linear-like contributions. Thus, the magnetization curve up to 50 kOe was analyzed by the use of a modified Langevin equation with the linear term against the magnetic field, H, as follows: 1 ð2Þ þ wshell H ; M ¼ N mcore cothx x mcore H ; kB T
400
300
200
80
Fig. 4. Temperature dependence of the out-of-phase component of the AC susceptibility, w’’, at f= 1 (a) and 10 Hz (b) for maghemite nanoparticles with D = 5.1 nm. The pressure range is the same as that of Fig. 3. The inset shows an enlargement of the rectangular area. The arrows indicate the blocking temperature (TB) at each pressure. The solid curve is a visual guide.
x¼
500
ΔE/k (K)
0.0002
0
1/TB (1/K)
χ" (emu/g)
0.0004
15
P (kbar)
0.0006
ð3Þ
where N is the particle number, and mcore is the magnetic moment of the core. In the frame of the core-shell model, the first and second terms on the right side of Eq. (2) correspond to the superparamagnetic core and shell contributions, respectively. The
1
0
5
2
10 P (kbar)
3
15
4
5
6
7
ln(2πf ) Fig. 6. Arrhe´nius plots of the inverse blocking temperature (1/TB) as a function of the frequency at various pressures for maghemite nanoparticles with D =5.1 nm. The solid line expresses Eq. (1) at each pressure. The inset shows the pressure dependence of the energy barrier (DE/kB), which is obtained from the slope of the Arrhe´nius plot. The solid curve is a visual guide.
shell contribution is modeled with high field susceptibility per one particle wshell, and the paramagnetic or antiferromagnetic behavior appears as the linear field dependence. The data analyses using Eqs. (2) and (3) did not fit the data with sufficient accuracy especially at low magnetic field. Thus we considered that the distribution of the magnetic moment of the core based on the size distribution (see Fig. 1 (a)) [24,25]. In low magnetic field, the size distribution of the shell is not so important because of the field dependence, whereas that of the core gives significant influence on magnetization development. Here, the experimental data were reproduced with the following equation, Z 1 ð4Þ f ðmcore Þdmcore þ wshell H ; M¼N mcore coth x x
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Fraction (%)
6 4 2 0
0
2 8 10 12 14 6 4 mcore (x10-18 emu/particle)
0
2 8 10 12 14 6 4 mcore (x10-18 emu/particle)
Fraction (%)
6
4
2
0
Fig. 7. Magnetization curve for magnetic fields up to 50 kOe of maghemite nanoparticles with D =5.1 nm at T= 5 K for P= 0 and 14.3 kbar. The value of M is evaluated with the unit mass of maghemite. The open circles represent the experimental data. The solid curve (a) represents the modified Langevin function Eqs. (4) and (5). The solid curve (b) shows the core contribution, which corresponds to the first term of the right side of Eq. (4), while a solid line (c) shows the shell contribution, which corresponds to the second term. The inset shows the distribution of the magnetic moment of the core (mcore), determined by the lognormal fit (solid red curve).
where, f(mcore) denotes a lognormal distribution function of mcore ( ) 1 ðln mcore =mm Þ2 : ð5Þ f ðmcore Þ ¼ pffiffiffiffiffiffi exp 2s2 2psmcore Here, mm is the medium value of the magnetic moment of the core, and s is the standard deviation of the distribution of log (mcore). The insets of Fig. 7 show the distribution of mcore with a lognormal type of distribution symmetry, used in analyzing the data for P= 0 and 14.3 kbar. In order to simplify the analysis procedure, the distribution of Eq. (5) was reproduced in the actual analysis with a discrete distribution divided into 60 parts. The solid line (b) expresses the first term of Eq. (4), while the solid line (c) expresses the second. The solid curve (a) shows the fitting data using the modified Langevin function Eqs. (4) and (5). For fitting parameters such as N= 5.68 1018 particles/g-Fe2O3, wshell =2.96 10-22 emu/particle (g-Fe2O3), mm =2.91 10 18 emu/ particle (g-Fe2O3) and s =0.60, we see a good agreement between the experimental data at ambient pressure and the modified Langevin function Eqs. (4) and (5). Bulk maghemite has the magnetic moment of 17.36 mB per unit cell [26]. Based on this reference value, the present value of (g-Fe2O3) (= 3.14 102 mB/particle 2.91 10 18 emu/particle (g-Fe2O3)) corresponds to the moment of maghemite nanoparticles with the diameter of the core, Dcore = 2.7 nm. This suggests the
Fig. 8. Pressure dependencies of the medium value of the magnetic moment of the core (mm) and the magnetic susceptibility of the shell contribution (wshell) for maghemite nanoparticles with D = 5.1 nm.
