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Electrical property of nanocrystalline γ-Fe2O3 under high pressure
Physica B 407 (2012) 1044–1046
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Electrical property of nanocrystalline g-Fe2O3 under high pressure Dongmei Zhang a,b,n, Chunhe Zang a, Yongsheng Zhang a, Yonghao Han b, Chunxiao Gao b,n, Yanxin Yang a, Ke Yu c a
Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang 471023, PR China National Laboratory of Superhard Materials, Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, PR China c Key Lab for Polar Materials and Devices of Ministry of Education and Department of Electronic Engineering, East China Normal University, Shanghai 200241, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 August 2011 Accepted 7 January 2012 Available online 13 January 2012
Using a microcircuit fabricated on a diamond anvil cell, in situ conductivity measurements on nanophase (NP) g-Fe2O3 are obtained under high pressure. For NP g-Fe2O3, the abrupt increase in electrical conductivity occurs at a pressure of 21.3 GPa, corresponding to a transition from maghemite to hematite. Above 26.4 GPa, conductivity increases smoothly with increasing pressure. No distinct abnormal change is observed during decompression, indicating that transformation is irreversible. The temperature-dependence of the conductivity of NP g-Fe2O3 was investigated at several pressures, indicating the electrical conductivity of the sample increases with increasing pressure and temperature, and that a remarkable phenomenon of discontinuity occurs at 400 K. The abnormal change is attributed to the electronic phase transitions of NP g-Fe2O3 due to the variation of inherent cation vacancies. Besides, the temperature-dependence of the electrical conductivity displays semiconductor-like behavior before 33.0 GPa. & 2012 Elsevier B.V. All rights reserved.
Keywords: High pressure Electronic transport Phase transition
1. Introduction Semiconductor nanomaterials, in comparison with bulk materials, have recently attracted much attention due to their exceptional properties. Among these materials, iron oxide nanoparticles play key roles in high-density data storage [1,2], ferrofluids [3], and biomedicine [4]. All these applications require particles with wellcharacterized structures and properties. However, due to their high surface area-to-volume ratio, nanoparticles frequently exhibit different electrical properties, identifying these properties is crucial to understanding their consequences in practical applications. Maghemite has an inverse spinel structure, which belongs to the space group P4332 (No. 212). Maghemite, g-Fe2O3, has a defective spinel structure similar to Fe3O4 but a larger number of cation vacancies [5,6]. Many studies have recently been conducted on the synthesis and structural and magnetic properties of g-Fe2O3 nanocrystallites using X-ray diffraction [7], electron magnetic resonance [8], and Mossbauer spectroscopy [9]. In particular, pressure-induced structural phase transitions have gained the most attention from research experts [10,11]. Despite all these efforts, however, the electrical transport properties of g-Fe2O3 have been rarely discussed, and this gap in the literature provides the motive for this study. The purpose of this study is to
n
Corresponding authors. Tel.: þ 86 379 65928281/þ 86 431 85168878. E-mail addresses: [email protected] (D. Zhang), [email protected] (C. Gao). 0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2012.01.086
investigate the variations of the resistivity of g-Fe2O3 with high pressure and moderate temperature using a microcircuit fabricated on a diamond anvil. The electron transport properties of the material are also characterized.
2. Experimental A Mao-Bell type diomand anvil cell and T301 stainless steel were used in our experiments. Pressure was measured by the ruby fluorescence method. The nanophase (NP) g-Fe2O3 (purity of 99.99c/o) sample was packed into a sample chamber and pressed firmly. In our microcircuit we chose molybdenum (Mo) for electrode and alumina (Al2O3) for the insulating and protect materials in the electrical conductivity measurement. The electrodes were fabricated in a manner similar to that described in a previous work [12–14], and a sketch of the completed into a van der Pauw-type [15] fourprobe circuit is shown in Fig. 1. A diagram of the microcircuit with a sample arranged in the DAC is presented in Fig. 2. The conductivity of the sample was calculated using the following formula: expðpLR1 sÞ þexpðpLR2 sÞ ¼ 1,
ð1Þ
where s and L are the conductivity and thickness of the sample, respectively, and R1 and R2 are electrical resistances with R1 ¼VDC/IAB and R2 ¼VAD/IBC. During measurement, the current IAB was applied across contacts A and B, and the potential difference VDC across contacts C and D was measured. Next, the current I2 was applied
D. Zhang et al. / Physica B 407 (2012) 1044–1046
1045
Fig. 1. Sketch map of the microcircuit used for resistivity measurements: 1, the Mo electrodes; 2, the aluminum layer; A–D, the four contact ends of the microcircuit.
