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Characterisation of magnetic materials by impedance spectroscopy
Solid State Ionics 40/41 ( 1990) 220-223 North-Holland
CHARACTERISATION J.T.S. IRVINE,
OF MAGNETIC
MATERIALS
BY IMPEDANCE
SPECTROSCOPY
A.R. WEST
Department of Chemistry, University ofAberdeen, Meston Walk, Old Aberdeen AB9 2lJE, Scotland, UK
E. AMANO,
A. HUANOSTA
and R. VALENZUELA
Institute de Investigaciones en Materiales, VNAM, Mexico DF 04510, Mexico
Impedance spectroscopy has been used to investigate the magnetic properties of (Ni,Zn)Fe,O,. Two magnetic relaxations were observed corresponding to domain wall bulging and domain rotation. At higher applied fields a second magnetic mechanism, involving irreversible domain movement, was also observed. An equivalent circuit consisting of two RL parallel elements and a Warburg-type magnetic impedance has been used to model these phenomena.
1. Introduction Impedance spectroscopy is a valuable technique for the characterisation of inhomogeneous electrical materials, utilising the different frequency dependences of the constituent components for their separation. The responses of most components, for example bulk and grain boundary impedances in electroceramics, take the form of electrical relaxations and can be modelled using simple RC parallel circuit elements. Each electrical component has its own characteristic relaxation time, given by the magnitude of the RC product and these may be separated in the frequency domain. Other components, particularly those related to diffusion, are associated with inclined spikes (often at 45 ’ ) in the impedance plane and can be modelled by Warburg-type impedances (constant phase elements) [ 11. ac magnetic properties show similar frequency dispersions to those exhibited by electrical properties. In particular, magnetic relaxations occur at high frequencies in magnetic materials [ 21. These are associated with reversible changes in magnetic structure, such as domain wall bulging. Other phenomena, which are associated with irreversible domain wall movement (hysteresis) are observed at low frequencies. Magnetic impedance spectroscopy would appear to be an ideal technique to investigate these phenomena. 0167-2738/90/s 03.50 0 Elsevier Science Publishers B.V. (North-Holland )
We have already shown how impedance spectroscopy can be used to characterise the electrical inhomogeneities in magnetic ceramics [ 3,4]. In this paper we show how impedance spectroscopy can be used to study the dynamics of domain movement in magnetic materials. Our investigations of magnetic relaxations in ferrites [ 4,s ] are briefly reviewed and new measurements on irreversible domain movement in (Ni,Zn)Fe*O, presented.
2. Experimental
The preparation of polycrystalline toroids of (Nio.~aZno.a4)Fez04 and the set-up used for impedance measurements have been described elsewhere [ 4,5]. For magnetic impedance measurements, a low capacitance coil was wound around the toroid. Measurements were performed over the frequency range 5 Hz to 13 MHz, generally using a signal of amplitude 0.1 V.
3. Magnetic relaxations The impedance
response
of a coil wound around
J. T.S. Irvine et al. /Impedance
( Ni,Zn)FezOa toroids indicates the presence of two, or more, impedance elements [ 5 1. Logarithmic plots of conductivity against frequency show clearly that the magnetic impedance of (Ni,Zn)Fe,O, consists of two components (fig. 1). Three plateaux are observed in these plots; the lowest frequency one corresponds to the resistance of the coil, the other two correspond to resistances associated with the magnetisation dynamics of the ferrite. The observed response could be modelled using an equivalent circuit consisting of two RL parallel elements in series with the resistance of the measuring coil (fig. 1). Each RL element corresponds to a magnetic relaxation, L being the inductance, which is proportional to the permeability, and R being a measure of the difficulty of reorganisation. The two magnetic mechanisms, associated with these RL elements, can be attributed to domain wall bulging (low frequency) and domain rotation (high frequency). Values of the resistive components can be readily extracted from log conductivity plots and the inductive components extracted from complex inductance plots, where L*=z*/jw [ 41. The resistive and inductive components due to both mechanisms tend to zero at the Curie transition, fig. 2, though well below the Curie transition, inductance increases with temperature. Impedance plane plots for magnetic relaxations show some similarity to admittance plots for electrical materials. This is a consequence of simple RCL circuit theory. For example, a single RL parallel ele-
spectroscopy for magnetic materials
221
I
750 -
/
(Nl,Zn),Fe204
R2
I
0
I
\1 I 150
I
50
100 T“C
80-
60L IpH 40-
20 9’
I 0
50
I
b
100
150
T/'C Fig. 2. Dependence temperature.
