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The fluctuation field and anomalous magnetic viscosity in commercial NdFeB alloys, AlNiCo and the bulk amorphous ferromagnets Nd60Fe30Al10 and Nd60Fe20Co10Al10
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 320 (2008) 2089–2093 www.elsevier.com/locate/jmmm
The fluctuation field and anomalous magnetic viscosity in commercial NdFeB alloys, AlNiCo and the bulk amorphous ferromagnets Nd60Fe30Al10 and Nd60Fe20Co10Al10 S.J. Collocott, J.B. Dunlop CSIRO Materials Science and Engineering, Lindfield, NSW 2070, Australia Received 27 July 2007; received in revised form 17 January 2008 Available online 25 March 2008
Abstract The fluctuation field, H f , is a useful parameter for characterising any ferromagnetic material that displays hysteresis, as it is a measure of the thermally activated rate processes that govern magnetisation reversals. Anomalous magnetic viscosity, i.e. nonmonotonic behaviour of the time dependent magnetisation, where the magnetisation is seen to increase, reach a peak, and then decrease, has been observed on both the upper and lower branches of minor loops or recoil curves in some ferromagnetic materials. Parameters relevant to the Preisach model are discussed as to their usefulness in predicting anomalous magnetic viscosity in ferromagnetic materials. This is done with reference to measurements of H f and the time dependent magnetisation in commercial NdFeB alloys, AlNiCo and the bulk amorphous ferromagnets Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 . Crown Copyright r 2008 Published by Elsevier B.V. All rights reserved. PACS: 75.60.d; 75.60.Ej; 75.60.Nt; 75.50.Bb Keywords: Fluctuation field; Anomalous magnetic viscosity; Preisach model
1. Introduction
the more general form
Time dependent magnetisation, under a constant applied magnetic field, which is observed in ferromagnetic materials, is a consequence of thermal activation processes which transform metastable states to stable states [1–3]. The time dependent magnetisation, MðtÞ, when measured on the major hysteresis loop over limited time scales, follows the well known expression [1]
H f ðH; tÞ ¼
MðtÞ ¼ M 0 þ S lnðt þ t0 Þ
(1)
where S is the magnetic viscosity parameter, M 0 a constant and t0 a fitting parameter to establish a reference time. The fluctuation field, H f , is defined by [4] Hf ¼
S wirr
(2)
where wirr is the irreversible magnetic susceptibility, or in Corresponding author. Tel.: +61 294137130; fax: +61 294137200.
E-mail address: [email protected] (S.J. Collocott).
SðH; tÞ wirr ðH; tÞ
(3)
which shows that H f may be time dependent [2]. It was Wohlfarth [4] who recognised the fundamental importance of the fluctuation field and the coercive force, in the interpretation of relaxation processes that lead to the time dependence of magnetisation in a wide range of magnetic materials. Anomalous magnetic viscosity, i.e. nonmonotonic behaviour of the time dependent magnetisation, where the magnetisation is seen to increase, reach a peak, and then decrease, has been observed on both the upper and lower branches of minor loops or recoil curves in the bulk amorphous ferromagnets Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 [5,6]. The Preisach model provides a framework for interpreting this behaviour, with the observed time dependent magnetisation the sum of contributions from hysterons, making opposite contributions to the magnetisation, in two
0304-8853/$ - see front matter Crown Copyright r 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.03.029
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regions (say A and B) of the Preisach plane, relaxing with very different time constants [6,7]. Bertotti [7, pp. 500–503] gives the following expressions for the time constants of the two sets of relaxing hysterons, which are a consequence of a double field reversal or two-step process, namely tA ¼ t0
(4)
and
H2 H1 tB ¼ t0 exp Hf
ture (294 K) in applied fields up to 1.5 MA/m, using a Lake Shore Vibrating Sample Magnetometer mounted on an electromagnet. The fluctuation field, H f , was determined using the method of Street and Brown [1] (frequently termed the waiting time method), based on the equation DH ¼
(5)
where t0 is viewed as a time interval over which the system updates its state, H 1 is the turning point on the major hysteresis loop, where the direction of the applied field is reversed to begin traversing the recoil curve (or minor hysteresis loop), and H 2 is the final field. For the case of the recoil curve that leads to the dc demagnetised state, H 2 equals zero and the magnetisation is zero. Eq. (5) shows that in the Preisach model, H f is an experimentally determined material parameter, and its value, in relation to H 1 and H 2 , plays a key role in determining the experimental conditions necessary for observation of nonmonotonic behaviour of the time dependent magnetisation, on recoil curves. Measurements of the time dependent magnetisation on the major hysteresis loop have been made for a range of commercial NdFeB magnet materials, AlNiCo and the bulk amorphous ferromagnets Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 , and H f determined for each material. The materials were selected to give a range of values for H f . For each material, time dependent magnetisation measurements were made on the recoil curve that connects a turning point on the major hysteresis loop to zero applied field (i.e. the recoil curve that leads to the dc demagnetised state) to probe for nonmonotonic behaviour. The usefulness of the Preisach model as a guide in predicting nonmonotonic behaviour in ferromagnetic materials is discussed.
