Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download ""

Transcription

1 1

2 URu2Si2 2

3 (n,l,m) + σ l: 4f (n=4,l=3) 5f (n=5,l=3) d 5 1. S L L=0(S), 1(P), 2(D), 3(F), 4(G), 5(H),... (2S+1) LJ 3

4 () d ~ > f >> > 1~10 ev 0.1~0.3 ev 1~100 K LS (Russell-Saunders) f 2 less than half-filled f 12 more than half-filled j-j << 4

5 f 1 (J=5/2) ρe(r) ρm(r) N S Jz 5

6 J=5/2 = ( ) J=5/2 6

7 (-1) l cf. E-H (-1) l+1 = ( :N, :S) 7

8 (m>0) l 0 (monopole) 1 (dipole) 2 (quadrupole) 3 (octupole) 4 (hexadecapole) 5 (dotriacontapole) 6 (tetrahexacontapole) 8

9 f n (Wigner-Eckart) M, M! (x,y,z ) (Jx,Jy,Jz )! 9

10 Jx, Jy, Jz Jx, Jy, Jz Mathematica Stevens 10

11 (q~0) (C ) : () ) PrInAg2 : (Γ3) 10 K x 2 -y 2 O. Suzuki et al.: JPSJ '06 11

12 X X ( 1998 ) X ( ) 4f ψ 2p X cf. X 4f E1 E2 E1 ev 12

13 (X ) Ce 0.7 La 0.3 B 6 $(IV ) Mannix$et$al.$PRL$95$117206$ 05 L 2 $ $:$2p"5d$(E1),$2p"4f$(E2) T$=$1$K,$Q=(3/2,3/2,3/2) $(Γ 5u ) ψ σ"σ $$:$6 [111] HK$and$Y.$Kuramoto$JPSJ$74$3139$ 05 E2 13

14 ( :) K.$Kuwahara$et$al.$JPSJ$76$(2007)$ R.$Shiina$et$al.$JPSJ$76$(2007)$ cαm(κ) F(κ) κ Q ( ) κ 14

15 cf. NMR/NQR xyz z xy y x 15

16 Hc > Hλ > HCEF J f r (Γ1g) = 16

17 (Oh) Oh J=5/2 4 O44 () 17

18 (Oh) () Γk ( ) = (2J+1)^2 ^2 18

19 Oh Γ3 J=4 19

20 Oh Γ3 4σz (Γ3 ) 4σx 20

21 Oh Γ3-18 sqrt(5) σy (Γ3 ) 40sqrt(15) σz 2 Γ3g () Γ3 Γ2u ( ) Γ3g ( ) 2 x

22 Oh Γ3 T. Onimaru et al.: PRL '11 Γ3 ()? 22

23 D4hx3 U 4+ (J=4) : UX2 (X=P, As, Sb, Bi), PrRu2Si2, UPt2Si2, URu2Si2 (?) J=4 x 3 URu2Si2 23

24 Oh Γ8 Ce 3+ (J=5/2) : Ce1-xLaxB6 ~ 540 K I. para II. AFQ (Γ5g) TRS III. AFQ (Γ5g) + AFM (Γ4u) IV. AFO (Γ5u) T. Tayama et al.: JPSJ '97 24

25 Th PrOs4Sb12 Th 4 Oh Γ4 Γ5 Γ4 (t) ~ 10 K Y. Aoki et al.: JPSJ '07 k=5 (θ~0) PrRu4P12 K. Iwasa et al.: PRB '05 AFQ: Γ5g SC AFH: Γ1g (scalar, hexadeca) 25

26 ( ) 2 i j i j J ~ t 2 / U RKKY () i j m1 m2 m1 m2 26

27 2 (J<0) D(k) k (=Q) -4J D(k) χ(q) (0,0) (π,0) (π,π) (0,0) +4J 27

28 () (i, x) z : (m) 28

29 () (Q) T < TN T < TN (0) [ ](0) [] (Q) [] 29

30 CeB6 R. Shiina et al.: JPSJ '97 Γ3g Γ5g Γ4u Γ4u Γ5u Γ2u NMR M. Takigawa et al.: JPSJ O. Sakai et al.: JPSJ X T. Matsumura et al.: PRL ξ(q) (001) (111) (110) σ (Q), η(q) 30

