Post on 24-Aug-2020
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)