kT lnðtÞ ¼ H f lnðtÞ qE=qHjM
(6)
In practice, the sample is first saturated magnetically in the forward direction and the field is then reduced, reversed on moving to the second quadrant, and then held constant. Measurements of the magnetisation, M, as a function of time are made at fixed incremental values of applied field, m0 H a , see Fig. 1. The intersection of lines of constant m0 M with the experimental curves, each at a constant applied field, gives the time, t. A plot, as is shown in Fig. 2, of m0 H a against lnðtÞ, results in a line, with the gradient, as is seen from Eq. (6), giving H f . Investigation of nonmonotonic behaviour of the time dependent magnetisation on a recoil line requires a twostep process. The sample is initially saturated magnetically, and the field is ramped in a negative direction to a turning point on the major hysteresis loop, H 1 , which is Step 1, followed by a second step, Step 2, where the field is ramped in a positive direction to a point H 2 on a recoil curve, where the field is held at a constant value. For the recoil curve that leads to the dc demagnetised state, H 1 is chosen such that when H 2 is equal to zero, M is equal to zero. For each sample H 1 was chosen for the recoil curve leading to dc demagnetisation, and the time dependent magnetisation was measured for a range of values of H 2 along the recoil curve to ascertain the presence or absence of nonmonotonic behaviour.
15
2. Experimental 10 5 µ0M (mT)
The NdFeB based materials studied were MQA-T, a commercial NdFeB HDDR anisotropic powder from Magnequench, and SPRAXC, a NdFeB two-phase nanocomposite isotropic powder from Neomax, along with AlNiCo, and the bulk amorphous ferromagnets Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 . The bulk amorphous samples were prepared using the method given in Ref. [6], and X-ray powder diffraction analysis showed each sample to be essentially amorphous, with only a trace (o1%) of crystallinity. The MQA-T and SPRAXC samples were prepared by fixing in epoxy resin, with the MQA-T powder aligned in a field of 80 kA/m. The AlNiCo sample was a polished sphere, about 5 mm in diameter. The Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 samples were in the form of rods about 6 mm long and 2 mm in diameter. Magnetic measurements were performed at room tempera-
0 -5 -10 -15
10
100
1000 Time (secs)
10000
100000
Fig. 1. Experimental results for SPRAXC for the decay of the magnetisation, m0 M, with the logarithm of time for fixed values of applied field ðm0 H a Þ of (E) 405:5 mT, (m) 406:5 mT, (’) 407:7 mT, () 408:4 mT and (.) 409:1 mT.
ARTICLE IN PRESS S.J. Collocott, J.B. Dunlop / Journal of Magnetism and Magnetic Materials 320 (2008) 2089–2093
-405
Table 1 Intrinsic coercivity, H ic , fluctuation field, H f , and turning point, H 1 , on the main loop which leads to the dc demagnetised state for the materials studied
-406 µ0Ha (mT)
2091
-407
-408
-409 3
4
5
6
7 8 In (t) (secs)
9
10
11
12
Fig. 2. m0 H a and lnðtÞ determined from the curves in Fig. 1. The average gradient of the lines is 1.3 mT, which is the fluctuation field.