existence of a shell with thickness of 1.2 nm for the particle size of D=5.1 nm. The present analytic result is consistent with the previous report by Milla´n et al. [17]. Herein the values of mm and wshell obtained by fitting the magnetization curve are shown in Fig. 8. In the analysis of the data under pressure, the value of N was fixed, and s hardly changed. When pressure was applied, mm decreased temporarily at the initial pressure, and reached a minimum at around 4 kbar. At P44 kbar, mm continued to increase with pressure in a linear fashion. The pressure dependence of wshell showed a behavior contrary to that of mm. The change of wshell per a particle surely reflects a change in the number of Fe3 + ions constituting the shell, and there is the change of up-and-down. Namely, the spatial region of the core is temporarily shrunk at PoPC ( 4 kbar), whereas at P4PC, the core region is re-stabilized due to restructuring. This suggests that the nanoparticle structure is quite sensitive to external stress. In order to obtain direct information on the intraparticle structural changes, we performed the XRD experiments under pressure at room temperature. 3.2. X-ray diffraction (XRD) measurements Synchrotron radiation powder X-ray diffraction (XRD) measurements of maghemite nanoparticles with D=5.1 nm were performed at pressures of up to 27.7 kbar. So as to confirm that the pressure response obtained for D= 5.1 nm is also unique for D410 nm, the data for D=12.8 nm are also presented. Fig. 9 shows the XRD patterns of maghemite nanoparticles with D= 5.1 and 12.8 nm. These diffraction patterns are consistent with the Rietveld simulation based on the space group P4332 with a= 8.34 A˚ (labeled with (a)). It reveals that vacancy sites are not ordered in the present magnetic nanoparticles. The intensities of these patterns were not perfectly reproduced by the Rietveld simulation especially around 2y = 161, owing to the broadening effects of the nano-scale size. The Rietveld simulation could not be an effective analytic approach, even if the effective backgrounds (b) and (c) are assumed. Fig. 10 shows the XRD patterns for P= 0 (a), 2.5 (b), 8.5 (c) and 14.8 kbar (d) as representative data for maghemite nanoparticles with D= 5.1 nm. In the experimental data shown in Fig. 10, the
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Fig. 9. X-ray diffraction (XRD) patterns of maghemite nanoparticles with D = 5.1 and 12.8 nm at room temperature and ambient pressure. The open circles and squares represent the experimental data for D =5.1 and 12.8 nm, respectively. The dotted curve (a) is the result of a simulation based on the bulk structure. The dotted curves (b) and (c) represent the assumed background data resulting from the fluorine oil and diamond anvils for D =5.1 and 12.8 nm, respectively.
