HAL Id: jpa-00228437

(1)

HAL Id: jpa-00228437

https://hal.archives-ouvertes.fr/jpa-00228437

Submitted on 1 Jan 1988

HAL

is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are published 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.

DOMAIN STRUCTURE VARIATION WITH THICKNESS OF Nd2Fe14B SINGLE CRYSTAL

Y. Luo, Q. Ji, N. Zhang, B. Han

To cite this version:

Y. Luo, Q. Ji, N. Zhang, B. Han. DOMAIN STRUCTURE VARIATION WITH THICKNESS OF Nd2Fe14B SINGLE CRYSTAL. Journal de Physique Colloques, 1988, 49 (C8), pp.C8-589-C8-590.

�10.1051/jphyscol:19888268�. �jpa-00228437�

(2)

JOURNAL DE PHYSIQUE

Colloque C8, Supplement an no 12, Tome 49, dkembre 1988

DOMAIN STRUCTURE VARIATION WITH

THICKNESS

OF Nd2Fe14B SINGLE

CRYSTAL

Y. Luo, Q. G. Ji, N. Zhang and B. S. Han

Central Iron and Steel Research Institute, Beijing, China

Abstract.

-

There is a critical thickness Lo along &axis of Nd2Fe14B single crystal, below which the maze domain appeaw in the basal plane, otherwise, a set of dot-like reverse domains appear among the basal domains. The formation of reverse domain was discussed and the domain wall energy was estimated.

The domain structure of NdzFel4B phase consists of 180' domain walls parallel to the easy axis and with- out transverse flux closure domains, but with cone- shaped reverse domains at surfaces perpendicular to easy axis, thus there is no magnetoelastic energy [I]

except the magnetostatic energy in the surface and d e main wall energy. The width of bar domains is given by 121:

where 7

-

domain wall energy, L

-

grain thickness, I,

-

saturation magnetization. The bar domains are far from flat plane, but are winding with each other. If sample surface is perpendicular t o oaxis, a character- istic maze domain pattern is observed. While sample surface is parallel to c-axis, a zebra-stripe pattern ap- pears. The average width and total energy of bar and maze domain structure should be the same [3]. To reveal the formation of cone-like domain and critical thickness is just purpose of present work.

Experiments

A cylinder sample $4 x 1.76 mm was cut from a Ndal?e14B single crystai prepared by levitation melt- ing. Sample surface is perpendicular to c-axis.

Results and discussion

1.

DOMAIN

STRUCTURE VARIATION WITH SAMPLE THICKNESS.

-

A set of domain patterns taken from basal plane of same sample but corresponding to differ- ent thickness was shown in figure 1. Domain patterns corresponding to L = 20 pm and 30 pm, respectively, are almost the same (see Figs. l a and b), but with the only difference in domain space. Domain structure changes with further thickness increase, as it can be seen from figure l c

(L

= 40 pm), where a lot of dot-like domains appear within basal domains. They

Fig. 1. - Domain patterns in basal plane of NdzFeleB ZingJe crystal with afferent thickness L a) 20 pm; b) 30

pm; c) 40 pm; d) 50 pm; e) 220 pm; f ) 800 pm.

are the bottom of cone-shaped reverse domains. Their appearance would effectively reduce magnetostatic energy in free surface of basal domain, although domain wall energy was increased. but the decrease of the for- mer is much greater than the increase of later, so total free energy of the system is reduced by formation of coneshaped reverse domains.

Domain space D, the number and size of reverse domains increase continuously with increasing sample thickness (comparing Figs. l c and d). A multiple lay-

'~nstitute of Physics, Academy Sinica, Beijing, China.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888268

(3)

C8

-

⁵⁹⁰ ^JOURNAL^DE^PHYSIQUE

ered reverse domains appear, if sample is thick enough (see Figs. l e and f). The measured D as a function of

L$

is shown in figure 2. For simple bar domain structure D is linear with L*, as in the case of L

<

^{40 pm.}

But D is no longer linear with

~ 3 ,

if dot-like reverse domains appear within basal domains. So the value of LO can be defined as the starting point of deviation from D o: L+ (i-e. Eq. (I)). The obtained Lo ⁼35 km (Fig. 2) is in good accordance with the observed value.

