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Magnetic properties of maghemite nanoparticle systems: surface anisotropy and interparticle interaction effects
Physica B 320 (2002) 122–126
Magnetic properties of maghemite nanoparticle systems: surface anisotropy and interparticle interaction effects D. Fiorania,*, A.M. Testaa, F. Lucarib, F. D’Oraziob, H. Romeroc a
ICMAT-CNR, Area della Ricerca di Roma, C.P. 10, 00010 Monterotondo Stazione, Rome, Italy b Dip. to di Fisica, Universita" di L’Aquila and INFM, 67010 Coppito-L’Aquila, Italy c Depto de Fisica, Fac. De Ciencias, Universidad de Los Andes, M!erida, Venezuela
Abstract The static and dynamic magnetic properties of powders of maghemite nanoparticles with average diameter D ¼ 2:7; 4.6 and 8.7 nm have been investigated by magnetisation, AC susceptibility at variable frequency (5ono104 Hz) and . Mossbauer spectroscopy measurements. The results provide an insight into the correlation between intra-particle and inter-particle effects. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Fine particles; Maghemite
1. Introduction The surface-to-volume ratio is large in nanoparticles (e.g. for a 4 nm, approx. 40% of atoms are on the surface) and hence surface effects play an important role in determining their magnetic behaviour [1]. The electronic, structural and magnetic properties are indeed modified near and at the surface, resulting in a site-specific anisotropy, spin disorder and weakened exchange coupling. Furthermore, the coupling between the different surfaces and core spin structures can lead to the exchange anisotropy [2]. Studies of ferrite nanoparticles [2–6] have provided clear evidences of an enhanced surface anisotropy, responsible for the non-saturation of the magnetization at low temperature, high coercivity and high-field irrever*Corresponding author. Tel.: +39-6-9067-2553; fax: +39-69067-2270. E-mail address: fi[email protected] (D. Fiorani).
sibility, and have suggested the occurrence, at low temperature, of a spin-glass- or semi-spin-glasslike freezing process at the surface layer, induced by competing exchange interactions and local anisotropy. Since surface phenomena influence the magnitude of the particle moment and possibly the interparticle distance, like in powders, where adsorbed species act as spacers, they affect the actual strength of the dipolar inter-particle interaction, which can itself influence the surface properties through local energy variations. In addition, if the particles are in close contact, inter-particle exchange can develop at sufficiently low temperature through the direct involvement of surface atoms. Aiming at investigating the inter-relation between surface and inter-particle interaction effects in g-Fe2O3 nanoparticles, we have studied by magnetization, AC susceptibility at variable fre. quency (5ono104 Hz) and Mossbauer spectroscopy measurements the static and dynamic
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 0 6 5 9 - 2
D. Fiorani et al. / Physica B 320 (2002) 122–126
properties of maghemite nanoparticles with average diameter D ¼ 2:7; 4.6 and 8.7 nm in the form of powders. Previously, we had investigated the magnetic properties [7] of particles of the same size, coming from the same starting batches, dispersed in polyvinilic alcohol (PVA) at different volume concentrations (Cv ): very diluted particle dispersion (Cv E1%; inter-particle distance dE5D; ‘‘IF’’ samples), representing the reference behaviour of almost non-interacting particles; concentrated particle dispersions (Cv E20%; dE1:5D; ‘‘IN’’ samples), where dipole–dipole inter-particle interactions are relevant. Dispersed nanoparticles exhibit low temperature enhanced surface anisotropy, responsible for the non-saturation of the magnetization [6]. The dynamical properties of IF samples are well described by the superparamagnetic Ne! el–Brown model [8], whereas those of IN samples by the modified superparamagnetic model accounting for inter-particle interactions [9], predicting an increase of the single particle anisotropy energy barrier with interactions, in agreement with results of Monte Carlo simulations [10].
123
55 kOe); AC susceptibility measurements were performed at different frequencies (5ono104 Hz) and at a field amplitude hAC ¼ 1 Oe, using a commercial susceptometer.
