Knight Shift Measurements on Superconducting Sr 2 RuO 4

Transcription

1 Knight Shift Measurements on Superconducting Sr 2 RuO 4 c b a Sr 2 RuO 4 Sr Ru O RuO 2 plane Layered Perovskite structure Maeno et al. Nature 372, 532 ( 94) K. Ishida A,B,. Murakawa, A. Mukuda, B Y. Kitaoka, B Z. Q. Mao, A * Y. Maeno, A A Dept. of Physics, Kyoto Univ. B Dept. of Material Physics, Osaka Univ. *Tulane Univ. ( USA)

2 Superconducting wave function Ψ( r 1, σ 1 : r 2, σ 2 ) = χ( σ 1, σ 2 ) ψ( r 1, r 2 ) d vector Spin part Orbital part Spin comp. NMR gives important information about both parts. Knight shift measurements : Spin susceptibility Nuclear spin-lattice relaxation rate 1/T 1 : Gap structure

3 Knight-Shift Measurement ( yperfine Interaction ) Interaction between nuclear spin and electronic spins Nuclear spins ( I ) are coupled with electronic spins ( S ) in the external magnetic field ( ). K μ e = γ e ħs amiltonian of the nuclear spins K= Z = -γ n ħ I + A I S = -γ n ħ I Loc μ n = γ n ħi A: yperfine coupling constant A Loc = - S A = γ n ħ - { S + δs } γ n ħ av. static dynamics Shift of the spectrum (Static properties) K = = A γ h Loc A n S = N A γ e γ n h 2 χ χ = M = N A γ h e S

4 Example of K- χ plot Sr 2 RuO 4 (Superconductor) Ru-NMR CaRuO 3 (Nearly Ferro. Metal) χ K ( % ) K spin A VV = 2μ B r -3 A hf = -222 koe/μb = 384kOe/μ B A hf = -25 koe/μb K = spin K = orb Ahf μ N AVV μ N B B A A χ χ spin VV ~ -4.5 % ~ 1 % Core polarization effect

5 Inner Core Polarization Effect by Unpaired d electrons apply Unpaired Ru-4d electron nul. K Negative isotropic field is induced 8π i Inner core { } 2 2 ψ ( ) ψ () i { } 2 2 ψ () ψ ( = CP χd i i ) 3 i i Sr 2 RuO 4 (SC.) c.f. SrRuO 3 (Ferro.) CaRuO 3 (NearlyFerro.) A hf ~ -25 koe/μ B int / M ~ -3 koe/μ B ~ -222 koe/μ B Ru-4d state is in the Fermi level in these Ruthenates

6 Knight-Shift Measurement at O site 17O-NMR K spinx ~ -.3 % K spiny ~.5 % O SrO c-axis O para Ru Ru Ru Ru O perp ext Ru O-2p orbitals O-2p orbitals hybridized with Ru- 4dxy orbitals are important.

7 17 O Knight Shift measurement K. Ishida et al.nature 395, 658 (98) Mukuda et al. J. Low Temp. Phys. 117, 1567 (99) Spin part in K K spinx = -.3 % K spiny =.5 % K spin y K spin x // ab ~ 3.5 koe FWM ~ 5Oe K spin y K spin x 11.2 koe 11.4 koe 6.5 koe 6.5 koe 3.2 koe 3.5 koe

8 Ru, 17 O Knight-shift measurements > 3 koe // ab 99 Ru //ab ~ 9 koe 17 O // ab ~ 6.5 koe Sr 2 RuO 4 Sr 2 RuO 4 K.Ishida. Mukuda, Y. Kitaoka et al. Phys. Rev. B 63 (21) 657(R). Knight-shift is unchanged in the SC state K.Ishida. Mukuda Y. Kitaoka et al. Nature. 396 (1998) 658. Spin-triplet superconductivity

9 KS behavior in the SC state T-dep. KS in Sr 2 RuO 4 igh-t c : singlet K. Ishida et al, J. Phys. Soc. Jpn. 63, 283 (93) K.Ishida et al. Phys. Rev. B 63, 657(R) CeCu 2 Si 2 : singlet UPt 3. Tou et al., Phys. Rev. Lett (96) K. Ueda et al., J. Phys. Soc. Jpn 56, 867 (87)

10 Other example (Spin-singlet Superconductor ) PuCoIn 5 (T c ~ 2 K ) N. Curro et al. Nature 434, 622 (5) CeCoIn 5 ( T c ~ 2.3 K ) Kumagai et al. PRL 97, (6) K orb K.S. decreases even near c2

11 Summary of the Knight-Shift Measurements so far Applied fields were controlled with an accuracy less than.5 degree. μ ( T ) // ab 17 O-NMR μ (T).8 9 mk.6.4 // c.44 T.5.55 T.15 T T ( K ).2 Ru-NMR δf δk T ( K ) Knight shift is unchanged in the field of μ ab >.55 T, μ c >.2 T.

