Development of a nuclear quadrupole based technique for measuring - PowerPoint PPT Presentation

Development of a nuclear quadrupole based technique for measuring charge homogeneity, and its application for YBCO

Outline: • What is charge homogeneity, and why is it interesting? • Current experimental methods for measuring charge homogeneity, and their drawbacks. • A new idea to tackle the problem. • Experimental results • Conclusions

Y 1 Ba 2 Cu 3 O 7-  YBCO 6 YBCO 7 c a b Planes O - Cu(2) Cu - Y - Ba - Cu(1) Chains

            2 2 2 2 2 2 2 2 2 2 2 2 Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu             3 3 3 3 3 3 3 3 3 3 3 3 <15% Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu

Motivation - Stripes • The stripes theory claims that one dimensional charge structures in the planes play a crucial role in the mechanism of superconductivity. inhomogeneity inhomogeneity • Higher doping  more stripes  Higher doping higher T c • There is partial experimental evidence for stripes.

Evidence for inhomogeneity using  SR Tetragonal Tetragonal Orthorhombic T c SC SC T N 200 Orthorhombic 180 400 160 140 Temperature [K] 300 120 100 200 80 60 100 Superconducting 40 Tg AF 20 0 0 6.3 6.4 6.5 6.6 6.7 6.8 6.9 Doping value - y Doping Value Low doping

• This result supports the presence of some magnetic structure (not necessarily in the form of stripes). • Increasing the doping decreases the inhomogeneity. • It looks as if the structure is a remainder of the AF phase.

Evidence for inhomogeneity using STM Bi 2 Sr 2 CaCu 2 O 8+  p  0.14 ± 0.02 p  0.18 ± 0.02   560 K.M.Lang et al, Nature, 415 , 412 (2002) Surface

Outline: Summary of the introduction • Motivation: what is • Some theories are based on structures charge homogeneity, and in the planes. why is it interesting? • What is the experimental • There is incomplete experimental evidence for evidence for such structures. homogeneity , and what are the drawbacks? • Our new idea how to deal with this problem. • Results • Conclusions TIME TO FALL Solution ASLEEP A new technique, based on the nuclear quadrupole interaction.

Electric quadrupole interaction  2 V V( r )  V   ij r r i j    0 V V V xx yy zz  V V         xx yy 0 1 V q zz V zz     1  y 0 0   2     1 V ij =  q    0 0   2   0 0 1 x         ˆ ˆ ˆ ˆ ˆ      2 2 2 q 2 2 2 2 Nucleus 3 ( ) H I I I I I I I x y z q z x y 6

• The quadrupole interaction is sensitive to the symmetry of the charge distribution, and can be a useful tool for our purpose. •  determines the homogeneity of the charge distribution:  =0 – Homogenous charge distribution  =1 – Inhomogenous charge distribution

 

The NQR Hamiltonian for spin 3/2    3 0 0    q    3 0 3 0   ˆ  H   q   6 0 3 0        0 0 3   1 0 0 0     q  2   2 0 1 0 0      1 ˆ   1 q H 3    q 2 3 0 0 1 0     0 0 0 1

NQR experimental setup

NQR Spectrum of YBCO <  >  63 Cu(2) 63 Cu(2) Y=7 T=100K V zz ||c 65 Cu(2) 65 Cu(2) 2 [a.u.] Tetragonal Orthorhombic Tetragonal T c T N Intensity/f 200 Orthorhombic 180 400 63 Cu(2) 63 Cu(2) 160 Y=6.675 T=100K ? 140 Temperature [K] 300 120 Cu(1) 100 Cu(1) 200 80 60 100 Superconducting 40 AF 20 0 0 6.3 6.4 6.5 6.6 6.7 6.8 6.9 Doping value - y Doping Value 26 27 28 29 30 31 32 Frequency [MHz] <> is known only for optimal doping

The EFG tensor for Cu(2) in YBCO 7 c a b V zz V zz Vxx<Vyy<Vzz V zz || c V yy V xx

YBCO in a magnetic field B o c Bo || c || Vzz  z a b

Orientation B o Z X

Orientation quality X-ray diffraction Unoriented Sample

V zz  Z Sample X  =0      1 0 0 0 0 ( ) 0 0 Sin         0 1 0 0 ( ) 0 0 0 Sin        q  3 ( ) B Cos t       1 0 0 1 0 0 0 0 ( ) 2 Sin       0 0 0 1   0 0 ( ) 0  Sin  0       0 ( ) ( ) 0 1 0 0 0 g Sin f Cos          q    ( ) 0 0 ( ) 2 0 1 0 0 g Sin f Cos            1 2 ( ) B Cos t        1 ( ) 0 0 ( ) f Cos g Sin 2 3 0 0 1 0           0 ( ) ( ) 0   f Cos g Sin 0 0 0 1    

Echo Intensity vs.  - Theoretical Result   1.0   0.8  Intensity[a.u] 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

Intensity (  =90)/Intensity (  =0) Intensity(  =90)\Intensity(  =0)  <> =0 < |  | > 0 |  |

NQR Spectrum of YBCO 63 Cu(2) 63 Cu(2) Y=7 T=100K <  >  YBCO 7 V zz ||c 65 Cu(2) 65 Cu(2) 2 [a.u.] YBCO 7-  Intensity/f 63 Cu(2) 63 Cu(2) Y=6.675 T=100K Cu(1) Cu(1) ? YBCO 6.675 26 27 28 29 30 31 32 Frequency [MHz]

H 1 YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 1.0 Intensity [a.u.] 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 0 0 50 50 100 100 150 150 200 200 250 250 300 300 350 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]

H 1  YBCO 7 1.0 Intensity [a.u.] 0.8 0.6 0.4 0.2 0.0 0 50 100 150 200 250 300 350  [degree]