THE MAGNETIZATION PROCESS IN HOT-PRESSED FERRITES STUDIED BY NEUTRON DEPOLARIZATION

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THE MAGNETIZATION PROCESS IN

HOT-PRESSED FERRITES STUDIED BY NEUTRON

DEPOLARIZATION

M. Rekveldt

To cite this version:

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THE MAGNETIZATION PROCESS IN HOT-PRESSED FERRITES STUDIED

BY NEUTRON DEPOLARIZATION

M. Th. REKVELDT

Interuniversitair Reactor Instituut, Delft, the Netherlands

Résumé. — On a étudié dans les trois dimensions la dépolarisation subie par un faisceau

mono-chromatique de neutrons polarisés après transmission à travers des échantillons de certains ferrites pressés à chaud. La matrice de dépolarisation (3 x 3) mesurée a été interprétée en fonction de l'aimantation, de la taille moyenne des domaines, des valeurs moyennes du carré du cosinus directeur de l'aimantation interne et du cosinus de l'angle entre les orientations des domaines adja-cents, vus perpendiculairement à l'aimantation moyenne. Un des ferrites présente une corrélation entre les domaines adjacents, ce qui indique un effet coopératif dans le renversement de l'aimanta-tion de l'échantillon.

Abstract. -— The depolarization of a monochromatic polarized neutron beam after transmission through some hot-pressed single domain ferrites has been studied in three dimensions. The measured (3 x 3) depolarization matrix has been interpreted in terms of the magnetization, the mean domain size, the mean square direction cosine of the inner magnetization and the mean direction cosine between the orientations of adjacent domains, seen perpendicular to the mean magnetization direction. As a result one of the ferrites shows a correlation between adjadent domains indicating a cooperative effect in reversing the magnetization of the sample.

1. Introduction. — The neutron depolarization

tech-nique has been subject of growing interest during the last decennium. The precession of the neutron polari-zation around a magnetic field makes the polaripolari-zation analyses of a polarized neutron beam after transmis-sion through a sample a useful and sensitive method in studying the magnetic properties of ferromagnetic domain structures [1-7], superconductors [8] and even magnetic critical phenomena [5, 9-12]. Experimentally the method makes use of a polarized monochromatic neutron beam (A = 1.6 A) obtained by

Bragg-reflec-tion from a magnetized Fe3Si single crystal (Fig. 1).

/VYL

D S

^ Ma V Q

Fia. 1. — Schematic view of the experimental set-up. Mp and

Ma give the magnetization directions of the polarizing and

ana-lyzing crystal, G is the guide field, Di and D2 are polarization turners. S is the sample holder and T the neutron detector. M is a neutron monitor counter, determining the measuring time of the detector. The row of arrows indicate the direction of polarization

of the beam.

The polarization of the beam can be analysed by mea-suring the intensity of the beam after reflection from a second Fe3Si-crystal. A polarization turner in front of

the sample consisting of two coils perpendicular to each other generating a magnetic field, enables one to obtain any required direction of the polarization vector at the sample position. At the sample position a ferromagnetic specimen can be placed in the (y — z) plane in a coil in which a magnetic field can be pro-duced up to 150 A/cm in the ^-direction. A second polarization turner behind the sample combined

with the analyzing Fe3Si crystal allows one to

ana-lyze successively any required component of the pola-rization vector of the beam transmitted through the sample in the x-direction. In this way a (3 x 3) depolarization matrix of the sample can be measured. For a more detailed description the reader is referred to earlier papers [4,5,6].

As described in these papers this depolarization matrix can be interpreted in terms of well-known domain parameters in the following way. The preces-sion of the neutron polarization around the local field in a domain can be described as the rotation

around a homogeneous field BJn0- In matrix form

P ( 0 = .D(n, cot) P(0)

where D(n, cot) is a pure rotation matrix, n is a unit vector in the direction of the magnetic induction, co is the Larmor precession frequency of the neutron in the

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C1-24 M. Th. REKVELDT

local field and t is the time that the neutron passes through that field, in this case the magnetic domain. The polarization change after transmission through a sample can be described by the average of the polarization changes through an array of N domains, being

a product of N rotation matrices, in formula :

P(t) =

1 ...

la

1

df, dt, dn, dn,.