3. Results and discussion Experimental results showing the decay of the magnetisation for a one-step process on the main hysteresis loop at a number of fixed fields, chosen to be close to the coercive field, for SPRAXC are shown in Fig. 1. Fig. 2 shows m0 H a against lnðtÞ, deduced from Fig. 1, for the determination of H f . Only data for SPRAXC are given, as it is representative of the behaviour shown by all the samples. The value of H f for each sample is reported in Table 1. The value of m0 H f obtained in Nd60 Fe30 Al10 is consistent with the value of 12–13 mT reported by Ref. [5], and interestingly the two bulk amorphous alloys exhibit a much larger value of H f , when compared to the crystalline MQAT, two-phase nanocomposite SPRAXC and AlNiCo. Ferguson et al. [8] in their study of sintered and melt-spun NdFeB report values for m0 H f of 5 and 8 mT, respectively, which are both larger than the values for MQAT (3.7 mT) and SPRAXC (1.3 mT), reported here. The behaviour of the time dependent magnetisation along the recoil curve, which leads to the dc demagnetised state, in bulk amorphous Nd60 Fe30 Al10 is shown in Fig. 3 (for data which show similar behaviour in Nd60 Fe20 Co10 Al10 see Ref. [6]). Initially at, and near, the turning point on the major hysteresis loop the magnetisation is seen to decrease with a logarithmic time dependence. From Fig. 3, it is seen that there are a range of experimental values of H 2 that result in a peak in the magnetisation, i.e. nonmonotonic behaviour is observed, with the time taken to reach the peak increasing from a few tens of seconds to 30,000 s as H 2 increases towards zero. For H 2 ¼ 0 the magnetisation is seen to increase monotonically with a logarithmic time dependence, i.e. spontaneous remagnetisation is observed. In Fig. 4, data are shown for SPRAXC for a range of experimental values of H 2 as the recoil curve is traversed. Both Nd60 Fe30 Al10 and SPRAXC exhibit similar behaviour at the turning point on the major
Material
m0 H ic (T)
m0 H f (mT)
m0 H 1 (mT)
Nd60 Fe30 Al10 Nd60 Fe20 Co10 Al10 MQAT SPRAXC AlNiCo
0.334 0.348 1.22 0.417 0.064
11.1 9.4 3.7 1.3 0.1
362.5 365.3 1250 695.8 105
hysteresis loop and at H 2 ¼ 0, but for SPRAXC there is no evidence of a peak in the magnetisation, at any value of H 2 , that would signify nonmonotonic behaviour. Rather, in SPRAXC as H 2 increases towards zero the rate of logarithmic decay of the magnetisation decreases, becomes almost constant with time, and then is seen to increase with time. The SPRAXC data shown in Fig. 4 are representative of, and qualitatively similar to, the other crystalline materials studied, MQAT and AlNiCo. The magnetic field history described by the two-step process (Step 1 is from magnetic saturation to H 1 , followed by Step 2 where the field is ramped in a positive direction from H 1 to H 2 ) can be represented in the Preisach plane. Here two portions of the state line relax, shown by arrows in Fig. 5, in opposite directions, with opposite contributions to the magnetisation. As is noted by Bertotti [7, p. 503], the Preisach approach predicts that as a function of time, the magnetisation first increases, reaching a maximum (peak), before decreasing i.e. nonmonotic behaviour. Of the materials studied, this predicted behaviour is observed experimentally in the two bulk amorphous alloys, Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 , but not in the crystalline materials SPRAXC, MQAT and AlNiCo. In the Preisach approach, one might speculate on the potential usefulness of Eq. (5) as a predictor of the material properties (H f ) and experimental conditions (H 1 and H 2 ) required for nonmonotonic behaviour. Eq. (5) can be rewritten as tB H2 H1 ln ¼ (7) t0 Hf In bulk amorphous Nd60 Fe30 Al10 nonmonotonic behaviour is observed for values of m0 H 2 ranging from 210 to 110 mT. This gives values ranging from 14 to 23 for the factor ðH 2 H 1 Þ=H f . Similarly, for Nd60 Fe20 Co10 Al10 values for the factor ðH 2 H 1 Þ=H f are in the range 14–25 [6]. Turning now to SPRAXC, if the factor ðH 2 H 1 Þ=H f is to have general applicability in predicting the experimental conditions required for observing nonmonotonic behaviour, it would imply that for SPRAXC nonmonotonic behaviour should be observed when m0 H 2 has a value of around 670 mT (from Eq. (7) with ðH 2 H 1 Þ=H f ¼ 20, m0 H 1 ¼ 695:8 mT and m0 H f ¼ 1:3 mT). As no nonmonotonic behaviour is observed in SPRAXC (or in the