Fig. 3. Conductivity of NP g-Fe2O3 as a function of pressure at room temperature.
Fig. 2. Cross-section of the designed diamond anvil.
across contacts B and C, and the potential difference V2 across contacts A and D was measured. The thickness of the sample under pressure was determined with a modified micrometer [16]. We also determined the contact condition using an I–V test and obtained an ideal, linear I–V curve, indicating that the contact between the electrode and sample was ohmic.
3. Results and discussion In situ conductivity measurements of NP g-Fe2O3 were carried out under high pressure and ambient temperature, as shown in Fig. 3. The slope vary in this pressure region widely depends on the nature and structure of the sample. If a discontinuity is observed in the relationship of electrical conductivity with pressure, it is probably due to the presence of different
crystallographic phases or the occurrence of a phase transition in the material being measured. Hence, electrical properties can reflect the structural phase transitions of a crystal by sharp variations in its electric conductivity. Qualitatively, three important remarks can be made from the analysis of Fig. 3. First, the conductivity increases smoothly with increasing pressure from 4.9 to 21.3 GPa, indicating that the application of pressure promotes electronic conduction. Second, abnormal electrical conductivity changes are observed at 21.3–26.4 GPa, which is consistent with the phase transformation of maghemite to hematite [6]. Third, at above 26.4 GPa, the conductivity increases sharply with increasing pressure. This indicates the completion of the phase transition at 26.4 GPa. Hence, the results of the experiment indicate that phase transformation begins at about 21.3 GPa and concludes at about 26.4 GPa. The electrical conductivity increases by two orders of magnitude when the pressure is decreased to ambient pressure. Moreover, no anomalies are observed in the conductivity with decreasing pressure. These results indicate that the phase transition process is irreversible because the increase in conductivity occurs with decreasing pressure. This phenomenon could be explained by the large number of defects in the energy levels among energy bands due to pressure. These defects are favorable for electron-hopping. In this study, the temperature-dependence of the conductivity of NP g-Fe2O3 was investigated at several pressures, the results of which are shown in Fig. 4. The electrical conductivity of NP g-Fe2O3 increases with increasing pressure and temperature. This result indicates that the higher the pressure and temperature are, the larger the electrical conductivity of NP g-Fe2O3. The s(T) curve exhibits semiconducting behavior until 33.0 GPa. To examine the temperature-dependence observed in detail, we attempted to fit the s(T) curve to a general semiconductor-activated type [17–19] or variable-range-hopping type [20,21]. The results indicate that the s(T) curve obeys neither the T 1 nor T 1/4 law at ambient pressure, implying that the semiconducting-like behavior of the nanocrystalline sample originates from some other conductive mechanism. To deepen our analysis of the effect of temperature on the electrical conductivity of NP g-Fe2O3, we show that M% ¼ 100½sðTÞsðaÞ=sðaÞ vs. T curves (Fig. 5) with varying pressure at 11.5, 15.7, 26.4, and 33.0 GPa, where s(a) is the electrical conductivity at ambient temperature. In Fig. 5, the M increases smoothly with increasing temperature and pressure. It should be noted that the M vs T curves are minor dependent of pressure and temperature at least up to 400 K. With further increase in
1046
D. Zhang et al. / Physica B 407 (2012) 1044–1046
4. Conclusions
Fig. 4. Plot of log s vs. T of NP g-Fe2O3 under several pressures.