3. Results and discussion
2. Experimental
The low-field (Ha ¼ 20 Oe) zero-field cooled (ZFC) susceptibility (wZFC ) (Fig. 1) shows a maximum at a temperature Tmax increasing with particle size (95 K for D ¼ 2:7 nm; 130 K for D ¼ 4:6 nm and E200 K for D ¼ 8:7 nm, for which the maximum is broader, indicating a larger distribution of particle size). Below Tmax the fieldcooled susceptibility (wFC ) splits from the ZFC curve and becomes almost temperature independent, as observed in spin-glass systems. On the other hand, a continuous Curie-like increase of wFC is observed for IF samples and an intermediate behaviour for IN samples. For the same particle size, wZFC decreases with increasing interparticle interactions, i.e. moving from IF to IN and to the powder sample. The real (w0 ) and imaginary (w00 ) components of the first harmonic of the AC susceptibility were
The preparation and characterisation of the materials are detailed in Ref. [6]. The samples were obtained by flocculating aqueous sols (pH=2) of g-Fe2O3 nanoparticles with average diameter D ¼ ð6/V S=pÞ1=3 ¼ 2:7; 4.6 and 8.7 nm, where /V S is the mean volume, by raising the pH up to 8 (cancelling the surface electrostatic charge), then washing and separating the precipitates by centrifuging and drying under reduced pressure. The Fe2O3 content determined by thermal analysis is 90, 95 and 95 wt% for 2.7, 4.6 and 8.7 nm, respectively, with the remaining percentage of physisorbed and chemisorbed water. The X-ray diffraction patterns are typical for the cubic (Fd3m) structure with lattice constant a=(0.83570.001) nm. TEM observations showed that the particles are roughly spheroidal with a lognormal distribution of the diameter D; whose average value is associated to the mean volume. Magnetization measurements were performed by a commercial SQUID magnetometer (Hmax ¼
Fig. 1. Zero-field and field-cooled susceptibility (H ¼ 20 Oe) vs. temperature (m: 2.7 nm; &: 4.6 nm; solid line: 8.7 nm).
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measured as a function of temperature (Fig. 2). w0 shows a sharp maximum at a frequency-dependent 0 temperature Tmax ðnÞ (e.g. for 2.7 nm particles, at 0 n ¼ 5 Hz, Tmax ¼ 97 K). For a given particle size, 0 Tmax increases with increasing interactions, e.g. for 0 2.7 nm particles, Tmax ð5 HzÞ ¼ 17 and 27 K for 0 IF and IN samples, respectively. Tmax ðnÞ is taken as the blocking temperature at which the relaxation time t equals the measuring time tm ¼ 1=n for a characteristic particle volume V ¼ R/V 2 S=/V S: The R factor, ranging between 1.1 and 1.3, is mainly determined by the width of the volume distribution [11]. From the frequency 0 dependence of Tmax ; the temperature variation of the relaxation time t was derived for 2.7 and 4.6 nm particles. This can be described neither by the Ne! el–Brown superparamagnetic model, like for IF samples, nor by the modified one, accounting for inter-particle interactions, like for IN samples [7]. t was found to diverge according to a power law, t ¼ t0 ½Tg =ðT Tg Þa ; like in collective disordered systems such as spin-glasses, with Tg corresponding to the temperature of the maximum of the ZFC susceptibility. For 2.7 nm particles, t0 ¼ 1011 s and a ¼ 7:6; for 4.6 nm
Fig. 2. Real (w0 ) and imaginary (w00 ) parts of AC susceptibility as a function of temperature at different frequencies for 2.7 nm particles.
