1 d 6 L S p p p p-d d 10Dq 1 ev p-d d 70 % 1: NiO [3] a b CI c [5] NiO Ni [ 1(a)] Ni 2+ d 8 d 7 d 8 + hν d 7 + e d 7 1(b) d 7 p Ni 2+ t 3 2g t3 2g e2

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1 d s p d 3d d d d d d d d d 1954 [1] d d 1970 I-II-VI 2 II-VI II 1:1 I III CuAlS 2 Al 3+ d 5 Fe 3+ d 5 S 3p d 6 L L [2] configuration interaction: CI d 5 1

2 1 d 6 L S p p p p-d d 10Dq 1 ev p-d d 70 % 1: NiO [3] a b CI c [5] NiO Ni [ 1(a)] Ni 2+ d 8 d 7 d 8 + hν d 7 + e d 7 1(b) d 7 p Ni 2+ t 3 2g t3 2g e2 2g S = 1 3 A 2g 4 T 1g, 2 T 1g, 2 E g 2

3 NiO [3] Ni Ni 3d Ni 3p d 7 p 3p 3p 6 3d 8 + hν 3p 5 3d 9 3p 5 3d 9 5p 6 3d 7 + e 3d d 8 d 7 + e Davis d p CI [4] Ψ g = α 0 d + β 0 L (1) d 3d Ψ f = α f d 2 + β f dl + γ f L 2 (2) d, d 2 d n, d n 1 L, dl d n+1 L, d n L d p d ε d, p ε p E(d) = ε d, E(L) = ε p (3) d p ε d > ε p E(d) < E(L) d E(d 2 ) = 2ε d + U, E(dL) = ε d ε p, E(L 2 ) = 2ε p (4) U d p p d (d 2 dl) ε d ε p U ε d ε p U > U 3

4 d d n 1 < U NiO L d n L d d n Davis NiO 6 Ni 3d t 2g e g p d 7 d 8 [5] =4.0 ev U =7.5 ev 1(c) < U d 8 L d 7 d 8 L d p 10Dq d M p+ m X q MX m (mq p) NiO M p+ =Ni 2+ X q =O 2 MX m (mq p) = NiO 10 6 N- MX (mq p 1) m N 1- MX (mq p+1) m N d n d n+1 L 4

5 2: N- N 1, N + 1- E h + E e E(d n d n+1 L) d d p ε d ε p 2 d U d n d n+1 L E(d n n(n 1) ) = E 0 + nε d + U 2 E(d n+1 n(n + 1) L) = E 0 + (n + 1)ε d ε p + U (5) 2 = ε d ε p + nu (5) E 0 p p-d d n d n+1 L 2 p-d d n (1) d n+1 L N 1- d n 1 d n L E(d n 1 ) = E 0 + (n 1)ε d + (n 1)(n 2) U (6) 2 5

6 d n 1 d n L U > U d n 1 d n L d n d n 1 + e < U d n L d n 1 d n d n L + e NiO CI 2 < U N + 1- d n+1 d n+2 L + U d n + e d n E h E e N- N 1- N + 1- E N,0 E N 1,0 E N+1,0 E gap = (E N 1,0 E N,0 )+(E N 1,0 E N,0 ) = E N 1,0 +E N+1,0 2E N 1,0 (7) p-d (5) (6) > U E gap = U < U E gap = > U d n +d n d n 1 +d n+1 Mott Hubbard ( ) < U d n + d n d n L + d n+1 2 p-d d n E(d n ) E n (> 0) [6] 6

7 3: a U eff, eff b U eff U, eff [6] 2 E n E n 1 E n+1 ( U eff U) E n E n+1 ( eff ) 3(a) U eff, eff n = 0, 1 n = 9, 10 E n = 0 n = 5 E n n = 5 3(b) n 5 n 4 3(b) 2 N 1- N- N + 1- N- N- N + 1- N 4 p d W p, W U 7

8 4: N 1, N + 1- (a) (b) p p d d W p W p > U U W < U 1 2 (W + W p) U W 1 2 (W + W p) -U 5 Zaanen-Sawatzky-Allen (ZSA) [7] U p -d p-d T pd = U 8

9 5: Zaanen-Sawatzky-Allen [7] NiO Ti V - d U- p p, U T pd [6], U, T pd W, W p (1) Z (2) v (3) 9

10 U (1) Z (2) v (3) (1), (2) d Z 2.5v, U Z + 0.5v (8) ev T pd 1 2 ev Z d p NiO T pd LaTiO 3 p U 2.5 ev 0.5 ev, 1.0 ev 6: (a) [8] (b) LaMO 3 [9] CT Mott 6(a) [8] n = 5 n = 4 (8)

