Emergence of heavy-fermion superconductivity by the ordering of nuclear spins

F. SteglichMax Planck Institute for Chemical Physics of Solids, Dresden

2015 Kamerlingh Onnes Prize:

Professor Gilbert Lonzarich for visionary experiments concerning the emergence of superconductivity among strongly correlated quasiparticles at the edge of magnetic order

Emergence of heavy-fermion superconductivity by the ordering of nuclear spins

AF heavy-fermion metals:

BUT: no SC in YbRh2Si2at T ≥ 10 mK

F. SteglichMax Planck Institute for Chemical Physics of Solids, Dresden

Outline:•heavy-fermion superconductors•SC below Tc = 2 mK in YbRh2Si2•outlook

Collaborators:E. Schuberth (WMI), M. Brando (CPfS), R. Yu (Renmin), Q. Si (Rice)

p →

↑TCePd2Si2

N.D. Mathur et al., Nature 394, 39 (1998)

Heavy-Fermion SuperconductorsTc(K)

CeCu2Si2 0.6 ('79 K)[p = 2.9 GPa: 2.3 ('84 GE/GR)] CeNi2Ge2 0.2 ('97 DA, '98 CA/GR) CeIrIn5 0.4 ('00 LANL)CeCoIn5 2.3 ('00 LANL)Ce2CoIn8 0.4 ('02 NA)Ce2PdIn8 0.7 ('09 WR)CePt3Si 0.7 ('03 VI)CeCu2Ge2 p > 0 0.6 ('92 GE)CePd2Si2 ‘‘ 0.4 ('98 CA) CeRh2Si2 ‘‘ 0.4 ('95 LANL)CeCu2 ‘‘ 0.15 ('97 GE/KA)CeIn3 ‘‘ 0.2 ('98 CA)CeRhIn5 ‘‘ 2.1 ('00 LANL)Ce2RhIn8 ‘‘ 1.1 ('03 LANL)CeRhSi3 ‘‘ 0.8 ('05 SE)CeIrSi3 ‘‘ 1.6 ('06 OS)CeCoGe3 ‘‘ 0.7 ('06 OS)Ce2Ni3Ge5 ‘‘ 0.26 ('06 OS)CeNiGe3 ‘‘ 0.4 ('06 OS)CePd5Al2 ‘‘ 0.57 (‘08 OS)CeRhGe2 ‘‘ 0.45 ('09 OS)CePt2In7 ‘‘ 2.1 (‘10 LANL)CeIrGe3 ‘‘ 1.5 (’10 OS)

UBe13 0.9 ('83 Z/LANL)UPt3 0.5 ('84 LANL)URu2Si2 1.5 ('84 K/DA)U2PtC2 1.5 (’84 LANL)UNi2Al3 1.2 ('91 DA)UPd2Al3 2.0 ('91 DA)URhGe 0.3 ('01 GR)UCoGe 3.0 ('07 AM/KA)UGe2 p > 0 0.7 ('00 CA/GR)UIr ‘‘ 0.14 ('04 OSNpPd5Al2 5.0 ('07 OS) PuCoGa5 18.5 ('02 LANL)PuRhGa5 8.7 ('03 KA)PuCoIn5 2.5 (’11 LANL)PuRhIn5 2.0 (‘12 LANL) Am metal p > 0 2.2 ('05 KA)

Tc(K) Ce3PdIn11 0.42 (`15 PR)Ce3PtIn11 0.32 (`15 PR) PrOs4Sb12 1.85 ('01 UCSD)PrIr2Zn20 0.05 ('10 HI)PrTi2Zn20 0.2 ('12 TO)β-YbAlB4 0.08 ('08 TO/IR)

►YbRh2Si2 0.002 ('14 M/DD)Eu metal p > 0 1.8-2.8 ('09 SL/OS)

YFe2Ge2 1.8 (`14 CA)CrAs p > 0 1.7 (`14 BEI/TO)

Field - cooled (fc) DC magnetization at T ≳ 1.4 mK[E. Schuberth et al., to be published]

TAF = 70 mKTc ≥ 2 mK: peak in MDC(T)

M/B

(10

-6 m

3 /mol

)

M/B

(10

-6 m

3 /mol

) 9

B

10 T T c AF

T B

8

YbRh2Si2 B ⊥ c

12 10

8 7 B ⊥ c (mT) 6

0.090 4 6 20

A 1 5

1 10 100

T (mK)

10 10 100 0

Superconductivity: zfc - MDC(T) & χAC(T)

M/B

(a.u

.)

χ′ a

c (S

I)

4

3

T B

2 B ⊥ c (mT) 1 0.418

0.055 0 0.028

C 0.012 -1

0.1 1 10 100

T (mK)

∆M/B

(ar

bitra

ry u

nits

)

0

YbRh2Si2

-2

-4

-6

-8 B ⊥ c

B (mT) 0.012 0.015 0.028 0.055 0.418

1 10 100

T (mK)

0.4

T c

0

-0.4

-0.8

D B = 0

1 10 100

T (mK)

T < Tc: large shielding

Tc = 2 mK

T < TB: partial shielding

field - cooled (fc) MDC(T): Meissner effect

M/B

(a.u

.)

