coexistence and competition of superconductivity and magnetism in ho 1- x dy x ni 2 b 2 c

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, Poh

ang 790-784, Republic of Korea

M. Ohashi and N. MoˆriInstitute for Solid State Physics, University of Tokyo,

M. SigristTheoretische Physik, ETH-Honggerberg, 8093 Zurich, Switzerland

Pohang Superconductivity Center Typed by Hyeonjin

Contents1. Introduction and Experiments2. Theory and Model3. Results and Discussion4. Summary

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)


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., PRL 72] RNi2B2C (TC = 0 ~16.6 K ) – Single phase.

[R. J. Cava et al., Nature 367]


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.


Superconducting Transition Temperature and de-Gennes Factor


Motivation



Electrical properties Layered structure. But!! It shows 3D nature. Large N(F) [ 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.



Crystal Structure Magnetic Structure



TC suppresion by Dy dopping into HoNi2B2

C. TN scales with de Ge

nnes factor. TC does not fit with d

e Gennes scaling B. K. Cho et al. PRL

77(1996)


Strange HC2 curve

[Canfield et al., Physics Today 51]



Neutron scattering Spiral phase

J. W. Lynn et al. PRB 55(1997)

Q=(0,0,2)

Q=(0,0,2)

Q=(0,0,2)


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 ( ).

SPAFSPAFSPSP

AFAF

SPSPAFAFM MMMMMTMTF 224422

22)()(

)()( 0 AFAFAF TTT )()( 0 SPSPSP TTT

SPAF

SPAF


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.

)(3)( 222

AFAF

SPSPAFAFAFAF TTMMTM

AFAFAF MMM

2222)3)(( MMMMTF AFSPAFAFAFAFAFAFM

222222

22))(( SP

SPAF

AFSPSPSPAFSPAFSP MMMMMT

)(),( 22222222 SPSPSPSPAFAFAFAF MMMMMMMM



Calculation of Gaussian Fluctuation.

Experiment for comparing.

F

AF

FAFAF

AFeMd

eMMdM

)(

)( 22

F

SP

FSPSP

SPedM

eMdMM

22

AF order

Spiral order



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


Theory and ModelsMossbauer Results

Temperature dependence of local magnetic field at the 57Fe nucleus in TbNi2B2C and HoNi2B2C



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

42

2

0

22 ||

2||)(2

2 AA

AAAA

SCbtaAi

mrdF

42

2

0

22 ||

2||)(2

2 BB

BBBB

btaAim

rd

1 20 0

2 2( . ) .A B A Bi ic c A A c c

222

221 |||| ASPBAF MM


3. Results and Discussion TC suppresion

The linearized Ginzburg-Landau equation.

BASPA MTa 12

2 ))((0

ABAFB MTa 12

1 ))((0


3. Results and Discussion

HC2 curve Comparison with the

experiments[Canfield et al., Physics Today 51]

HoNi2B2CDyNi2B2C



Pressure Effects Transport experiments of H

o0.9Dy0.1Ni2B2C and Ho0.6Dy0.4

Ni2B2C. 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 expSolid circle – TN in expSolid line – TN in theoryDotted line – TC in theory[J.-H. Choi, PRB 65]



Reentrant behavior of Ho1-xDyxNi2B2C

B. K. Cho et al., PRL 77 (1996)

Schematic diagram for the resistivity data



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., PRL 77 (1996)



Qualitative description for Dy1-xTbxNi2B2C

Magnetic structureJ. H. Choi et al. (1999)



TC suppression of Dy1-xTbxNi2B2C Tb has different type of magnetic order from Dy and H

o. 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.


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.


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.

coexistence and competition of superconductivity and magnetism in ho 1- x dy x ni 2 b 2 c

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