11 eff, U eff 3 p-d LaMO 3 6(b) M [9] 5 ZSA Ti, V U < U 5 U T pd p-d T eff 10 nt pd n d p d T eff 10 n d n d n+1 L d 10 n Ti, V T eff ZSA T eff 1 2 (W + W p) U W 2T eff U Ti, V 7: Zaanen-Sawatzky-Allen [10] U T pd 11

12 ZSA (W + W p) 0 < 0 [10] d n d n+1 L 2 E e + E h 2 d n+1 L < 0 p-d d n+1 L < 0 Cu Cu 3+ : d 8 NaCuO 2 d 9 L LiNiO 2 Ni 3+ : d 7 NiO Ni (111) 1 Li < 0 p p d S 10Dq d p-d d 4, d 5, d 6, d 7 CuO 4 d 3 d 8 2 d n e g p-d [T pd (e g )/T pd (t 2g ) 2 e g 12

13 d n+1 L ] LaCoO 3 (Co 3+ : d 6, S = 0) NaCuO 2 (S = 0) LiNiO 3 (S = 1/2) 4d d p-d T pd SrRuO 3 Ru 4+ : d 4 Ru 4+ S = 1 S 2Sµ B µ B p-d d p p Ψ g = α d n + β d n+1 L (2 α 2 + β 2 )µ B S n 5 NiO Ni 1.8µ B α 2 S(S + 1)µ B p-d 8: Ni-O-Ni Ni 3d x 2 y 2 (a): (b): 13

14 9: MO [11] [11] NiO Ni-O-Ni Ni 2 O 2+ Ni Ni 2+ e g d x 2 y 2 d 3z 2 r2, z Ni-O 2 8 d 3z 2 r2 2 Ni d 1, d 2 p z L d x 2 y 2 p d x 2 y 2 Ni 8(a) d 1 d 2 Ni d 1 L L d 2 = eff E(, ) = 2t2 (< 0) (9) eff t d 3z 2 r 2-p z NiO 6 T pd (e g ) t T pd (e g )/ 3 Ni 8(b) d 1 d 2 d 1 L L d 2 d 1 d 1 d 2 d 2 = U eff L L = 2 eff E(, ) = 2t2 eff (1 + t2 2 eff + t 2 U eff eff )(< 0) (10) 14

15 H = JS 1 S 2 J J = t4 S 2 ( 1 eff 2 eff + 1 U eff eff ) (11) J T N = 2JZS(S + 1)/3k B k B : Z: NiO Z = 6 NaCl MO 9 [11] 10: RMnO 3 (a) LaMnO 3 Mn (b) NiO Ni 2+ e g Cu 2+ d 9 S = 1 2 Ni3+ t 3 2g t3 2g e1 g S = 2 Mn 3+ t 3 2g e1 g e g d x 2 y 2 d 3z 2 r 2 R 1 x Sr x MnO 3 R 1 x Ca x MnO 3 R 3+ 3 RMnO 3 Mn 3+ : d 4 Mn-O-Mn Mn 2 O 4+ Mn d 3z 2 r 2 t d x 2 y 2 t ( t << t ) Mn e g d 3z 2 r 2 15

16 NiO Mn e g d x 2 y 2 t Mn t 3 2g e g Mn(1) d 3z 2 r 2 Mn(2) d x 2 y 2 Mn(1) d 3z 2 r 2 Mn(2) d 3z 2 r 2 Mn(1) Mn(2) d 2,3z 2 r 2 d 2,x 2 y 2 d 2,3z 2 r 2 d 2,x 2 y 2 d 2,3z 2 r 2 d 2,x 2 y 2 Mn(1) Mn(2) Mn Mn 10(a) [12] BiMnO 3 e g [13] LaMnO 3 MnO 6 x, y d 3x 2 r 2 d 3y 2 r 2 ab c 10(b) d d CI CI (1) 10Dq, B, C, U, T pd 10Dq B C (2) p-d 16

