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Magnetization reversal in granular powder systems
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) e493–e495
Magnetization reversal in granular powder systems M. El-Hiloa,*, A. Rousanb, A. Al-Hattaba,b b
a Department of Physics, University of Bahrain, P.O. Box 32038, Isa Town, Bahrain Department of Physical Sciences, Jordan University of Science and Technology, P.O. Box 3030, Irbid, Jordan
Abstract In this paper, the magnetization reversal in substituted BaFe122xCoxTixO19 nanoparticles is examined. Measurements of fluctuation field (Hf ) have shown that the behavior of Hf is greatly influenced by the substitution level (x). At x ¼ 0:71; Hf is observed to be slowly varying with field, which is expected for a particulate system when both distributions (anisotropy fields and particle volumes) have comparable standard deviations. Hence a constant behavior of Hf with field cannot be used as an indication of single activation energy in the system. r 2003 Elsevier B.V. All rights reserved. PACS: 75.60.lr; 75.60.jk Keywords: Magnetization reversal; Doped barium ferrite; Fluctuation field
In magnetic materials, it is well known that the magnetization reversal is a time-dependent process and analysis of this phenomenon is usually interpreted in terms of fluctuation fields (Hf ). The concept of Hf was first suggested by Ne! el [1] and then used to describe the effects of thermal activation on magnetization reversal i.e. field description of kT. Accordingly, the fluctuation field is usually determined by linking thermal and field changes in the irreversible component of magnetization [2]. Consequently, the fluctuation field is governed by the activation energy for magnetic reversal since it is derived from measurements of changes in the irreversible component of magnetization. In systems where activation energies are distributed, the fluctuation field is defined and interpreted as follows [3]: kT DH Hf ¼ ¼ ; ð1Þ qDEB ðHÞ=qH DEB ¼DEc DlnðtÞ Mirr where DEB is the activation energy for magnetization reversal and DEc ¼ kT lnðtm f0 Þ is the critical energy barrier for reversal with tm is the measuring time and f0 is the frequency factor. In this technique, Hf values can *Corresponding author. Tel.: +973-9202656; fax: +973682582. E-mail address: [email protected] (M. El-Hilo).
be estimated from a series of Mirr ðH; tÞ curves. These curves will be used to generate plots of reverse field H vs. lnðtÞ at constant Mirr and Hf is the slope of the variation. The aim of this study is to investigate the effects of different contributions to the distribution of activation energies (anisotropies and volumes) on the behavior of fluctuation fields. The samples examined were in the form of compressed BaFe122xCoxTixO19 powder. Three samples with different substitution levels x ¼ 0:71; x ¼ 0:76 and x ¼ 0:82 were studied. These powders were prepared by the conventional glass crystallization method. Detailed preparation process, geometric and magnetic characterization of these systems was the subject of a previous study [4]. Measurements of remanence magnetization curves (Mirr ) and families of time-dependent curves at different reverse fields were made. The time dependence data for the total magnetization (Mtot ) were corrected for the reversible component of magnetization; since Hf has to be evaluated at constant Mirr : The correction was made using the DCD method where Mirr ðH; tÞ ¼ Mtot ðH; tÞ ½Mtot ðH; tf Þ Mtot ð0; tf Þ [5]. All magnetic measurements were made at room temperature using a VSM system model MicroMagTM 3900 supplied by Princeton Measurement Co.). Fig. 1 shows a family of reduced irreversible magnetization (Mirr =Ms ) versus lnðtÞ curves measured
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.279
ARTICLE IN PRESS M. El-Hilo et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e493–e495
0.10
20
0.05
15
Fluctuation Field Hf(Oe)
Reduced Irrev. Magnetization Mirr/Ms