of R (a)
and
L (b)
components
on
ment has the same impedance plane response as the admittance plane response of an RC series element. More generally, it is possible to transform a simple inductive circuit into a capacitive circuit with the same immittance response by interchanging the following three sets of parameters: - impedance o admittance, series o parallel and inductance o capacitance.
log0
0
I
2
3
L
5
6
7
log f (Hz1
Fig. 1. Plot of conductivity against circuit used to model this response.
frequency.
Inset, equivalent
4. Magnetic hysteresis The response observed in magnetic impedance measurements of (Ni,Zn)Fe204 changes as the ap-
J. T.S. Irvine et al. /Impedance
222
plied voltage signal is increased. These changes are apparent in both log conductivity plots (fig. 3), where the low frequency magnetic relaxation is masked at higher voltages, and in inductance versus frequency plots (fig. 4)) where the low frequency inductance is greatly enhanced. This increase in inductance indicates that an additional magnetic mechanism becomes important at higher applied magnetic fields. The dependence of this mechanism upon applied field indicates that it is related to hysteresis. The most likely mechanism to give rise to hysteresis involves irreversible domain wall movement. The impedance response for (Ni,Zn)Fe20, mea-
0
log 0 .(ohm? -1
-31 0
1
I
1
/
1
1
2
3
4
5
b
7
spectroscopy for magnetic materials
sured at 112’ C, using applied voltages of 0.1 and 1.O V, is shown in fig. 5. The response at 0.1 V, where hysteresis is not an important mechanism, corresponds to the low frequency part of an impedance semicircle. The response at 1 V, where hysteresis is an important magnetic mechanism, shows an additional element at low frequencies. This additional element takes the form of an inclined spike in the impedance plane, and is reminiscent of the Warburgtype impedances associated with diffusion in electrical impedance measurements. This similarity is not surprising as hysteresis involves the domain wall moving in a series of jumps through the lattice [ 6 1. Domain walls normally pass through imperfections or defects in magnetic materials. Applying a small magnetic field causes the domain wall to bulge in the direction of the magnetic field, but the wall remains pinned at these imperfections. Applying a larger magnetic field causes the domain wall to jump from being pinned at one set of imperfections to being pinned at another set (Barkhausen effect ). A magnetic Warburg impedance, ZIn,= A,/%+jA& (where A is a function of voltage) has been introduced to model the observed response. This element is the inverse of the electrical Warburg impedance, but corresponds to the electrical admittance Warburg, in accordance with the electrical to
log f (Hz) Fig. 3. Conductivity voltages.
against
frequency,
using different
applied
I
20 400
I
I
I/ /
1
0 IV
I
._
15
1
I
I
ov
flc
-&I
r&A-l
Z"(ohms I
Ll
t
L2
10 zooLI,uHI
5
log10
Fig. 4. Inductance
f (Hz1
against frequency,
at different applied voltages.
lNi,Zn)
Fe204
112oc
1
Fig. 5. Impedance plane response ( P = Z’ + jZ” ) using 0.1 and 1.0 V applied voltages. Inset, equivalent circuit used to model this response.