particles, t0 ¼ 1011 s and a ¼ 7:0 [7]. The values of the critical exponent are similar to those reported for spin-glasses [12] and determined by Monte Carlo simulations. The existence of a collective glassy-like dynamics of particle moments is supported by previous observations of ageing effects in the relaxation of the ZFC magnetization [7]. For 2.7 and 4.6 nm particles, with decreasing temperature, w00 first increases in proximity of 0 Tmax ðnÞ; then shows a frequency-dependent variation, decreases rapidly below 60–50 K and finally becomes frequency independent below 40 K (Fig. 2). The results suggest that both samples enter into a different dynamical regime characterized by a strong slowing down of the dynamics. The frequency independence of w00 at low temperature is similar to the behaviour observed in spin glasses well below the freezing temperature, where the spin disorder can be considered quasi static. Such a complex temperature dependence of w00 is not observed for 8.7 nm particles, as well as in IF and IN samples of 2.7 and 4.6 nm particles, down to the lowest temperature investigated. . Mossbauer spectra are well fitted using a broad distribution of hyperfine fields Hhyp ; similar to spin-glasses [13]. On the other hand, for IF and IN samples the spectra are well interpreted in terms of a collection of up–down superparamagnetic relaxation processes with a distribution of relaxation times [6]. For 2.7 nm and 4.6 nm particles, the thermal variation of the standard deviation s of the distribution of the hyperfine field Hhyp flattens off below E60 K and that of the average /Hhyp S below E30 K, indicating an almost complete freezing of spins fluctuations below this tempera. ture. Mossbauer experiments performed on 4.6 nm particles in a field of 60 kOe, applied parallel to the g-ray direction, gave evidence that surface spins gradually freeze and finally reach a semi-spinglass-like state below 30 K [13]. Magnetisation vs. applied field measurements were performed at different temperatures. Between Tmax and 60 K the cycles are almost unhysteretic, with vanishing remanence and coercive field. Below 60 K, the loops open up with a strong increase of remanence and coercive field and the behaviour of the virgin magnetization curve
D. Fiorani et al. / Physica B 320 (2002) 122–126
changes (Fig. 3). At low temperature, for 2.7 and 4.6 nm, the magnetization does not saturate at the maximum field value, unlike for 8.7 nm particles, and the highest value M0 ðH ¼ 55 kOeÞ decreases with decreasing particle size (M0 ¼ 72; 55 and 48 emu/g for 8.7, 4.6 and 2.7 nm, respectively). The reduction of the magnetization with respect to the bulk saturation value (80 emu/g [14]) is mainly determined by surface spin canting and disorder, due to broken bonds and frustration of antiferromagnetic exchange interactions, whose effect becomes more and more important with decreasing particle size. Both the coercive field Hc and the irreversibility field Hirr (the field above which the cycle is reversible) increase with decreasing particle size, reflecting an increase of macroscopic anisotropy: at 5 K, Hc ¼ 200; 510 and 680 Oe for D ¼ 8:7; 4.6 and 2.7 nm, respectively; Hirr ¼ 2:6; 6 and 20 kOe for D ¼ 8:7; 4.6, 2.7 nm, respectively. From Hirr ; an effective anisotropy volume constant Keff can be deduced as Keff ¼ ð1=2ÞMs Hirr ; where Ms is the extrapolated value of the saturation magnetization. Keff is found to increase with decreasing size: at 5 the values are 4.7 105, 8.6 105 and 2.5 106 erg/cm3 for 8.7, 4.6 and
Fig. 3. Magnetization vs. applied field at T ¼ 5 K for 2.7 (solid line) and 4.6 (line and symbols) nm particles.