Demagnetizing energy of system can be expressed as

E d = Edl

+

^Edz

,

where ^{E d l}and Edz is demagnetizing energy per unit surface caused by interaction of leakage between basal domains, and between reverse domains and basal domain, respectively.

Edl = 1.71 I:D (1

-

n x ' / ~ ~ ) ~

,

where TX'/D~

- area of reverse domains per unit surface, (1

-

^?rx2

/

D ~ )

-

fraction of reducing basal domain area. Ed, = 1.71

12

^D'

,

where D'

-

width of invented strip reverse domain, the area of which is equal to total area of dot-like domains per unit surface, D' = xx2/D,

Fig. 2.

-

D ^we. LZ 1 curve.

2. CALCULATION OF WALL ENERGY. - The wall energy can be expressed as

for NdzFel*B, 4x1, = 16.2 kG [4], L and

D

can be determined from figures l a and b. The calculated wall energy y = 30 m ~ / m ' is in accordance with the value reported by Sagawa [5].

3. FORMATION OF CONE-LIKE DOMAIN AND CRITICAL

Lo

. -

Although the size of cone-shaped reverse domdn inserted in the middle of each basal domain changes with domain space, but their geometric shape remains the same, namely the cone angle 0 of cone-shaped domain keeps constant. This can be confirmed by ob- serving domain pattern in the surface parallel to c-axis (Fig. 3). The measured 8 = 6

-

^'⁸ and radius of cone domain x = D/4.

Fig. 3.

-

Longitudinal section of cone-shaped reverse do- mains ( !/ *axis of Nd2FellB single crystal).

Wall energy of system can be expressed as Er = E,,

+

R,, where & l = l ~ / ~ - wall energy of basal domain,

&,

-

wall energy of cone-shaped domain, it can be

expressed as: Erz = yx a c (812) 2 x ' / ~ ~ . Total free energy of system is as follows

where Eo = 1.71 I ~ D . + ?LID, i.e. the free energy of simple strip domain system, AE is free energy dif- ference between simple maze domains and system with dot-like reverse domains. since x/D

<<

1, we only keep terms with (x/D)' in expansion of AE, then A E can be expressed approximately as

A E = y (~Tx'/D~) csc (812)

-

1.71 1;2az'/~ (3) i) If A E = 0 , then E = &, this is the critical state between simple maze domain system and system with reverse domains and

2x7 csc (8/2) x ~ / D ~ = 1.71 1:2ax2/D

SO

DO = y csc (8/2)

/

(1.71 12)

.

To take 8 = 7', 7 = 30 rn~/m', I, = 0.1289 T, then Do = 1.7 pm, this value is consistent with the measured one.

ii) If A E

>

0, then E

>

Eo, i.e. free energy of system with reverse domains is greater than that of simple maze domain system, so the stable domain structure should be the later, this is in good accordance with the observed fact.

iii) If A E

<

^0,then E

<

^I& ^andD

>

Do, the stable domain structure is that with dot-like reverse domain.

111 Luo, Yang, Zhang, Nin, Su, Xiujin, Acta Metall.

Sinica 23 (1987) A136.

121 Kittel, C., Rev. Mod. Phys. 2 1 (1949) 541.

[3] Kaczer, J., IEEE Trans. Magn. MAG-6 (1970) 442.

[4] Koon, N. C., Das, B. N., Rubenstein, M., J. Appl.

Phys. 57 (1985) 4091.

[5] Sagawa, M. et al., Proc. of 8th In%. Workshop on h e - E a r t h Magnets (ed. K. J. Stmat), Dayton, Ohio (May 1985) p. 587.