17 (3) p d d d 11: NiO Ni 2+ N- 3 p d 9 L NiO d d Ni 2+ S = 1 t 6 2g e2 g 3 A 2g t 2g e g t 5 2g e3 g 3 T 2g hν =1.2 ev B, C 10Dq 11 Ni 2+ d 8 S = 1 3 F d 9 L 3 A 2g 3 T 1g 3 T 2g L 10Dq 3 A 2g e g d 9 L 2T pd (e g ) 2 / 3 T 2g e g t 2g 1 [T pd (e g ) 2 +T pd (t 2g ) 2 ]/ T pd (e g ) 2T pd (t 2g ) 3 T 2g 3 A 2g 3 4 [T pd(e g ) 2 ]/ 10Dq p-d e g t 2g 0.3 ev 10Dq 2 3 ev 17

18 12: ZnS Zn N- [15] ZnS ZnSe CdTe II-VI Zn 2+ Cd 2+ 2 p-d p-d e t Dq ZnS [14] d n d n+1 L e t 2 [15] 12 N e, t 2 g 18

19 d n 1 d n L U 2 N NaCuO 2 Cu 3+ d n L p-d d n L 13: ZnS [15] 12 ZnS d 5 19

20 Mn 2+ (d 5 ) d 4 d 5 Cr 2+ (d 4 ) AFeO 3 A: 2 6 SrFeO 3 CaFeO Ca Sr (d ) W - - AFeO 3 ( 14) A Ca Fe-O-Fe 180 p Fe 3d - V Cr Ti V 2 O 3, NiS 2 x Se x, NiS 1 x Se x AFeO 3 W Ca 1 x Sr x VO 3 Y 1 x La x TiO 3 x - W U U/W NiS NiS 1 x Se x - [16] ( )NiO 4 ev NiO 2p NiS 3p 2.5 ev d 8 d 9 L 20

21 14: AMO 3 (a) (b) NiS NiAs NiS Ni-Ni d W p W p 0.14 ev NiS d 9 t 3 2g t3 2g e2 g e g 2 E g d 8 L Ni e g S 3p 2 E g NiS e g e g (1) 260 K (2) S Se (3) (1) (2) S Se p-d d (3) 15 Se NiS 1 x Se x (3) kbar - NiS NiO d 7 d 8 L 21

22 15: NiS 1 x Se x [16] NiS 6 [17] d-d p-d - NiS 6 α d 8 + β d 9 L +... N- 3 A 2g d 9 N E g, d 8 L N 1-2 E g U d U 4 NiS 2 NiS 2 x Se x 16 NiS 1 x Se x [18] NiS 1 x Se x NiS 2 Ni 2+ S 2 2 NaCl NiS ev S Se x 0.5 x 1.0 NiS 1 x Se x - [19] Ni 22

23 16: NiS 2 x Se x [18] Se - NiS 2 x Se x NiS 1 x Se x Ni S - 10 V 2 O 3 NiS 2 x Se x V Ti V Cr U W U d 1 U/W - 17 U/W 1 U/W U/W 23

24 17: d 1 [20] d n U/W /W - 18 n = U/W 1 - n RMO 3 R 3+ Sr 2+ Ca 2+ M d Sr 2+ Ca 2+ 24

25 a B m ε 0 a B = h 2 ε 0 /m e 2 x a B x 1/3 = 0.25 U/W 1 ε 0 m a B x U/W 1 a B x x = 0.5 x = : n-u/w /W - 18 n-u/w n- /W AMO 3 A: 19 U/W /W A U/W /W A M d p U 25

26 19: AMO 3 A 14 W n = La 1 x Sr x TiO 3 [21] LaTiO 3 (d 1 ) La 3+ x 0.03 Sr 2+ SrTiO 3 (d 0 ) d Sr 2+ La 3+ 0 < x < 1 n( 1 x) x γt m n 1 La 2 x Sr x CuO 4 - La 1 x Sr x TiO 3 La 2 CuO 4 x 0.05 x γt x 0.05) [22] La 1 x Sr x TiO 3 La 2 x Sr x CuO 4 26

27 18 Mn La 1 x Sr x MnO 3 - LaMnO La 3+ Sr 2+ x 0.1 x = 0.3 T c =350K x < : La 1 x Sr x MnO 3 [23] La 2 x Sr x NiO 4 R 1 x A x MnO 3 La 1 x Sr x FeO 3 x 1/2, 1/3 La 2 x Sr x NiO 4 Ni 2+ Ni 3+ R 1 x A x MnO 3 Mn 3+ Mn 4+ La 1 x Sr x MnO 3 La Nd Nd 0.5 Sr 0.5 MnO 3 T co =160 27

