Magnetic states of lightly hole- doped cuprates in the clean limit as seen via zero-field muon spin spectroscopy Kitaoka Lab Kaneda Takuya F. Coneri, S. Sanna, K. Zheng, J. Lord, and R. De Renzi, Phy. Rev. B 81, (2010)

Contents Introduction High-T c cuprate superconductors Measurement muon spin rotation (μSR) Result Phase diagram of YBa 2 Cu 3 O 6+y Conclusion

LaSrCuO YBaCuO BiCaSrCuO TlCaBaCuO HgCaBaCuO TlCaBaCuO HgCaBaCuO （ under high pressure ） HgCaBaCuO （ under high pressure ） Nb NbC V 3 Si NbN Nb 3 Sn Pb Nb 3 Ge Nb-Al-Ge liquid nitrogen Hg LaBaCuO T c (K) (year) Increase of Transition Temperature (T c ) Cuprate Superconductor High-T c Cuprate Superconductors Introduction

crystal structure of La-Ba-Cu-O La 3+ 2-x Ba 2+ x CuO 4 Cu 2+x CuO 2 面 電荷供給層 La (Ba) electric conductivity with hole doping Superconductivity emerges with optimal doping. Cu O La(Ba) High-T c Cuprate Superconductors Introduction charge reservoir CuO 2 layer charge reservoir La 2 CuO 4 d(x 2 -y 2 ) Cu +2 (3d 9 ) 3d(x 2 -y 2 ) Cu(3d 10 4s 1 ) 3d(3z 2 -r 2 ) 3d(xy) 3d(yz, zx) La 3+ →Ba 2+

In order to understand the ground state of cuprate superconductor, careful study about its underdoped region is required. High-T c Cuprate Superconductors Introduction AFM SC AFM charge reservoir CuO 2 layer

sample YBa 2 Cu 3 O 6+y for various oxygen-content y various hole density h CuO-chain CuO 2 plane hole density T (K)

spin: I = ½ gyromagnetic ratio: MHz/T mean lifetime: 2.2μs What is μSR (muon spin rotation) ? Measurement Property of Muon It’s very sensitive even to low magnetic field. pion mean lifetime: 26ns

sample internal field positron counter muon (μ + ) positron Internal field about t μs later… Internal field is determined from time dependence of muon asymmetry. What is μSR (muon spin rotation) ? Measurement H SμSμ detected!! The positron emission in the muon decay is asymmetric. many muons Eech muon has different life.

μSR Result Result h=0.02 h=0.04 h=0.07 hole density T (K) only depend on muon’s life damped oscillation static field Internal field is not static.

TNTN hole density T (K) T N drop rapidly with increasing the hole density h. For h =0.035, m(h,T) deviates from power-law behavior (dashed line) and an upturn (solid line) appears. m :magnetization h :hole density B AO :internal field at the apical oxygen Temperature dependence of the moment Result Thermally activated regime (high temperature) & Re-entrant regime (low temperature) Thermally activated Re-entrant

Activation temperature T A Result TATA hole dependence of T A extrapolation of the m(h,T) power-law hole doping

Phase diagram Result AFM SC Re-entrant Thermally activated Re-entrant regime Holes are localized. Spins are freezing. The moment recovers to 0.6μ B. Thermally activated regime Holes are delocalized. AFM phase is separeted into two regimes. AFM phase vanishes at SC phase emerges at QCP!!

holespin Holes in CuO 2 layer… Holes are localized. Spins are freezing. Holes are delocalized.

There are two distinct regimes in AFM phase. In re-entrant regime holes are localized and spins are freezing. The critical hole density h c and h s have the same value. And the value h = is a quantum critical point (QCP) for the cuprate clean limit. Conclusion Re-entrant and Thermally Activated

3d x 2 -y 2, 3z 2 -r 2 xy, yz, zx x 2 -y 2 xy 3z 2 -r 2 yz, zx 正方晶歪み 結晶場分裂 Solving the degeneracy of 3d-orbital Appendix

Magnetic volume fraction

Appendix Power-law

Appendix Equations

Appendix Equations