0

. p ( n ~ n,, t,

...

t,) D(n,, cot,) D(n,, cot,) P(0).

Here

I

dn means averaging only over the orientations

of the unit vector n and p(n,

...

n,, t,

...

t,) is a norma- lized weight function giving the probability of finding a matrix row with configuration (n,

...

n,, t,

...

t,). Assuming no correlation between the different domain orientations and the different interaction times one can factorize this probability function into a product of probability functions for each domain separately and a theoretical depolarization matrix can be derived written in terms of

and B, which can be determined from a measured depolarization matrix. Here the brackets denote an average over the part of the sample illuminated by the neutron beam, B, is the spontaneous magnetic

induction within the domains, B, is the ith component

of the local magnetic induction, B is the mean magnetic induction over the same part of the sample as mentioned, m is the reduced magnetization (m = BIB,), y ,

are the mean square direction cosines of the local magnetization and 6 is the mean domain size in the neutron transmission direction. It should be noted that in field dependent measurements where the polarization vector rotates over 90 degrees and more around the mean magnetization, from the mean square direc- tion cosines only y, in the field direction can be deter- mined.

This theoretical interpretation can be extended by taking into account the correlations between the orientations of adjacent domains, expressed by

and

At zero magnetization K is the mean direction cosine between adjacent domains seen in the transmission- direction of the neutrons and y: the mean square direction cosine of the orientations in which the correlation K occurs. Owing to this correlation the probability function p(n,

...

n,, t,

...

t , ) can not be factorized anymore, which makes the derivation of the theoretical depolarization matrix very complicated.

Under the assumptions that for each domain cot 4 1,

yi

does not depend on the sequence number i and j

for [ i-j

1

2 1 and the correlation parameter K is not to close to one, a theoretical depolarization matrix can be derived in terms of

These quantities can be determined from a measured depolarization matrix in their dependence on an applied magnetic field or other parameters as tempera- ture and mechanical stress.

2. Experiments.

-

Depolarization experiments have

been carried out on some hotpressed single domain ferrites of dimensions (4 x 1 x 0.2) cm3, obtained from Dr. U. Enz of the Philips Laboratories in Eindho- ven, the Netherlands. The cross-section of the neutron

beam amounts (8 x 8) mm2. In addition to the pro-

perties of the ferrites as composition, spontaneous magnetic induction and grain size mentioned in the figures 2 (ferrite 1) and figure 3 (ferrite 2), ferrite 1 is a commercial ferrite [13], with a coercive field of 2 A/cm

FIG. 2. - The upper figure gives the reduced magnetization m as a function of H in NiZn ferrite (ferrite 1). The lower two figures give the mean domain size 6 and the mean square y-component of the inner magnetization as a function of the reduced magnetization. The open and closed circles in the lower figures and the upper figure correspond to each other. The dotted line in the lower figure gives the calculated result of a theoretical

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FIG. 3.

-

AS in figure 2 for MgMn ferrite (ferrite 2).

measured with a field amplitude of 7 Alcm. Ferrite 2 has a coercive field of

+

10 A/cm measured with an induction meter at the same field amplitude as in the depolarization experiments. An insert in figure 3 gives a complete (B-H) curve in arbitrary units obtained with an induction meter. Measurements have been perform- ed with varying magnetic field up to 50 A/cm in the y-direction. The long ends of the ferrites were fastened in a magnetic yoke to short circuit the magnetic flux of the specimen and the coil. The results have been plotted in the figures 2 and 3, where together with the magneti- zation curve determined with the depolarization technique, y, and 6 are plotted as a function of the reduced magnetization m. When one accounts for the correlation between neighbouring domains, 6 and y, in the figures 2 and 3 should be replaced by

6

(s)

and y

(E)

1 + K + Y y I(=) 1 + K

respectively.