The in situ conductivity of NP g-Fe2O3 was measured under various high pressures, and the temperature-dependence of conductivity under several pressures was investigated using a microcircuit fabricated on a DAC. The electrical conductivity increased smoothly up to 21.3 GPa, and a discontinuous variation in conductivity occurred from 21.3–26.4 GPa, beyond which the electrical conductivity once again increased gradual. Hence, the transformation of maghemite to hematite was believed to begin at 21.3 GPa and end at 26.4 GPa. The electrical conductivity decreased as the pressure decreased, indicating that transformation with the application of pressure was irreversible. The temperature-dependence experiment results showed that below 400 K, the conductivity of NP g-Fe2O3 changes very little with increasing pressure and temperature. However, above 400 K, the effect of temperature on electrical conductivity was significant. We suggest that an electron phase transition occurs at 400 K due to the variation of cation vacancies in the octahedral positions vacancies sites. Besides, the results also showed that NP g-Fe2O3 displayed the transport behavior of a semiconductor up to 33.0 GPa.
Acknowledgments The authors wish to acknowledge financial support from the NSF of China (Grant nos. 10874053, 11074094, 50802033, 91014004, and 60876014), and the NSF of Henan Province (Grant nos. 072300410180 and 2010B140009). The project was also sponsored by Program for Science and Technology Innovation Talents in the Universities of Henan Province (Grant no. 2008HASTIT029), and the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (No.104100510018).). References
Fig. 5. Plot of M% ¼ 100½sðTÞsðaÞ=sðaÞ vs. T of NP g-Fe2O3 under several pressures.
temperature, a remarkable phenomenon of discontinuity occurs at 400 K, and does not move with pressure. Above 400 K, the effect of temperature starts to increase with pressure increase, indicating the variation of conduction mechanism. The fundamental structure of maghemite remains in the inverse spinel Fe3O4 (magnetite) and the presence of vacancies is distributed in the cation sublattice. Hence, g-Fe2O3 is expected to be an insulator. Otherwise, serna et al. suggested that NP g-Fe2O3 presents structural disorders not only on the surface layer but also in the interior of the particles [22].The different degrees of order-disorder at different sites change with increasing temperature, result in electron phase transition. This electron phase transition may be explained by the conduction being dominated by charge carriers hopping between metal-ions vacancies sites. The application of temperature promotes hopping and electronic (hole) conduction, the two effects approximately offsetting each other. In the low temperature region(o400 K), the conductivity increases slowly with increasing temperature, indicating that hopping conduction is dominant. In the high temperature region( 4400 K), the slope of the s(T) curve becomes steep indicating that electronic (or hole) conduction is dominant.