J. TX Irvine et al. /Impedance
magnetic immittance transformation detailed above. The equivalent circuit shown in fig. 5, can be used to model the observed hysteresis and relaxation processes in (Ni,Zn)Fe*O,. This circuit gives the same impedance response as is seen in figs. 3-5. The Warburg has been placed in series with the inductance associated with domain bulging and in parallel with the associated resistance. This circuit gives a reasonable model of the hysteresis and relaxation processes as both mechanisms involve movement of the domain walls. Two alternative circuits have been discounted as these would give unrealistic impedance responses. If the magnetic Warburg was placed in series with the two RL parallel elements, the contribution of irreversible wall movement to the impedance would not tend to zero at high frequencies. Alternatively, placing the magnetic Warburg in parallel with both the resistance and inductance would not give the observed 45” spike at low frequencies.
spectroscopy for magnetic materials
terials. Both reversible and irreversible changes in the domain structure can be studied. Combination with electrical impedance spectroscopy, which allows characterisation of the electrical inhomogeneities, gives a technique which affords a wide-ranging characterisation of magnetic materials.
Acknowledgement We thank the British Council and Conacyt for supporting the Aberdeen-Mexico collaboration programme and the Royal Society of Edinburgh for a BP Research Fellowship (JTSI).
References [ 1] I.D. Raistrick,
[2]
[ 31 5. Conclusions [4]
Magnetic impedance spectroscopy is a powerful technique that can give a great deal of information about the magnetisation dynamics in magnetic ma-
223
[5] [6]
J.R. Macdonald and D.R. Franceschetti, in: Impedance spectroscopy, ed. J.R. Macdonald (Wiley, New York, 1987) chap. 2. G.T. Rado, Rev. Mod. Phys. 25 (1953) 81. J.T.S. Irvine, A. Huanosta, R. Valenzuela and A.R. West, J. Am. Ceram. Sot., to be published. J.T.S. Irvine, A. Huanosta, R. Valenzuela and A.R. West, in: Proc. 5th Int. Conf. Ferrites, Bombay, 1989, to be published. J.T.S. Irvine, A. Huanosta, R. Valenzuela and A.R. West, IEEE Trans. Magn., submitted for publication. H.J. Williams and W. Schockley, Phys. Rev. 75 (1949) 178.
CHARACTERISATION J.T.S. IRVINE,
OF MAGNETIC
MATERIALS
BY IMPEDANCE
SPECTROSCOPY
A.R. WEST
Department of Chemistry, University ofAberdeen, Meston Walk, Old Aberdeen AB9 2lJE, Scotland, UK
E. AMANO,
A. HUANOSTA
and R. VALENZUELA
Institute de Investigaciones en Materiales, VNAM, Mexico DF 04510, Mexico
Impedance spectroscopy has been used to investigate the magnetic properties of (Ni,Zn)Fe,O,. Two magnetic relaxations were observed corresponding to domain wall bulging and domain rotation. At higher applied fields a second magnetic mechanism, involving irreversible domain movement, was also observed. An equivalent circuit consisting of two RL parallel elements and a Warburg-type magnetic impedance has been used to model these phenomena.
1. Introduction Impedance spectroscopy is a valuable technique for the characterisation of inhomogeneous electrical materials, utilising the different frequency dependences of the constituent components for their separation. The responses of most components, for example bulk and grain boundary impedances in electroceramics, take the form of electrical relaxations and can be modelled using simple RC parallel circuit elements. Each electrical component has its own characteristic relaxation time, given by the magnitude of the RC product and these may be separated in the frequency domain. Other components, particularly those related to diffusion, are associated with inclined spikes (often at 45 ’ ) in the impedance plane and can be modelled by Warburg-type impedances (constant phase elements) [ 11. ac magnetic properties show similar frequency dispersions to those exhibited by electrical properties. In particular, magnetic relaxations occur at high frequencies in magnetic materials [ 21. These are associated with reversible changes in magnetic structure, such as domain wall bulging. Other phenomena, which are associated with irreversible domain wall movement (hysteresis) are observed at low frequencies. Magnetic impedance spectroscopy would appear to be an ideal technique to investigate these phenomena. 0167-2738/90/s 03.50 0 Elsevier Science Publishers B.V. (North-Holland )
We have already shown how impedance spectroscopy can be used to characterise the electrical inhomogeneities in magnetic ceramics [ 3,4]. In this paper we show how impedance spectroscopy can be used to study the dynamics of domain movement in magnetic materials. Our investigations of magnetic relaxations in ferrites [ 4,s ] are briefly reviewed and new measurements on irreversible domain movement in (Ni,Zn)Fe*O, presented.
