HAL Id: jpa-00214025
https://hal.archives-ouvertes.fr/jpa-00214025
Submitted on 1 Jan 1971
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
NEUTRON DEPOLARISATION AS A METHOD TO DETERMINE THE MAGNETIZATION, THE MEAN
DOMAIN SIZE AND THE MEAN SQUARE
COMPONENTS OF THE INNER MAGNETIZATION OF FERROMAGNETS
M. Th. Rekveldt
To cite this version:
M. Th. Rekveldt. NEUTRON DEPOLARISATION AS A METHOD TO DETERMINE THE MAG- NETIZATION, THE MEAN DOMAIN SIZE AND THE MEAN SQUARE COMPONENTS OF THE INNER MAGNETIZATION OF FERROMAGNETS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-579-C1-581. �10.1051/jphyscol:19711200�. �jpa-00214025�
JOURNAL DE PHYSIQUE Colloque C 1, supplkment au no 2-3, Tome 32, Fe'orier-Mars 1971, page C 1 - 579
NEUTRON DEPOLARISATION AS A METHOD TO DETERMINE THE MAGNETIZATION, THE MEAN DOMAIN SIZE AND
THE MEAN SQUARE COMPONENTS
OF THE INNER MAGNETIZATION OF FERROMAGNETS
M. TH. REKVELDT
Interuniversitair Reactor Instituut, Delft, the Netherlands
RCsumC. - Un faisceau de neutrons monochromatique et polarise traverse un echantillon ferromagnetique devant et derriere lequel a ete place un tourneur de polarisation qui permet de determiner une (3 x 3) matrice de d6polarisation dont on calcule la magnetisation, la grandeur moyenne du domaine et la moyenne des carres des composantes de la magnktisation interne (dans le domaine). Les rksultats d'experiences sur des lames de nickel sous tension montrent l'utilite de la methode pour la determination des differentes propriBtes magnetiques dans l'echantillon.
Abstract. - A monochromatic polarised neutron beam passes through the ferromagnetic sample, in front of and behind which a polarisation turner is placed. With help of these turners a (3 x 3) depolarisation matrix can be measured, from which the magnetization, the mean domain size and the mean square components of the inner magnetization in the domain can be calculated. The results of experiments on nickel foils under stress show the usefulness of the method in determining various magnetic properties in bulk material.
FIG. 1. - Experimental set-up. At the sample position of the depolarisation apparatus any polarisation direction can be obtained and from these any component can be analysed.
A monochromatic polarised neutron beam can be ple position, the second one turns the polarisation obtained by reflection from a (200) plane of a magne- vector from the x, y or z direction back to the optimal tized Co(92) Fe(8) crystal (Fig. 1). The polarisation direction to be analysed by the second analysing
crystal.
of the beam can be analysed by measuring the inten- sity of the beam after reflection from a second Co(92) Fe(8) crystal [I]. D. ter Haar [2] and 0. Steinsvoll 131 showed that the polarisation of the beam behaves like a classical polarisation vector. When the beam passes a magnetic field the polarisation-vector turns around the field with a frequency corresponding to the Larmor precession frequency during the time that a neutron from the beam is present in that field. Two polarisation turners have been built, consisting of three coils perpendicular t o each other, in which a magnetic field can be produced. In front of and behind the field-free sampleholder a polarisation-turner is placed, the first one turns the polarisation vector of the neutrons into either x, y or z direction at the sam-
Mp-Ma=rnognet~ratton dlrectlon p ~ ~ o r 1 5 0 t 0 r - O ~ O I ~ S ~ ~ O , c r y ~ l a l G = gutdeleid
D, - 4 =polor~sotlanturnen S = sornpldholder T =counter
where D(m, t) is a pure rotation matrix, m is a unit vector in the direction of the magnetic induction and t is the time that the neutron passes through the domain.
The polarisation change after transmission through N domains is found to be a product of N matrices, each of them representing the polarisation change in one domain. The ~esulting polarisation after trans- mission through a ferromagnetic foil is found by averageing over all possible rows of matrices
At the sample position a ferromagnetic foil can be placed in the (y - z) plane in a coil, in which amagnetic field in the y-direction can be produced up to 200 Oe.
The foil-ends are magnetically closed by a soft iron magnetic yoke to reduce demagnetizing forces. The foil can be put under tension variable up to about 10 kg.mm-2 in the y-direction. In this way a (3 x 3) depolarisation matrix can be measured as a function of field strength and tension.
This depolarisation matrix can be interpreted in terms of well-known domain parameters in the follow- ing way. As mentioned the polarisation change in a homogeneous field B,/y,, can be described as a rotation of the polarisation-vector around the local field direction within each domain. In matrix form
P(t) = D(m, t) .P(O)
where the Nl matrices in a row are numbered by i, the K possible orientations of m by ji and the rele- vant row by I.
