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doi:10.1016/j.ph

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Physica B 378–380 (2006) 1025–1026

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The origin of new high-temperature superconductorPuCoGa5 and, its implications

Yunkyu Banga,, A.V. Balatskyb, F. Wastinc, J.D. Thompsonb

aDepartment of Physics, Chonnam National University, Kwangju 500-757, Republic of KoreabLos Alamos National Laboratory, Los Alamos, NM 87545, USA

cEuropean Commission, Joint Research Centre, Institute for Transuranium Elements, Post Office 2340, D-76175 Karlsruhe, Germany

Abstract

We examined possible pairing bosons in PuCoGa5. We found that the antiferromagnetic (AFM) spin-fluctuation scattering is most

consistent with the experimental data of resistivity rðTÞ, successfully explaining the anomalous temperature dependence at low

temperatures ½T4=3 as well as the saturation behavior at high temperatures. The extracted characteristic energy scale of spin

fluctuations ðosf150KÞ and the dimensionless coupling constant l3–4 are consistent with the experimental T c ¼ 18:5K of PuCoGa5and predicts a d-wave-like unconventional pairing symmetry. Our prediction is confirmed by the recent NMR experiments [N. Curro,

et al., Nature 434 (2005) 622].

r 2006 Elsevier B.V. All rights reserved.

PACS: 71.10.Hf; 71.27.+a; 75.30.Mb

Keywords: PuCoGa5; Superconductivity; Antiferromagnetic spin fluctuations

1. Introduction

Recently, superconductivity (SC) was found in PuCoGa5at the amazingly high transition temperature ðT cÞ of18.5K [1,2], which is an order of magnitude larger valuethan the previous highest T c in f-electron-based super-conducting compounds [3]. Therefore, understanding theorigin of this 18.5K transition temperature in PuCoGa5should not only provide important information on thepuzzling behavior of f-electrons but also shed light onthe origin of the high transition temperature in cupratesuperconductors.

In this paper, we examine two possible bosonic scatter-ing mechanisms, namely, phonons and antiferromagnetic(AFM) spin fluctuations, to consistently understand theexperimental DC-resistivity rðTÞ. More details can befound in the previously published paper [4].

e front matter r 2006 Elsevier B.V. All rights reserved.

ysb.2006.01.446

ng author. Tel.: +8262 530 3363; fax: +82 62 530 3369.

ss: ykbang@chonnam.ac.kr (Y. Bang).

2. Formalism

The DC-conductivity is calculated by the Kubo formulaas follows:

sðTÞ ¼_e2

3Z ~Nð0Þh~v2iFS

Zdo4T

1

cosh2½o=2T

" #1

ImSRðT ;oÞ, ð1Þ

where ImSRðT ;oÞ is the electron self-energy calculated byBorn approximation with the spectral density of a Bosonicfluctuations Bðq;oÞ as

ImSRðT ;oþ iZÞ ¼ g2Nð0Þ

Zdo0

2pX

q

pBðq;o0Þ

½nðo0Þ þ f ðoþ o0Þ. ð2Þ

In Eq. (1), ~Nð0Þ and ~v are the renormalized density of statesand Fermi velocity, respectively, by the bosonic scatteringand Z is the wave function renormalization parameterZ ¼ 1þ qReSðoÞ=qo. The explicit dependence on Z in

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0 50 100 150 200 250 3000

50

100

150

200

250

300

T(K)

ρ(µΩ

cm)

Exp (PuCoGa5)

Theory (I0=150K)

0 500

50

Fig. 1. Theoretical calculation with Z ¼ 4:6 (open blue circles) and the

experimental resistivity rðTÞ [2] (red solid line). Input parameters are

osf ¼ 150K, a ¼ 1, g ¼ 77mJ=K2 mol, and ~vexp ¼ 4:78 106 cm=s and

rimp ¼ 15mO cm is added. Inset: closeup view of low-temperature region.

For better fitting, ~vexp ¼ 5:28 106 cm=s and rimp ¼ 19mO cm are used.

0 50 100 150 200 250 3000

50

100

150

200

250

300

350

T(K)

ρ(µΩ

cm)

Exp (PuCoGa5)

Theory (Z=2, Tθ=240K)

Theory (Z=2, Tθ=150K)

0 500

50

Fig. 2. Theoretical calculations of resistivity rðTÞ for Z ¼ 2 with two

different Einstein phonon frequencies: yD ¼ 240K, g ¼ 77mJ=K2 mol,

and ~vexp ¼ 6:1 106 cm=s (open green squares); yD ¼ 150K, and ~vexp ¼5:6 106 cm=s (open blue circles). Inset: closeup view of low-temperature

region.

Y. Bang et al. / Physica B 378–380 (2006) 1025–10261026

Eq. (1) is actually strongly weakened by the factImSðT ;oÞ½ZðTÞ 1.

3. Results

Spin fluctuations: We choose the mean field type spinrelaxational mode for AFM fluctuations of Bðq;oÞ ¼Co=ð½IðTÞ þ bðqQÞ22 þ ½o=G2Þ. IðTÞ ¼ I0 þ aT is theparameter controlling the distance from a magneticquantum critical point, and G IðTÞ ¼ osf ðTÞ defines thecharacteristic energy scale of the fluctuations. Fig. 1 showsthe calculated result compared with the experimentalrexpðTÞ. The overall fitting is satisfactory from low to hightemperatures. The saturation behavior at high tempera-tures is well reproduced with the temperature dependentIðTÞ. The inset shows the perfect fit with the experimentalobservation rðTÞT4=3 [2] for TcoTo50K, while thecorrect theoretical form of rðTÞ at low temperatures isT2=ð150Kþ TÞ.

Phonons: For phonon scattering, we assumed an Einsteinphonon Bðq;oÞdðo yDÞ. Fig. 2 shows the theoreticalresistivity rtheorðTÞ calculated with yD ¼ 240 and 150K incomparison with the experimental data. Either case doesnot show any saturation at high temperatures and alsoshows a clear deviation between rphðTÞ exp½yD=T andrexpðTÞT4=3 at low-temperatures.

4. Discussion and summary

We found that the AFM spin fluctuations is the bestscattering boson to explain the resistivity data over the

temperature region of TcoTo300K. The AFM spinfluctuations naturally lead to a D-wave like unconventionalpairing. And the Allen–Dynes formula [5] with l ¼ Z

1 ¼ 3:6 and hoiosf ¼ 150K produces T c35K, which isa reasonable value when accounting for other effectsreducing T c such as impurities, etc. The recent NMRmeasurements of PuCoGa5 [1] indeed identified the d-wavelike unconventional gap symmetry in PuCoGa5. Havingconfirmed the AFMmediating D-wave like unconventionalsuperconductor with Tc20K leads us to suspect that theAFM spin-fluctuation mediating SC pairing might be anunifying paring mechanism from CeMð¼ Co;Rh; IrÞIn5to high-temperature cuprate superconductors having Tc

scaling with osf .

Acknowledgments

We thank M. J. Graf, J. Sarrao, N. Curro fordiscussions. Work at Los Alamos was performed underthe auspices of the US DOE. Y. B. has been supported byChonnam National University Fund.

References

[1] N. Curro, et al., Nature 434 (2005) 622.

[2] J.L. Sarrao, et al., Nature 420 (2002) 297.

[3] C. Petrovic, et al., J. Phys.: Condens. Matter 13 (2001) L337.

[4] Y. Bang, et al., Phys. Rev. B 70 (2004) 104512.

[5] W.L. McMillan, Phys. Rev. 167 (1968) 331.