Hall Effect in Sr 14− x Ca x Cu 24 O 41

1. Hall Effect inSr14−xCaxCu24O41 E. Tafra1, B. Korin-Hamzić2, M. Basletić1, A. Hamzić1, M. Dressel3, J. Akimitsu4 Department of Physics, Faculty of Science, University of Zagreb, Croatia Institute of Physics, Zagreb, Croatia 1. Physikalisches Institut, Universität Stuttgart, Germany Department of Physics, Aoyama-Gakuin University, Kanagawa, Japan

2. outline • introduction to Sr14−xCaxCu24O41 • structure → anisotropy • distribution of self-doped holes • results (0 ≤x≤ 11.5) • electrical resistivity vs T • Hall coefficient vs T • discussion • estimation of effective number of carriers neff • relation to high-Tccuprates

3. A14 Cu2O3 ladders CuO2 chains b=12.9 Å CuO2plane cC cL high-Tc2D cuprates a=11.4 Å chains: ladders:cC=2.75 Å cL=3.9 Å 10·cC≈7·cL≈27.5 Å c a structure of Sr14−xCaxCu24O41 • isoelectronic substitution of Sr by Ca → change in properties • quasi-1D behaviour: anisotropy of conductivity: sc/sa 10 , sc/sb 103 – 104 [T. Vuletić, et al., Phys. Rep. (2006)] • ladders and chains structures are incommensurable → intrinsic source of disorder

4. Sr14−xCaxCu24O41 properties • superconductivity occurs forx≥10 under pressure (p= 3-5 GPa) for T≤12K [Uehara et al., JPSJ (1996)][Nagata et al., PRL (1998)] • system is intrinsically hole doped: average Cu valence = +2.25 → 6 self-doped holes per f.u. • Ca substitution → holes are transferred from the chains to the ladders [Osafune et al., PRL (1997)] [Mizuno et al., JPSJ (1997)] [Motoyama et al., PRB (1997)][Kato et al., Phys. C (1996)] • precise amount of hole transfer is still under disscusion: experiments give contradictory results

5. Motivation for Hall effect measurements • number of holes in ladders n: ◊ NEXAFS[Nückeret al., PRB (2000)] Δ NMR[Piskunov et al., PRB (2005)] □ optical[Osafune et al., PRL (1998)] XAS[Rusydi et al., PRB (2007)] Δ • why Hall effect: • long missing basic experiment • holes in chains are localized [T. Vuletić, et al., Phys. Rep. (2006)] • in La2-xSrxCuO4: n = V/eRH= x, for small x [Ono et al., PRB (2007)]

6. resistivity vs temperature • measured in two geometries • j||a and j||c • x≤ 9: • ρ ~ exp(∆ / T) • x = 11.5(T>80 K): • dρa / dT < 0 • dρc / dT > 0 • change in slope: • transition to CDW [Vuletić et al. PRL (2003)]

7. Hall coefficient vs temperature • geometry: • full symbols: j||a, B||b • empty symbols: j||c, B||b • no difference in RH • dashed lines: • scaled ρa • x≤ 9: RH ~ exp(∆ / T) ∆~ 1000 K (x = 0) to ∆~ 100 K (x = 9) • solid black line: • RH = V/4necalculated assuming n=1 hole/f.u.

8. effective number of carriers • effective number of carriers (●): neff = V/(4eRH) • number of holes in ladders n: ◊ NEXAFS [Nückeret al., PRB (2000)] Δ NMR [Piskunov et al., PRB (2005)] □ optical [Osafune et al., PRL (1998)] XAS [Rusydi et al., PRB (2007)] • also neff from RH at 1GPa (○) [Nakanishi et al., JPSJ (1998)] Δ • minor change in number of carriers is responsible for pronounced change in resistivity with x • our results in good agreement with NMR and NEXAFS

9. Sr2.5Ca11.5Cu24O41 • Sr2.5Ca11.5Cu24O41 • dρc / dT > 0 • dρa / dT < 0 • dRH(T)/ dT < 0 • neff = 1.33 → neff (per Cu) = 0.09 • comparison with La1.92Sr0.08CuO4: n (per Cu) = 0.08 [Ando et al.,PRL 92 (2004)] [Ando et al.,PRL 93 (2004)] • La1.92Sr0.08CuO4 • dρab / dT > 0 • dRH(T)/ dT < 0 ~ T-1 ~ T1

10. cot(ΘH)inSr2.5Ca11.5Cu24O41 • cot(ΘH)~ T2 • common for HTC • explanation of thatbehavior still underdebate • Sr2.5Ca11.5Cu24O41 T >140 K • cot(ΘH)~ T2 • that behavior is not changed by the increased anisotropy cot(ΘH)=ρab/RHB [Ando et al.,PRL 92 (2004)] cot(ΘH)=ρc/RHB

11. Conclusion • Hall coefficient RH: • positive, hole-like, temperature dependent • x < 11.5, RH ~ exp(∆ / T) • x = 11.5 • ρc ~ T1 ;ρa ~RH ~ T-1 • cot(ΘH)~ T2 → common for HTC → independent of anisotropy of ladder plane • effective number of carriers neff~ 1/RH • comparison with number of holes in ladders n • good agreement with NEXAFS and NMR results • minor change in number of carriers → responsible for pronounced change in resistivity with x

12. Hall effect in Sr14−xCaxCu24O41 • two geometries: • j||a, B||b→ all samples • j||c, B||b → x = 0 and 11.5 • particular care for temperature stabilization • three pairs of Hall contacts • better statistics • self-compensation of magnetoresistance

13. Sr14−xCaxCu24O41 and Bechgaard-Fabre salts [Korin-Hamzić et al.,PRB 67 (2003)] [Moser et al.,PRL 84 (2000)]

14. RH and ρ vs temperature • RH and ρ vs T for x = 0 • RH(T) ~ ρ(T) • no marked changes in RH at TCDW • TCDW values in agreement with [Vuletić et al. PRL (2003)]

15. [T. Vuletić, et al., Phys. Rep. (2006)] Sr14−xCaxCu24O41 superconductivity • occurs forx≥10 under pressure (p= 3-8 GPa) for T<12K [Nagata et al., J. Phys. Soc. Jpn. (1997)] • occurs by carrier doping in low-dimensional antiferromagnetic spin structure

16. distribution of doped holes • Madelung potential calculations: [Mizuno et al., J. Phys. Soc. Jpn. (1997)] • x=0: nL=0 • x>0: nL>0 • optical conductivity: [Osafune et al., Phys. Rev. Lett. (1998)] • x=0: nL=1 • x=11: nL=2.8 • NEXAFS: [Nückeret al., Phys. Rev. B. (2000)] • x=0: nL=0.8 • x=12: nL=1.1 • NMR: [Piskunov et al., Phys. Rev. B. (2005)] • nL(x=12)-nL(x=0)=0.42 • applied pressure: nL ↑ • XAS [Rusydi et al., Phys. Rev. B. (2007)] • x=0: nL=2.8 • x=11: nL=4.4