1. Coexistence and Competition of Superconductivity and Magnetism in Ho 1-x Dy x Ni 2 B 2 C 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. Typed by Hyeonjin Pohang Superconductivity CenterPage 2  Contents  Introduction and Experiments  Theory and Model  Results and Discussion  Summary  B. K. Cho, P. C. Canfield, and D. C. Johnston Phys. 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)

3. Typed by Hyeonjin Pohang Superconductivity CenterPage 3 1. Introduction and Experiments  History  Magnetic Superconductor containing the rare-earth atoms  RMo 6 S 8, RMo 6 Se 8, and RRh 4 B 4 (1970s)  YPd 5 B 3 C 0.3 with T C = 23 K – Multi phase [R. Nagarajan et al., PRL 72 ]  RNi 2 B 2 C ( T C = 0 ~ 16.6 K ) – Single phase. [R. J. Cava et al., Nature 367 ]

4. Typed by Hyeonjin Pohang Superconductivity CenterPage 4 1. Introduction and Experiments  Special Feature of Borocarbides  There exists of compounds to compare  RNi 2 B 2 C ; R = Y, Dy, Ho, Tb, Tm, Er, Lu, Gd  Underline - magnetism, Red - superconductivity  TmNi 2 B 2 C - T C = 11 K, T N = 1.5 K  DyNi 2 B 2 C - T C = 6 K, T N = 10 K  HoNi 2 B 2 C - T C = 8 K, T N = 5 K  High quality samples can be produced in single crystal form.

5. Typed by Hyeonjin Pohang Superconductivity CenterPage 5 Superconducting Transition Temperature and de-Gennes Factor

6. Typed by Hyeonjin Pohang Superconductivity CenterPage 6 Motivation

7. Typed by Hyeonjin Pohang Superconductivity CenterPage 7 Motivation

8. Typed by Hyeonjin Pohang Superconductivity CenterPage 8 1. Introduction and Experiments  Electrical properties  Layered structure. But!! It shows 3D nature.  Large N(  F ) [ 2.4 states/eV Ni ] – relatively high T C.  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.

9. Typed by Hyeonjin Pohang Superconductivity CenterPage 9 1. Introduction and Experiments  Crystal Structure  Magnetic Structure

10. Typed by Hyeonjin Pohang Superconductivity CenterPage 10 1. Introduction and Experiments  T C suppresion by Dy dopping into HoNi 2 B 2 C.  T N scales with de Gennes factor.  T C does not fit with de Gennes scaling  B. K. Cho et al. PRL 77(1996)

11. Typed by Hyeonjin Pohang Superconductivity CenterPage 11  Strange H C2 curve [Canfield et al., Physics Today 51 ]

12. Typed by Hyeonjin Pohang Superconductivity CenterPage 12 1. Introduction and Experiments  Neutron scattering  Spiral phase J. W. Lynn et al. PRB 55(1997) Q=(0,0,2  )

13. Typed by Hyeonjin Pohang Superconductivity CenterPage 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 ( ).

14. Typed by Hyeonjin Pohang Superconductivity CenterPage 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.

15. Typed by Hyeonjin Pohang Superconductivity CenterPage 15 2. Theory and Models  Calculation of  Gaussian Fluctuation.  Experiment for comparing. AF order Spiral order

16. Typed by Hyeonjin Pohang Superconductivity CenterPage 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

17. Typed by Hyeonjin Pohang Superconductivity CenterPage 17 Theory and Models Mossbauer Results Temperature dependence of local magnetic field at the 57Fe nucleus in TbNi 2 B 2 C and HoNi 2 B 2 C

18. Typed by Hyeonjin Pohang Superconductivity CenterPage 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

19. Typed by Hyeonjin Pohang Superconductivity CenterPage 19 3. Results and Discussion  T C suppresion  The linearized Ginzburg-Landau equation.

20. Typed by Hyeonjin Pohang Superconductivity CenterPage 20 3. Results and Discussion  H C2 curve  Comparison with the experiments [Canfield et al., Physics Today 51 ] HoNi 2 B 2 C DyNi 2 B 2 C

21. Typed by Hyeonjin Pohang Superconductivity CenterPage 21 3. Results and Discussion  Pressure Effects  Transport experiments of Ho 0.9 Dy 0.1 Ni 2 B 2 C and Ho 0.6 Dy 0.4 Ni 2 B 2 C.  For T N <T C,  dT C /dp ~ -0.64 K/Pa. -0.49 K/Pa [Michor, PRB 61 ]  dT N /dp ~ 0.48 K/Pa. 0.482 K/Pa [Michor]  For T N >T C,  T C ~ almost constants. Solid square – T C in exp Solid circle – T N in exp Solid line – T N in theory Dotted line – T C in theory [J.-H. Choi, PRB 65 ]

22. Typed by Hyeonjin Pohang Superconductivity CenterPage 22 3. Results and Discussion  Reentrant behavior of Ho 1-x Dy x Ni 2 B 2 C B. K. Cho et al., PRL 77 (1996) Schematic diagram for the resistivity data

23. Typed by Hyeonjin Pohang Superconductivity CenterPage 23 3. Results and Discussion  Qualitative description for Lu 1-x Dy x Ni 2 B 2 C  From the DyNi 2 B 2 C 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., PRL 77 (1996)

24. Typed by Hyeonjin Pohang Superconductivity CenterPage 24 3. Results and Discussion  Qualitative description for Dy 1-x Tb x Ni 2 B 2 C Magnetic structure J. H. Choi et al. (1999)

25. Typed by Hyeonjin Pohang Superconductivity CenterPage 25 3. Results and Discussion  T C suppression of Dy 1-x Tb x Ni 2 B 2 C  Tb has different type of magnetic order from Dy and Ho.  The magnetic field at Ni site is not zero in TbNi 2 B 2 C at T < T N  Tb suppresses the superconductivity from Ni bands unlike Ho and Dy.  Breakdown of the de Gennes scaling of T N.  Since Tb and Dy has different type of magnetic order, they suppress each other and T N is lower than expected from the de Gennes scaling.

26. Typed by Hyeonjin Pohang Superconductivity CenterPage 26 4. Summary  RNi 2 B 2 C is multi-band system unlike the cuprate.  There are many contributions for the superconductivity.  In HoNi 2 B 2 C and DyNi 2 B 2 C, 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.  T C and T N in Ho  H C2 of Ho Ni 2 B 2 C and Dy Ni 2 B 2 C.  Pressure dependence.  Reentrance behavior of Ho Ni 2 B 2 C.

27. Typed by Hyeonjin Pohang Superconductivity CenterPage 27 4. Summary  In Lu 1-x Dy x Ni 2 B 2 C, 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 Dy 1-x Tb x Ni 2 B 2 C, the structure of the antiferromagnetic order is different from Ho 1- x Dy x Ni 2 B 2 C.  The antiferromagnetic order suppresses the superconductivity from Ni bands.