125
2.7 nm, respectively. Such values are much larger than the magnetocrystalline anisotropy constant of the bulk material (Kmc ¼ 4:7 104 erg/cm3). They are of the same order of magnitude of those obtained from the analysis of the frequency dependence of the blocking temperature on the corresponding IF samples [11], confirming the dominant contribution of the intrinsic surface anisotropy to the total anisotropy energy. For 4.6 nm particles, the deduced surface anisotropy constant is Ks ¼ Keff D=6E7:0 102 erg/cm2. This value is of the same order of magnitude as that derived by means of ferromagnetic resonance experiments on g-Fe2O3 particles of similar size [15]. Below 60 K, increasing the magnetic field, the virgin curve first crosses the loop at a sizedependent field H1 ; lies outside the cycle for a certain field range and finally enters the loop again at higher fields (Fig. 3). H1 increases with decreasing particle size: at 5 K, H1 ¼ 330; 750 and 1220 Oe for D ¼ 8:7; 4.6 and 2.7 nm, respectively. Moreover, the virgin curve shows a S shape with a change of curvature at a size-dependent characteristic field H (Fig. 4), which is found to increase with decreasing particle size: at 5 K, H ¼ 450; 1220 and 1610 Oe for D ¼ 8:7; 4.6 and 2.7 nm, respectively. With increasing temperature, the virgin magnetization curve progressively enters the loop for the whole field range and both H1 and H decrease until they vanish around 60 K (Fig. 4, inset). Such features are not observed in IF samples, in absence of inter-particle interactions, whereas are clearly observed, although weaker, in concentrated dispersion consisting of aggregates of particles (FLOC samples). An intermediate behaviour is observed for IN samples, where inter-particle interactions are much weaker. Therefore, the observed features are related to inter-particle interactions effects. The behaviour of the virgin magnetization curve indicates a high stability of the particle system against the application of the magnetic field. This should be due to the presence of short-range correlated regions of particle moments forming closed magnetic circuits, minimizing the magnetostatic energy, coherently with the decrease of the low field susceptibility with increasing inter-particle interactions. The S shape
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D. Fiorani et al. / Physica B 320 (2002) 122–126
Summarizing, the results show that the static and dynamical properties of maghemite nanoparticles in the form of powders are governed by inter-particle interactions and surface effects. Inter-particle interactions lead to a collective freezing of particle moments at a size-dependent temperature Tg : At lower temperatures, at which surface spins fluctuations slow down and finally freeze, surface effects too play a role in determining the resulting magnetic state of the particle assembly.
References
Fig. 4. Field derivative (dM=dH) of the virgin magnetization vs. applied field at 5 K for 2.7 nm (m), 4.6 nm (&) and 8.7 nm ( ) particles. Inset: the peak field H of dM=dH; normalized to the value at 5 K, as a function of temperature for 2.7 nm (m), 4.6 nm (&) and 8.7 nm ( ) particles. Solid lines are guide for the eye.
of the virgin curve may be related to an actual random pinning of particle moments within the agglomerates. Such effects are more marked as the particle size decreases, suggesting a possible concomitant role of the particle surface, e.g. through exchange (actually super-exchange through hydroxyl groups at the surface) interparticle interactions at low temperatures, at which surface spin fluctuations are frozen.
[1] J.L. Dormann, D. Fiorani, E. Tronc, Adv. Chem. Phys. 98 (1997) 283. [2] A.E. Berkowitz, K. Takano, J. Magn. Magn. Mater. 200 (1999) 552. [3] R.H. Kodama, et al., Phys. Rev. Lett. 77 (1996) 394. [4] R.H. Kodama, A.E. Berkowitz, Phys. Rev. B 59 (1999) 6321. [5] B. Martinez, et al., Phys. Rev. Lett. 80 (1998) 181. [6] E. Tronc, et al., J. Magn. Magn. Mater. 221 (2000) 63. [7] J.L. Dormann, et al., J. Magn. Magn. Mater. 187 (1998) L139. [8] L. N!eel, J. Phys. Radium 15 (1954) 225. [9] J.L. Dormann, L. Bessais, D. Fiorani, J. Phys. C 21 (1998) 2015. [10] R.W. Chantrell, et al., J. Magn. Magn. Mater. 196–197 (1999) 118. [11] J.L. Dormann, et al., Mater. Sci. Forum 235–238 (1997) 669. [12] N. Bontemps, et al., J. Magn. Magn. Mater. 54–57 (1986) 1. [13] E. Tronc, et al., unpublished. [14] M.D. Coey, Phys. Rev. Lett. 27 (1971) 1140. [15] F. Gazeau, et al., J. Magn. Magn. Mater. 196 (1998) 175.