e494
H (Oe)
Constant
-1000
0
Mirr/Ms=0 -1020
-0.05
-1040 -1060
-0.10 -2
-1
0
1
2
3
4
5
6
7
ln(t)
Applied Reverse Field H (Oe)
Slope=Hf=9.8 Oe
Mirr/Ms=0.0 Mirr/Ms=-0.05
1075 Slope=Hf=9.7 Oe 1050
1025
1000
-1
0
1
2
3
4
5
6
ln(t) Fig. 2. The variation of applied reverse field with D lnðtÞ at different constants of Mirr =Ms for the sample with x ¼ 0:82:
at different reverse fields near the coercive field for sample with x ¼ 0:82: From these data values of lnðtÞ and reverse fields at constant levels of magnetization were obtained. Fig. 2 shows the variation of applied reverse field with lnðtÞ at different constant values of reduced irreversible magnetization Mirr =Ms ; 0.05 and 0 which exhibited linear behavior. According to Eq. (1), the slope DH=D lnðtÞ at each constant level of Mirr gives the fluctuation field associated with the activation energy above which thermal activation was taking place in the range of field increment. Fig. 3 shows the obtained variation of Hf with field for all samples examined using the DH=D lnðtÞ technique. These data show clearly the effects of different contributions to the distribution of activation energies on the behavior of Hf : For sample with x ¼ 0:71; the
A1(x=0.71) A2(x=0.76) A3(x=0.82)
5
0 8
Fig. 1. Family of Mirr ðH; tÞ versus lnðtÞ curves measured near the coercive field for s the ample with x ¼ 0:82:
1100
10
500
1000 1500 2000 Applied Reverse Field H(Oe)
2500
Fig. 3. The variation of fluctuation fields with reverse field.
behavior of Hf is slowly varying with field which is what expected for particulate systems when both distributions (anisotropy fields f ðHK Þ and particle volumes F ðV Þ) have comparable standard deviations [3]. Thus a constant Hf behavior can be observed in systems that contain a distribution of activation energies. Hence a constant Hf behavior may give ambiguous information about single activation energy process in the system. In addition, a constant Hf behavior is expected for a weak domain wall reversal mechanism [6]. Hence a constant value of Hf also cannot be used to distinguish between reversal mechanisms such as coherent rotation or week domain wall pinning. For samples with x ¼ 0:76 and x ¼ 0:82; the behavior of Hf with field exhibited a minimum near the coercive field that shifts toward lower fields with increasing the substitution level. This behavior arises when the mean of the distribution of activation energies (DE0 ¼ Km Vm ) shifts toward lower values, and the distribution of anisotropy fields becomes narrower than the distribution of particle volumes [4]. From geometrical data, the average particle volumes are Vm ¼ 3:2 1017 cm3 for samples with x ¼ 0:71 and x ¼ 0:76; and Vm ¼ 3:1 1017 cm3 for sample with x ¼ 0:82 [4]. From this fact, changes in the particle volume distribution in these samples are very small and changes in the behavior of Hf with x can be mainly attributed to changes in the anisotropy field distribution. Accordingly the increases in the substitution level in these systems not only lower the mean anisotropy field but also give rise to a narrower distribution of anisotropy fields. From this study it can be concluded that the behavior of fluctuation fields in particulate systems is governed by the nature of the distribution of activation energies that usually arises from distributions of both particle volumes and anisotropy fields.
ARTICLE IN PRESS M. El-Hilo et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e493–e495
References [1] L. N!eel, J. Phys. Radium 11 (1950) 49. [2] R. Street, J.C. Woolley, P.B. Smith, Proc. Phys. Soc. B 65 (1952) 679. [3] M. El-Hilo, K. O’Grady, R.W. Chantrell, J. Magn. Magn. Mater. 248 (2002) 360.
e495
[4] M. El-Hilo, H. Pfeiffe, K. O’Grady, W. Schuppel, . E. Sinn, . . P. Gorrnert, M. Rosler, D.P.E. Dickson, R. Wchantrell, J. Magn. Magn. Mater. 129 (1994) 339. [5] D.C. Crew, S.H. Farrant, P.G. McCormic, R.W. Street, J. Magn. Magn. Mater. 163 (1996) 229. [6] P. Gaunt, J. Appl. Phys. 59 (1986) 4129.