28 21: Sm 0.5 Sr 0.5 MnO 3 [24] K [24] 21 CE Mn 4+ t 3 2g Mn 3+ t 3 2g e1 g e g Mn 3+ e g Mn 4+ e g e g Mn 4+ t 3 2g e g Mn LaMnO 3 La 0.5 Sr 0.5 MnO 3 A Nd 0.5 Sr 0.5 MnO 3 Pr 0.5 Ca 0.5 MnO 3 T co La 0.5 Sr 0.5 MnO 3 Sm 0.5 Sr 0.5 MnO 3 Pr 0.5 Ca 0.5 MnO 3 A Mn-O-Mn e g La 1 x Sr x FeO 3 x =2/3 Mn Ni Fe 3+ : Fe 4+ = 1 : 2 Fe 3+ : Fe 5+ = 2 : 1 [25, 26] Fe 4+ 2Fe 4+ Fe 3+ +Fe 5+ 28

29 CaFeO 3 Fe 4+ : d 4 Fe 4+ 6 E gap (7) E gap < 0 Fe 4+ d 4 d 5 L [(3.3.1)] Fe 5+ d 4 d 5 L 2 Fe 4+ d d 5 p Fe - VO 2 V 4+ : d 1 - T t = 350 K [27] VO 2 VO 6 O-O t 2g V d xy V - [1] 1969 [2] T. Kambara, K. Suzuki and K. Gondaira, J. Phys. Soc. Jpn. 39, 764 (1975) [3] M. R. Thuler, R. L. Benbow, and Z. Hurych, Phys. Rev. B 27, 2082 (1983). [4] L. C. Davis, Phys. Rev. B 25, 1912 (1982). [5] A. Fujimori, F. Minami, and S. Sugano, Phys. Rev. B 29, 5225 (1984); A. Fujimori and F. Minami, Phys. Rev. B 30, 957 (1984). 29

30 [6] 1993 [7] J. Zaanen, G. A. Sawatzky and J. W. Allen, Phys. Rev. Lett. 55, 418 (1985). [8] T. Saitoh, A. E. Bocquet, T. Mizokawa, and A. Fujimori, Phys. Rev. B 52, 7934 (1995). [9] T. Arima, Y. Tokura, and J. B. Torrance, Phys. Rev. B 48, (1993). [10] T. Mizokawa, A. Fujimori, H. Namatame, K. Akeyama, and N. Kosugi, Phys. Rev. B 49, 7193 (1994). [11] J. Zaanen and G. A. Sawatzky, Can. J. Phys. 62, 1262 (1987). [12] T. Mizokawa and A. Fujimori, Phys. Rev. B 56, R686 (1997). [13] K. I. Kugel and D. I. Khomskii, Sov. Phys.-JETP 37, 725 (1973). [14] 24, 737 (1989). [15] T. Mizokawa and A. Fujimori, Phys. Rev. B 48, (1993). [16] M. Matoba, S. Anzai and A. Fujimori, J. Phys. Soc. Jpn. 60, 4230 (1991). [17] M. Nakamura, A. Sekiyama, H. Namatame, H. Kino, A. Fujimori, A. Misu, H. Ikoma, M. Matoba, and S. Anzai, Phys. Rev. Lett. 73, 2891 (1994). [18] G. Czyzek, J. Fink, H. Schmidt, G. Krill, M.F. Lapierre, P. Paissod, F. Gautier and C. Robert, J. Magn. Magn. Mater. 3, 58 (1976). [19] S. Miyasaka, H. Takagi, Y. Sekine, H. Takahashi, N. Môri, and R. J. Cava, submitted to Phys. Rev. B (1997) [20] A. Fujimori, I. Hase, H. Namatame, Y. Fujishima, Y. Tokura, H. Eisaki, S. Uchida, K. Takegahara, and F.M.F. de Groot, Phys. Rev. Lett. 69, 1796 (1992). [21] Y. Tokura, Y. Taguchi, Y. Okada, Y. Fujishima, T. Arima, K. Kumagai and Y. Iye, Phys. Rev. Lett. 70, 2126 (1993). 30

31 [22] N. Momono, M. Ido, T. Nakano, M. Oda, Y. Okajima and K. Yamaya, Physica C 233, 395 (1994). [23] A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido and Y. Tokura, Phys. Rev. B 51, (1995). [24] 31, 124 (1997). [25] M. Takano, J. Kawachi, N. Nakanishi and Y. Tokura, J. Solid State Chem. 39, 75 (1981). [26] P.D. Battle, T.C. Gibb and P. Lightfoot, J. Solid State Chem. 84, 271 (1990). [27] A. Zylbersztejn and N.F. Mott, Phys. Rev. B 11, 4383 (1975). 31

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