ARTICLE IN PRESS S.J. Collocott, J.B. Dunlop / Journal of Magnetism and Magnetic Materials 320 (2008) 2089–2093
2092
-9.3
-50
-7.2
-60
-9.4
-70
-7.4 -9.5
-80 -90
-7.6
-9.6
µ0M (mT)
-100 101
102
103
104
105
-9.7
101
102
103
104
105
-7.8
-15.2
101
102
103
104
105
104
105
5 -1.6 4
-1.8
-15.4
-15.6
-2.0
3
-2.2
2
-2.4
1
-2.6
-15.8 101
102
103
104
105
101
102
103
104
0
105
101
102
103
Time (secs)
µ0M (mT)
Fig. 3. Magnetisation, m0 M, as a function of time in Nd60 Fe30 Al10 , on the recoil curve that leads to the dc demagnetised state, commencing at (a) the turning point on the main loop (m0 H 1 ) 362:5 mT, and for values of m0 H 2 , (b) 210 mT, (c) 180 mT, (d) 140 mT, (e) 110 mT and (f) 0 mT.
-540
-515
-500
-545
-520
-505
-550
-525
-510
-555
-530
-515
-560 101
102
103
104
-535 101
102
103
104
-520 101
-410
-320
20
-415
-325
15
-420
-330
10
-425
-335
5
-430 101
102
103
104
-340 101
102 103 Time (secs)
104
0 101
102
103
104
102
103
104
Fig. 4. Magnetisation, m0 M, as a function of time for SPRAXC along the recoil curve that leads to the dc demagnetised state, commencing at (a) the turning point on the main loop (m0 H 1 ) 695:8 mT, and for values of m0 H 2 , (b) 675:5 mT, (c) 662:5 mT, (d) 500 mT, (e) 342:3 mT and (f) 0 mT.
ARTICLE IN PRESS S.J. Collocott, J.B. Dunlop / Journal of Magnetism and Magnetic Materials 320 (2008) 2089–2093
hu Area B
H
H2
hc
Area A
+
2093
structure inhibits these relaxation processes due to pinning sites that inhibit domain-wall motion processes. In summary, values of the fluctuation field in Nd60 Fe30 Al10 , Nd60 Fe20 Co10 Al10 , MQAT, SPRAXC and AlNiCo are reported. Nonmonotonic behaviour is observed in the bulk amorphous ferromagnetic materials, but not in the crystalline ferromagnetic materials studied. Whilst the Preisach model provides a suitable theoretical approach for explaining any observed nonmonotonic behaviour, it is not useful as a predictor of the experimental conditions required for the observation of nonmonotonic behaviour.
+
H1 Fig. 5. The Preisach description of relaxation following a two-step magnetic field history [6]: Step 1 is from magnetic saturation to H 1 , followed by Step 2 where the field is ramped in a positive direction from H 1 to H 2 .
other crystalline materials studied), the factor ðH 2 H 1 Þ=H f obviously has no general usefulness as a predictor of nonmonotonic behaviour. Of more importance is the difference in the microstructure between the amorphous and crystalline materials. In the amorphous materials the local fields, which drive the observed magnetisation, relax readily and at a rate that is easily accessible in terms of experimental time scales (a few tens of seconds to a few tens of thousands of seconds). In the crystalline materials the
Acknowledgement The authors thank Satsohi Hirosawa, Neomax Co. Ltd., for supplying the SPRAXC material.
References [1] [2] [3] [4] [5]
R. Street, S.D. Brown, J. Appl. Phys. 78 (1994) 6386. A. Lyberatos, R.W. Chantrell, J. Phys. Condens. Matter 9 (1997) 2623. L. Folks, R. Street, J. Appl. Phys. 78 (1994) 6391. E.P. Wohlfarth, J. Phys. F Met. Phys. 14 (1984) L155. L. Wang, J. Ding, Y. Li, Y.P. Feng, X.Z. Wang, Phys. J. Mag. Mag. Mater. 206 (1999) 127. [6] S.J. Collocott, J.B. Dunlop, Phys. Rev. B 66 (2002) 224420. [7] G. Bertotti, in: Hysteresis in Magnetism, Academic Press, San Diego, 1998. [8] G.B. Ferguson, K. O’Grady, J. Popplewell, R.W. Chantrell, et al., J. Appl. Phys. 69 (1991) 5495.