Magnetic properties of maghemite nanoparticle systems: surface anisotropy and interparticle interaction effects D. Fiorania,*, A.M. Testaa, F. Lucarib, F. D’Oraziob, H. Romeroc a
ICMAT-CNR, Area della Ricerca di Roma, C.P. 10, 00010 Monterotondo Stazione, Rome, Italy b Dip. to di Fisica, Universita" di L’Aquila and INFM, 67010 Coppito-L’Aquila, Italy c Depto de Fisica, Fac. De Ciencias, Universidad de Los Andes, M!erida, Venezuela
Abstract The static and dynamic magnetic properties of powders of maghemite nanoparticles with average diameter D ¼ 2:7; 4.6 and 8.7 nm have been investigated by magnetisation, AC susceptibility at variable frequency (5ono104 Hz) and . Mossbauer spectroscopy measurements. The results provide an insight into the correlation between intra-particle and inter-particle effects. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Fine particles; Maghemite
1. Introduction The surface-to-volume ratio is large in nanoparticles (e.g. for a 4 nm, approx. 40% of atoms are on the surface) and hence surface effects play an important role in determining their magnetic behaviour [1]. The electronic, structural and magnetic properties are indeed modified near and at the surface, resulting in a site-specific anisotropy, spin disorder and weakened exchange coupling. Furthermore, the coupling between the different surfaces and core spin structures can lead to the exchange anisotropy [2]. Studies of ferrite nanoparticles [2–6] have provided clear evidences of an enhanced surface anisotropy, responsible for the non-saturation of the magnetization at low temperature, high coercivity and high-field irrever*Corresponding author. Tel.: +39-6-9067-2553; fax: +39-69067-2270. E-mail address: fi[email protected] (D. Fiorani).
sibility, and have suggested the occurrence, at low temperature, of a spin-glass- or semi-spin-glasslike freezing process at the surface layer, induced by competing exchange interactions and local anisotropy. Since surface phenomena influence the magnitude of the particle moment and possibly the interparticle distance, like in powders, where adsorbed species act as spacers, they affect the actual strength of the dipolar inter-particle interaction, which can itself influence the surface properties through local energy variations. In addition, if the particles are in close contact, inter-particle exchange can develop at sufficiently low temperature through the direct involvement of surface atoms. Aiming at investigating the inter-relation between surface and inter-particle interaction effects in g-Fe2O3 nanoparticles, we have studied by magnetization, AC susceptibility at variable fre. quency (5ono104 Hz) and Mossbauer spectroscopy measurements the static and dynamic
0921-4526/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 2 ) 0 0 6 5 9 - 2
D. Fiorani et al. / Physica B 320 (2002) 122–126
properties of maghemite nanoparticles with average diameter D ¼ 2:7; 4.6 and 8.7 nm in the form of powders. Previously, we had investigated the magnetic properties [7] of particles of the same size, coming from the same starting batches, dispersed in polyvinilic alcohol (PVA) at different volume concentrations (Cv ): very diluted particle dispersion (Cv E1%; inter-particle distance dE5D; ‘‘IF’’ samples), representing the reference behaviour of almost non-interacting particles; concentrated particle dispersions (Cv E20%; dE1:5D; ‘‘IN’’ samples), where dipole–dipole inter-particle interactions are relevant. Dispersed nanoparticles exhibit low temperature enhanced surface anisotropy, responsible for the non-saturation of the magnetization [6]. The dynamical properties of IF samples are well described by the superparamagnetic Ne! el–Brown model [8], whereas those of IN samples by the modified superparamagnetic model accounting for inter-particle interactions [9], predicting an increase of the single particle anisotropy energy barrier with interactions, in agreement with results of Monte Carlo simulations [10].
123
55 kOe); AC susceptibility measurements were performed at different frequencies (5ono104 Hz) and at a field amplitude hAC ¼ 1 Oe, using a commercial susceptometer.
