Magnetism and Superconductivity

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Magnetism and Superconductivity
T. Park, H-O. Lee, R. Movshovich, E. D. Bauer, F.
Ronning, V. A. Sidorov, JDT with special thanks
to Z. Fisk, R. Urbano, N. J. Curro, J. L.
Sarrao, A. Bianchi, M. Nicklas, O. Stockert, B-L.
Young, Y. Tokiwa, and M. Kenzelmann
Outline ? conventional superconductivity and
magnetism ? magnetism and unconventional
superconductors ? recent results --
CeCoIn5 -- CeRhIn5 ? summary
Sungkyunkwan University, June, 2009
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conventional superconductivity
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1
2
2
? creates electron pairs with zero net momentum
and spin (L0, S0) whose energy is lower by an
amount ? relative to unpaired electrons ? finite
energy gap between paired and unpaired electrons
? temporary lattice distortion of positively
charged ions provides attractive interaction
between negatively charged conduction electrons
of opposite spin and momentum
? temperature below which pairs form, the
superconducting transition temperature Tc ? ?/kB,
a function of how the lattice of positive ions
responds to the presence of negatively charged
electrons ? once formed below Tc, electron pairs
move with exactly zero resistancea perfect
conductor but also a perfect diamagnet, hence
superconductivity
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manifestation of the superconducting gap
? jump in specific heat ?C at Tc exponential
decrease in C below Tc as gap opens and removes
electronic density of states at EF
? nuclear relaxation rate 1/T1 just below Tc, an
initial increase in 1/T1, a hallmark of
superconducting pairs with L0, S0, followed by
an exponential decrease at TltTc
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conventional superconductivity and magnetism
? superconducting electron pairs satisfy certain
rules, including that pairs are unchanged if the
momentum and spin of each electron is reversed
(k,?),(-k,?) L0, S0
(-k,?),(k,?) L0, S0

? introducing a tiny number of magnetic
impurities with spin S ? interaction (JS?s) of
spin S with conduction electron spin s breaks the
rule (by randomizing relative phase of two
time-reversed electron states) and Tc ? 0
Tc03.2 K
S
J
? example lt1 Ce magnetic impurities in
conventional superconductor LaAl2
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superconductivity in the presence of strong
paramagnetism
? completely unexpected discovery by Steglich et
al. of superconductivity in CeCu2Si2 a material
with 1023 Ce impurities ? equally surprising,
huge T-linear contribution to specific heat (C ?
?T) just above Tc ? huge ? ? m ? effective mass
of conduction electrons 1000me ? jump in
specific heat at Tc ? ? ? very heavy electrons
form superconducting pairs ? unlike conventional
superconductors, where energy scale of itinerant
electrons kBTF 104 kBTc, characteristic energy
scale of heavy electrons ? kBTc ? 1st example of
an unconventional, high-Tc superconductor