Journal of Magnetism and Magnetic Materials 320 (2008) 2089–2093 www.elsevier.com/locate/jmmm
The fluctuation field and anomalous magnetic viscosity in commercial NdFeB alloys, AlNiCo and the bulk amorphous ferromagnets Nd60Fe30Al10 and Nd60Fe20Co10Al10 S.J. Collocott, J.B. Dunlop CSIRO Materials Science and Engineering, Lindfield, NSW 2070, Australia Received 27 July 2007; received in revised form 17 January 2008 Available online 25 March 2008
Abstract The fluctuation field, H f , is a useful parameter for characterising any ferromagnetic material that displays hysteresis, as it is a measure of the thermally activated rate processes that govern magnetisation reversals. Anomalous magnetic viscosity, i.e. nonmonotonic behaviour of the time dependent magnetisation, where the magnetisation is seen to increase, reach a peak, and then decrease, has been observed on both the upper and lower branches of minor loops or recoil curves in some ferromagnetic materials. Parameters relevant to the Preisach model are discussed as to their usefulness in predicting anomalous magnetic viscosity in ferromagnetic materials. This is done with reference to measurements of H f and the time dependent magnetisation in commercial NdFeB alloys, AlNiCo and the bulk amorphous ferromagnets Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 . Crown Copyright r 2008 Published by Elsevier B.V. All rights reserved. PACS: 75.60.d; 75.60.Ej; 75.60.Nt; 75.50.Bb Keywords: Fluctuation field; Anomalous magnetic viscosity; Preisach model
1. Introduction
the more general form
Time dependent magnetisation, under a constant applied magnetic field, which is observed in ferromagnetic materials, is a consequence of thermal activation processes which transform metastable states to stable states [1–3]. The time dependent magnetisation, MðtÞ, when measured on the major hysteresis loop over limited time scales, follows the well known expression [1]
H f ðH; tÞ ¼
MðtÞ ¼ M 0 þ S lnðt þ t0 Þ
(1)
where S is the magnetic viscosity parameter, M 0 a constant and t0 a fitting parameter to establish a reference time. The fluctuation field, H f , is defined by [4] Hf ¼
S wirr
(2)
where wirr is the irreversible magnetic susceptibility, or in Corresponding author. Tel.: +61 294137130; fax: +61 294137200.
E-mail address: [email protected] (S.J. Collocott).
SðH; tÞ wirr ðH; tÞ
(3)
which shows that H f may be time dependent [2]. It was Wohlfarth [4] who recognised the fundamental importance of the fluctuation field and the coercive force, in the interpretation of relaxation processes that lead to the time dependence of magnetisation in a wide range of magnetic materials. Anomalous magnetic viscosity, i.e. nonmonotonic behaviour of the time dependent magnetisation, where the magnetisation is seen to increase, reach a peak, and then decrease, has been observed on both the upper and lower branches of minor loops or recoil curves in the bulk amorphous ferromagnets Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 [5,6]. The Preisach model provides a framework for interpreting this behaviour, with the observed time dependent magnetisation the sum of contributions from hysterons, making opposite contributions to the magnetisation, in two
0304-8853/$ - see front matter Crown Copyright r 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.03.029
ARTICLE IN PRESS 2090
S.J. Collocott, J.B. Dunlop / Journal of Magnetism and Magnetic Materials 320 (2008) 2089–2093
regions (say A and B) of the Preisach plane, relaxing with very different time constants [6,7]. Bertotti [7, pp. 500–503] gives the following expressions for the time constants of the two sets of relaxing hysterons, which are a consequence of a double field reversal or two-step process, namely tA ¼ t0
(4)
and
H2 H1 tB ¼ t0 exp Hf
ture (294 K) in applied fields up to 1.5 MA/m, using a Lake Shore Vibrating Sample Magnetometer mounted on an electromagnet. The fluctuation field, H f , was determined using the method of Street and Brown [1] (frequently termed the waiting time method), based on the equation DH ¼
(5)