3. Discussion. - The following model will be used in the discussion of the results. An isotropic distribution of domain orientations within a cone with apex angle 2 0 gives rise to a reduced magnetization

( m 1=0.5 (l+cos 0) and yy=(4

I

m 1'-2

1

rn )+1)/3. For 0 = 4 2 a half spherical distribution is found, corresponding to the case of remanence where

/

m

I

= 0.5 and y, = 113. If it is supposed further that

the magnetization may vary in the region

-

0.5 < m

<

0.5 without changing the angle distribution of the absolute magnetization of the domains, then y, = 113 in this region. A dotted line in the figures of y,(m) gives the results of this model. The results in figure 2 for the remanence and y,(m) can reasonably be explained by such an isotropic model. Figure 2 also shows a domain size which is nearly independent of the magnetization and of the order of the grain size of 2 pm. This indicates that the correla- tion parameter K is constant for all m and most likely zero on basis of its definition which makes a correlation very unlikely at higher values of m. The apparent increase of the domain size for ] m

I

> 0.7

may be due to a systematic error in m as a consequence of which 6 determined from a quantity like ~ : ( 1 - m2) 6 becomes too large if m is chosen to large.

In contrast ferrite 2 shows quite a different beha- viour. The remanence at zero field is about 0.7 which strongly exceeds the remanence in ferrite 1 that can be related to an isotropic distribution of domain orientations. This difference may arise when the grains in ferrite 1 have an uniaxial magnetic anisotropy whereas the grains in ferrite 2 have a polyaxial aniso- tropy with a preference for the easy axis to be nearest to the magnetization direction. Assuming further that the crystallografic direction of the grains are at random, a rough calculation of the magnetic remanences gives a qualitative agreement with the observation. The

domain size 6 in figure 3 shows apparently a magneti-

zation dependence which can be the result of existing correlations between neighbouring domains. In order to explain this it is likely that the mean domain size 6 is independent of m and does not exceed the grain size of about 0.8 pm. So the observed dependence of 6 on m is interpreted as a variation of the factor (1

+

K)/(1

-

K) which is supposed to be equal to one at the higher values of m, where the value found for 6 indeed coincides satisfactorily with the grain size of ferrite 2. Using this model the effect of K arises at increasing m at m =

-

0.5, reaches its maximum of

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C1-26 M. Th. REKVELDT

least several grain sizes running capriciously along the easy magnetization. This may explain why this corre-

direction of the magnetizing field. It is clear that lation is probably absent in the ferrite 1 where we

such a correlation preferentially occurs in materials suggested that the grains have uniaxial magnetic

where the grains have more than one orientation of anisotropy.

References

[ I ] DRABKIN, G. M., ZABIDAROW, E. I., KASMAN, Ya. A., [8] WEBER, H. W., PFEIFFER, K., RAUCH, H., Z. Phys. 244 (1971)

OKOROKOV, A. I., SOY. Phys. JETP29 (1969) 261. 383.

[2] RAUCH, H., Z. Phys. 197 (1966) 373. [9] REKVELDT, M . Th., Proceedings ICM-73, V (1973) 617.

DI M ~S.

v.,

~R ~~V. A., ~~so,,. ~phys. JETP ~ ~, ,31 (1970) 1101 RAUCK H., s~tDL.9 E., ZEILINGER, A.9 Z. Angew. Phys. 32

111. (1975) 109.

[ l l ] DRABKIN, G. M., OKOROKOV, A. I., RUNOV, V. V. SOY.

[4] REKVELDT, M. Th., J. Physique Colloq. 32 (1971) C5-79. _{Phys. JETP}_Lett.₁₅_{(1972) 324.}

[5] REKVELDT, M. Th., Thesis, Delft (1972). _{[12] MALPEV,}_S._{V., RUBAN,}_V._V.,SOY. Phys. JETP35(1972) 222.

[6] REKVELDT, M. Th., Z. Phys. 259 (1973) 391. [13] Type nr. 4B 1 in Philips Data Handbook, Components and

[7] REKVELDT, M . Th., J. of Magn. and Magn. Mat. 1 (1976) Materials, part 4a, april 1975.