• C ?T
• ?1J/molK2
• ? m?1000me

?
F. Steglich et al., Phys. Rev. Lett. 43, 1892
(1979)
? no magnetism in LaCu2Si2 and not
superconducting ? magnetism necessary for
superconductivity in CeCu2Si2
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subsequent discoveries
antiferromagnetic state
anti- ferromagnetic state
??????
??????
??????
D. Jaccard et al., Phys. Lett. A 163, 475 (1992)
R. Movshovich et al., PRB 53, 8241 (1996)
F. M. Grosche et al., Physica B 224, 50 (1996)
? antiferromagnetic to superconducting transition
with applied pressure in a family of materials
with the CeCu2Si2 structure type ? near order of
magnitude variation in critical pressures , but
unit cell volumes at Pc and maximum Tcs
comparable and essentially identical to those of
CeCu2Si2 ? a guiding principle for where to look
near the T0 magnetic-nonmagnetic boundary (a
magnetic quantum-critical point)
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a lattice of Ce impurities
? one Ce impurity in a metallic host, eg., in
LaCu2Si2 interaction JS?s ? polarization of
conduction electron spins s antiparallel to spin
S on magnetic Ce ? creates zero net spin through
the Kondo effect ? strongly enhanced m or
equivalently large T-linear specific heat ?/Kondo
ion ? periodic array of moments, e.g. CeCu2Si2,
interacting through the indirect RKKY interaction
? long range magnetic order at TN
s
s
S
s
s
S
S
s
? competition between Kondo and RKKY, both of
which depend on magnetic exchange J ?
non-monotonic variation of TN as a function of
some parameter, e.g. pressure, that tunes
magnitude of J
S
S
? T-P phase diagrams of Ce122 compounds as
expected from this simple model, with
superconductivity appearing near the T0
magnetically ordered-magnetically disordered
boundary at Jc, i.e., a quantum-critical point,
where fluctuations of the magnetic order induce a
strange metallic state
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unconventional superconductivity mediated by
magnetic fluctuations
?
? an attractive interaction between itinerant
electrons mediated by magnetic fluctuations
? also produces an energy gap and superconducting
electron pairs but pairs with finite angular and
spin momenta, L ? 0 S ? 0 (? unconventional)
?
? because L ? 0 and S ? 0 is allowed,
superconducting energy gap ?(k) goes to zero at
gap nodes on the Fermi surface ? finite N(EF) as
T?0 and, consequently, a power-law temperature
dependence of physical properties below Tc ?
illustrated L2, S0 spin-singlet, d-wave gap
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evidence for unconventional superconductivity in
CeCoIn5
? power laws in C/T, 1/T1, etc below Tc and no
peak in 1/T1 -- all consistent with L2, S0
pairs (R. Movshovich et al., PRL 86, 5152 (2001)
S. Ozcan et al. EPL 62, 412 (2003) Y. Kohori et
al., PRB 64, 134526 (2001))
Tc
T
? 4-fold modulation of in-plane thermal
conductivity ? gap with dx2-y2 symmetry (K.
Izawa et al., PRL 87, 057002 (2001))
? sign change of order parameter from
point-contact spectroscopy ? dx2-y2 gap (W. K.
Park et al., PRL 100, 177001 (2008))
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magnetic fluctuations in CeCoIn5
? no long range, static magnetic order for H0,
but just above Tc, magnetic fluctuations at Q
(½,½,½) ? in the superconducting state, spin
fluctuations sharply peaked at E0 0.60 meV
develops by shifting magnetic spectral weight
from low to higher energy ? non-trivial relation
between SC and magnetic fluctuations
Q (½,½,½)
? spin resonance in high-Tc cuprates, with E0/2?
? 0.6 -- compared to E0/2? ? 0.5 in CeCoIn5 ? not
unique to CeCoIn5 spin gap below Tc also in
CeCu2Si2, with energy scale 0.2 meV and
correspondingly lower Tc
O. Stockert et al.,Physica B 403, 973(2008).
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proximity to magnetic order in CeCoIn5
? Cd substitution for In adds 1 hole/substituted
Cd and induces AFM that coexists with bulk
superconductivity (L.Pham et al., PRL 97, 056404
(2006)) entropy below 6K independent of ground
state ? same electrons involved in both orders ?
microscopic coexistence of large-moment
antiferromagnetism with Q (½,½,½) for x1
(from NQR R. Urbano et al., PRL 99, 146402
(2007) from neutrons M. Nicklas et al., PRB 76,
052401(2007))
? development of magnetic intensity arrested
abruptly at Tc and finite below ? strong coupling
of coexisting long-range magnetic order and
unconventional superconductivity
CeCo(In.99Co.01)5 (1/2,1/2,1/2)
a
Tc
TN
? undoped CeCoIn5 very near magnetic order
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field-induced coexistence of magnetism and
superconductivity
A. Bianchi et al., PRL 91, 187004 (2003)