where t0 is viewed as a time interval over which the system updates its state, H 1 is the turning point on the major hysteresis loop, where the direction of the applied field is reversed to begin traversing the recoil curve (or minor hysteresis loop), and H 2 is the final field. For the case of the recoil curve that leads to the dc demagnetised state, H 2 equals zero and the magnetisation is zero. Eq. (5) shows that in the Preisach model, H f is an experimentally determined material parameter, and its value, in relation to H 1 and H 2 , plays a key role in determining the experimental conditions necessary for observation of nonmonotonic behaviour of the time dependent magnetisation, on recoil curves. Measurements of the time dependent magnetisation on the major hysteresis loop have been made for a range of commercial NdFeB magnet materials, AlNiCo and the bulk amorphous ferromagnets Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 , and H f determined for each material. The materials were selected to give a range of values for H f . For each material, time dependent magnetisation measurements were made on the recoil curve that connects a turning point on the major hysteresis loop to zero applied field (i.e. the recoil curve that leads to the dc demagnetised state) to probe for nonmonotonic behaviour. The usefulness of the Preisach model as a guide in predicting nonmonotonic behaviour in ferromagnetic materials is discussed.
kT lnðtÞ ¼ H f lnðtÞ qE=qHjM
(6)
In practice, the sample is first saturated magnetically in the forward direction and the field is then reduced, reversed on moving to the second quadrant, and then held constant. Measurements of the magnetisation, M, as a function of time are made at fixed incremental values of applied field, m0 H a , see Fig. 1. The intersection of lines of constant m0 M with the experimental curves, each at a constant applied field, gives the time, t. A plot, as is shown in Fig. 2, of m0 H a against lnðtÞ, results in a line, with the gradient, as is seen from Eq. (6), giving H f . Investigation of nonmonotonic behaviour of the time dependent magnetisation on a recoil line requires a twostep process. The sample is initially saturated magnetically, and the field is ramped in a negative direction to a turning point on the major hysteresis loop, H 1 , which is Step 1, followed by a second step, Step 2, where the field is ramped in a positive direction to a point H 2 on a recoil curve, where the field is held at a constant value. For the recoil curve that leads to the dc demagnetised state, H 1 is chosen such that when H 2 is equal to zero, M is equal to zero. For each sample H 1 was chosen for the recoil curve leading to dc demagnetisation, and the time dependent magnetisation was measured for a range of values of H 2 along the recoil curve to ascertain the presence or absence of nonmonotonic behaviour.
15
2. Experimental 10 5 µ0M (mT)
The NdFeB based materials studied were MQA-T, a commercial NdFeB HDDR anisotropic powder from Magnequench, and SPRAXC, a NdFeB two-phase nanocomposite isotropic powder from Neomax, along with AlNiCo, and the bulk amorphous ferromagnets Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 . The bulk amorphous samples were prepared using the method given in Ref. [6], and X-ray powder diffraction analysis showed each sample to be essentially amorphous, with only a trace (o1%) of crystallinity. The MQA-T and SPRAXC samples were prepared by fixing in epoxy resin, with the MQA-T powder aligned in a field of 80 kA/m. The AlNiCo sample was a polished sphere, about 5 mm in diameter. The Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 samples were in the form of rods about 6 mm long and 2 mm in diameter. Magnetic measurements were performed at room tempera-
0 -5 -10 -15
10
100
1000 Time (secs)
10000
100000
Fig. 1. Experimental results for SPRAXC for the decay of the magnetisation, m0 M, with the logarithm of time for fixed values of applied field ðm0 H a Þ of (E) 405:5 mT, (m) 406:5 mT, (’) 407:7 mT, () 408:4 mT and (.) 409:1 mT.
ARTICLE IN PRESS S.J. Collocott, J.B. Dunlop / Journal of Magnetism and Magnetic Materials 320 (2008) 2089–2093
-405
Table 1 Intrinsic coercivity, H ic , fluctuation field, H f , and turning point, H 1 , on the main loop which leads to the dc demagnetised state for the materials studied
-406 µ0Ha (mT)
2091
-407
-408
-409 3
4
5
6
7 8 In (t) (secs)
9
10
11
12
Fig. 2. m0 H a and lnðtÞ determined from the curves in Fig. 1. The average gradient of the lines is 1.3 mT, which is the fluctuation field.
