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Influence of the particle size and intrinsic magnetic characteristics on the coercivity of sintered magnets
Journal of Magnetism and Magnetic Materials 104-107 (1992) 1143-1144 North-Holland
AI4=
Influence of the particle size and intrinsic magnetic characteristics on the coercivity of sintered magnets G. Turilli, A. Paoluzi, M. Lucenti and L. Pareti lstituto Maspec - CNR, Via Chiacari 18/+4, 43100 Parma, Italy
Using sintered specimens of Ba-hexaferrite powders as a model system, a study was made of the dependence of coercivity on the particle dimensions and on the temperature from RT up to the Curie temperature. The temperature behaviour of the coercive and anisotropy field are the same in single-domain particle specimens while they are rather different in polydomain particle specimens. However, the coercivity behaviour of both systems can be fitted well up to 350 ° C using a simple relation between He, H A, and M~. Further contributions to the coercivity have to be taken into account at higher temperatures. The coercivity in hard magnetic materials has been the subject of many investigations and several models have been developed [1], in particular with regard to hexaferrites based permanent magnets [2]. The Mbexaferrites have received a lot of attention because they constitute a model system [3-5] due to their stability, their well-known intrinsic properties and to the ease in obtaining particles with different aspect ratios and sizes (typically 0.05 ~xm-0.5 mm). To distinguish between effects due either to the m o r p h o l o g y / size or intrinsic magnetic properties of the particles, we have investigated the coercivity of sintered M-hexaferrites powders having dimensions larger and smaller than that of the critical domain size as a function of both dimension and temperature from R T to the Curie temperature (T c = 457 ° C). Powders having different dimensions, in the polydomain region >_ 2 Ixm, were obtained grinding for different times pellets of B a - M ferrites and measured by the Fisher method. Samples, which were in the shape of small cylinders, were obtained by pressing isostatically and then sintering the powders for 1 h at 1100 °C. Samples made of particles having dimensions in the range of that of a single domain, i.e. < 1 ~xm, and in the transition region 1-2 Ixm were obtained by sintering at different temperatures (800-1000 ° C) single-domain powders. The phase identification was performed by the thermomagnetic analysis, Tc = 457 ° C, and their single- or polydomain status was verified by transverse susceptibility measurements Xt [6]. Moreover, using the Xt method the anisotropy field was measured in the case of single-domain particle samples. The anisotropy field value of polydomain samples was measured by the singular point detection (SPD) technique. The magnetization curve and the coercive field values were determined using a computer-controlled vibrating sample m a g n e t o m e t e r in a field ranging from - 19 to 19 kOe. The coercive field values as a function of the particles dimension are shown in fig. 1. As expected, there is a sharp decrease of the coercivity in the proximity of the single-polydomain transition region. This behaviour is explained by a change of the coercivity
5.0 4.0 3.0 ~2.0 1.0 ill,i
0.0
;--rijidlllll~-ill
0
5 10 15 20 25 Particle size/Critical domain size Fig. 1. Coercive field as a function of the normalized particle size dimension. mechanism from a coherent rotation to a domain wall nucleation and displacement [1]. In the polydomain region the coercivity is practically invariant from 10 to 20 Ixm and it is however, small compared with the corresponding variation in the grain dimension. It has to be noted that such a decrease in the coercivity indicates that a further increase of the number of domain walls in a multidomain particle is not relevant for establishing the coercivity value. This seems to confirm that the nucleation mechanism is the main factor responsible for the coercivity in M-hexaferrites. In fact, in the case of a domain wall pinning mechanism a distinct variation of H c would be expected from an increased number of domain walls. The coercivity values shown in fig. 1 are smaller than that expected at the corresponding grain dimensions. This is due to the methods used to prepare the samples which induce a distribution in the dimension and morphology of the particles. The effects of such a distribution are particularly important in the transition and single domain regions. The temperature dependence of the coercivity in a single- and a polydomain particle specimen is corn-