After carrying out the averageing procedure, we
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711200
C 1 - 580 M. TH. REKVELDT find a (3 x 3) matrix with four independent elements,
which can be measured and from which the five 1
averaged domain parameters < rn; >, < m: >,
< rn; >, < m,, > and < 3: 6 > can be calculated.
T
Here BS is the spontaneous magnetic induction, which is assumed to be known and < 6 > the mean
domain size in the direction of transmission. -1 In the averageing procedure a few assumptions are made about the domain structure, which generally are not fulfilled. At first the correlation between the magnetization orientations of neighbouring domains is the same as it is for all other domains, 20 secondly there is no correlation between the domain 15 size and the magnetization orientation of the domain, and thirdly a gaussian distribution function for the 'O domain size is assumed, from which the distribution width has to be chosen. The errors introduced with the last two assumptions are in general such that the O mean domain size found from the measurements is slightly different from the real one. In accordance to the first assumption, in first approximation it can be said that domains separated by 180° walls in a row, 0.8 do not affect the neutron-polarisation, with the conse- O6 quence that the formulae derived are not usable for CM ferromagnets with 180° walls only. On the other hand a2 this property can be used to determine the mean direc- tion of 1800 walls.
Measurements are done on polycrystalline Ni-foil
(purity 0,999) of dimensions 40 x 10 x 0.12 mm3. FIG. 2. -The reduced magnetization m as a function-of the Before the experiments the samples were annealed field H, the mean domain size < 6 > and the mean~s~uare for 2 hours at 900 centigrade. y-component of the inner magnetization as a function of the
magnetization in the y-direction at two different transmission In order to illustrate how 1800 walls influence the angles and a tension of 7 kg.--2 in the y-direction. The arrows results two experiments will be discussed, one perfor- indicate whenever the magnetization increases or decreases.
med with the foil under tension and the other after tension has been taken away. Measurements have
been done when the transmission direction is perpen- @=O after (r.7lcp/hm2 @ -35 after @7kqtnm2
dicular to the foil (@ = 00) and when the transmission 1
direction makes an angle of 350 with the normal on ,,,
the foilplane in the (x - y) plane (@ = 350). In both t
cases the magnetization curves calculated from the o depolarisation measurements (Fig. 2 and 3) are in very good agreement with the results obtained by other
techniques. -I
In general the mean domain size < 6 > is increas- ing with increasing magnetization, even at tensions up to 7 kg.mm-2. This means that there is still wall movement.
The most interesting result is the presence of a hysteresis both in < 6 > and < m: > as a function l5 of m, which is much more pronounced at @ = 35O 10
than it is at @ = 00. This may be due to the appearance at a certain value of m of a number of 1800 walls parallel to the x-direction with the domain magnetiza- 0
tion in the (x - z) plane. It is clear that these 1800 walls are seen by transmission at @ = 350 and not by perpendicular transmission. Because domains separated by 1800 walls in the transmission direction a do affect the neutron polarisation much less, a smal- 0.6
ler depolarisation will be found at @ = 35O and therefore an apparently smaller domain size calculated.
Also the mean square magnetization in the (x - z) 0.
plane seems to be smaller and thus an increased 0
< m; > will be measured. This picture is consistent
with the results (Fig. 2), if it is assumed that the FIG. 3. - AS in figure 2, except that the tension is released.
NEUTRON DEPOLARISATION AS A METHOD TO DETERMINE THE MAGNETIZATION C 1 - 581 number of 1800 walls is increasing when m changes
from 0.1 to - 0.3 and decreasing when m changes from - 0.3 to - 1.
After the tension has been released (Fig. 3) a similar explanation can be given, though in this case the number of 1800 walls is increasing when m changes from 0.7 to 0.3 and decreasing when m changes from 0.3 to - 0.1. The magnetization direction of the
domains as well as the direction of the 1800 domain walls is in the y-direction.
As a general conclusion, this depolarisation method turns out to be a valuable technique which supple- ments other methods in determining magnetic proper- ties. In contrast to other techniques to study domain structure it enables one to measure magnetic quantities in the bulk material.
References
[I] NATHANS (R.), SHULL (C. G.), SHIRANE (G.) and [2] TER HAAR (D.), Fluctuation, Relaxation and Reso- ANDRESEN (A.), J . Phys. Chem. Solids 1959, nance in Magnetic Systems, Oliver and Boyd,
10, 138. Edinburgh and London, 1961.
[3] STEINSVOLL (O.), Kjeller Report KR-65, 1963