12 T dependence of 11 K at = 44 Oe 59Oe 3.28 Mz 11 Ru NMR at 44 Oe at 3.19 Mz 11 Ru 87 Sr Ru-NMR //c κ ~ 2.3 Δ 11 K c (%) // c ~ 45 Oe Sr 2 RuO 4 ~ 44 Oe NMR Intensity (a.u.) 117 mk 9 mk 48 mk 28 mk 18 mk Frequency (Mz) Intensity (arb.unit.) 18 mk 44 Oe 9 mk 44 Oe 18 mk 45 Oe 11 Ru Frequency (Mz) T (K) δk ~ 1% δ =4.4 Oe δf = γ δ ~ 1 kz Within the experimental accuracy, 11 K is invariant with T.

13 dependence of the Ru Knight Shift at Low T 11 K (%) SC state (koe) 9 85 mk Normal state Within the experimental accuracy, 11 K S (~ 2%) is unchanged across T c. (Oe) sweep χ ac C/T T ( K )

14 17 O NMR at ``D phase μ (T) C e /T ( mj / K 2 mol ) Knight-shift measurement // [1 ] perpt (K) K spin ~.47 % -induced DOS μ (T) c-axis O perp R u ext NMR Intensity (arb. units) O para K spin x K s ~ -.15 % T 65 mk 5 mk 4 mk 3 mk 2 mk 18 mk 16 mk Frequency from Mz (kz) 17 O NMR NMR Intensity (arb. units) O perp K spin y K s ~.45 % T 65 mk 5 mk 4 mk 3 mk 25 mk 2 mk 18 mk 16 mk Frequency from Mz (kz)

15 Summary KS was measured in the wider-field range shown below, but the decrease of KS was not observed in the range. // ab ( > 55 Oe ) // c ( > 2 Oe ) c2 ( koe ) Orbital moment d -vector Akima et al. ( ρ ) Akima et al. // ab T ( K ) d =zδ ( sink x + i sink y ) (A state) Spin <S z > = (Oe) sweep ` ± χ AC C/T T sweep í ` ± c2 (T) // c T ( K ) Orbital moment Spin Due to Meissner effect, precise measurement of KS was impossible [parallel to the c-axis ] d-vector [in ab (RuO 2 ) plane ]

16 The effect of the spin-orbit interaction at Ru-4d orbitals (λl s) F d c F d//c ~ UJ λ 2 /W 3 ΔT c ~.1 T c flip ~ 1 koe χ c /χ ab ~ 1.2 Y. Yanase and M. Ogata JPSJ 72, 673 (23). The symmetry breaking interaction in the d-vector space is in the second order with respect to λ. This is the order estimation. DC susceptibility The normal state DC susceptibility is almost isotropic. χ ( 1-3 emu / mol ) The anisotropy in the spin space seems to be small. Anisotropic energy is reduced to ~ ab χ c ( 1-3 emu / mol ) 1..5 c Ikeda & Nomura Sr 2 RuO 4 χ. c (T) = 3.86 x χ ab (T) χ ab ( 1-3 emu / mol ) Temperature ( K )

17 UPt 3 : Spin-triplet Multi-phase superconductor Tc1 ~.58 K, Tc2 ~.53 K Magnetic anomaly T M ~ 5 K

18 Ginzburg Landau Parameter κ κ ~ 2.7 in // c (Sr 2 RuO 4 ) small κ Cooper pair large κ ξ Excited quasiparticle(qp) ξ Estimation the ratio of the spin susceptibility from the excited QP is needed. Specific heat data (Deguchi et al.,) is used for estimating the QP s contribution.

19 Superconducting Parameter in Sr2RuO4