[1] See the review by J.L. Dormann, D. Fiorani, E. Tronc, on Magnetic Relaxation in Fine-Particle Systems, in: I. Prigogine, S.A. Rice (Eds.), Adv. Chem. Phys., Vol. XCVIII, John Wiley, New York, 1997, pp. 283–494. [2] D.E. Speliotis, J. Magn. Magn. Mater. 193 (1999) 29. [3] F.L. Calderon, T. Stora, O.M. Monval, P. Poulin, J. Bibette, Phys. Rev. Lett. 64 (1990) 539. [4] C.C. Berry, A.S.G. Curtis, J. Phys. D 36 (2003) R198. [5] C. Greaves, J. Solid State Chem. 49 (1983) 325. [6] O scar Iglesias, Amı lcar Labarta, Phys. Rev. B 63 (2001) 184416. [7] J.Z. Jiang, J. StaunOlsen, L. Gerward, S. Mroup, Europhys. Lett. 44 (5) (1998) 620. [8] P. Dutta, A. Manivannan, M.S. Seehra, N. Shah, G.P. Huffman, Phy. Rev. B 70 (2004) 174428-1. [9] Takateru Kawakami, Saburo Nasu, Toshio Tsutsui, Takahiro Yamada, Shoichi Endo, Mikio, Midio Takano, Tsutomu Katamoto, J. Phys. Soc. Jpn. 72 (10) (2003) 2640. [10] Z.W. Wang, S.K. Saxena, Solid State Commun. 123 (2002) 195. [11] S.M. Clark, S.G. Prilliman, C.K. Erdonmez, A.P. Alivisatos, Nanotechnology 16 (2005) 2813. [12] C.X. Gao, Y.H. Han, Y.Z. Ma, A. White, H.W. Liu, J.F. Luo, M. Li, C.Y. He, A.M. Hao, X.W. Huang, Y.W. Pan, G.T. Zou, Rev. Sci. Instrum 76 (2005) 083912. [13] Y.H. Han, C.X. Gao, Y.Z. Ma, H.W. Liu, Y.W. Pan, J.F. Luo, M. Li, C.Y. He, X.W. Huang, G.T. Zou, Appl. Phys. Lett. 86 (2005) 064104(1). [14] A.M Hao, C.X Gao, M. Li, C.Y. He, X.W. Huang, G.T. Zou, Y.J. Tian, Y.Z. Ma, J. Appl. Phys. 101 (2007) 053701-1. [15] L.J. van der Pauw, Philips Tech. Rev. 20 (1958) 220. [16] M. Li, C.X. Gao, G. Peng, Rev. Sci. Instrum. (2007) 075106(7). [17] A.L. Chen, P.Y. Yu, R.D. Taylor, Phys. Rev. Lett. 71 (1993) 4011. [18] B.M. Riggleman, H.G. Drickamer, J. Chem. Phys. 38 (1963) 2721. [19] D. DiMarzio, M. Croft, N. Sakai, Phys. Rev. B 35 (1987) 8891. [20] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1. [21] N.F. Mott, Phil. Mag. 19 (1969) 835. [22] C.J. Serna, F. Bodker, S. Morup, M.P. Morales, F. Sandiumenge, S. VeintemillasVerdauguer, Solid State Commun. 118 (2001) 437.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Electrical property of nanocrystalline g-Fe2O3 under high pressure Dongmei Zhang a,b,n, Chunhe Zang a, Yongsheng Zhang a, Yonghao Han b, Chunxiao Gao b,n, Yanxin Yang a, Ke Yu c a
Department of Mathematics and Physics, Luoyang Institute of Science and Technology, Luoyang 471023, PR China National Laboratory of Superhard Materials, Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, PR China c Key Lab for Polar Materials and Devices of Ministry of Education and Department of Electronic Engineering, East China Normal University, Shanghai 200241, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 8 August 2011 Accepted 7 January 2012 Available online 13 January 2012
Using a microcircuit fabricated on a diamond anvil cell, in situ conductivity measurements on nanophase (NP) g-Fe2O3 are obtained under high pressure. For NP g-Fe2O3, the abrupt increase in electrical conductivity occurs at a pressure of 21.3 GPa, corresponding to a transition from maghemite to hematite. Above 26.4 GPa, conductivity increases smoothly with increasing pressure. No distinct abnormal change is observed during decompression, indicating that transformation is irreversible. The temperature-dependence of the conductivity of NP g-Fe2O3 was investigated at several pressures, indicating the electrical conductivity of the sample increases with increasing pressure and temperature, and that a remarkable phenomenon of discontinuity occurs at 400 K. The abnormal change is attributed to the electronic phase transitions of NP g-Fe2O3 due to the variation of inherent cation vacancies. Besides, the temperature-dependence of the electrical conductivity displays semiconductor-like behavior before 33.0 GPa. & 2012 Elsevier B.V. All rights reserved.