3. Results and discussion
2. Experimental
The low-field (Ha ¼ 20 Oe) zero-field cooled (ZFC) susceptibility (wZFC ) (Fig. 1) shows a maximum at a temperature Tmax increasing with particle size (95 K for D ¼ 2:7 nm; 130 K for D ¼ 4:6 nm and E200 K for D ¼ 8:7 nm, for which the maximum is broader, indicating a larger distribution of particle size). Below Tmax the fieldcooled susceptibility (wFC ) splits from the ZFC curve and becomes almost temperature independent, as observed in spin-glass systems. On the other hand, a continuous Curie-like increase of wFC is observed for IF samples and an intermediate behaviour for IN samples. For the same particle size, wZFC decreases with increasing interparticle interactions, i.e. moving from IF to IN and to the powder sample. The real (w0 ) and imaginary (w00 ) components of the first harmonic of the AC susceptibility were
The preparation and characterisation of the materials are detailed in Ref. [6]. The samples were obtained by flocculating aqueous sols (pH=2) of g-Fe2O3 nanoparticles with average diameter D ¼ ð6/V S=pÞ1=3 ¼ 2:7; 4.6 and 8.7 nm, where /V S is the mean volume, by raising the pH up to 8 (cancelling the surface electrostatic charge), then washing and separating the precipitates by centrifuging and drying under reduced pressure. The Fe2O3 content determined by thermal analysis is 90, 95 and 95 wt% for 2.7, 4.6 and 8.7 nm, respectively, with the remaining percentage of physisorbed and chemisorbed water. The X-ray diffraction patterns are typical for the cubic (Fd3m) structure with lattice constant a=(0.83570.001) nm. TEM observations showed that the particles are roughly spheroidal with a lognormal distribution of the diameter D; whose average value is associated to the mean volume. Magnetization measurements were performed by a commercial SQUID magnetometer (Hmax ¼
Fig. 1. Zero-field and field-cooled susceptibility (H ¼ 20 Oe) vs. temperature (m: 2.7 nm; &: 4.6 nm; solid line: 8.7 nm).
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measured as a function of temperature (Fig. 2). w0 shows a sharp maximum at a frequency-dependent 0 temperature Tmax ðnÞ (e.g. for 2.7 nm particles, at 0 n ¼ 5 Hz, Tmax ¼ 97 K). For a given particle size, 0 Tmax increases with increasing interactions, e.g. for 0 2.7 nm particles, Tmax ð5 HzÞ ¼ 17 and 27 K for 0 IF and IN samples, respectively. Tmax ðnÞ is taken as the blocking temperature at which the relaxation time t equals the measuring time tm ¼ 1=n for a characteristic particle volume V ¼ R/V 2 S=/V S: The R factor, ranging between 1.1 and 1.3, is mainly determined by the width of the volume distribution [11]. From the frequency 0 dependence of Tmax ; the temperature variation of the relaxation time t was derived for 2.7 and 4.6 nm particles. This can be described neither by the Ne! el–Brown superparamagnetic model, like for IF samples, nor by the modified one, accounting for inter-particle interactions, like for IN samples [7]. t was found to diverge according to a power law, t ¼ t0 ½Tg =ðT Tg Þa ; like in collective disordered systems such as spin-glasses, with Tg corresponding to the temperature of the maximum of the ZFC susceptibility. For 2.7 nm particles, t0 ¼ 1011 s and a ¼ 7:6; for 4.6 nm
Fig. 2. Real (w0 ) and imaginary (w00 ) parts of AC susceptibility as a function of temperature at different frequencies for 2.7 nm particles.
