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Dynamic behavior of superparamagnetic iso-oriented magnesioferrite nanoparticles
ARTICLE IN PRESS
Physica B 384 (2006) 300–302 www.elsevier.com/locate/physb
Dynamic behavior of superparamagnetic iso-oriented magnesioferrite nanoparticles W.S.D. Folly1, S. Soriano, J.P. Sinnecker, M.A. Novak Instituto de Fı´sica-UFRJ, CP 68528, Cidade Universita´ria, 21941-972, Rio de Janeiro, Brazil
Abstract Small magnetic particle systems generally present complex magnetic behaviors, which are due to the similarity of effects arising from distribution of size, shape, orientation of anisotropy axis and interparticle interactions that can jeopardize the comparison between experimental results and theoretical models. The system formed by magnesioferrite (MgFe2O4) nanoparticles precipitated in dilute solid solutions of iron in MgO (magnesiowu¨stite) is interesting since the insulating single crystal matrix impose nanoparticles iso-orientation, and the interparticle interactions are negligible. In addition it is easy to change its average particle size by sample annealing. In this work, we present some dynamic magnetic properties of this system and its relation with the evolution of the average particle sizes with annealing time. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50; 75.40; 75.10 Keywords: Nanomagnetism; Magnetic relaxation; Superparamagnetism
1. Introduction The great majority of nanosized magnetic particles systems present non-uniformities of size, anisotropy axis orientation and shape. These structural characteristics may make difficult the application of theoretical models and the determination of some magnetic properties, for instance, the anisotropy field on the blocking temperature. This occurs because some observable physical properties of the system depend simultaneously of the size, the orientation and the shape of the particles. Thus, it is important to study systems in which some of these difficulties may be overcome. In this work, we present some new results about an interesting nanostructured magnetic system in which all the particles present octahedral shape and are oriented in the same direction [1]: the magnesioferrite precipitates in a magnesiowu¨stite matrix. Corresponding author. Tel.: +55 21 25627330; fax: +55 21 25627368.
E-mail address: [email protected] (M.A. Novak). Present address: Centro Brasileiro de Pesquisas Fı´ sicas, 22290-180, Rio de Janeiro, Brazil. 1
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.07.005
When a single crystalline solid solution of iron in magnesium oxide (magnesiowu¨stite) is annealed at certain temperature, the nucleation and coarsening of magnesioferrite (MgFe2O4) phase occurs. The obtained magnesioferrite nanoparticles have their crystalline lattices oriented with respect to the matrix host lattice [1]. Due to this feature, the measurement of magnetic anisotropy field and other physical properties [2,3] of this system are extremely eased. The system presents a cubic magnetocrystalline anisotropy with the easy axis parallel to the /1 0 0S directions and the hard axis in the /1 1 0S directions. In addition by increasing the annealing time one has the opportunity to modify the size distribution of the particles.
2. Experimental procedure In order to investigate the magnetic relaxation process in this system, we performed AC susceptibility measurements over a wide frequency range [4] (0.01 Hz–120 kHz) and DC magnetization as function of time at different temperatures of samples annealed at 700 1C during 2, 3, 8 and 1400 h. At frequencies below 10 Hz and in DC magnetization
ARTICLE IN PRESS W.S.D. Folly et al. / Physica B 384 (2006) 300–302
measurements we used a Cryogenic S600 SQUID magnetometer with an AC option. Measurements at frequencies between 10 Hz and 10 kHz were performed with a Quantum Design Model 6000 PPMS system and finally, at frequencies above 10 kHz, we used a homemade AC susceptometer. Figs. 1a and b show respectively the real w0 and imaginary w00 components of the AC susceptibility of the sample annealed at 700 1C for 3 h and Fig. 1c shows the Arrhenius plots, obtained from w00 maxima of samples annealed for different times. We can notice in this figure that the Arrhenius law t ¼ t0 eDE=kB T is obeyed over a wide range of relaxation time for all studied samples. In addition to our AC susceptibility determination of relaxation time, we measured the relaxation of DC magnetization at different temperatures using the following protocol: at each temperature we apply a persistent field of 250 Oe for 500 s and measure the magnetization, then set the field to zero and measure the remanent magnetization
301
for 2500 s. All measurements were done with the field oriented along the easy /1 0 0S direction. The decay of the magnetization does not follow an exponential law, but a linear decay with logarithm of time (see Fig. 2). The magnetic viscosity defined by SðT; HÞ ¼
qM q lnðtÞ
(1)
was determined and is shown in Figs. 3 and 4. A logarithmic time dependence is known to be followed by many granular magnetic systems due to a wide distribution of relaxation time [5] within the experimental measuring time window (between 100 and 2500 s in our case). It was not possible to extract from those data a dominant relaxation time equivalent to the maxima in w00 for time above 100 s. An accurate analysis of magnetic viscosity at low-temperature limit can give information
5x10-3
7.0 K 12.7K
0.2 (a)
1 2
4x10-3
17.7K
0.1 m (emu)
χ (arb. units)
3 4 (1) 0.01Hz
0.0 1
2
3x10-3
(2) 0.1 Hz
(b) 3
20.2K
25.1K
(3) 1 kHz
4
30.1K
(4) 100 kHz 0.01
35.1 K
2x10-3 100.0
1000.0 t (s)
0.00
0
10
20
30
40
Fig. 2. Logarithmic plot of total magnetic moment of the sample annealed for 1400 h as a function of time.