contribution of the background, including the diamond anvils and FC77 (see Fig. 9), was subtracted. At first, the data for 2y =12–181 at P =0 kbar (a) are reproduced by the summation of seven diffraction peaks with Lorentzian shape, based on P4332. The diffraction pattern around 2y = 161 was well fitted with the summation of three Lorentzians with the plane indices (3 1 0), (3 1 1) and (2 2 2). Given these situation, using both the diffraction peak angle on the dominant diffraction peak (3 1 1) and the full-width at halfmaximum (FWHM) of the diffraction peak, the lattice constant (a) of the cubic lattice and the particle size of the core, Dcore, were estimated. The Dcore was calculated from the values of the FWHM and the diffraction peak angle using the Scherrer’s formula, as follows: Dcore ¼
0:9l ; bcosy
ð6Þ
where b is the FWHM of the diffraction peak expressed in radians, and y is the diffraction peak angle. At ambient pressure, Dcore was estimated to be 3.8 nm. Then, the thickness of the shell was calculated to be about 0.65 nm for D= 5.1 nm. Dcore =3.8 nm from the XRD measurement is slightly larger than Dcore = 2.7 nm estimated by the magnetic measurement. The above two estimated values are derived from independent physical measurements, nevertheless they are not so far each other. We think that the deviation is explained with that the entire core with the structural periodicity may not have the perfect magnetic order. Fig. 11 shows the pressure dependencies of the diameter of the core Dcore estimated from the XRD measurement and the lattice constant (a) of the cubic lattice for the maghemite nanoparticles with D=5.1 nm. The Dcore estimated from XRD measurement reached a minimum at around 2.5 kbar, and the qualitative behavior was consistent with those of the magnetic data such as MFC–ZFC(T), Tp, TB, DE and mm. As for the lattice constant of the cubic lattice, the lattice shrinkage tended to saturate in the pressure region of 2.5–10.7 kbar. At pressures above 10.7 kbar, the lattice shrinkage restarted. This
Fig. 10. XRD patterns of maghemite nanoparticles with D = 5.1 nm at room temperature for P = 0 (a), 2.5 (b), 8.5 (c) and 14.8 kbar (d). The open squares represent the experimental data. The data for 2y = 12–181 at P = 0 kbar (a) could be reproduced by the summation of seven diffraction peaks with Lorentzian shape, based on P4332. The diffraction pattern around 2y = 161 was fitted using the sum of three Lorentzians (red solid curve). The diffraction peaks of (3 1 0) and (2 2 2) are reproduced by the green solid curves, while that of (3 1 1) is reproduced by the blue solid curve. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
successive shrinkage for P410.7 kbar surely corresponds to the restructuring of the particle. After the 27.7 kbar pressure was released, the diffraction pattern almost recovered to that of the initial state, and, within the considered pressure region, the elasticity of maghemite nanoparticle remained intact. Fig. 12 shows the pressure dependencies of the volume of the entire nanoparticle and that of the core. In the shell region, the unit cell cannot be defined, because the shell region does not have the structural periodicity. Here, we suppose that the shrinkage ratio of the shell should be equal to that of the core under pressure, since the intrinsic composition is uniform over the entire particle. Under pressure, the particle volume, Vparticle, was calculated based on the following assumption: the initial particle
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Fig. 11. Pressure dependencies of the diameter of the core, Dcore, and the lattice constant a of the cubic lattice for maghemite nanoparticles with D =5.1 nm.
Fig. 13. XRD patterns of maghemite nanoparticles with D = 12.8 nm at room temperature for P =0 (a), 3.3 (b), 12.3 (c) and 33.6 kbar (d). The open squares represent the experimental data. The data for 2y = 12–181 at P = 0 kbar (a) could be reproduced by the summation of seven diffraction peaks with Lorentzian shape, based on P4332. The diffraction pattern around 2y = 161 was fitted by using the sum of three Lorentzians (red solid curve). The diffraction peaks of (3 1 0) and (2 2 2) are reproduced by the green solid curves, while that of (3 1 1) is reproduced by the blue solid curve. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 12. Pressure dependencies of the volume of the entire nanoparticle, Vparticle, and that of the core, Vcore, for maghemite nanoparticles with D =5.1 nm.
diameter, D, is 5.1 nm, and the shrinkage ratio of the entire nanoparticle is the same as that of the unit cell in the core under pressure. The core volume Vcore was calculated using the diameter of the core, Dcore. The residual volume after subtracting the core volume from the particle volume at each pressure corresponded to the volume of the shell, Vshell ( =Vparticle Vcore). Vcore reached a minimum at 2.5 kbar, and thereafter increased with increasing pressure. At P= 2.5 kbar, Vcore was reduced to almost half of the initial volume, and the decrease ratio was much larger than that of Vparticle. This suggests that the ratio of the core region against the particle temporarily became quite small under pressure. For D=12.8 nm, the data corresponding to Figs. 10–12 for D= 5.1 nm are presented in Figs. 13–15, respectively. The essential pressure response was similar to that for D= 5.1 nm. Fig. 16 shows the ratios of Vcore, and Vshell, to Vparticle, under pressure for both
Fig. 14. Pressure dependencies of the diameter of the core, Dcore, and the lattice constant a of the cubic lattice for maghemite nanoparticles with D= 12.8 nm.