0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
1144
G. Turilli et al. / Influence of particle size and intrinsic magnetic characteristics
20.0 16.0
A
A
A
A
&
& & A A A
12.0
A zx
8.0 ,
A
•
4.0
A
0.0 0
100
200
300 400 500 T(°C) Fig. 2. Temperature dependence of the measured coercive field (solid dots), effective anisotropy field after correction for shape anisotropy (triangles) and calculated coercive field (H~ = 0 . 4 8 H A e f f ) (solid diamonds) in a single-domain sample. 20.0
1000 O•OOo
16.0
800 ~
~12.0
600 ,
~8.0
400 '~-
4.0 0.0
I
i
i
I
i
i
±
200 =
~ EI
0
200 300 400 500 T(°C) Fig. 3. Temperature dependence of the anisotropy field (e) and coercive field ( A ) in a polydomain sample. 100
pared with the temperature behaviour of the anisotropy field in figs. 2 and 3, respectively. As can be seen, the behaviour of H c in single-domain particles, where the magnetization reverses coherently, is qualitatively very similar to that of the effective anisotropy field obtained after correction for the shape anisotropy, although its value is lower than that predicted by the relation H~ = 0.48H A and an interaction factor Neff must be taken into account to obtain a good fit of the data up to 350 ° C using H c ( r ) = OtHA(T ) - 4"rrNeffms(T),
(1)
where a = 0.35 and Ncff = 0.44 for single-domain particles. On the other hand, in the polydomain region, the increment of H c with temperature is much larger than that of the magnetocrystalline anisotropy and it is independent of the particle dimension. In particular, H~ reaches its highest value at a temperature around
T = 325 ° C which does not correspond to the temperature where the anisotropy field reaches its maximum. Such a feature is observed in the case of single-domain specimens where both H A and H c have their maximum around T = 230 ° C. It is worth noting that the observed increase of Hc from the R T value to its maximum is about 20% in single-domain and larger than 100% in polydomain specimens irrespective of their particle dimension. It should be noted that, in the polydomain region, the dimension of the particles has little influence on the H~ value and no influence at all on its temperature dependence. An attempt to fit the temperature dependence of H c in polydomain specimens using eq. (1), where ~ H A is now a nucleation field, gave a reasonable result again up to 350 ° C, even if the correlation factor of the fitting is worse than that found in the single-domain specimens. With increasing particle dimension both the coefficients c~ and N~tf were found to decrease, in agreement with a weakening of the nucleation field and particle interaction. The failure of the fitting above 350 ° C in both single- and polydomain specimens can be attributed to an oversimplification of the model [eq. (1)]. In particular, it has to be noted that the critical domain size increases with increasing temperature [1] and this can be particularly important in influencing the coercivity in the transition region (fig. 1), where the coercivity depends strongly on the grain dimension. This effect is evident when analyzing the temperature dependence of the coercive field of particles having dimension in the transition region where it is observed that the curves relative to different grain size collapse into a single curve above 400 ° C. In the case of polydomain specimens, where nucleation is still the main responsible for the coercivity, domain wall dynamics, as a function of temperature, have to play a role in the definition of the coercivity [5]. A calculation of the wall thickness, as a function of temperature shows a minimum located at T = 400 ° C. Therefore, an additional term involving the domain wall characteristics (thickness, energy, etc.) should be included in eq. (1) and calculations are in progress for both cases. This work was funded by grants from the Progetto Finalizzato M S T A of the CNR. References
[1] H. Zijlstra, in: Ferromagnetic Materials vol. 3, ed. E.P. Wohlfarth (North-Holland, Amsterdam, 1982). [2] F. Kools, J, de Phys. 46 (1985) C6-349. [3] P. Grohs and K.A. Hempel, IEEE Trans. Magn. MAG-20 (1984) 1633. [4] D. Givord, J. Magn. Magn. Mater. 83 (1990) 183. [5] R.A. Schippan and K.A. Hempel, J. Magn. Magn. Mater. 38 (1983) 319. [6] L. Pareti and G. Turilli, J. Appl. Phys. 61 (1987) 5098.