T (K) 1x102
1x10-5
S (dm /d ln (t))
τ (s)
0.018
2h 3h
(c)
8h 1400h 10-12 0.00
0.05
0.10
0.15
0.012
0.006 S = 1.2 * 10-3 * T1 /2
0.20
1/ T ( K-1) Fig. 1. Real (a) and imaginary (b) component of the magnetic susceptibility of the sample annealed for 3 h measured in different frequencies and the Arrhenius plot (c) for samples annealed during 2, 3, 8 and 1400 h.
0.000
0
5
10
15
20 T (K)
25
30
35
40
Fig. 3. Magnetic viscosity as a function of temperature for the sample annealed for 1400 h.
ARTICLE IN PRESS W.S.D. Folly et al. / Physica B 384 (2006) 300–302
302
3. Conclusion
S (dm /d ln (t))
4x10-4
3x10-4
2x10-4
1x10-4
0
0
4
8
12
16
20
T (K) Fig. 4. Magnetic viscosity as a function of temperature for the sample annealed for 2 h.
about the possible occurrence of quantum tunneling of magnetization. If the relaxation process is dominated by thermal activation, the viscosity is expected to vanish, limT!0 SðT; HÞ ¼ 0. Otherwise, if the magnetic viscosity presents a finite value when T-0, the relaxation of the magnetization may be due to quantum tunneling. The magnetic viscosity of an iso-oriented magnetic particle system, whose magnetization relaxes by thermal activation, was predicted to present a temperature dependence S / T 1=a with a ¼ 2 at very low temperatures [6,7]. In the present system, this behavior seems to be followed down to the lowest measured temperature. In Figs. 3 and 4 we show the results for two samples annealed during a short period of time (2 h), as well as in the case of a long time annealing (1400 h). The maximum in S reflects, in this system, a different distribution of sizes for both samples, with larger sizes in the sample annealed for 1400 h.
We presented here the study of dynamic magnetic process of the iso-oriented magnetic nanoparticles of magnesioferrite in magnesiowu¨stite matrix which is a promising system to study magnetic properties of nanomagnetic particles. Besides having iso-oriented nanoparticles imposed by the single crystal matrix, it allows an easy control of the particle size distribution by appropriate choice of annealing time and temperature. The dynamical properties as probed by AC susceptibility measurements present an Arrhenius behavior in a wide temperature and time range rarely observed in other granular materials. The magnetic viscosity data at low temperatures indicates that the magnetization relaxation of this system is predominantly thermal activated. The possibility of quantum tunneling of the magnetization may be checked with measurements well below 1 K.
Acknowledgements The authors acknowledge FAPERJ, CAPES, CNPq, Instituto de Nanocieˆncias and ALFAII Project ‘‘HIFIELD’’n II-0147-FI for financial support.
References [1] [2] [3] [4]
G.P. Wirtz, M.E. Fine, J. Am. Ceram. Soc. 51 (1968) 402. R.S. de Biasi, T.C. Devezas, J. Appl. Phys. 49 (1978) 4. W.S.D. Folly, R.S. de Biasi, Braz. J. Phys. 31 (2001) 398. M.A. Novak, W.S.D. Folly, J.P. Sinnecker, S. Soriano, J. Magn. Magn. Mater. 294 (2) (2005) 133. [5] R. Street, J.C. Woolley, Proc. Phys. Soc. A 62 (1949) 562. [6] S.H. Charap, J. Appl. Phys. 63 (1988) 2054. [7] V.M. Tobin, S. Schultz, C.H. Chan, S.B. Oserof, IEEE Trans. Magn. MAG-24 (6) (1988) 2880.