χ′ac

(SI)

4

3

T B

2 B ⊥ c (mT) 1 0.418

0.055 0 0.028

C 0.012 -1

0.1 1 10 100

T (mK)

peak in fc - M(T) at Tc≌ 2 mK

T < Tc: flux expulsion („Meissner effect“)

Meissner volume ~ 3%: strong pinning!

Nuclear specific heat C(T) & entropy SI(T)∆C

/T (J/

K2 mol)

C/T (

J/K2 mo

l)

S / S

I

I,tot

A

10000 T A

YbRh2Si2

1000

100

10

1

0.1

µYb/µB

0.15 0.05 0.01 0.00

B (mT) 59.6

2.4

B ⊥ c

1500

TA

1000

1 10 100 T (mK)

1

500

B 0

B = 2.4 mT

0.9

C 0.8

1 2 3 4 5 6

T (mK) 0 2 4 6 8 10 12

T (mK)

C(T,B) =CQ(T) + CZ(T,μ4f(B))

Phys.Stat.Sol.B 247,737(2010)

ΔC (T) = C(T, B = 2.4 mT) – C(T,0)

T ≥ 10 mK: SI(T) = SI,totSI,tot ≈ 1.8 Rln 2

171Yb (I = 1/2, 14.3%)173Yb (I = 5/2, 16.1%)

Field-cooled DC magnetization at very low fields

M vs. 1/T M vs. TM

(arb

itrar

y un

its)

T (m

K)

M (a

rbitr

ary

units

)

B

c

A YbRh2Si2

0

1 T T L H T A

0 -1 T

-20

-2 1.8 2 2.2

T (mK)

2

-40

B ⊥ c B = 0.09 mT 0 0.2 0.4 0.6 0.8 1

1/T (1/mK)

C

1 0 2 4 6 8 10 12

B (mT)

B ≲ 3 mT: TA > Tc

- dBc2/dT∣Tc = Bc2‘ ≃ 25 T/K

New T – B phase diagram of YbRh2Si2T

(mK)

B (m

T)

400 200

100

40

20

YbRh2Si2

PM

0.5

0

A + SC 1.8 2

T (mK)

10

AF 4 B

2

1 A + SC

B ⊥ c

0 10 20 30 40 50 60 70 80 90 B (mT)

Bc2‘ ≈ 25 T/K,cf. CeCu2Si2

(m* ≈ several 100 mel :heavy – fermion SC)

geff (~TA/BA) ≈ 0.03 – 0.06 → hybrid A phase: (dominating) nuclear AF order

Three - component GL theory by R. Yu & Q. Si

T

A T T T

I A AF hf

T T T hyb AF

B

m AF

SC

T T hyb AF

T ≤ TAF = 70 mK:ΦAF with QAF

T ≤ Thyb = TA = 2.3 mK: ΦJ, ΦI with Q1 ≠ QAF

(- λΦJΦI )

Below TA: hybrid order competes with primary order→ system approaches QCP→ superconductivity develops, driven by quantum critical fluctuations

λ (~ Ahf = 102 T/μB ) ≈ 25 mK

Qutlook: Interplay betweensuperconductivity and quantum criticality

Heavy - fermion superconductivity robust at AF QCP

• Conventional (3D - SDW) QCP,CeCu2Si2presumably also: CePd2Si2, CeIn3, ….

• Unconventional (Kondo destroying) QCP,CeRhIn5 (H. Shishido et al. '05; T. Park et al. '06, G. Knebel et al. `08)presumably also:β -YbAlB4 (S. Nakatsuji et al. '08)

• Link to doped Mott insulatorse.g., cuprates, organic charge – transfer salts

new example: YbRh2Si2Kondo breakdown QCP: (T=0) 4f-orbital selective Mott transition

Happy Birthday, Gil !

Erwin Schuberth: PrNi5 nuclear demag (Tmin = 0.4 mK)

Determination of heat capacity C*(T) using M(T) of YbRh2Si2 as internal thermometer -

via heat - pulse (C* = ΔQ/ΔT) and relaxation (τ = R⋅C*) method

First-order nature of superconducting transition

(10-6

m3 /m

ol)

χ′ ,

χ′′

ac

ac

10

YbRh2Si2 8 B ⊥ c

6

B = 28 mT, 2.5 µT ac B = 0 (earth), 2.5 µT ac

4 B = 0 (earth), 2.5 µT ac B = 0 (earth), 10 µT ac

from T. Westerkamp et al. 2

0

-2 1 10 100 1000

T (mK)

T ≤ Tc:

increase in χ’’(T)

superconducting transition: 1st order

Superconductivity along with Nuclear Kondo effect

(in the Absence of Nuclear Order)?

Nuclear Kondo temperature TK,nucl = TF,eff exp(-TF,eff/ Thf)

Thf ≈ 25 mK, TF,eff ≈ TK ≈ 25 K: TK,nucl = TKexp(-1000)

Mass enhancement: m*/mel ≈ D(104 K)/TK,nucl = 400/exp(-1000)(“superheavy” fermions)

For superheavy-fermion SC TK,nucl ≥ 10 Tc !

Even if TK,nucl ≈ 25 mK → mass enhancement ≈ 400 000 !

Kondo temperature TK = D exp(-D/J)