AI4=
Influence of the particle size and intrinsic magnetic characteristics on the coercivity of sintered magnets G. Turilli, A. Paoluzi, M. Lucenti and L. Pareti lstituto Maspec - CNR, Via Chiacari 18/+4, 43100 Parma, Italy
Using sintered specimens of Ba-hexaferrite powders as a model system, a study was made of the dependence of coercivity on the particle dimensions and on the temperature from RT up to the Curie temperature. The temperature behaviour of the coercive and anisotropy field are the same in single-domain particle specimens while they are rather different in polydomain particle specimens. However, the coercivity behaviour of both systems can be fitted well up to 350 ° C using a simple relation between He, H A, and M~. Further contributions to the coercivity have to be taken into account at higher temperatures. The coercivity in hard magnetic materials has been the subject of many investigations and several models have been developed [1], in particular with regard to hexaferrites based permanent magnets [2]. The Mbexaferrites have received a lot of attention because they constitute a model system [3-5] due to their stability, their well-known intrinsic properties and to the ease in obtaining particles with different aspect ratios and sizes (typically 0.05 ~xm-0.5 mm). To distinguish between effects due either to the m o r p h o l o g y / size or intrinsic magnetic properties of the particles, we have investigated the coercivity of sintered M-hexaferrites powders having dimensions larger and smaller than that of the critical domain size as a function of both dimension and temperature from R T to the Curie temperature (T c = 457 ° C). Powders having different dimensions, in the polydomain region >_ 2 Ixm, were obtained grinding for different times pellets of B a - M ferrites and measured by the Fisher method. Samples, which were in the shape of small cylinders, were obtained by pressing isostatically and then sintering the powders for 1 h at 1100 °C. Samples made of particles having dimensions in the range of that of a single domain, i.e. < 1 ~xm, and in the transition region 1-2 Ixm were obtained by sintering at different temperatures (800-1000 ° C) single-domain powders. The phase identification was performed by the thermomagnetic analysis, Tc = 457 ° C, and their single- or polydomain status was verified by transverse susceptibility measurements Xt [6]. Moreover, using the Xt method the anisotropy field was measured in the case of single-domain particle samples. The anisotropy field value of polydomain samples was measured by the singular point detection (SPD) technique. The magnetization curve and the coercive field values were determined using a computer-controlled vibrating sample m a g n e t o m e t e r in a field ranging from - 19 to 19 kOe. The coercive field values as a function of the particles dimension are shown in fig. 1. As expected, there is a sharp decrease of the coercivity in the proximity of the single-polydomain transition region. This behaviour is explained by a change of the coercivity
5.0 4.0 3.0 ~2.0 1.0 ill,i
0.0
;--rijidlllll~-ill
0
5 10 15 20 25 Particle size/Critical domain size Fig. 1. Coercive field as a function of the normalized particle size dimension. mechanism from a coherent rotation to a domain wall nucleation and displacement [1]. In the polydomain region the coercivity is practically invariant from 10 to 20 Ixm and it is however, small compared with the corresponding variation in the grain dimension. It has to be noted that such a decrease in the coercivity indicates that a further increase of the number of domain walls in a multidomain particle is not relevant for establishing the coercivity value. This seems to confirm that the nucleation mechanism is the main factor responsible for the coercivity in M-hexaferrites. In fact, in the case of a domain wall pinning mechanism a distinct variation of H c would be expected from an increased number of domain walls. The coercivity values shown in fig. 1 are smaller than that expected at the corresponding grain dimensions. This is due to the methods used to prepare the samples which induce a distribution in the dimension and morphology of the particles. The effects of such a distribution are particularly important in the transition and single domain regions. The temperature dependence of the coercivity in a single- and a polydomain particle specimen is corn-