Physica B 384 (2006) 300–302 www.elsevier.com/locate/physb
Dynamic behavior of superparamagnetic iso-oriented magnesioferrite nanoparticles W.S.D. Folly1, S. Soriano, J.P. Sinnecker, M.A. Novak Instituto de Fı´sica-UFRJ, CP 68528, Cidade Universita´ria, 21941-972, Rio de Janeiro, Brazil
Abstract Small magnetic particle systems generally present complex magnetic behaviors, which are due to the similarity of effects arising from distribution of size, shape, orientation of anisotropy axis and interparticle interactions that can jeopardize the comparison between experimental results and theoretical models. The system formed by magnesioferrite (MgFe2O4) nanoparticles precipitated in dilute solid solutions of iron in MgO (magnesiowu¨stite) is interesting since the insulating single crystal matrix impose nanoparticles iso-orientation, and the interparticle interactions are negligible. In addition it is easy to change its average particle size by sample annealing. In this work, we present some dynamic magnetic properties of this system and its relation with the evolution of the average particle sizes with annealing time. r 2006 Elsevier B.V. All rights reserved. PACS: 75.50; 75.40; 75.10 Keywords: Nanomagnetism; Magnetic relaxation; Superparamagnetism
1. Introduction The great majority of nanosized magnetic particles systems present non-uniformities of size, anisotropy axis orientation and shape. These structural characteristics may make difficult the application of theoretical models and the determination of some magnetic properties, for instance, the anisotropy field on the blocking temperature. This occurs because some observable physical properties of the system depend simultaneously of the size, the orientation and the shape of the particles. Thus, it is important to study systems in which some of these difficulties may be overcome. In this work, we present some new results about an interesting nanostructured magnetic system in which all the particles present octahedral shape and are oriented in the same direction [1]: the magnesioferrite precipitates in a magnesiowu¨stite matrix. Corresponding author. Tel.: +55 21 25627330; fax: +55 21 25627368.
E-mail address: [email protected] (M.A. Novak). Present address: Centro Brasileiro de Pesquisas Fı´ sicas, 22290-180, Rio de Janeiro, Brazil. 1
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.07.005
When a single crystalline solid solution of iron in magnesium oxide (magnesiowu¨stite) is annealed at certain temperature, the nucleation and coarsening of magnesioferrite (MgFe2O4) phase occurs. The obtained magnesioferrite nanoparticles have their crystalline lattices oriented with respect to the matrix host lattice [1]. Due to this feature, the measurement of magnetic anisotropy field and other physical properties [2,3] of this system are extremely eased. The system presents a cubic magnetocrystalline anisotropy with the easy axis parallel to the /1 0 0S directions and the hard axis in the /1 1 0S directions. In addition by increasing the annealing time one has the opportunity to modify the size distribution of the particles.
2. Experimental procedure In order to investigate the magnetic relaxation process in this system, we performed AC susceptibility measurements over a wide frequency range [4] (0.01 Hz–120 kHz) and DC magnetization as function of time at different temperatures of samples annealed at 700 1C during 2, 3, 8 and 1400 h. At frequencies below 10 Hz and in DC magnetization
ARTICLE IN PRESS W.S.D. Folly et al. / Physica B 384 (2006) 300–302
measurements we used a Cryogenic S600 SQUID magnetometer with an AC option. Measurements at frequencies between 10 Hz and 10 kHz were performed with a Quantum Design Model 6000 PPMS system and finally, at frequencies above 10 kHz, we used a homemade AC susceptometer. Figs. 1a and b show respectively the real w0 and imaginary w00 components of the AC susceptibility of the sample annealed at 700 1C for 3 h and Fig. 1c shows the Arrhenius plots, obtained from w00 maxima of samples annealed for different times. We can notice in this figure that the Arrhenius law t ¼ t0 eDE=kB T is obeyed over a wide range of relaxation time for all studied samples. In addition to our AC susceptibility determination of relaxation time, we measured the relaxation of DC magnetization at different temperatures using the following protocol: at each temperature we apply a persistent field of 250 Oe for 500 s and measure the magnetization, then set the field to zero and measure the remanent magnetization
301
for 2500 s. All measurements were done with the field oriented along the easy /1 0 0S direction. The decay of the magnetization does not follow an exponential law, but a linear decay with logarithm of time (see Fig. 2). The magnetic viscosity defined by SðT; HÞ ¼
qM q lnðtÞ
(1)
was determined and is shown in Figs. 3 and 4. A logarithmic time dependence is known to be followed by many granular magnetic systems due to a wide distribution of relaxation time [5] within the experimental measuring time window (between 100 and 2500 s in our case). It was not possible to extract from those data a dominant relaxation time equivalent to the maxima in w00 for time above 100 s. An accurate analysis of magnetic viscosity at low-temperature limit can give information
5x10-3
7.0 K 12.7K
0.2 (a)
1 2
4x10-3
17.7K
0.1 m (emu)
χ (arb. units)
3 4 (1) 0.01Hz
0.0 1
2
3x10-3
(2) 0.1 Hz
(b) 3
20.2K
25.1K
(3) 1 kHz
4
30.1K
(4) 100 kHz 0.01
35.1 K
2x10-3 100.0
1000.0 t (s)
0.00
0
10
20
30
40
Fig. 2. Logarithmic plot of total magnetic moment of the sample annealed for 1400 h as a function of time.
