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Magnetization reversal in microparticles of barium ferrite
M A G N E T I Z A T I O N R E V E R S A L IN M I C R O P A R T I C L E S OF B A R I U M F E R R I T E W. ROOS, C. V O I G T , H. D E D E R I C H S and K. A. H E M P E L Institut fur Werkstoffe der Elektrotechnik, R W T H Aachen, Fed. Rep. Germany
To study the magnetization process of polycrystalline barium ferrite we have measured the magnetization loops of representative single particles with diameters of the order of 1 /~m. The measurements show that the magnetization reversal is determined by nucleation. Domain wall motion has not been observed.
1. Introduction
3. Results and discussion
Stoner and Wohlfarth [1] have calculated the hysteresis loop of an assembly of non-interacting uniaxial single-domain particles in which the magnetization reversal occurs by rotation in unison. But the coercive force predicted by this theory usually exceeds the observed value considerably. In order to clarify this discrepancy and to get direct information about the mechanism of magnetization reversal we have investigated the hysteresis loop of very small individual particles of polycrystalline barium ferrite.
Figure 1 shows a typical magnetization curve of a sample with dimensions of about 3/~m. The field H has been applied parallel to the easy axis. The hysteresis curve is considerably distorted by the diamagnetism of the gold wire. F r o m the coercivity it can be seen that the sample is representative of the behaviour of barium ferrite powder. The magnetization reversal is essentially determined by a large magnetization j u m p following nucleation. The nucleation field strength H n ~ 250 kA m - ~ differs markedly from the anisotropy field H A ~ 1265 kA m - 1 which was determined from microwave resonance measurements. To explain the shape of the hysteresis curve we also have measured minor loops. F r o m fig. 2 it can be seen that the minor loops are reversible and always parallel to the outer hysteresis branches. Apparently no change of magnetization occurs along the minor loops. This behaviour is in contrast to SmCo 5 where pinning of domain walls is
2. Experimental Measurements were carried out with a modified version of the vibrating reed magnetometer [2]. The reed was made of gold wire of 18/~m diameter and 1 cm length. The gold wire was glued to a piece of piezoelectric ceramic in order to convert the mechanical vibrations directly to an ac-voltage. Using a lock-in-amplifier a magnetic m o m e n t as small as 10 -9 A cm 2 can be resolved. This m o m e n t corresponds to a barium ferrite particle of about 1 /~m size at room temperature. Commerical barium ferrite was ground in a laboratory mill for 2.5 h and annealed at 950 ° C for 1 h. The annealed powder showed a particle distribution between 0.1 /~m and 5/~m and a coercive force of 280 kA / m - i . Single particles of this powder were fixed in wax at one end of the gold wire. To study the angular variation of magnetization the samples were oriented by heating up the wax in a field of 1000 kA m -1.
MI
-6°°
Fig. 1. Typical magnetization loop of a barium ferrite sample of about 3 ~m size.
Journal of Magnetism and Magnetic Materials 15-18 (1980) 1455-1456 ©North Holland
1455
W. Roos et al./ Magnetization reversal in microparticles of BaFel2Ol9
1456 ¢
t l
ii I ,
.,!
~q q,
J;
"\
kMm 410
350 '
3i @
-26G ~
2'!0
•
1~1
H Fig. 2. Minor loops of the hysteresis curve shown in fig. 1. The shape of the hysteresis is the result of an agglomeration of particles with different size.
the dominant mechanism [3]. The observed hysteresis loop is that of an agglomeration of particles having different size (fig. 2). These agglomerations can clearly be recognized in electron micrographs. All particles have rectangular hysteresis curve which differ in remanence and coercivity (nucleation field). The nucleation field depends on imperfections of the lattice and stray fields at sharp edges of the particles. From the large magnetization jump at 250 kA m-1 we obtain precise information about the angular variation of the nucleation field strength H n. Figure 3 shows the measured angular dependence of the reduced nucleation field strength a n = H J H A and in addition the reduced coercivity Mac = M H c / H A obtained from investigations on oriented polycrystalline barium ferrite. Furthermore fig. 3 contains the reduced coercivity Masw = MHSW/HA and the reduced critical field a sw = Hsw//HA according to the Stoner-Wohlfarth (SW) theory. A large difference between the nucleation field a n and the critical field a sw is observed. This explains why the coercivity of polycrystalline barium ferrite is considerably smaller than predicted by the SW theory. The agreement between the coercivity Mac and the nucleation field strength a n in the range of 0 < v ~ 0 < 70 ° confirms that the
. . . . . . . . .
"~
9 Fig. 3. Angular variation of the reduced nucleation field strength a, = H n / H A (HA: anisotropy field). The reduced coercivity Mac = M H c / H A is obtained from investigations at polycrystalline oriented barium ferrite, a sw = HkSW/HA is the reduced critical field strength and Masw = M H S W / H A the reduced coercivity according to SW theory Ill. 00 is the angle between the easy axis and the magnetic field H.
investigated particle is representative of the powder behaviour.
4. Conclusion The present investigation shows that the demagnetization curve of barium ferrite is determined by nucleation. Domain wall motion has not been observed. The angular variation of the critical field can neither be described by the Stoner-Wohlfarth theory nor by the Kondorsky relation as has been assumed in the models proposed by Ratnam and Buessem [4] and Haneda and Kojima [51. References [1] E. C. Stoner and E. P. Wohlfarth, Phil. Trans. Roy. Soc. A240 (1948) 599. [2] H. Zijlstra, Rev. Sci. Instrum. 41 (1970) 1241. [3] H. Zijlstra, J. Appl. Phys. 41 (1970) 4881. [4] D. V. Ratnam and W. R. Buessem, J. Appl. Phys. 43 (1972) 1291. [5l K. Haneda and H. Kojima, J. Appl. Phys. 44 (1973) 3760.