2. Experimental
The preparation of polycrystalline toroids of (Nio.~aZno.a4)Fez04 and the set-up used for impedance measurements have been described elsewhere [ 4,5]. For magnetic impedance measurements, a low capacitance coil was wound around the toroid. Measurements were performed over the frequency range 5 Hz to 13 MHz, generally using a signal of amplitude 0.1 V.
3. Magnetic relaxations The impedance
response
of a coil wound around
J. T.S. Irvine et al. /Impedance
( Ni,Zn)FezOa toroids indicates the presence of two, or more, impedance elements [ 5 1. Logarithmic plots of conductivity against frequency show clearly that the magnetic impedance of (Ni,Zn)Fe,O, consists of two components (fig. 1). Three plateaux are observed in these plots; the lowest frequency one corresponds to the resistance of the coil, the other two correspond to resistances associated with the magnetisation dynamics of the ferrite. The observed response could be modelled using an equivalent circuit consisting of two RL parallel elements in series with the resistance of the measuring coil (fig. 1). Each RL element corresponds to a magnetic relaxation, L being the inductance, which is proportional to the permeability, and R being a measure of the difficulty of reorganisation. The two magnetic mechanisms, associated with these RL elements, can be attributed to domain wall bulging (low frequency) and domain rotation (high frequency). Values of the resistive components can be readily extracted from log conductivity plots and the inductive components extracted from complex inductance plots, where L*=z*/jw [ 41. The resistive and inductive components due to both mechanisms tend to zero at the Curie transition, fig. 2, though well below the Curie transition, inductance increases with temperature. Impedance plane plots for magnetic relaxations show some similarity to admittance plots for electrical materials. This is a consequence of simple RCL circuit theory. For example, a single RL parallel ele-
spectroscopy for magnetic materials
221
I
750 -
/
(Nl,Zn),Fe204
R2
I
0
I
\1 I 150
I
50
100 T“C
80-
60L IpH 40-
20 9’
I 0
50
I
b
100
150
T/'C Fig. 2. Dependence temperature.
of R (a)
and
L (b)
components
on
ment has the same impedance plane response as the admittance plane response of an RC series element. More generally, it is possible to transform a simple inductive circuit into a capacitive circuit with the same immittance response by interchanging the following three sets of parameters: - impedance o admittance, series o parallel and inductance o capacitance.
log0
0
I
2
3
L
5
6
7
log f (Hz1
Fig. 1. Plot of conductivity against circuit used to model this response.
frequency.
