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III. .
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(>0,10-5 - 10-2) : 1. , , , , , . : Na, NO, F - (). 2. : ; , ; . : Mn2+,Gd3+,U4+. , , , . 3. , , . 4. >. 5. . . . , , , , , , , . , , . N , ( ). =1Е, = 1/ (12 ) 1.2З10-29З106 = 1.2З10-23. Н kT =1/2З1.38З10-23З300 = 2.1З10-21, .. 175 . , , . , : exp(U/kT) = exp (MHcos/kT). , - (+d):

p ( ) =

exp(





0

MH cos ) sin d kT . MH exp( cos ) sin d kT


(3.1)

:


I = NM cos = NM cos p ( )d = NM
0


0

exp(


MH cos ) cos sin d kT


0

MH exp( cos ) sin d kT

(3.2)

/kT = , cos=x,

I = NM (

exp + exp(- ) 1 1 - ) = NM (cth - ) = NML( ), exp - exp(- )

. 3.1.

(3.3) L()= [cth-1/] - . L() , .3.1, , , I NM, . - , 3


( ) ~1/ = NM/(1/2 kT) ~ 1.2З10-23/2.1З10-21~0.005. . . I = (NM/3) = NM2/3kT. , = I/H = NM2/3kT - .

(3.5) (3.6)

. - . z , z- Mz = gЕBJz, (3.7) Jz 2J+1 -J +J.

I = NgM

B

J z =- J J



J

J z exp(

J z =- J



gЕ B HJ z ) kT 2J + 1 2J + 1 1 cth( )- = NgЕ B [ cth( )] . gЕ B 2J 2J 2J 2J exp( HJ z ) kT

(3.8)



BJ ( ) = [

2J + 1 2J + 1 1 cth( )- cth( )] 2J 2J 2J 2J

(3.9)

. .3.2 Cr3+, Fe3+ Gd3+ [W.E. Henry, Phys. Rev., 88 (1952), 552]. J . <<1

BJ ( ) =

J +1 [(J + 1)2 + J 2 ]( J + 1 ) 3 - + ..... 3J 90 J 3

(3.10)

J (3.10) , (3.10) (3.5). .., (J ). , = JЕBH/kT (3.10) , -: (3.11) = Ng2J(J+1) ЕB 2/3kT. , (2.11) (3.6), Meff = g[J(J+1)]1/2ЕB. (3.12) Meff . . J0 (1.29) ЕBH , . 3.1. . , . (1.32) MJ = 3+ 3+ Cr , Fe J*gJЕB, - L* S*. .. , Gd3+. , . , , L* = 0, J* = S* gJ = gS =2. .. = S =2S*ЕB, , . , , ?Л (quenched). , . . 4


. ~1/T () , , . - . = 3 5s25p6 Xe. La 4f- , Ce3+- 4f1 4f- , 4f13 ,Yb3+ Lu3+4f14. 3+ 1.11A0(Ce3+) 0.94 A0(Yb3+) - " ". 4f- 0.3 . 4f . (2J+1)- . - - (3.11) (3.13) gJЕB/kBT<<1 =M/H= N/V p2ЕB2/3kBT, p=g[J(J+1)]1/2 (3.14) Ce3+ 4f15s2p6 2F(L=3)5/2 p() = 2.54 ()=2.4 3 Pr3+ 4f25s2p6 H(L=4)4 ()=3.58 ()=3.5 ()=0.84 () =1.5 Sm3+ 4f55s2p6 6H5/2 Pr3+ 4f65s2p6 7F0 ()=0 () =3.4 , L-S , kBT . L S J, . . ( ), - (3.11) MNp2ЕB(ЕBH/kBT) p=g[J(J+1)] (3.15) (), . . 3.3 , , (J)=g[J(J+1)]1/2, - (S)=2[S(S+1)]1/2 3.3. (J) 2 Ti3+,V4+ 3d1 D3/2 1.55 3+ 32 V 3 d2 F3 4 3d3 F3/23 Cr3+,V2+, Mn4+ 2+ 3+ 4 5 Cr , Mn 3d D0 6 3d5 F5/2 Fe3+, Mn2+ 5 Fe2+ 3 d6 D4 4 Co2+ 3d7 F9/2 3 F4 5.59 Ni2+ 2 Cu2+ 3d9 D5/2 (S) 1.73 1.63 0.77 4.90 5.92 6.70 6.63 2.83 3.55 3d-. p() 1.8 2.83 2.8 3.87 3.7, 3.8, 4.0 0 4.8, 5.0 5.92 5.9 4.90 5.4 3.87 4.8 3.2 1.73 1.9