Keywords: High pressure Electronic transport Phase transition
1. Introduction Semiconductor nanomaterials, in comparison with bulk materials, have recently attracted much attention due to their exceptional properties. Among these materials, iron oxide nanoparticles play key roles in high-density data storage [1,2], ferrofluids [3], and biomedicine [4]. All these applications require particles with wellcharacterized structures and properties. However, due to their high surface area-to-volume ratio, nanoparticles frequently exhibit different electrical properties, identifying these properties is crucial to understanding their consequences in practical applications. Maghemite has an inverse spinel structure, which belongs to the space group P4332 (No. 212). Maghemite, g-Fe2O3, has a defective spinel structure similar to Fe3O4 but a larger number of cation vacancies [5,6]. Many studies have recently been conducted on the synthesis and structural and magnetic properties of g-Fe2O3 nanocrystallites using X-ray diffraction [7], electron magnetic resonance [8], and Mossbauer spectroscopy [9]. In particular, pressure-induced structural phase transitions have gained the most attention from research experts [10,11]. Despite all these efforts, however, the electrical transport properties of g-Fe2O3 have been rarely discussed, and this gap in the literature provides the motive for this study. The purpose of this study is to
n
Corresponding authors. Tel.: þ 86 379 65928281/þ 86 431 85168878. E-mail addresses: [email protected] (D. Zhang), [email protected] (C. Gao). 0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2012.01.086
investigate the variations of the resistivity of g-Fe2O3 with high pressure and moderate temperature using a microcircuit fabricated on a diamond anvil. The electron transport properties of the material are also characterized.
2. Experimental A Mao-Bell type diomand anvil cell and T301 stainless steel were used in our experiments. Pressure was measured by the ruby fluorescence method. The nanophase (NP) g-Fe2O3 (purity of 99.99c/o) sample was packed into a sample chamber and pressed firmly. In our microcircuit we chose molybdenum (Mo) for electrode and alumina (Al2O3) for the insulating and protect materials in the electrical conductivity measurement. The electrodes were fabricated in a manner similar to that described in a previous work [12–14], and a sketch of the completed into a van der Pauw-type [15] fourprobe circuit is shown in Fig. 1. A diagram of the microcircuit with a sample arranged in the DAC is presented in Fig. 2. The conductivity of the sample was calculated using the following formula: expðpLR1 sÞ þexpðpLR2 sÞ ¼ 1,
ð1Þ
where s and L are the conductivity and thickness of the sample, respectively, and R1 and R2 are electrical resistances with R1 ¼VDC/IAB and R2 ¼VAD/IBC. During measurement, the current IAB was applied across contacts A and B, and the potential difference VDC across contacts C and D was measured. Next, the current I2 was applied
D. Zhang et al. / Physica B 407 (2012) 1044–1046
1045
Fig. 1. Sketch map of the microcircuit used for resistivity measurements: 1, the Mo electrodes; 2, the aluminum layer; A–D, the four contact ends of the microcircuit.
Fig. 3. Conductivity of NP g-Fe2O3 as a function of pressure at room temperature.
Fig. 2. Cross-section of the designed diamond anvil.
across contacts B and C, and the potential difference V2 across contacts A and D was measured. The thickness of the sample under pressure was determined with a modified micrometer [16]. We also determined the contact condition using an I–V test and obtained an ideal, linear I–V curve, indicating that the contact between the electrode and sample was ohmic.