particles, t0 ¼ 1011 s and a ¼ 7:0 [7]. The values of the critical exponent are similar to those reported for spin-glasses [12] and determined by Monte Carlo simulations. The existence of a collective glassy-like dynamics of particle moments is supported by previous observations of ageing effects in the relaxation of the ZFC magnetization [7]. For 2.7 and 4.6 nm particles, with decreasing temperature, w00 first increases in proximity of 0 Tmax ðnÞ; then shows a frequency-dependent variation, decreases rapidly below 60–50 K and finally becomes frequency independent below 40 K (Fig. 2). The results suggest that both samples enter into a different dynamical regime characterized by a strong slowing down of the dynamics. The frequency independence of w00 at low temperature is similar to the behaviour observed in spin glasses well below the freezing temperature, where the spin disorder can be considered quasi static. Such a complex temperature dependence of w00 is not observed for 8.7 nm particles, as well as in IF and IN samples of 2.7 and 4.6 nm particles, down to the lowest temperature investigated. . Mossbauer spectra are well fitted using a broad distribution of hyperfine fields Hhyp ; similar to spin-glasses [13]. On the other hand, for IF and IN samples the spectra are well interpreted in terms of a collection of up–down superparamagnetic relaxation processes with a distribution of relaxation times [6]. For 2.7 nm and 4.6 nm particles, the thermal variation of the standard deviation s of the distribution of the hyperfine field Hhyp flattens off below E60 K and that of the average /Hhyp S below E30 K, indicating an almost complete freezing of spins fluctuations below this tempera. ture. Mossbauer experiments performed on 4.6 nm particles in a field of 60 kOe, applied parallel to the g-ray direction, gave evidence that surface spins gradually freeze and finally reach a semi-spinglass-like state below 30 K [13]. Magnetisation vs. applied field measurements were performed at different temperatures. Between Tmax and 60 K the cycles are almost unhysteretic, with vanishing remanence and coercive field. Below 60 K, the loops open up with a strong increase of remanence and coercive field and the behaviour of the virgin magnetization curve
D. Fiorani et al. / Physica B 320 (2002) 122–126
changes (Fig. 3). At low temperature, for 2.7 and 4.6 nm, the magnetization does not saturate at the maximum field value, unlike for 8.7 nm particles, and the highest value M0 ðH ¼ 55 kOeÞ decreases with decreasing particle size (M0 ¼ 72; 55 and 48 emu/g for 8.7, 4.6 and 2.7 nm, respectively). The reduction of the magnetization with respect to the bulk saturation value (80 emu/g [14]) is mainly determined by surface spin canting and disorder, due to broken bonds and frustration of antiferromagnetic exchange interactions, whose effect becomes more and more important with decreasing particle size. Both the coercive field Hc and the irreversibility field Hirr (the field above which the cycle is reversible) increase with decreasing particle size, reflecting an increase of macroscopic anisotropy: at 5 K, Hc ¼ 200; 510 and 680 Oe for D ¼ 8:7; 4.6 and 2.7 nm, respectively; Hirr ¼ 2:6; 6 and 20 kOe for D ¼ 8:7; 4.6, 2.7 nm, respectively. From Hirr ; an effective anisotropy volume constant Keff can be deduced as Keff ¼ ð1=2ÞMs Hirr ; where Ms is the extrapolated value of the saturation magnetization. Keff is found to increase with decreasing size: at 5 the values are 4.7 105, 8.6 105 and 2.5 106 erg/cm3 for 8.7, 4.6 and
Fig. 3. Magnetization vs. applied field at T ¼ 5 K for 2.7 (solid line) and 4.6 (line and symbols) nm particles.
