Coexistence and Competition of Superconductivity and Magnetism in Ho 1- x Dy x Ni 2 B 2 C

1. Coexistence and Competition of Superconductivity and Magnetism in Ho1-xDyxNi2B2C Hyeon-Jin Doh, Jae-Hyuk Choi, Heon-Jung Kim, Eun Mi Choi, H. B. Kim, B. K. Cho and Sung-Ik Lee National Creative Research Initiative Center for Superconductivity and Department of Physics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea M. Ohashi and N. Moˆri Institute for Solid State Physics, University of Tokyo, M. Sigrist Theoretische Physik, ETH-Honggerberg, 8093 Zurich, Switzerland

2. B. K. Cho, P. C. Canfield, and D. C. JohnstonPhys. Rev. Lett. 77, 163-166 (1996), PRL 77(1996) • Hyeonjin Doh, Manfred Sigrist, B.K. Cho, Sung-Ik Lee Phys. Rev. Lett. 83(25), 5350-5353 (1999/12/20) • Jae-Hyuk Choi, Hyeonjin Doh, Eun-Mi Choi, and Sung-Ik Lee, M. Ohashi and N. Mori. Phys. Rev. B 65(2), 024520(6) (2002) • Jae-Hyuk Choi, Heon-Jung Kim, H. B. Kim, Hyeon-Jin Doh, Sung-Ik Lee, and B.K. Cho. Phys. Rev. B 72(05), 054516 (2005) • Contents • Introduction and Experiments • Theory and Model • Results and Discussion • Summary Pohang Superconductivity Center

3. 1. Introduction and Experiments • History • Magnetic Superconductor containing the rare-earth atoms • RMo6S8, RMo6Se8, and RRh4B4 (1970s) • YPd5B3C0.3 with TC = 23 K – Multi phase [R. Nagarajan et al., PRL72] • RNi2B2C (TC = 0 ~16.6 K ) – Single phase. [R. J. Cava et al., Nature367] Pohang Superconductivity Center

4. 1. Introduction and Experiments • Special Feature of Borocarbides • There exists of compounds to compare • RNi2B2C ; R = Y, Dy, Ho, Tb, Tm, Er, Lu, Gd • Underline - magnetism, Red - superconductivity • TmNi2B2C - TC = 11 K,TN = 1.5 K • DyNi2B2C - TC = 6 K,TN = 10 K • HoNi2B2C - TC = 8 K,TN = 5 K • High quality samples can be produced in single crystal form. Pohang Superconductivity Center

5. Superconducting Transition Temperature and de-Gennes Factor Pohang Superconductivity Center

6. Motivation Pohang Superconductivity Center

7. Motivation Pohang Superconductivity Center

8. 1. Introduction and Experiments • Electrical properties • Layered structure. But!! It shows 3D nature. • Large N(eF) [ 2.4 states/eV Ni] – relatively high TC. • Multiband system. • All bands contribute to the superconductivity. • Most contribution comes from Ni(3d). • Magnetic properties • Originated from the 4f orbitals of the rare-earth atoms. – RKKY interaction between the local moments. • Large Spin-Orbit coupling. -Strong anisotropy; Crystal Electric Field Effects. Pohang Superconductivity Center

9. 1. Introduction and Experiments • Magnetic Structure • Crystal Structure Pohang Superconductivity Center

10. 1. Introduction and Experiments • TC suppresion by Dy dopping into HoNi2B2C. • TN scales with de Gennes factor. • TC does not fit with de Gennes scaling • B. K. Cho et al. PRL 77(1996) Pohang Superconductivity Center

11. Strange HC2curve [Canfield et al., Physics Today 51] Pohang Superconductivity Center

12. 1. Introduction and Experiments • Neutron scattering • Spiral phase Q=(0,0,2p) Q=(0,0,2p) Q=(0,0,2p) J. W. Lynn et al. PRB 55(1997) Pohang Superconductivity Center

13. 2. Theory and Models • Model for the magnetic order • The free energy from spin degree of freedom. • Here, and • - Coupling between antiferromagnetic order and the spiral order. Two orders compete each other ( ). Pohang Superconductivity Center

14. 2. Theory and Models • Magnetic fluctuation • Antiferromagnetic order. • Antiferromagnetic fluctuation. • Mean Field Calculation by using. • The increase of the free energy due to the magnetic fluctuation. Pohang Superconductivity Center