3. Results and discussion In situ conductivity measurements of NP g-Fe2O3 were carried out under high pressure and ambient temperature, as shown in Fig. 3. The slope vary in this pressure region widely depends on the nature and structure of the sample. If a discontinuity is observed in the relationship of electrical conductivity with pressure, it is probably due to the presence of different
crystallographic phases or the occurrence of a phase transition in the material being measured. Hence, electrical properties can reflect the structural phase transitions of a crystal by sharp variations in its electric conductivity. Qualitatively, three important remarks can be made from the analysis of Fig. 3. First, the conductivity increases smoothly with increasing pressure from 4.9 to 21.3 GPa, indicating that the application of pressure promotes electronic conduction. Second, abnormal electrical conductivity changes are observed at 21.3–26.4 GPa, which is consistent with the phase transformation of maghemite to hematite [6]. Third, at above 26.4 GPa, the conductivity increases sharply with increasing pressure. This indicates the completion of the phase transition at 26.4 GPa. Hence, the results of the experiment indicate that phase transformation begins at about 21.3 GPa and concludes at about 26.4 GPa. The electrical conductivity increases by two orders of magnitude when the pressure is decreased to ambient pressure. Moreover, no anomalies are observed in the conductivity with decreasing pressure. These results indicate that the phase transition process is irreversible because the increase in conductivity occurs with decreasing pressure. This phenomenon could be explained by the large number of defects in the energy levels among energy bands due to pressure. These defects are favorable for electron-hopping. In this study, the temperature-dependence of the conductivity of NP g-Fe2O3 was investigated at several pressures, the results of which are shown in Fig. 4. The electrical conductivity of NP g-Fe2O3 increases with increasing pressure and temperature. This result indicates that the higher the pressure and temperature are, the larger the electrical conductivity of NP g-Fe2O3. The s(T) curve exhibits semiconducting behavior until 33.0 GPa. To examine the temperature-dependence observed in detail, we attempted to fit the s(T) curve to a general semiconductor-activated type [17–19] or variable-range-hopping type [20,21]. The results indicate that the s(T) curve obeys neither the T 1 nor T 1/4 law at ambient pressure, implying that the semiconducting-like behavior of the nanocrystalline sample originates from some other conductive mechanism. To deepen our analysis of the effect of temperature on the electrical conductivity of NP g-Fe2O3, we show that M% ¼ 100½sðTÞsðaÞ=sðaÞ vs. T curves (Fig. 5) with varying pressure at 11.5, 15.7, 26.4, and 33.0 GPa, where s(a) is the electrical conductivity at ambient temperature. In Fig. 5, the M increases smoothly with increasing temperature and pressure. It should be noted that the M vs T curves are minor dependent of pressure and temperature at least up to 400 K. With further increase in
1046
D. Zhang et al. / Physica B 407 (2012) 1044–1046
4. Conclusions
Fig. 4. Plot of log s vs. T of NP g-Fe2O3 under several pressures.
The in situ conductivity of NP g-Fe2O3 was measured under various high pressures, and the temperature-dependence of conductivity under several pressures was investigated using a microcircuit fabricated on a DAC. The electrical conductivity increased smoothly up to 21.3 GPa, and a discontinuous variation in conductivity occurred from 21.3–26.4 GPa, beyond which the electrical conductivity once again increased gradual. Hence, the transformation of maghemite to hematite was believed to begin at 21.3 GPa and end at 26.4 GPa. The electrical conductivity decreased as the pressure decreased, indicating that transformation with the application of pressure was irreversible. The temperature-dependence experiment results showed that below 400 K, the conductivity of NP g-Fe2O3 changes very little with increasing pressure and temperature. However, above 400 K, the effect of temperature on electrical conductivity was significant. We suggest that an electron phase transition occurs at 400 K due to the variation of cation vacancies in the octahedral positions vacancies sites. Besides, the results also showed that NP g-Fe2O3 displayed the transport behavior of a semiconductor up to 33.0 GPa.
Acknowledgments The authors wish to acknowledge financial support from the NSF of China (Grant nos. 10874053, 11074094, 50802033, 91014004, and 60876014), and the NSF of Henan Province (Grant nos. 072300410180 and 2010B140009). The project was also sponsored by Program for Science and Technology Innovation Talents in the Universities of Henan Province (Grant no. 2008HASTIT029), and the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (No.104100510018).). References
Fig. 5. Plot of M% ¼ 100½sðTÞsðaÞ=sðaÞ vs. T of NP g-Fe2O3 under several pressures.
