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108  Magnetic Properties of Materials Sec. 4.9-•

tude. It should be realized that the measured susceptibility includes a

diamagnetic contribution which has not been considered in the present

section. However, since susceptibilities are additive quantities, and since

Xdia 10-5 according to the results in section .!, we  see that "dia # Xpara

at room temperature and below.

$or many applications in electrical engineering, it is a good appro"i%mation to ta&e the relative permeability 'r   o( paramagnetic substances

equal to unity. )s (ar as applications o( paramagnetic materials are con%

cerned, we may mention here that paramagnetic salts are the wor&ing

material used in obtaining very low temperatures * # 1+- by adiabatic

demagnetization: the principle o( this method is discussed in the boo&s by

ittel and by e&&er, given in the list o( general re(erences. )lso,

 paramagnetic salts have entered the group o( electrical engineering mate%

rials a (ew years ago because they are the essential material used in the

solid state maser *microwave ampli(ication through stimulated emission

 by radiation-. /he principle o( operation o( a maser is discussed in van der 

iels boo& *page 230 ((-, cited in the general re(erences.

4.10 4ome properties o(

(erromagnetic materials

5ach (er romagnet ic

material has a

characteristic temperature

above which its properties

are qui te di((erent (rom

those below thattemperature. /his

temperature is called the

 ferromagnet ic Curie

temperature and wil l be

denoted here by O f. In this

section we shall discuss

 brie(ly some o( the

characteristic (eatures o( 

(erromagnetic behavior in

the two te mp er atur e

regions.

*i- T > O f . In the region

above the (erromagnetic

6urie temperature, the

 behavior o( a (erromagnetic

material is somewhat similar 

to that o( a paramagnetic

material. /hus. there e"ists a

unique relationship between

 B and H, and between M and

 H. 7ne can thus de(ine the

susceptibility X = MH 9 'r   : 

1, where " and !r   have a

de(inite meaning. In this

region, the susceptibility

depends on /emperature in

accordance with the so%called

Curie"#eiss $a%

 & ' !r ( ) '

C * +T ( -

(or 

T > Of 

Sec. 4.) Magnetic roperties of Materia$s 1 0 3

1 "

t

Fig. 4.21. 4chematic represen%tation o( the hysteresis loop (or a (erromagnetic material. /he

virgin curve starts at the origin.

Of 0

Fig. 4.20. /he reciprocal o( the

susceptibility as a (unction o( temperature (or a (erromagneticmaterial above the (erromag%netic 6urie temperature, Of. /he

 paramagnetic 6urie temperat ureis obtained by e"trapolation o( 

the straight portion o( the curve

which satis(ies the 6 urie%;eiss

/

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*.!

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evident (rom the values given

in /able .2 (or high%

 permeability materials. 'pon

reducing the value o(  H (rom

the saturation region to zero, it

is observed that there remains

a (lu" density

+remanent f$u densit3-.

4ince 5f ' 0, the material

must be spon%

0(