0312-8853/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved
1144
G. Turilli et al. / Influence of particle size and intrinsic magnetic characteristics
20.0 16.0
A
A
A
A
&
& & A A A
12.0
A zx
8.0 ,
A
•
4.0
A
0.0 0
100
200
300 400 500 T(°C) Fig. 2. Temperature dependence of the measured coercive field (solid dots), effective anisotropy field after correction for shape anisotropy (triangles) and calculated coercive field (H~ = 0 . 4 8 H A e f f ) (solid diamonds) in a single-domain sample. 20.0
1000 O•OOo
16.0
800 ~
~12.0
600 ,
~8.0
400 '~-
4.0 0.0
I
i
i
I
i
i
±
200 =
~ EI
0
200 300 400 500 T(°C) Fig. 3. Temperature dependence of the anisotropy field (e) and coercive field ( A ) in a polydomain sample. 100
pared with the temperature behaviour of the anisotropy field in figs. 2 and 3, respectively. As can be seen, the behaviour of H c in single-domain particles, where the magnetization reverses coherently, is qualitatively very similar to that of the effective anisotropy field obtained after correction for the shape anisotropy, although its value is lower than that predicted by the relation H~ = 0.48H A and an interaction factor Neff must be taken into account to obtain a good fit of the data up to 350 ° C using H c ( r ) = OtHA(T ) - 4"rrNeffms(T),
(1)
where a = 0.35 and Ncff = 0.44 for single-domain particles. On the other hand, in the polydomain region, the increment of H c with temperature is much larger than that of the magnetocrystalline anisotropy and it is independent of the particle dimension. In particular, H~ reaches its highest value at a temperature around
T = 325 ° C which does not correspond to the temperature where the anisotropy field reaches its maximum. Such a feature is observed in the case of single-domain specimens where both H A and H c have their maximum around T = 230 ° C. It is worth noting that the observed increase of Hc from the R T value to its maximum is about 20% in single-domain and larger than 100% in polydomain specimens irrespective of their particle dimension. It should be noted that, in the polydomain region, the dimension of the particles has little influence on the H~ value and no influence at all on its temperature dependence. An attempt to fit the temperature dependence of H c in polydomain specimens using eq. (1), where ~ H A is now a nucleation field, gave a reasonable result again up to 350 ° C, even if the correlation factor of the fitting is worse than that found in the single-domain specimens. With increasing particle dimension both the coefficients c~ and N~tf were found to decrease, in agreement with a weakening of the nucleation field and particle interaction. The failure of the fitting above 350 ° C in both single- and polydomain specimens can be attributed to an oversimplification of the model [eq. (1)]. In particular, it has to be noted that the critical domain size increases with increasing temperature [1] and this can be particularly important in influencing the coercivity in the transition region (fig. 1), where the coercivity depends strongly on the grain dimension. This effect is evident when analyzing the temperature dependence of the coercive field of particles having dimension in the transition region where it is observed that the curves relative to different grain size collapse into a single curve above 400 ° C. In the case of polydomain specimens, where nucleation is still the main responsible for the coercivity, domain wall dynamics, as a function of temperature, have to play a role in the definition of the coercivity [5]. A calculation of the wall thickness, as a function of temperature shows a minimum located at T = 400 ° C. Therefore, an additional term involving the domain wall characteristics (thickness, energy, etc.) should be included in eq. (1) and calculations are in progress for both cases. This work was funded by grants from the Progetto Finalizzato M S T A of the CNR. References
[1] H. Zijlstra, in: Ferromagnetic Materials vol. 3, ed. E.P. Wohlfarth (North-Holland, Amsterdam, 1982). [2] F. Kools, J, de Phys. 46 (1985) C6-349. [3] P. Grohs and K.A. Hempel, IEEE Trans. Magn. MAG-20 (1984) 1633. [4] D. Givord, J. Magn. Magn. Mater. 83 (1990) 183. [5] R.A. Schippan and K.A. Hempel, J. Magn. Magn. Mater. 38 (1983) 319. [6] L. Pareti and G. Turilli, J. Appl. Phys. 61 (1987) 5098.