Journal of Magnetism and Magnetic Materials 272–276 (2004) e493–e495
Magnetization reversal in granular powder systems M. El-Hiloa,*, A. Rousanb, A. Al-Hattaba,b b
a Department of Physics, University of Bahrain, P.O. Box 32038, Isa Town, Bahrain Department of Physical Sciences, Jordan University of Science and Technology, P.O. Box 3030, Irbid, Jordan
Abstract In this paper, the magnetization reversal in substituted BaFe122xCoxTixO19 nanoparticles is examined. Measurements of fluctuation field (Hf ) have shown that the behavior of Hf is greatly influenced by the substitution level (x). At x ¼ 0:71; Hf is observed to be slowly varying with field, which is expected for a particulate system when both distributions (anisotropy fields and particle volumes) have comparable standard deviations. Hence a constant behavior of Hf with field cannot be used as an indication of single activation energy in the system. r 2003 Elsevier B.V. All rights reserved. PACS: 75.60.lr; 75.60.jk Keywords: Magnetization reversal; Doped barium ferrite; Fluctuation field
In magnetic materials, it is well known that the magnetization reversal is a time-dependent process and analysis of this phenomenon is usually interpreted in terms of fluctuation fields (Hf ). The concept of Hf was first suggested by Ne! el [1] and then used to describe the effects of thermal activation on magnetization reversal i.e. field description of kT. Accordingly, the fluctuation field is usually determined by linking thermal and field changes in the irreversible component of magnetization [2]. Consequently, the fluctuation field is governed by the activation energy for magnetic reversal since it is derived from measurements of changes in the irreversible component of magnetization. In systems where activation energies are distributed, the fluctuation field is defined and interpreted as follows [3]: kT DH Hf ¼ ¼ ; ð1Þ qDEB ðHÞ=qH DEB ¼DEc DlnðtÞ Mirr where DEB is the activation energy for magnetization reversal and DEc ¼ kT lnðtm f0 Þ is the critical energy barrier for reversal with tm is the measuring time and f0 is the frequency factor. In this technique, Hf values can *Corresponding author. Tel.: +973-9202656; fax: +973682582. E-mail address: [email protected] (M. El-Hilo).
be estimated from a series of Mirr ðH; tÞ curves. These curves will be used to generate plots of reverse field H vs. lnðtÞ at constant Mirr and Hf is the slope of the variation. The aim of this study is to investigate the effects of different contributions to the distribution of activation energies (anisotropies and volumes) on the behavior of fluctuation fields. The samples examined were in the form of compressed BaFe122xCoxTixO19 powder. Three samples with different substitution levels x ¼ 0:71; x ¼ 0:76 and x ¼ 0:82 were studied. These powders were prepared by the conventional glass crystallization method. Detailed preparation process, geometric and magnetic characterization of these systems was the subject of a previous study [4]. Measurements of remanence magnetization curves (Mirr ) and families of time-dependent curves at different reverse fields were made. The time dependence data for the total magnetization (Mtot ) were corrected for the reversible component of magnetization; since Hf has to be evaluated at constant Mirr : The correction was made using the DCD method where Mirr ðH; tÞ ¼ Mtot ðH; tÞ ½Mtot ðH; tf Þ Mtot ð0; tf Þ [5]. All magnetic measurements were made at room temperature using a VSM system model MicroMagTM 3900 supplied by Princeton Measurement Co.). Fig. 1 shows a family of reduced irreversible magnetization (Mirr =Ms ) versus lnðtÞ curves measured
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.11.279
ARTICLE IN PRESS M. El-Hilo et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e493–e495
0.10
20
0.05
15
Fluctuation Field Hf(Oe)
Reduced Irrev. Magnetization Mirr/Ms
e494
H (Oe)
Constant
-1000
0
Mirr/Ms=0 -1020
-0.05