31 T > Tc T < Tc Γ1g 31

32 Oh3 Γ1g α = dipole (z), k=0 () O20(Q) Jz(Q) Oxy(Q) Txyz(Q) (C4v Γ4 ) 32

33 Ce1-xLaxB6 IV HK & Y. Kuramoto: JPSJ '01 K. Kubo & Y. Kuramoto: JPSJ C44 ( ) 33

34 (2 ) k 0 () (Holstein-Primakoff ) HK and Y. Kuramoto JPSJ R. Shiina et al. JPSJ HK et al. JPSJ ( ) bi : HP b2 b1 34

35 T=0 α = 1 35

36 PrOs4Sb12 Y. Aoki et al.: JPSJ R. Shiina et al.: JPSJ Q 36

37 URu2Si2 R. Okazaki et al. Science & T* M.B. Maple et al. PRL 56 (1986) 185 E. Hassinger, et al. PRB 77 (2008)

38 URu2Si21. E. Hassinger, et al. PRB 77 (2008) D. Aoki et al. JPSJ 78 (2009) st order (Ising ) T0, TN, Tx (HM, HAF) 38

39 URu2Si22. H. Amitsuka (Private commun.) G.J. Nieuwenhuys PRB 35 (1987) 5260 H c H a T > T* (T* ~ 50 K) H//c : CW H//a : VV Hc2 H. Ohkuni et al Phil. Mag. B 79 (1999) D FS 39

40 URu2Si23. C. Broholm et al. PRB 43 (1991) T = 1 K Q=(1,0,0) Q=(1,0,0) ( Q=(100)) 40

41 URu2Si23. AFM A. Villaume et al. PRB 78 (2008) D. Aoki et al. JPSJ 78 (2009) GPa 41

42 URu2Si2 cf. Doniach T URu2Si2 Tcoh T* Torder T0 T* T0! QCP 0, AFM () 42

43 URu2Si2 Y. Kuramoto, 46 (1991) 98 Y. Kuramoto, Physica B 156&157 (1989) 789 NCA cf. DMFT N. Sato et al., JPSJ 54 (1985) 1923 T. Tayama et al., JPSJ 66 (1997)

44 URu2Si2 (NMR) 29 Si NMR T. Kohara et al. Solid State Commun. 59 (1986) 603 5f (HF) 5f 44

45 URu2Si2 ( 2) G.J. Nieuwenhuys PRB 35 (1987) 5260 U 4+ (5f 2 ) J=4 3 H4 D4h ( ) 500 K 170 K PrRu2Si2 : R. Michalski et al. J. Phys. Condens. Matter 12 (2000) 7609 PrRu2Si2 : A. Mulders et al. PRB 56 (1997) 8752 UPt2Si2 : G.J. Nieuwenhuys PRB 35 (1987) 5260 RRu2Si2 (R=Th,Y,La) + Pr, U : A. Morishita et al. JMMM 310 (2007) K cf. Haule-Kotliar LDA + DMFT [ Γ2 - Γ1 (1) ] Nature Phys. 5 (2009) 796; EPL 89 (2010)

46 URu2Si2 170 K Jz> 0, 4 50 K z xy(x 2 -y 2 ) xyz(x 2 -y 2 )! 46

47 URu2Si2 z () xy(x 2 -y 2 ) () xyz(x 2 -y 2 ) z=0 z=c/2 47

48 URu2Si2 ( 1) (a) 1.5 (b) 1.5 T N (p) 1 T 0 (p) 1 H 0 (p) T / T 0 H / H 0 AFH 0.5 AFH AFM 0.5 AFM p [GPa] p [GPa]

49 URu2Si2 ( 3) (a) (b) ω ω ζ ζ ζ ζ ζ ζ ζ ζ (101) (100) (100) (110) (101) (100) (100) (110) Jz INS ξ : ξ INS Jz : Jx, Jy () 49

50 URu2Si2 ( ) Q=(1,0,0) :, H0 Q*=(1,0.4,0) :, cf. F. Bourdarot et al. PRL 90 (2003) P. Santini et al. PRL 85 (2000) 654 HK, arxiv:

51 URu2Si2 X E2 H. Amitsuka, et al. J. Phys. Conf. Series 200 (2010)

52 URu2Si2 AF x 2 -y 2 F H c [110] Oxy [110] O22 [100] Oxy RXS [110] 52