磁性Ⅰ講義予定 H18. 物質系講義 1．孤立イオンの磁性 2．結晶 …

1 H18.. I II .. ( . Hund .. r r r s = g B s hs : . eh B = = 10 23 J/T : . 2mc = 10-20 erg/G Bohr magneton). g = . r e r r r r IS evr = [r v ] ( p = mv ). = = ( . 2c v c 2c . e r r r ev I = 2 = . S = r [r p ] . 2 r 2mc r = l r hl : .. r r e r r c r r 1 r r [ ]. mv = p + A(r ) ( A(r ) = H r : vector potential). 2. r e r r = [r v ]. 2c e r r e2. = [r p] 2 [r A]. 2mc 2mc [ ]. r e2 r r r r . = l 2. r H (r H )r 2. 4mc . H r r r r e2. Edia = dH = l H + 2 2. r 2 . H. 0 8mc . dEdia N atom e 2 N n e 2. M = = 2. H x 2. + y 2. = atom e 2. r 2. H. electron dH 4mc electron 6mc dM N atom ne e 2 2. dia = = 2. r dH 6 mc & = 3 10 6 n emu/mole n = 1 ~ 100.)

2 R 2 1A dia e e . r N atom ne e 2 r f = Edia = 2. r H H. 2. 6mc r = dia H H .. ( .. 1 n , l, lz, sz, . n l lz sz 1 0. 2 0, 1. 3 0, 1, 2 -l~+l +1/2, -1/2. 4 0, 1, 2, 3 (2(2 l+1) . s, p, d, f . ( r ) r r r r . = B g si + li = B ( gS + L ) r r S = si He Li Na F Cl r r L = li S = 0, L = 0 . 3d, 4d, 4f, 5f, shells). 2(2l+1)=10.. n (3d)n: 10n . No n . 10 9 8 10-n+1).. e2. U = r r ij ri r j Hund . S . S L . LS S+1)(2L+1) .. Ti4+, Ti3+, V3+, Cr3+, Mn3+, Fe3+, Fe2+, Co2+, Ni2+, Cu2+, Cu+. V 4+, Mn4+, Mn2+. ne 0 1 2 3 4 5 6 7 8 9 10. S. L.. Ti4+, Ti3+, V3+, Cr3+, Mn3+, Fe3+, Fe2+, Co2+, Ni2+, Cu2+, Cu+. V 4+, Mn4+, Mn2+. ne 0 1 2 3 4 5 6 7 8 9 10.

3 S 0 1/2 1 3/2 2 5/2 2 3/2 1 1/2 0. L 0 2 3 3 2 0 2 3 3 2 0. l . LS .. B . e . Ze r r 1 r r [ l ]. r r Ze r B 3 r I 3 I Zev = p r r m . r r r r . Hls = li si = L S =. 2 S 2l+1 . r i r r r . L = li S = si = 2l+1 . i i 2S. h2 1 dV Ze 2. = V : effective potential ( ). 2m 2 c 2 r dr r r r r 4f J = L + S . J = L S ne 2l + 1. L S J L+S . J = L + S ne 2l + 1. ( ) ( ). r r r r r r = B 2 S + L = B J + S = (1 + ) J. r r r 1 J J S . r r J,M S J,M ' = J,M J J,M ' Wigner-Eckert . r r r r r r r J S = J ( J + 1), J S = L, J ( J + 1) 2 J S + S ( S + 1) = L( L + 1). J ( J + 1) + S ( S + 1) L( L + 1). =. 2 J ( J + 1). r 3 S ( S + 1) L( L + 1) Lande's g-factor = g J B J , g J = 1 + = +.

4 2 J ( J + 1).. 2 2 . a (r ) b (r ). 1 . 1 a (1) a (1) b (1) b (1) . 2 a (2) a (2) b (2) b (2) 4 . 1 a (1) (1) b (1) (1). =. 2 a (2) (2) b (2) (2) a (r ) b (r ). ( =1 ). 2 [ a (1) b (2) a (2) b (1)] (1) (2). = (1 2 ) [ (1) (2) (1) (2) (2) (1) (2) (1)]. a b a b = (1. 2 ) [ (1) (2) (1) (2) (2) (1) (2) (1)]. a b a b = (1. 2 ) [ (1) (2) (2) (1)] (1) (2). a b a b 2 . e2. H = H0 (1) + H0 (2) + H0 a = Ea a H0 b = Eb b r12. 1 .. H = H = Ea + Eb e2 r r e2 r r + a (1) b (2) a (1) b (2)dr1dr2 a (1) b (2) a (2) b (1)dr1dr2. r12 r12. Kab: Jab: . Coulomb integral exchange integral e2 r r H = H = Ea + Eb + a (1) b (2) a (1) b (2)dr1dr2. r12. = Ea + Eb + K ab K ab > 0.

5 E2 r r H = H = Ea + Eb a (1) b (2) a (2) b (1)dr1dr2. r12. = J ab J ab > 0.. K ab J ab 0 0 0 .. 0 K ab J ab 0 . H = Ea + Eb + . 0 J ab K ab 0.. K ab J ab . 0 0 0.. r r r S = s 1+ s2. S z = 1.. Et = K ab J ab 1. ( + ) S = 1 S z = 0 triplet 2 S = 1.. z Es = K ab + J ab 1. (. ) S =0 singlet 2. 1. ( + ) = 12 [ a (1) b (2) a (2) b (1)][ (1) (2) + (2) (1)]. 2. 1. ( ) = 12 [ a (1) b (2) + a (2) b (1)][ (1) (2) (2) (1)]. 2. 1 r r . H = K ab J ab + 2 s1 s2 . 2 . r v r v S ( S + 1) = 2 s ( s + 1) + 2 s1 s2 s1 s2 = 1 / 4 (triplet), 3 / 4 (singlet). triplet .. r r r r triplet 1. [ a (r1 ) b (r2 ) a (r2 ) b (r1 )]. 2 r r r1 = r2 . singlet 1. [ a (rr1 ) b (rr2 ) + a (rr2 ) b (rr1 )].

6 2. r r r1 = r2 .. Sz=1/2. H . S=1/2. H . Sz= 1/2. M = (n+ n ) . exp( H k BT ) exp( H k BT ). = . exp( H k BT ) + exp( H k BT ). 2 H. 2. k BT = Curie's law k BT.. Jz = J. Jz = J +1. r r r r H = H = g J B J H. J z = J 1. Jz = J. J. ( g J B M )exp( g J B MH k BT ). (H , T ) = M = J. J. exp( g J B MH k BT ). M = J. g J B JH 2J +1 2J +1 1 x . = g J B J BJ BJ ( x) = coth x coth . k BT 2J 2J 2J 2J . Brillouin . d . J = .. =. ( g J B ) J ( J + 1). 2.. dH H =0 3k BT Curie's law