15. AF order Spiral order 2. Theory and Models • Calculation of • Gaussian Fluctuation. • Experiment for comparing. Pohang Superconductivity Center

16. 2. Theory and Models • Superconducting order • Multiple bands system. • Ni(3d), B(2p)-C(2p), and R(5d) • All bands contribute the superconductivity. • In ordered states, the magnetic moments are cancelled in Ni plain. • Two order parameter. • From Ni band. • From the bands other than Ni. Observation of a Pair-Breaking Field at the Ni Site in Nonsuperconducting ReNi2B2C, PRL 76, 507-510 (1996) E. Baggio-Saitovitch, Brazil Pohang Superconductivity Center

17. Theory and ModelsMossbauer Results Temperature dependence of local magnetic field at the 57Fe nucleus in TbNi2B2C and HoNi2B2C Pohang Superconductivity Center

18. 2. Theory and Models • Free energy for two superconducting orders. • A- superconducting order from Ni(3d)bands. • B- superconducting order from the other bands. • 1,2 - Josepsen coupling between A and A Pohang Superconductivity Center

19. 3. Results and Discussion • TC suppresion • The linearized Ginzburg-Landau equation. Pohang Superconductivity Center

20. 3. Results and Discussion • HC2curve • Comparison with the experiments [Canfield et al., Physics Today 51] HoNi2B2C DyNi2B2C Pohang Superconductivity Center

21. 3. Results and Discussion • Pressure Effects • Transport experiments of Ho0.9Dy0.1Ni2B2C and Ho0.6Dy0.4Ni2B2C. • For TN<TC, • dTC/dp ~ -0.64 K/Pa.-0.49 K/Pa [Michor, PRB 61] • dTN/dp ~ 0.48 K/Pa.0.482 K/Pa [Michor] • For TN>TC, • TC ~ almost constants. Solid square –TC in exp Solid circle –TNin exp Solid line –TNin theory Dotted line –TCin theory [J.-H. Choi, PRB 65] Pohang Superconductivity Center

22. 3. Results and Discussion B. K. Cho et al., PRL77 (1996) • Reentrant behavior of Ho1-xDyxNi2B2C Schematic diagram for the resistivity data Pohang Superconductivity Center

23. 3. Results and Discussion • Qualitative description for Lu1-xDyxNi2B2C • From the DyNi2B2C side, if we put in Lu instead of Dy, this breaks the balance which makes zero field at Ni site. • Lu acts as magnetic impurity, through Lu has no magnetic moments. • Increasing Dy reduces the magnetic fluctuation. This enhances the superconductivity. B. K. Cho et al., PRL77 (1996) Pohang Superconductivity Center

24. 3. Results and Discussion • Qualitative description for Dy1-xTbxNi2B2C J. H. Choi et al. (1999) Magnetic structure Pohang Superconductivity Center

25. 3. Results and Discussion • TC suppression of Dy1-xTbxNi2B2C • Tb has different type of magnetic order from Dy and Ho. • The magnetic field at Ni site is not zero in TbNi2B2C at T < TN • Tb suppresses the superconductivity from Ni bands unlike Ho and Dy. • Breakdown of the de Gennes scaling of TN. • Since Tb and Dy has different type of magnetic order, they suppress each other and TN is lower than expected from the de Gennes scaling. Pohang Superconductivity Center

26. 4. Summary • RNi2B2C is multi-band system unlike the cuprate. • There are many contributions for the superconductivity. • In HoNi2B2C and DyNi2B2C, two superconducting order parameters are introduced due to the magnetism. • One interacts with the antiferromagnetic order and the other does not. • Phenomenological theory describes well. • TC and TN in Ho • HC2 of HoNi2B2C and DyNi2B2C. • Pressure dependence. • Reentrance behavior of HoNi2B2C. Pohang Superconductivity Center

27. 4. Summary • In Lu1-xDyxNi2B2C, Lu breaks the balance of the magnetic field and generate the field at Ni site. • Lu acts as a magnetic impurity in the Dy background. • In Dy1-xTbxNi2B2C, the structure of the antiferromagnetic order is different from Ho1-xDyxNi2B2C. • The antiferromagnetic order suppresses the superconductivity from Ni bands. Pohang Superconductivity Center