-1040 -1060
-0.10 -2
-1
0
1
2
3
4
5
6
7
ln(t)
Applied Reverse Field H (Oe)
Slope=Hf=9.8 Oe
Mirr/Ms=0.0 Mirr/Ms=-0.05
1075 Slope=Hf=9.7 Oe 1050
1025
1000
-1
0
1
2
3
4
5
6
ln(t) Fig. 2. The variation of applied reverse field with D lnðtÞ at different constants of Mirr =Ms for the sample with x ¼ 0:82:
at different reverse fields near the coercive field for sample with x ¼ 0:82: From these data values of lnðtÞ and reverse fields at constant levels of magnetization were obtained. Fig. 2 shows the variation of applied reverse field with lnðtÞ at different constant values of reduced irreversible magnetization Mirr =Ms ; 0.05 and 0 which exhibited linear behavior. According to Eq. (1), the slope DH=D lnðtÞ at each constant level of Mirr gives the fluctuation field associated with the activation energy above which thermal activation was taking place in the range of field increment. Fig. 3 shows the obtained variation of Hf with field for all samples examined using the DH=D lnðtÞ technique. These data show clearly the effects of different contributions to the distribution of activation energies on the behavior of Hf : For sample with x ¼ 0:71; the
A1(x=0.71) A2(x=0.76) A3(x=0.82)
5
0 8
Fig. 1. Family of Mirr ðH; tÞ versus lnðtÞ curves measured near the coercive field for s the ample with x ¼ 0:82:
1100
10
500
1000 1500 2000 Applied Reverse Field H(Oe)
2500
Fig. 3. The variation of fluctuation fields with reverse field.
behavior of Hf is slowly varying with field which is what expected for particulate systems when both distributions (anisotropy fields f ðHK Þ and particle volumes F ðV Þ) have comparable standard deviations [3]. Thus a constant Hf behavior can be observed in systems that contain a distribution of activation energies. Hence a constant Hf behavior may give ambiguous information about single activation energy process in the system. In addition, a constant Hf behavior is expected for a weak domain wall reversal mechanism [6]. Hence a constant value of Hf also cannot be used to distinguish between reversal mechanisms such as coherent rotation or week domain wall pinning. For samples with x ¼ 0:76 and x ¼ 0:82; the behavior of Hf with field exhibited a minimum near the coercive field that shifts toward lower fields with increasing the substitution level. This behavior arises when the mean of the distribution of activation energies (DE0 ¼ Km Vm ) shifts toward lower values, and the distribution of anisotropy fields becomes narrower than the distribution of particle volumes [4]. From geometrical data, the average particle volumes are Vm ¼ 3:2 1017 cm3 for samples with x ¼ 0:71 and x ¼ 0:76; and Vm ¼ 3:1 1017 cm3 for sample with x ¼ 0:82 [4]. From this fact, changes in the particle volume distribution in these samples are very small and changes in the behavior of Hf with x can be mainly attributed to changes in the anisotropy field distribution. Accordingly the increases in the substitution level in these systems not only lower the mean anisotropy field but also give rise to a narrower distribution of anisotropy fields. From this study it can be concluded that the behavior of fluctuation fields in particulate systems is governed by the nature of the distribution of activation energies that usually arises from distributions of both particle volumes and anisotropy fields.
ARTICLE IN PRESS M. El-Hilo et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e493–e495
References [1] L. N!eel, J. Phys. Radium 11 (1950) 49. [2] R. Street, J.C. Woolley, P.B. Smith, Proc. Phys. Soc. B 65 (1952) 679. [3] M. El-Hilo, K. O’Grady, R.W. Chantrell, J. Magn. Magn. Mater. 248 (2002) 360.
e495
[4] M. El-Hilo, H. Pfeiffe, K. O’Grady, W. Schuppel, . E. Sinn, . . P. Gorrnert, M. Rosler, D.P.E. Dickson, R. Wchantrell, J. Magn. Magn. Mater. 129 (1994) 339. [5] D.C. Crew, S.H. Farrant, P.G. McCormic, R.W. Street, J. Magn. Magn. Mater. 163 (1996) 229. [6] P. Gaunt, J. Appl. Phys. 59 (1986) 4129.