1. Hall Effect in Sr 14−x Ca x Cu 24 O 41 E. Tafra 1, B. Korin-Hamzić 2, M. Basletić 1, A. Hamzić 1, M. Dressel 3, J. Akimitsu 4 1.Department of Physics, Faculty of Science, University of Zagreb, Croatia 2.Institute of Physics, Zagreb, Croatia 3.1. Physikalisches Institut, Universität Stuttgart, Germany 4.Department of Physics, Aoyama-Gakuin University, Kanagawa, Japan

2. outline introduction to Sr 14−x Ca x Cu 24 O 41  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 n eff  relation to high-T c cuprates

3. structure of Sr 14−x Ca x Cu 24 O 41 isoelectronic substitution of Sr by Ca → change in properties b=12.9 Å a=11.4 Å A 14 Cu 2 O 3 ladders CuO 2 chains cCcC chains: ladders: c C =2.75 Å c L =3.9 Å 10·c C ≈7·c L ≈27.5 Å cLcL ladders and chains structures are incommensurable → intrinsic source of disorder CuO 2 plane high-T c 2D cuprates quasi-1D behaviour: anisotropy of conductivity:  c /  a  10,  c /  b  10 3 – 10 4 [T. Vuletić, et al., Phys. Rep. (2006)] a c

4. Sr 14−x Ca x Cu 24 O 41 properties superconductivity occurs for x ≥ 10 under pressure (p = 3-5 GPa) for T ≤ 12 K [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 [Nücker et 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 La 2-x Sr x CuO 4 : n = V/eR H = 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) :  dρ a / dT < 0  dρ c / 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 R H dashed lines:  scaled ρ a  x ≤ 9: R H ~ exp(∆ / T) ∆ ~ 1000 K (x = 0) to ∆ ~ 100 K (x = 9) solid black line:  R H = V/4ne calculated assuming n=1 hole/f.u.

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

9. Sr 2.5 Ca 11.5 Cu 24 O 41  dρ c / dT > 0  dρ a / dT < 0  dR H (T) / dT < 0  n eff = 1.33 → n eff (per Cu) = 0.09 comparison with La 1.92 Sr 0.08 CuO 4 : n (per Cu) = 0.08 [Ando et al.,PRL 92 (2004)] [Ando et al.,PRL 93 (2004)] La 1.92 Sr 0.08 CuO 4  dρ ab / dT > 0  dR H (T) / dT < 0 ~ T 1 ~ T -1

10. cot(Θ H ) in Sr 2.5 Ca 11.5 Cu 24 O 41 cot(Θ H ) ~ T 2  common for HTC  explanation of that behavior still under debate Sr 2.5 Ca 11.5 Cu 24 O 41 T > 140 K  cot(Θ H ) ~ T 2  that behavior is not changed by the increased anisotropy cot(Θ H )=ρ ab /R H B cot(Θ H )=ρ c /R H B [Ando et al.,PRL 92 (2004)]

11. Conclusion Hall coefficient R H :  positive, hole-like, temperature dependent  x < 11.5, R H ~ exp(∆ / T) x = 11.5  ρ c ~ T 1 ;ρ a ~ R H ~ T -1  cot(Θ H ) ~ T 2 → common for HTC → independent of anisotropy of ladder plane effective number of carriers n eff ~ 1/R H  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 Sr 14−x Ca x Cu 24 O 41 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. Sr 14−x Ca x Cu 24 O 41 and Bechgaard- Fabre salts [Korin-Hamzić et al.,PRB 67 (2003)] [Moser et al.,PRL 84 (2000)]

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

15. Sr 14−x Ca x Cu 24 O 41 superconductivity occurs for x ≥ 10 under pressure (p = 3-8 GPa) for T < 12 K [Nagata et al., J. Phys. Soc. Jpn. (1997)] occurs by carrier doping in low- dimensional antiferromagnetic spin structure [T. Vuletić, et al., Phys. Rep. (2006)]

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