Double hysteresis loops in ferromagnetic crystals

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Double hysteresis loops in ferromagnetic crystals

A.A. Hirsch

To cite this version:

A.A. Hirsch. Double hysteresis loops in ferromagnetic crystals. J. Phys. Radium, 1959, 20 (2-3),

pp.262-263. �10.1051/jphysrad:01959002002-3026200�. �jpa-00236031�

262

DOUBLE HYSTERESIS LOOPS IN FERROMAGNETIC CRYSTALS

By ^{A. A.} HIRSCH,

Department ^of Physics, Technion-Israel Institute of Technology, Haifa, ^Israel.

Résumé.

Un monodomaine présentant ^une anisotropie ^mixte magnéto-cristalline ^{et uni-} axiale peut ^{donner une} courbe d’aimantation composée de deux boucles asymétriques ^reliées par

un segment, ^le long duquel l’aimantation est réversible. Le processus d’aimantation irréversible

commence à partir ^d’un champ critique. ^Ce cycle ^{double pourrait être une} explication possible ^du

mécanisme d’aimantation ^des matériaux ayant ^des cycles étirés, ^comme les Perminvars.

Abstract.

A single domain with mixed magnetocrystalline and uniaxial anisotropies ^can

show a magnetization ^curve composed ^{of two} asymmetric loops ^connected by ^{a section over which}

the magnetization is reversible. The irreversible process starts at acritical field. The double

loop ^{could be a} possible explanation ^for the mechanism ^of magnetization ⁱⁿ materials with con-

tricted loops ^as Perminvars.

LE JOURNAL DE PHYSIQUE ^{ET LE RADIUM TOME} 20, FÉVRIER-MARS 1959,

Single ferromagnetic domains of cubic structure may show double hysteresis loops [1, 2]. ^The

transition of the ordinary hysteresis loop ^into

the double loop depens ^{on :}

1° the magnitude ^{of the} magnetic ^{uniaxial ani-} sotropy and its direction with respect ^{to that of} the magnetic ^{field and to} that of the crystallogra- phics axes ;

20 the ratio of the constants of uniaxial aniso-

tropy ^and magnetocrystalline anisotropy.

The magnetization ^{in the direction of the} magne- tic field, I, ^{is obtained} by minimising ^{the free}

energy of the crystal. ^{For a} prolate spheroidal

domain whose polar ^{axis lies} along ^the [100] ^direc- tion, ^the values of 1 are given by ^the following expressions :

for a magnetic field, H, ^{in a} [001] ^{direct ion.}

where Ii is the magnetocrystalline ^constant.

Ta is the spontaneous magnetization ^and Na, Nb

are the demagnetization coefficients along ^the polar

and equatorial ^{axes. A} rectangular magnetization loop ^can be derived from these relations for a posi-

tive K. The shape ^{of this} loop changes ^with changing ^{value of the factor F. For F =} 0.5 the

loop becomes -double. In case of a negative K,

the magnetization loop ^is ordinary and its coercive force is equal ^{to zero} for F == - 0.5.

When the magnetic ^{field lies} along ^the polar

axis of the domain, ^the magnetization loop ^is rectangular ^{for .K} > 0 and its coercive force increases with increasing ^{factor F.}

Two double hystérésis loops ^{of a} crystal ^with

a positive K ^are illustrated in figure ^{1 for F - 0.5}

and F =1.

FIG. 1.

Thé inverse slope ^{of the} magnetization ^{curve for}

low-fields and small values of f ^is given hy

where f ⁼ I/Is. ^This portion ^{of the} curve corres-

ponds ^{to stable} equilibrium directions of the _magne- tization vector.

For large ^{values of} f ^and low-fields (at ^a crystal

field which corresponds ^{to a} sharply increasing magnetization), the inverse slope ^of magnetization

curve is expressed by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01959002002-3026200

263

This portion ^{of the curve shows non-stable} equilibruim directions of Is.

Fm. 2.

Fic.3.

The condition dHO,,,, ^{dI = 0 leads to the following}

relation for thé ;critical field :

It is supposed ^{that the} theory ^of the double

hysteresis loop ^{can be} applied ^for analysis ^{of the} magnetization ^{curves of} single-crystal cobalt fer- rite which are measured by ^{Foner and Artman} [3].

The magnetocrystalline anisotropy ^{constant deriv-}

ed from equation (2) ^and (4) ^{is of the same order}

of magnitude ^as calculated by ^these investigators.

Figure ^{2 shows the} magnetization ^{curve of a} crystal with"a negative ^{K for F .- - 0. 5.}

A composite magnetization loop ^{of two domains} with magnetocrystalline ^constants of différent

signs is shown’in figure ³ (F1 - 0.5, F2 - - 0.5

and K1 ^{= -} K2). Loops of simila.r shape ^have

been measured by ^several investigators ^{in Per-}

minvar. The mechanism of the magnetization ^of

a double loop ^can give ^{also a} possible explanation

for the magnetic behaviour of this material.

REFERENCES’

[1] ^HIRSCH (A. A.), Bull. Res. Couns. Israel, 1957, ⁶ A, ^276.

[2] ^HIRSCH (A. A.), Bull. Res. Couns. Israel, 1958, ⁷ F, ⁱⁿ print.

[3] ^FONER (S.) and ARTMAN (J. O.), ^J. Appl. Physics, 1958, 29, ^443.

DISCUSSION

Mr. Artman and Foner.

VGe would like to

point ^{out that a} single ^domain analysis ^{does not} applyto our problem. ^As discussed by ^{us in detail}

at this çonference, ^{in order to} explain ^{our results it}

is essential that a multi-domain structure exist.

Mr. ^Hirsch.

^In multi-domain materials

having ^{some ordered domain} arrangement ^{it is} possible ^{to have a} magnetization process which

occur only by domain rotation. when the external

magnetic ^{field lies in a direction} perpendicular

to the walls of the domains, ^the magnetization ^is

rotational.