Isotope Effect in Nuclear Magnetic Resonance Spectra of Germanium Single Crystals.

Transcription

1 Isotope Effect n Nuclea Magnetc Resonance Specta of Gemanum Sngle Cystals. Theoetcal goup: B.Z.Maln, S.K.San, Kazan State Unvesty, Russa Expemenal goups: S.V.Vehovs, A.V.Ananyev, A.P.Geasheno Insttute of metal physcs, Russan Academy of Scence, Eatenbug, Russa A.Yu.Yaubovs, V.I.Ozhogn, A.V.Thomov Russan Reseach Cente Kuchatov Insttute, Mosow, Russa A.Tone Ecole Supeeue de Physque et de Chme Industelles, Pas, Fance

2 Outlne Intoducton examples of sotopc effects n solds Fomulaton of poblem Isotopc mechansms edstbuton of phonon specta local defomatons Expemental data Model exact soluton fo neaest pa of defects NMR-lne shape n the method of moments model of Ge lattce wth sotopc defects Conclusons

3 Examples Isotopc effect n supeconductos T c (Mg 11 B )=39K T c (Mg 10 B )=40,K Stong themal conductvty dependence of sotopc content n Ge ( 70 Ge)/(Ge nat ) 8 tmes Isotopc stuctue of optcal specta 6 L x7 L 1-x YF 4 :E ω 0.0 cm -1 (0.6GHz) 3

4 6 Lx 7 L1-xYF4:E ntesty 6534, 6534,3 6534,4 6534,5 fequency, cm , 6538,3 6538,4 fequency, cm -1 4

5 Poblem fomulaton Ge - cystal Resonance hν = γ!h z 73 Ge(nat)=7.73% I=9/ µ= µ N Q= cm Resonance? I z = 9/ Intensty I z = -9/ Inhomogeneous boadenng

6 Redstbuton of phonon spectum Hamonc appoxmaton: Φ = Φ 1 Φ ˆ " ξ " ξ! Dynamc dsplacement ξ Phonons fequences and polazaton vectos: " " ( ˆ D( q) ω ( q) 1ˆ ) ξ ( q) = 0, ˆ " 1 D( q) = Φ ˆ m L " " qx e " " L. densty of states 73 Ge - 74 Ge fequency, cm -1 6

7 Local defomatons u statc dsplacement Anhamonc appoxmaton: 1 " ˆ " 1 " ( ) ˆ " Φ = Φ ( ) Φ ξ + u + Φ ξ + u +...! 3! Φ 1 1 = 0 u = Φ ξξ u Φ 7

8 Expemental data Examples Isotopc content, % 70 Ge 7 Ge 73 Ge 74 Ge 76 Ge 100g 100g 4 Ge-nat Ge-74m Ge Ge-70/ n ca ~ 10 1 cm -3 n ds ~ 10 4 cm -3 H=1 T H [0 0 1] Mass dsode chaactestc: H [1 1 1] g n = m n m 1 n 8

9 π/ pulse FID Foue tansfom H [001] H [111] Ge-nat 73 Ge % Ge-nat Ge-74m 73 Ge - 3.8% Ge-74m Ge Ge - 0.1% Ge

10 Magnetc Hamltonan Η = Η Z + Η Q + Η dd, Zeeman pat: Η Z = γ! HI z, Dpole-dpole pat: Η dd = 1 γ! j 1 j 1 3z j j ( 3I I I I ) z zj j Quadupole pat: Η 4I e Q Q = z + ( I 1) ( I 1) ( 3I I ) E ( ) zz 10

11 73 Ge 73 Ge <δu 1 >= nm/u.m. T=300K <δu >= nm/u.m. T=300K No changes n local symmety δe αβ =0 Local symmety ae changed δe αβ 0 11

12 Exact soluton a) H [0 0 1] b) H [1 1 1] c) Neaest magnetc pa (0 0 0) - (a/4 a/4 a/4) Pa n second shell (0 0 0) - (a/ a/ 0) 1

13 13 73 Ge δe αβ εαβ, γδ αβγδ αβ ε δ S E def = 11 5, S y x z m m a a E def zz + + = σ σ δ δ δ π δ Effect of nonlocal defomaton: ( ) + + = = eff loc zz z z y y x x z Z E δ δ δ γ δ 4 1 4, ) ( 1 Effect of local defomaton:

14 Method of moments Magnetc moment: M m, 4 3γ! c = I( I + 1) 4(π ) L 1 L 3 1 3z L L Quadupole moment: Lne shape: M q 3e Q(mI + 1), ( I z ) = ( m g) δe 8π! I(I 1) L zz (L) f < m I m 1 > m= 9 / x m= 7 / [(m 1) b / 4 + d ( ν ) = ( f ( ν ) dν ) m= 9 / 1/ π m= 7 / ] < 1/ ν exp [(m 1) b m I x m 1 > / 4 + d ] b=m q, (I z ) d=m m, 14

15 expement theoy Ge-nat H [0 0 1] Ge-nat H [1 1 1] Intensty Intensty Ge-74 H [0 0 1] Ge-74 H [1 1 1]

16 expement theoy Ge-70 H [0 0 1] Ge-70 H [1 1 1] Ge-70/76 H [0 0 1] Ge-70/76 H [1 1 1]

17 Model of Ge lattce Adabatc Bond Chage Model (ABCM) Phys.Rev. 15, 4789 (1977) phonons densty of states - Ge atom, -Z eff - Bond chage, Z eff, m= fequency, cm -1 Lattce wth defects: [ M ω Φ ] G( ω) = 1 Dayson equaton: 1 G( ω) = G0( ω) G0( ω)(1 + δmω G0( ω)) δmω G0( ω) Local defomatons: 1 δu = Gˆ ( ω = 0) Φ ˆ ( ξξ ξξ ) 0 17

18 Tempeatue dependence of lne shape H [0 0 1] Ge-nat T=0K T=78K T=300K H [1 1 1] Ge-nat H [0 0 1] Ge-74 H [1 1 1] Ge

19 Conclusons NMR-specta of 73 Ge n Ge cystals wth dffeent sotopc contents have been measued. Theoetcal model of NMR-lne shape of gemanum cystal wth sotopc defects was deved, and the mechansm of NMR-lne boadenng was nvestgated. It was shown, that sotopc local defomatons causes quadupole boadenng n NMR specta of nucle wth nonzeo quadupole moment, whch can be measued. 19