temperature, a remarkable phenomenon of discontinuity occurs at 400 K, and does not move with pressure. Above 400 K, the effect of temperature starts to increase with pressure increase, indicating the variation of conduction mechanism. The fundamental structure of maghemite remains in the inverse spinel Fe3O4 (magnetite) and the presence of vacancies is distributed in the cation sublattice. Hence, g-Fe2O3 is expected to be an insulator. Otherwise, serna et al. suggested that NP g-Fe2O3 presents structural disorders not only on the surface layer but also in the interior of the particles [22].The different degrees of order-disorder at different sites change with increasing temperature, result in electron phase transition. This electron phase transition may be explained by the conduction being dominated by charge carriers hopping between metal-ions vacancies sites. The application of temperature promotes hopping and electronic (hole) conduction, the two effects approximately offsetting each other. In the low temperature region(o400 K), the conductivity increases slowly with increasing temperature, indicating that hopping conduction is dominant. In the high temperature region( 4400 K), the slope of the s(T) curve becomes steep indicating that electronic (or hole) conduction is dominant.
[1] See the review by J.L. Dormann, D. Fiorani, E. Tronc, on Magnetic Relaxation in Fine-Particle Systems, in: I. Prigogine, S.A. Rice (Eds.), Adv. Chem. Phys., Vol. XCVIII, John Wiley, New York, 1997, pp. 283–494. [2] D.E. Speliotis, J. Magn. Magn. Mater. 193 (1999) 29. [3] F.L. Calderon, T. Stora, O.M. Monval, P. Poulin, J. Bibette, Phys. Rev. Lett. 64 (1990) 539. [4] C.C. Berry, A.S.G. Curtis, J. Phys. D 36 (2003) R198. [5] C. Greaves, J. Solid State Chem. 49 (1983) 325. [6] O scar Iglesias, Amı lcar Labarta, Phys. Rev. B 63 (2001) 184416. [7] J.Z. Jiang, J. StaunOlsen, L. Gerward, S. Mroup, Europhys. Lett. 44 (5) (1998) 620. [8] P. Dutta, A. Manivannan, M.S. Seehra, N. Shah, G.P. Huffman, Phy. Rev. B 70 (2004) 174428-1. [9] Takateru Kawakami, Saburo Nasu, Toshio Tsutsui, Takahiro Yamada, Shoichi Endo, Mikio, Midio Takano, Tsutomu Katamoto, J. Phys. Soc. Jpn. 72 (10) (2003) 2640. [10] Z.W. Wang, S.K. Saxena, Solid State Commun. 123 (2002) 195. [11] S.M. Clark, S.G. Prilliman, C.K. Erdonmez, A.P. Alivisatos, Nanotechnology 16 (2005) 2813. [12] C.X. Gao, Y.H. Han, Y.Z. Ma, A. White, H.W. Liu, J.F. Luo, M. Li, C.Y. He, A.M. Hao, X.W. Huang, Y.W. Pan, G.T. Zou, Rev. Sci. Instrum 76 (2005) 083912. [13] Y.H. Han, C.X. Gao, Y.Z. Ma, H.W. Liu, Y.W. Pan, J.F. Luo, M. Li, C.Y. He, X.W. Huang, G.T. Zou, Appl. Phys. Lett. 86 (2005) 064104(1). [14] A.M Hao, C.X Gao, M. Li, C.Y. He, X.W. Huang, G.T. Zou, Y.J. Tian, Y.Z. Ma, J. Appl. Phys. 101 (2007) 053701-1. [15] L.J. van der Pauw, Philips Tech. Rev. 20 (1958) 220. [16] M. Li, C.X. Gao, G. Peng, Rev. Sci. Instrum. (2007) 075106(7). [17] A.L. Chen, P.Y. Yu, R.D. Taylor, Phys. Rev. Lett. 71 (1993) 4011. [18] B.M. Riggleman, H.G. Drickamer, J. Chem. Phys. 38 (1963) 2721. [19] D. DiMarzio, M. Croft, N. Sakai, Phys. Rev. B 35 (1987) 8891. [20] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1. [21] N.F. Mott, Phil. Mag. 19 (1969) 835. [22] C.J. Serna, F. Bodker, S. Morup, M.P. Morales, F. Sandiumenge, S. VeintemillasVerdauguer, Solid State Commun. 118 (2001) 437.