D=5.1 and 12.8 nm. Indeed, these ratios, Vcore/Vparticle and Vshell/ Vparticle, are the same as the ratios of the number of Fe3 + ions constituting the core and shell to that constituting the entire particle. In particular for D=5.1 nm, the number of Fe3 + ions
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constituting the core, Ncore, was reduced to a half of the initial value at 2.5 kbar, and increased at pressures above 2.5 kbar. Finally, Ncore at P= 27.7 kbar exceeded the initial value in the case of D= 5.1 nm. These results indicate that the core is eroded by the shell under small stress, and the region without structural periodicity is enlarged. However, the larger stress saturates the particle shrinkage, and thereafter the core region is restructured and stabilized. Our series of magnetic measurement results are well explained by the change in Ncore, estimated through XRD measurements. In the maghemite nanoparticles with D= 25 nm, a Raman spectroscopic study has been already done in the pressure range up to 57.5 GPa [27], and it has been reported that the g phase transforms to the a phase at P= 13.5 GPa. The stability of g-phase seen in the present experiment is consistent with the above Raman spectroscopy.
Fig. 15. Pressure dependencies of the volume of the entire nanoparticle, Vparticle, and that of the core, Vcore, for maghemite nanoparticles with D =12.8 nm.
4. Discussion In principle, changes in magnetic properties observed with the application of pressure may be attributed to interparticle and/or intraparticle effects. In the case of interparticle effects, dipolar interactions are more plausible than exchange ones, since the nanoparticles are coated with polymer. In a regular array of identical dipoles, the transition temperature associated to dipolar interactions is given by [3] Td ¼
a0 m0 m2 4pkB d3
ð7Þ
with a0 being of the order of 1–10, m0 is the magnetic permeability of vacuum, m is the magnetic moment, and herein corresponds to mm. d is the distance between neighboring dipoles. This expression has also been used to estimate the ordering temperature in systems of randomly distributed particles, where m and d are average values [3]. For the nanocomposite with D= 5.1 nm, considering a0 =10, d =13.8 nm (estimated from D and from the maghemite mass concentration) and mm (see Fig. 8), Td = 0.5 K at ambient pressure, which means that dipolar interactions do not play an important role in the present discussion, even considering that at the highest pressure the total volume shrinks to half. If the random field of the dipole–dipole interaction induces a glassy behavior, one can ascertain the sign based on the non-linear AC susceptibility. In the present study, at all pressures, no non-linear response was detected in the AC susceptibility measurement for D=5.1 and 12.8 nm. In this view we should focus our attention on only intraparticle effects. In ferromagnetic nanoparticles, the energy barrier is expressed as proportional to volume (V) considering an effective anisotropy constant (Keff) as DE =KeffV. This expression is also used in ferrimagnetic nanoparticles. As mentioned above, the change of Vparticle reflects intrinsic shrinkage, while Vcore does both shrinkage and change of the number of Fe3 + ions constituting the core. For 2.5rPr10.7 kbar, the shrinkage of Vparticle is small, and the change of the numbers of Fe3 + ions constituting core and shell appears dominantly. Thus, for 2.5rPr10.7 kbar, combining information of DE/kB (P) (from Fig. 6) with information of Vparticle (P) and Vcore (P) as Fig. 17(a), we find out that DE/kB is approximately proportional to Vcore (P). Then, in the core-shell model, surface anisotropy (KS) is sometimes relevant, being expressed as an extra term, such as [19]
DE ¼ Kcore Vcore þ Ks S:
ð8Þ
Fig. 16. Pressure dependence of the ratios of the core volume, Vcore, and the shell volume, Vshell, to the volume of the entire particle, Vparticle, for D =5.1 (a) and 12.8 nm (b). These ratios are the same as the ratios of Fe3 + ions constituting the core and the shell to the number of Fe3 + ions constituting the entire particle.