To study the magnetization process of polycrystalline barium ferrite we have measured the magnetization loops of representative single particles with diameters of the order of 1 /~m. The measurements show that the magnetization reversal is determined by nucleation. Domain wall motion has not been observed.
1. Introduction
3. Results and discussion
Stoner and Wohlfarth [1] have calculated the hysteresis loop of an assembly of non-interacting uniaxial single-domain particles in which the magnetization reversal occurs by rotation in unison. But the coercive force predicted by this theory usually exceeds the observed value considerably. In order to clarify this discrepancy and to get direct information about the mechanism of magnetization reversal we have investigated the hysteresis loop of very small individual particles of polycrystalline barium ferrite.
Figure 1 shows a typical magnetization curve of a sample with dimensions of about 3/~m. The field H has been applied parallel to the easy axis. The hysteresis curve is considerably distorted by the diamagnetism of the gold wire. F r o m the coercivity it can be seen that the sample is representative of the behaviour of barium ferrite powder. The magnetization reversal is essentially determined by a large magnetization j u m p following nucleation. The nucleation field strength H n ~ 250 kA m - ~ differs markedly from the anisotropy field H A ~ 1265 kA m - 1 which was determined from microwave resonance measurements. To explain the shape of the hysteresis curve we also have measured minor loops. F r o m fig. 2 it can be seen that the minor loops are reversible and always parallel to the outer hysteresis branches. Apparently no change of magnetization occurs along the minor loops. This behaviour is in contrast to SmCo 5 where pinning of domain walls is
2. Experimental Measurements were carried out with a modified version of the vibrating reed magnetometer [2]. The reed was made of gold wire of 18/~m diameter and 1 cm length. The gold wire was glued to a piece of piezoelectric ceramic in order to convert the mechanical vibrations directly to an ac-voltage. Using a lock-in-amplifier a magnetic m o m e n t as small as 10 -9 A cm 2 can be resolved. This m o m e n t corresponds to a barium ferrite particle of about 1 /~m size at room temperature. Commerical barium ferrite was ground in a laboratory mill for 2.5 h and annealed at 950 ° C for 1 h. The annealed powder showed a particle distribution between 0.1 /~m and 5/~m and a coercive force of 280 kA / m - i . Single particles of this powder were fixed in wax at one end of the gold wire. To study the angular variation of magnetization the samples were oriented by heating up the wax in a field of 1000 kA m -1.
MI
-6°°
Fig. 1. Typical magnetization loop of a barium ferrite sample of about 3 ~m size.
Journal of Magnetism and Magnetic Materials 15-18 (1980) 1455-1456 ©North Holland
1455
W. Roos et al./ Magnetization reversal in microparticles of BaFel2Ol9
1456 ¢
t l
ii I ,
.,!
~q q,
J;
"\
kMm 410
350 '
3i @
-26G ~
2'!0
•
1~1
H Fig. 2. Minor loops of the hysteresis curve shown in fig. 1. The shape of the hysteresis is the result of an agglomeration of particles with different size.
the dominant mechanism [3]. The observed hysteresis loop is that of an agglomeration of particles having different size (fig. 2). These agglomerations can clearly be recognized in electron micrographs. All particles have rectangular hysteresis curve which differ in remanence and coercivity (nucleation field). The nucleation field depends on imperfections of the lattice and stray fields at sharp edges of the particles. From the large magnetization jump at 250 kA m-1 we obtain precise information about the angular variation of the nucleation field strength H n. Figure 3 shows the measured angular dependence of the reduced nucleation field strength a n = H J H A and in addition the reduced coercivity Mac = M H c / H A obtained from investigations on oriented polycrystalline barium ferrite. Furthermore fig. 3 contains the reduced coercivity Masw = MHSW/HA and the reduced critical field a sw = Hsw//HA according to the Stoner-Wohlfarth (SW) theory. A large difference between the nucleation field a n and the critical field a sw is observed. This explains why the coercivity of polycrystalline barium ferrite is considerably smaller than predicted by the SW theory. The agreement between the coercivity Mac and the nucleation field strength a n in the range of 0 < v ~ 0 < 70 ° confirms that the
. . . . . . . . .
"~
9 Fig. 3. Angular variation of the reduced nucleation field strength a, = H n / H A (HA: anisotropy field). The reduced coercivity Mac = M H c / H A is obtained from investigations at polycrystalline oriented barium ferrite, a sw = HkSW/HA is the reduced critical field strength and Masw = M H S W / H A the reduced coercivity according to SW theory Ill. 00 is the angle between the easy axis and the magnetic field H.
investigated particle is representative of the powder behaviour.
4. Conclusion The present investigation shows that the demagnetization curve of barium ferrite is determined by nucleation. Domain wall motion has not been observed. The angular variation of the critical field can neither be described by the Stoner-Wohlfarth theory nor by the Kondorsky relation as has been assumed in the models proposed by Ratnam and Buessem [4] and Haneda and Kojima [51. References [1] E. C. Stoner and E. P. Wohlfarth, Phil. Trans. Roy. Soc. A240 (1948) 599. [2] H. Zijlstra, Rev. Sci. Instrum. 41 (1970) 1241. [3] H. Zijlstra, J. Appl. Phys. 41 (1970) 4881. [4] D. V. Ratnam and W. R. Buessem, J. Appl. Phys. 43 (1972) 1291. [5l K. Haneda and H. Kojima, J. Appl. Phys. 44 (1973) 3760.