3. Results and discussion Experimental results showing the decay of the magnetisation for a one-step process on the main hysteresis loop at a number of fixed fields, chosen to be close to the coercive field, for SPRAXC are shown in Fig. 1. Fig. 2 shows m0 H a against lnðtÞ, deduced from Fig. 1, for the determination of H f . Only data for SPRAXC are given, as it is representative of the behaviour shown by all the samples. The value of H f for each sample is reported in Table 1. The value of m0 H f obtained in Nd60 Fe30 Al10 is consistent with the value of 12–13 mT reported by Ref. [5], and interestingly the two bulk amorphous alloys exhibit a much larger value of H f , when compared to the crystalline MQAT, two-phase nanocomposite SPRAXC and AlNiCo. Ferguson et al. [8] in their study of sintered and melt-spun NdFeB report values for m0 H f of 5 and 8 mT, respectively, which are both larger than the values for MQAT (3.7 mT) and SPRAXC (1.3 mT), reported here. The behaviour of the time dependent magnetisation along the recoil curve, which leads to the dc demagnetised state, in bulk amorphous Nd60 Fe30 Al10 is shown in Fig. 3 (for data which show similar behaviour in Nd60 Fe20 Co10 Al10 see Ref. [6]). Initially at, and near, the turning point on the major hysteresis loop the magnetisation is seen to decrease with a logarithmic time dependence. From Fig. 3, it is seen that there are a range of experimental values of H 2 that result in a peak in the magnetisation, i.e. nonmonotonic behaviour is observed, with the time taken to reach the peak increasing from a few tens of seconds to 30,000 s as H 2 increases towards zero. For H 2 ¼ 0 the magnetisation is seen to increase monotonically with a logarithmic time dependence, i.e. spontaneous remagnetisation is observed. In Fig. 4, data are shown for SPRAXC for a range of experimental values of H 2 as the recoil curve is traversed. Both Nd60 Fe30 Al10 and SPRAXC exhibit similar behaviour at the turning point on the major
Material
m0 H ic (T)
m0 H f (mT)
m0 H 1 (mT)
Nd60 Fe30 Al10 Nd60 Fe20 Co10 Al10 MQAT SPRAXC AlNiCo
0.334 0.348 1.22 0.417 0.064
11.1 9.4 3.7 1.3 0.1
362.5 365.3 1250 695.8 105
hysteresis loop and at H 2 ¼ 0, but for SPRAXC there is no evidence of a peak in the magnetisation, at any value of H 2 , that would signify nonmonotonic behaviour. Rather, in SPRAXC as H 2 increases towards zero the rate of logarithmic decay of the magnetisation decreases, becomes almost constant with time, and then is seen to increase with time. The SPRAXC data shown in Fig. 4 are representative of, and qualitatively similar to, the other crystalline materials studied, MQAT and AlNiCo. The magnetic field history described by the two-step process (Step 1 is from magnetic saturation to H 1 , followed by Step 2 where the field is ramped in a positive direction from H 1 to H 2 ) can be represented in the Preisach plane. Here two portions of the state line relax, shown by arrows in Fig. 5, in opposite directions, with opposite contributions to the magnetisation. As is noted by Bertotti [7, p. 503], the Preisach approach predicts that as a function of time, the magnetisation first increases, reaching a maximum (peak), before decreasing i.e. nonmonotic behaviour. Of the materials studied, this predicted behaviour is observed experimentally in the two bulk amorphous alloys, Nd60 Fe30 Al10 and Nd60 Fe20 Co10 Al10 , but not in the crystalline materials SPRAXC, MQAT and AlNiCo. In the Preisach approach, one might speculate on the potential usefulness of Eq. (5) as a predictor of the material properties (H f ) and experimental conditions (H 1 and H 2 ) required for nonmonotonic behaviour. Eq. (5) can be rewritten as tB H2 H1 ln ¼ (7) t0 Hf In bulk amorphous