, (S)=2[S(S+1)]1/2, . . . , Lx, Ly, Lz . , Lz, L2. , . Lz , L2 . Lz , . B(L+g0S). z Lz, .. , Lz. 5


- , S, - (3.2) - S L, , , g-, , , 2, . : g>2, 3d , g=2, 1/2, g<2, <1/2. (abc) (3.16) e=Ax2 + By2 - (A+B)z2 , - . x,y,z 2 = 0, . , Lz , = 0, . , , . x, y, z. - ( -) 3- . , , (3.19). , - (Jahn-Teller effect), , Mn3+ Cu2+ . . - , 4f- - , 5s 5p , Fe 3d- . , 3d , . . : ) L-S -, J; ) 2L+1 - L, , , . 3.3. pz , z, , px py. , px py - . L . , >>H, . . J=0. , , 1 , . , , L .3.3 = l, S = 2lз1/2 = l J = |L-S| = 0. ( 2J+1 = 1). (1.43) (J =0), . , , 2- (1.43) . .. (1.43) (3.17) E0=(e2/8m)H2<0(xi2+yi2)0> - n <0ЕBH(L+g0S)n>2 / (En-E0). (3.18) = -N/V 2E0/H2 = -N/V{e2/4mc2<0(xi2+yi2)0>-2ЕB2 n <0Lz+g0Sz2n> / (En-E0)}. 6


, 1- . 2- , .. En > E0. .. () . , - (J. Van Vleek, 1927). , .. , , , , : = n - E0 >> kBT. (3.19) J 0 . (, ) , , . , , . : , Eu3+ , Sm3+; E1-E0 300 -1 (0.04 ) (Eu3+), paraVV = const (T) 10-2 < 100 .

. . . , . , -ЕB/V, g0 = 2, SH +ЕB/V, SH, M=ЕB(n+ - n-) (3.20)

. 3.3. . gБ(E)dE - V (?+Л -, ?-Л - () ) ? +dE. (3.21) : gБ(E)=1/2g(E) (H=0), (3.22) SH E = -gЕBH, H0 (3.23) g+(E)=1/2g(E+ЕBH); g-(E)=1/2g(E-ЕBH). (3.23) (3.24) nБ=dEgБ(E)f(E), f=1/(e(E - Е)+1). , . n=n++n- (3.25) (3.26) Е. (-Е >> kBT, fexp [-(E-Е)]) , (3.11) ( M=N/V JBJ(JH)) J = 1/2. , - . g(E) EF, ЕBB ~ 10-4 F, 104 , ЕBB: (3.25) gБ(E)=1/2g(EБЕBH)=1/2g(E)Б1/2ЕBHg'(E)f(E); (3.26) nБ=1/2g(E)f(E)dEБ1/2ЕBHdEg'(E)f(E). n=g(E)f(E)dE, H=0, , , H=0: 7


Е=EF[1+((kBT/EF)2)]. (3.27) (3.21) (3.26) (3.28) M=ЕB2Hg'(E)f(E)dE. , , (3.29) M=ЕB2Hg(E)(-f/E)dE. T=0 : -f/E=(E-EF) M=ЕB2Hg(EF), =ЕB2g(EF) (3.30) . -f/E (kBT/EF)2 (3.30) (T104). , ( ~ 1/T). g(EF)=mkF/h22 , , P=(/2)2(a0kF), =e2/hc=1/137, P=(2.59/(rs /a0)*10-6 ~ 10-6. (3.31) Pauli ion teor par = par (T/TF). P ~ 0.66 10-6, Pexp = 2.0 10-4. . , H. , - (H) - - c=eB/mc>>1. , (H) () H. . . , L=-1/3P (3.32) , , () - . - . , L= 2/3P .

. 3.4. (T).

8