T (K) 1x102
1x10-5
S (dm /d ln (t))
τ (s)
0.018
2h 3h
(c)
8h 1400h 10-12 0.00
0.05
0.10
0.15
0.012
0.006 S = 1.2 * 10-3 * T1 /2
0.20
1/ T ( K-1) Fig. 1. Real (a) and imaginary (b) component of the magnetic susceptibility of the sample annealed for 3 h measured in different frequencies and the Arrhenius plot (c) for samples annealed during 2, 3, 8 and 1400 h.
0.000
0
5
10
15
20 T (K)
25
30
35
40
Fig. 3. Magnetic viscosity as a function of temperature for the sample annealed for 1400 h.
ARTICLE IN PRESS W.S.D. Folly et al. / Physica B 384 (2006) 300–302
302
3. Conclusion
S (dm /d ln (t))
4x10-4
3x10-4
2x10-4
1x10-4
0
0
4
8
12
16
20
T (K) Fig. 4. Magnetic viscosity as a function of temperature for the sample annealed for 2 h.
about the possible occurrence of quantum tunneling of magnetization. If the relaxation process is dominated by thermal activation, the viscosity is expected to vanish, limT!0 SðT; HÞ ¼ 0. Otherwise, if the magnetic viscosity presents a finite value when T-0, the relaxation of the magnetization may be due to quantum tunneling. The magnetic viscosity of an iso-oriented magnetic particle system, whose magnetization relaxes by thermal activation, was predicted to present a temperature dependence S / T 1=a with a ¼ 2 at very low temperatures [6,7]. In the present system, this behavior seems to be followed down to the lowest measured temperature. In Figs. 3 and 4 we show the results for two samples annealed during a short period of time (2 h), as well as in the case of a long time annealing (1400 h). The maximum in S reflects, in this system, a different distribution of sizes for both samples, with larger sizes in the sample annealed for 1400 h.
We presented here the study of dynamic magnetic process of the iso-oriented magnetic nanoparticles of magnesioferrite in magnesiowu¨stite matrix which is a promising system to study magnetic properties of nanomagnetic particles. Besides having iso-oriented nanoparticles imposed by the single crystal matrix, it allows an easy control of the particle size distribution by appropriate choice of annealing time and temperature. The dynamical properties as probed by AC susceptibility measurements present an Arrhenius behavior in a wide temperature and time range rarely observed in other granular materials. The magnetic viscosity data at low temperatures indicates that the magnetization relaxation of this system is predominantly thermal activated. The possibility of quantum tunneling of the magnetization may be checked with measurements well below 1 K.
Acknowledgements The authors acknowledge FAPERJ, CAPES, CNPq, Instituto de Nanocieˆncias and ALFAII Project ‘‘HIFIELD’’n II-0147-FI for financial support.
References [1] [2] [3] [4]
G.P. Wirtz, M.E. Fine, J. Am. Ceram. Soc. 51 (1968) 402. R.S. de Biasi, T.C. Devezas, J. Appl. Phys. 49 (1978) 4. W.S.D. Folly, R.S. de Biasi, Braz. J. Phys. 31 (2001) 398. M.A. Novak, W.S.D. Folly, J.P. Sinnecker, S. Soriano, J. Magn. Magn. Mater. 294 (2) (2005) 133. [5] R. Street, J.C. Woolley, Proc. Phys. Soc. A 62 (1949) 562. [6] S.H. Charap, J. Appl. Phys. 63 (1988) 2054. [7] V.M. Tobin, S. Schultz, C.H. Chan, S.B. Oserof, IEEE Trans. Magn. MAG-24 (6) (1988) 2880.