Nd60 Fe30 Al10 nonmonotonic behaviour is observed for values of m0 H 2 ranging from 210 to 110 mT. This gives values ranging from 14 to 23 for the factor ðH 2 H 1 Þ=H f . Similarly, for Nd60 Fe20 Co10 Al10 values for the factor ðH 2 H 1 Þ=H f are in the range 14–25 [6]. Turning now to SPRAXC, if the factor ðH 2 H 1 Þ=H f is to have general applicability in predicting the experimental conditions required for observing nonmonotonic behaviour, it would imply that for SPRAXC nonmonotonic behaviour should be observed when m0 H 2 has a value of around 670 mT (from Eq. (7) with ðH 2 H 1 Þ=H f ¼ 20, m0 H 1 ¼ 695:8 mT and m0 H f ¼ 1:3 mT). As no nonmonotonic behaviour is observed in SPRAXC (or in the
ARTICLE IN PRESS S.J. Collocott, J.B. Dunlop / Journal of Magnetism and Magnetic Materials 320 (2008) 2089–2093
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Fig. 3. Magnetisation, m0 M, as a function of time in Nd60 Fe30 Al10 , on the recoil curve that leads to the dc demagnetised state, commencing at (a) the turning point on the main loop (m0 H 1 ) 362:5 mT, and for values of m0 H 2 , (b) 210 mT, (c) 180 mT, (d) 140 mT, (e) 110 mT and (f) 0 mT.
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Fig. 4. Magnetisation, m0 M, as a function of time for SPRAXC along the recoil curve that leads to the dc demagnetised state, commencing at (a) the turning point on the main loop (m0 H 1 ) 695:8 mT, and for values of m0 H 2 , (b) 675:5 mT, (c) 662:5 mT, (d) 500 mT, (e) 342:3 mT and (f) 0 mT.
ARTICLE IN PRESS S.J. Collocott, J.B. Dunlop / Journal of Magnetism and Magnetic Materials 320 (2008) 2089–2093
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structure inhibits these relaxation processes due to pinning sites that inhibit domain-wall motion processes. In summary, values of the fluctuation field in Nd60 Fe30 Al10 , Nd60 Fe20 Co10 Al10 , MQAT, SPRAXC and AlNiCo are reported. Nonmonotonic behaviour is observed in the bulk amorphous ferromagnetic materials, but not in the crystalline ferromagnetic materials studied. Whilst the Preisach model provides a suitable theoretical approach for explaining any observed nonmonotonic behaviour, it is not useful as a predictor of the experimental conditions required for the observation of nonmonotonic behaviour.
+
H1 Fig. 5. The Preisach description of relaxation following a two-step magnetic field history [6]: Step 1 is from magnetic saturation to H 1 , followed by Step 2 where the field is ramped in a positive direction from H 1 to H 2 .
other crystalline materials studied), the factor ðH 2 H 1 Þ=H f obviously has no general usefulness as a predictor of nonmonotonic behaviour. Of more importance is the difference in the microstructure between the amorphous and crystalline materials. In the amorphous materials the local fields, which drive the observed magnetisation, relax readily and at a rate that is easily accessible in terms of experimental time scales (a few tens of seconds to a few tens of thousands of seconds). In the crystalline materials the
Acknowledgement The authors thank Satsohi Hirosawa, Neomax Co. Ltd., for supplying the SPRAXC material.
References [1] [2] [3] [4] [5]
R. Street, S.D. Brown, J. Appl. Phys. 78 (1994) 6386. A. Lyberatos, R.W. Chantrell, J. Phys. Condens. Matter 9 (1997) 2623. L. Folks, R. Street, J. Appl. Phys. 78 (1994) 6391. E.P. Wohlfarth, J. Phys. F Met. Phys. 14 (1984) L155. L. Wang, J. Ding, Y. Li, Y.P. Feng, X.Z. Wang, Phys. J. Mag. Mag. Mater. 206 (1999) 127. [6] S.J. Collocott, J.B. Dunlop, Phys. Rev. B 66 (2002) 224420. [7] G. Bertotti, in: Hysteresis in Magnetism, Academic Press, San Diego, 1998. [8] G.B. Ferguson, K. O’Grady, J. Popplewell, R.W. Chantrell, et al., J. Appl. Phys. 69 (1991) 5495.