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resonance measurement (K1 = 2.5 105 erg/cm3) [28], and that found in maghemite nanoparticles (K1 = 3.6–6 106 erg/cm3) [29]. At the same time, DE/kB extrapolates to 246 710 K at Vcore = 0, corresponding to the energy barrier associated to the shell. Considering D(P)= 5.0 nm for 2.5rPr10.7 kbar according to Fig. 12, one can determine KS = 4.2 10 2 erg/cm2. This value is of the order of that previously found for maghemite nanoparticles (KS = 6 10 2 erg/cm2) and Fe2.93O4 nanoparticles (KS = 2.9 10 2 erg/cm2) [30,31], and about one order of magnitude lower than that found in Co nanoparticles by magnetic measurement (KS =2–3 10 1 erg/cm2) [32]. A similar analysis is made by plotting mm as a function of Vcore and Vparticle (Fig. 17 (b)). As in the case of DE/kB, for 2.5rPr10.7 kbar, mm is approximately proportional to Vcore. On the other hand, considering DE/kB and mm obtained at different pressures (Fig. 17 (c)), one finds that they are quite proportional over the entire pressure region, showing that they have a similar dependence on P. In other words, the change of DE/kB and mm with P has most probably the same physical origin related to the change of the number of Fe3 + ions constituting the core against P. As explained in Section 3, Tp, TB, DE, mm, and Vcore exhibited similar pressure dependence. First, mm is connected with Vcore as shown in Fig. 17 (b). Second, DE is expressed as a function of Vcore as Eq. (8). Finally, Tp is intrinsically the same as TB, and they are connected with DE. Thus, all physical quantities listed above are connected each other, suggesting that a down-and-up fluctuation of the number of Fe3 + ions constituting the core.
5. Conclusion
Fig. 17. (a) Anisotropy energy barrier DE/kB as a function of Vcore and Vparticle for maghemite nanoparticles with D = 5.1 nm. Solid line represents the best linear fitting against DE/kB vs Vcore and dotted line its extrapolation for Vcore = 0 for 2.5 rP r 10.7 kbar. (b) The medium value of the core magnetic moment mm as a function of Vcore and Vparticle for maghemite nanoparticles with D = 5.1 nm. Solid line represents the best linear fitting against mm vs Vcore for 2.5 rP r 10.7 kbar. (c) DE/kB as a function of mm for maghemite nanoparticles with D =5.1 nm. Solid line represents the best linear fitting.
Here, Kcore is the effective anisotropy constant per unit volume of the core, and S is the surface area of the particle. From the slope of the curve for 2.5rP r10.7 kbar and Kcore = 7.7 105 erg/cm3. This value is between that found for the magnetocrystalline anisotropy (K1) of single-domain particle of maghemite by ferromagnetic
The effects of pressure on the g phase of Fe2O3 (maghemite) nanoparticles with a diameter of 5.1 and 12.8 nm were studied through magnetic measurements and powder X-ray diffraction (XRD) measurements. An experimental data series revealed that the anisotropy energy barrier DE/kB and the effective value of the magnetic moment of the core decrease against the initial pressure (P r3.8 kbar), recovering at P Z3.8 kbar. This was interpreted as a pressure-induced down-and-up fluctuation of the number of Fe3 + ions constituting the core. These experimental findings indicate that the core/shell structure of nanoparticles with vacancy site is unstable against external stress, and under high pressure, the core can be restructured. For 2.5rPr10.7 kbar, DE/kB is approximately proportional to the volume associated to the ordered fraction of the nanoparticles as seen from XRD, Vcore. From this dependence it is possible to separate the core/shell contribution to DE/kB and estimate core and surface anisotropy constants, with the core one being of the order of magnetocrystaline anisotropy of maghemite. In this view, applying pressure constitutes an elegant way of changing the core/shell ratio in an identical system in order to separate core from surface anisotropy.
Acknowledgments This work in Japan was supported by the CREST project of the Japan Science and Technology Agency (JST) and a Grant-in-Aid for Young Scientists (B) (19750118) from the MEXT of Japan. The work in Zaragoza has been supported by the research grants MAT2007-61621 and CSD2007-00010 from the Ministry of Education. The Aveiro-Zaragoza collaboration has been supported by the Integrated Spanish-Portuguese Action PT2009-0131. N. J. O. Silva acknowledges CSIC for an I3P contract and FCT for a Ciencia
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