Inset, equivalent
4. Magnetic hysteresis The response observed in magnetic impedance measurements of (Ni,Zn)Fe204 changes as the ap-
J. T.S. Irvine et al. /Impedance
222
plied voltage signal is increased. These changes are apparent in both log conductivity plots (fig. 3), where the low frequency magnetic relaxation is masked at higher voltages, and in inductance versus frequency plots (fig. 4)) where the low frequency inductance is greatly enhanced. This increase in inductance indicates that an additional magnetic mechanism becomes important at higher applied magnetic fields. The dependence of this mechanism upon applied field indicates that it is related to hysteresis. The most likely mechanism to give rise to hysteresis involves irreversible domain wall movement. The impedance response for (Ni,Zn)Fe20, mea-
0
log 0 .(ohm? -1
-31 0
1
I
1
/
1
1
2
3
4
5
b
7
spectroscopy for magnetic materials
sured at 112’ C, using applied voltages of 0.1 and 1.O V, is shown in fig. 5. The response at 0.1 V, where hysteresis is not an important mechanism, corresponds to the low frequency part of an impedance semicircle. The response at 1 V, where hysteresis is an important magnetic mechanism, shows an additional element at low frequencies. This additional element takes the form of an inclined spike in the impedance plane, and is reminiscent of the Warburgtype impedances associated with diffusion in electrical impedance measurements. This similarity is not surprising as hysteresis involves the domain wall moving in a series of jumps through the lattice [ 6 1. Domain walls normally pass through imperfections or defects in magnetic materials. Applying a small magnetic field causes the domain wall to bulge in the direction of the magnetic field, but the wall remains pinned at these imperfections. Applying a larger magnetic field causes the domain wall to jump from being pinned at one set of imperfections to being pinned at another set (Barkhausen effect ). A magnetic Warburg impedance, ZIn,= A,/%+jA& (where A is a function of voltage) has been introduced to model the observed response. This element is the inverse of the electrical Warburg impedance, but corresponds to the electrical admittance Warburg, in accordance with the electrical to
log f (Hz) Fig. 3. Conductivity voltages.
against
frequency,
using different
applied
I
20 400
I
I
I/ /
1
0 IV
I
._
15
1
I
I
ov
flc
-&I
r&A-l
Z"(ohms I
Ll
t
L2
10 zooLI,uHI
5
log10
Fig. 4. Inductance
f (Hz1
against frequency,
at different applied voltages.
lNi,Zn)
Fe204
112oc
1
Fig. 5. Impedance plane response ( P = Z’ + jZ” ) using 0.1 and 1.0 V applied voltages. Inset, equivalent circuit used to model this response.
J. TX Irvine et al. /Impedance
magnetic immittance transformation detailed above. The equivalent circuit shown in fig. 5, can be used to model the observed hysteresis and relaxation processes in (Ni,Zn)Fe*O,. This circuit gives the same impedance response as is seen in figs. 3-5. The Warburg has been placed in series with the inductance associated with domain bulging and in parallel with the associated resistance. This circuit gives a reasonable model of the hysteresis and relaxation processes as both mechanisms involve movement of the domain walls. Two alternative circuits have been discounted as these would give unrealistic impedance responses. If the magnetic Warburg was placed in series with the two RL parallel elements, the contribution of irreversible wall movement to the impedance would not tend to zero at high frequencies. Alternatively, placing the magnetic Warburg in parallel with both the resistance and inductance would not give the observed 45” spike at low frequencies.
spectroscopy for magnetic materials
terials. Both reversible and irreversible changes in the domain structure can be studied. Combination with electrical impedance spectroscopy, which allows characterisation of the electrical inhomogeneities, gives a technique which affords a wide-ranging characterisation of magnetic materials.
Acknowledgement We thank the British Council and Conacyt for supporting the Aberdeen-Mexico collaboration programme and the Royal Society of Edinburgh for a BP Research Fellowship (JTSI).
References [ 1] I.D. Raistrick,
[2]
[ 31 5. Conclusions [4]
Magnetic impedance spectroscopy is a powerful technique that can give a great deal of information about the magnetisation dynamics in magnetic ma-
223
[5] [6]
J.R. Macdonald and D.R. Franceschetti, in: Impedance spectroscopy, ed. J.R. Macdonald (Wiley, New York, 1987) chap. 2. G.T. Rado, Rev. Mod. Phys. 25 (1953) 81. J.T.S. Irvine, A. Huanosta, R. Valenzuela and A.R. West, J. Am. Ceram. Sot., to be published. J.T.S. Irvine, A. Huanosta, R. Valenzuela and A.R. West, in: Proc. 5th Int. Conf. Ferrites, Bombay, 1989, to be published. J.T.S. Irvine, A. Huanosta, R. Valenzuela and A.R. West, IEEE Trans. Magn., submitted for publication. H.J. Williams and W. Schockley, Phys. Rev. 75 (1949) 178.