125
2.7 nm, respectively. Such values are much larger than the magnetocrystalline anisotropy constant of the bulk material (Kmc ¼ 4:7 104 erg/cm3). They are of the same order of magnitude of those obtained from the analysis of the frequency dependence of the blocking temperature on the corresponding IF samples [11], confirming the dominant contribution of the intrinsic surface anisotropy to the total anisotropy energy. For 4.6 nm particles, the deduced surface anisotropy constant is Ks ¼ Keff D=6E7:0 102 erg/cm2. This value is of the same order of magnitude as that derived by means of ferromagnetic resonance experiments on g-Fe2O3 particles of similar size [15]. Below 60 K, increasing the magnetic field, the virgin curve first crosses the loop at a sizedependent field H1 ; lies outside the cycle for a certain field range and finally enters the loop again at higher fields (Fig. 3). H1 increases with decreasing particle size: at 5 K, H1 ¼ 330; 750 and 1220 Oe for D ¼ 8:7; 4.6 and 2.7 nm, respectively. Moreover, the virgin curve shows a S shape with a change of curvature at a size-dependent characteristic field H (Fig. 4), which is found to increase with decreasing particle size: at 5 K, H ¼ 450; 1220 and 1610 Oe for D ¼ 8:7; 4.6 and 2.7 nm, respectively. With increasing temperature, the virgin magnetization curve progressively enters the loop for the whole field range and both H1 and H decrease until they vanish around 60 K (Fig. 4, inset). Such features are not observed in IF samples, in absence of inter-particle interactions, whereas are clearly observed, although weaker, in concentrated dispersion consisting of aggregates of particles (FLOC samples). An intermediate behaviour is observed for IN samples, where inter-particle interactions are much weaker. Therefore, the observed features are related to inter-particle interactions effects. The behaviour of the virgin magnetization curve indicates a high stability of the particle system against the application of the magnetic field. This should be due to the presence of short-range correlated regions of particle moments forming closed magnetic circuits, minimizing the magnetostatic energy, coherently with the decrease of the low field susceptibility with increasing inter-particle interactions. The S shape
126
D. Fiorani et al. / Physica B 320 (2002) 122–126
Summarizing, the results show that the static and dynamical properties of maghemite nanoparticles in the form of powders are governed by inter-particle interactions and surface effects. Inter-particle interactions lead to a collective freezing of particle moments at a size-dependent temperature Tg : At lower temperatures, at which surface spins fluctuations slow down and finally freeze, surface effects too play a role in determining the resulting magnetic state of the particle assembly.
References
Fig. 4. Field derivative (dM=dH) of the virgin magnetization vs. applied field at 5 K for 2.7 nm (m), 4.6 nm (&) and 8.7 nm ( ) particles. Inset: the peak field H of dM=dH; normalized to the value at 5 K, as a function of temperature for 2.7 nm (m), 4.6 nm (&) and 8.7 nm ( ) particles. Solid lines are guide for the eye.
of the virgin curve may be related to an actual random pinning of particle moments within the agglomerates. Such effects are more marked as the particle size decreases, suggesting a possible concomitant role of the particle surface, e.g. through exchange (actually super-exchange through hydroxyl groups at the surface) interparticle interactions at low temperatures, at which surface spin fluctuations are frozen.
[1] J.L. Dormann, D. Fiorani, E. Tronc, Adv. Chem. Phys. 98 (1997) 283. [2] A.E. Berkowitz, K. Takano, J. Magn. Magn. Mater. 200 (1999) 552. [3] R.H. Kodama, et al., Phys. Rev. Lett. 77 (1996) 394. [4] R.H. Kodama, A.E. Berkowitz, Phys. Rev. B 59 (1999) 6321. [5] B. Martinez, et al., Phys. Rev. Lett. 80 (1998) 181. [6] E. Tronc, et al., J. Magn. Magn. Mater. 221 (2000) 63. [7] J.L. Dormann, et al., J. Magn. Magn. Mater. 187 (1998) L139. [8] L. N!eel, J. Phys. Radium 15 (1954) 225. [9] J.L. Dormann, L. Bessais, D. Fiorani, J. Phys. C 21 (1998) 2015. [10] R.W. Chantrell, et al., J. Magn. Magn. Mater. 196–197 (1999) 118. [11] J.L. Dormann, et al., Mater. Sci. Forum 235–238 (1997) 669. [12] N. Bontemps, et al., J. Magn. Magn. Mater. 54–57 (1986) 1. [13] E. Tronc, et al., unpublished. [14] M.D. Coey, Phys. Rev. Lett. 27 (1971) 1140. [15] F. Gazeau, et al., J. Magn. Magn. Mater. 196 (1998) 175.