M. Kenzelmann et al., Science 321, 1652 (2008)
CeCoIn5
T2
strange metal
SC
? CeCoIn5 as with all superconductors, a
sufficiently high magnetic field suppresses Tc to
T0 unlike other superconductors, a new
thermodynamic phase transition at T2(H) inside
the low-T, high-H superconducting state ? now
shown to be magnetic by NMR (B.-L. Young et al.,
PRL 98, 036402 (2007)) and by neutrons
field-induced Q(q,q, ½) not the expected (½, ½,
½) and M0? 0.15?B
? an entirely new relationship between magnetism
and unconventional superconductivity
superconductivity necessary for magnetic order
? not understood but perhaps the result of
CeCoIn5s proximity to a T0 magnetic transition
in the absence of a field or Cd doping, as
inferred from it strange normal state
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similarity of CeCoIn5 to CeRhIn5 under pressure
? smaller cell volume of CeCoIn5 ? similar to
CeRhIn5 near P2
? near-identical Tc and C/T
? at Hc2(0), C/T ? -lnT/T in CeCoIn5 and
diverges in CeRhIn5 near P2 ? strange normal
state
A.Bianchi et al., PRL 91, 257001(2003) T. Park
et al., Nature 440, 65 (2006)
? also H-induced magnetic order below Tc, but
relationship between magnetism and SC different
(exists only in SC state of CeCoIn5, extends into
strange normal state of CeRhIn5 (T. Park et
al., PNAS 105, 6825 (2008))
strange normal state
SC
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origin of the strange normal state and
superconductivity in CeRhIn5
P2
P2
T. Park et al., Nature 456, 366 (2008)
? unusual sublinear T?, ? ? 0.85, resistivity
that emanates from the quantum-critical point P2
and that characterizes the strange normal state
? nearly constant ?ab/?c centered on P2 and
extending from Tc to 300K ? local nature of
quantum-critical fluctuations that scatter
electrons
? highest Tc and highest scattering rate
coincident near P2 ? absolute resistivity at P2
for ?ab and ?c ? chemically disordered CeCoIn5,
where disorder scattering kills SC (J. Paglione
et al., Nature Phys. 3, 703 (2007)) ? not
disorder scattering in CeRhIn5 vs P but
scattering from critical fluctuations at P2 that
favor superconductivity
P2
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nodal superconductivity in CeRhIn5
P1.47 GPa lt P1
P2.3 GPa ? P2
? at P lt P1and T lt Tc, 4-fold modulation of C/T
for H rotation in basal plane ? d-wave symmetry
? at P ? P2 and T lt Tc, also 4-fold modulation of
C/T for H rotation in basal plane ? d-wave
symmetry
T. Park et al., PRL 101, 177002 (2008)
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comparison to expectations of Doniach model
? CeRhIn5 evolution of TN(P) and emergence of a
strange metal as TN?0, as expected from
competing Kondo and RKKY interactions
? problem solved! strange metal and
unconventional superconductivity a result of this
competition
CeRhIn5
CeCoIn5
strange metal
? BUT, TK ltlt TN over a wide P range not
expected from this simple competition and 1st
time to be demonstrated in any Kondo lattice
system (H-O. Lee et al, unpublished) ? essential
physics of CeRhIn5 (and CeCoIn5) not captured
completely by a simple competition and new
concepts are required, eg, Y-f. Yang, Z. Fisk,
H-O. Lee et al., Nature 454, 611 (2008)
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summary

• ? unconventional superconductivity and magnetism
• ? difficult to prove, but almost certainly
  unconventional superconductivity magnetically
  mediated by fluctuations arising from proximity
  of these heavy-fermion compounds to a magnetic
  quantum-critical point
• ? unlike conventional superconductivity and
  its relation to magnetism, for which there are
  microscopic theories, no equivalent theory for
  magnetically mediated superconductivity or for
  the strange normal state out of which
  unconventional superconductivity emerges or for
  field-induced magnetism in the superconducting
  state
• ? a very fundamental problem related to
  physics of trapped ultracold atoms, paired quark
  condensates at high nucleon densities, deconfined
  field theories, .
• ? search for new examples
• ? historically, guided by the Doniach model
  and empirical observation that unconventional
  superconductivity appears near a T0
  magnetic/non-magnetic boundary
• ? still a useful guide, but now finding that
  Doniach model is incomplete and that new concepts
  are required
• ? CeCoIn5, CeRhIn5, and heavy-electron systems in
  general -- exciting opportunities to discover new
  quantum states of matter and to address
  challenging, fundamental questions in many-body
  physics, magnetism, superconductivity, and
  quantum criticality

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