Spin dynamics in cuprate superconductors

1
Spin dynamics in cuprate superconductors
CIAR Superconductivity Program

• T. E. Mason
• Spallation Neutron Source Project

Harrison Hot Springs Dec. 9, 2000
2
Neutron Scattering and Spin Fluctuations

• excitations characterized by c(Q,w) è a measure
  of absorption at (Q,w).
• neutron scattering measures
• S(Q,w) c(Q,w) n(w)1.
• note Q è0, recover uniform susceptibility.
• the proportionality constant involves magnetic
  moment direction and form factor.

3
co(Q,w) for Metals

• Excitations are electron-hole pairs
• Lindhard susceptibility
• As T è0 states near eF dominate
• Note NMR relaxation rate

4
Facilities

• Neutron scattering measurements were carried out
  using TAS6 (RITA) at Risø, IN20 at the ILL , and
  MARI at ISIS.

5
(La,Nd)2-xSrxCuO4
Vaknin et al (1987)

• Pure La2CuO4 is an insulating antiferromagnet
  with quasi-two-dimensional magnetic interactions
• Doping with Sr (or Ba) suppresses TN, introduces
  holes in the CuO2 planes, and leads to
  superconductivity (maximum Tc39 K for x0.15)

6
Paramagnetic Critical Scattering

• Antiferromagnetic correlations in La2CuO4 above
  TN are well described by renormalized classical
  model (see Keimer et al (1992) and Birgeneau et
  al (1995))

7
La2CuO4 Spin Wave Response
(Hayden et al, 1991)
(Hayden et al, 1990)

• The magnetic excitations of undoped La2CuO4 are
  well described by (renormalized) classical spin
  wave theory for the 2D spin 1/2 Heisenberg
  antiferromagnet

8
Stripe Ordering

• Tranquada et al have shown that static, long
  range ordering of spin and charge occurs in
  (La,Nd)2-xSrxCuO4 pinned to the LTT structural
  distortion at x1/8.

9
Effect of Doping

• The high energy magnetic excitations in nearly
  optimally doped La2-xSrxCuO4 retain the
  characteristics of the antiferromagnet
• slightly softened maximum energy
• same periodicity with broader momentum
  distribution

10
Energy Integrated Response

• The correlation length extracted from S(Q)
  decreases from 6.2 Å in La2CuO4 (T295 K) to 3.7
  Å (ao) in La1.86Sr0.14CuO4 (17 K) however the
  bulk of the spin fluctuations are still AF in
  nature.

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Local Susceptibility

• A new energy scale (25 meV) is present in the
  metallic sample

12
Low Energy Excitations in the Metallic State
x0.075
x0.14
(Yamada et al, 1998)
1 meV, 12 K
2 meV, 35 K (gtTc)

• For metallic compositions the low energy response
  has shifted away from the commensurate (p,p)
  position along the (p,0) direction.
• The peaks are well defined (xgtao/Öx).

13
Normal State Energy Dependence

• As the frequency is increased the peaks become
  less well defined.
• The response is qualitatively quite similar to
  that of the spin density wave system Cr, above TN.

14
Increased Energy, Temperature Have Similar Effects

• A combination of polarized and unpolarized
  measurements have permitted a reliable
  determination of the Q and w dependence of the
  magnetic response over a wide range of
  temperature.

15
Temperature Dependence

• The magnetic intensity drops off rapidly with T.
• The peak susceptibility varies as 1/T2 between Tc
  (35 K) and 350 K.
• This trend is interrupted by superconductivity
  below Tc the response is suppressed.
• The inverse length scale extracted from
  resolution corrected fits to the lineshape
  increases systematically with increasing T or w.

16
w,T Scaling

• The inverse length scale which characterizes the
  peak width at a given energy and temperature is
  well described by

• In the T,w è0 limit k è ko0.034Å for x0.14
  and 0.06 Å for x0.17
• The fact that w and k enter with the same
  exponent implies z 1where z is the dynamical
  exponent. Together with the 1/T2 susceptibility
  this implies h1.

The inset shows cP/w vs T varying with an
exponent of 3 for z1 this implies h0.
Ambiguity because of ko.
17
Quantum Criticality

• Taken together these results reveal that
  La1.86Sr0.14CuO4 is close to a quantum critical
  point characterized by exponents z1, h0. These
  exponents are consistent with expectations for
  the QCP associated with 2D insulating magnets
  (Sachdev and Ye, 1992 Chubukov et al, 1994).
• Alternatively z1, h1 would be expected for 1D
  quantum antiferromagnets (Luther Peschel,
  1975).
• The similarity of the dynamic fluctuations to the
  patterns observed in the ordered stripe phases
  for Nd doped sample suggests a connection.

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Link to Commensurate Stripe Instability?

• The observation that the residual ko for
  La1.83Sr0.17CuO4 is larger points to lower
  doping...
• The low energy length scale extracted from
  studies at various doping levels becomes
  anomalously large near x1/8 the concentration
  for which commensurate stripe order occurs nearby
  in phase space and for which short range
  structural features have been observed in
  La2-x(Ba,Sr)xCuO4.

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Recap - Normal State

• Insulator, MFL
• broad, commensurate response
• La2-x(Ba,Sr)xCuO4 (x0.05)

• Insulator, Antiferromagnet
• spin waves
• La2CuO4 (x0)

• Metal incommensurate response
• La2-xSrxCuO4 (x0.14, 0.17)

Temperature and energy dependence of c for the
metallic samples suggests proximity to T0 QCP.
20
YBa2Cu3O6x Spin Dynamics

• Spin dynamics of antiferromagnetically ordered
  Y123 also well described by (renormalized)
  classical spin wave theory, including bi-layer
  coupling (see work by Tranquada et al,
  Rossat-Mignod et al, and Hayden et al)

21
Superconducting YBa2Cu3O7-x

• Low energy, commensurate Q(p,p ), acoustic
  mode response in the normal state of four
  different compositions of YBa2Cu3O7-x measured at
  100 K.
• As the doping is increased the feature at (p ,p )
  broadens and weakens, and there is very little
  normal state response at the commensurate
  position for the overdoped sample. From Bourges
  et al. (1998).

22
Incommensurate fluctuations in YBa2Cu3O7-x

• Images of the magnetic scattering from
  YBa2Cu3O6.6 above and below Tc at 34 and 24.5 meV
  in the two dimensional reciprocal space of the
  CuO2 planes.
• At the lower energy (e,f) an incommensurate
  response, described by the model shown in d,
  appears at the positions noted in the schematic
  map, a. The resonance appears at the (p, p)
  position (b,c) in the superconducting state. From
  Mook et al. (1998a).

23
The (p,p) resonance

• Variation of the (p, p) resonance energy with
  superconducting transition temperature, Tc. From
  Bourges (1998).
• A similar feature is also seen in BSSCO (Keimer
  et al)

24
The resonance in underdoped Y123

• Temperature dependence of the 35 meV resonance in
  YBa2Cu3O6.6 with temperature.
• A broadened response at (p,p) persists in the
  normal state for underdoped compositions. From
  Mook et al. (1998b).

25
Superconductivity in LSCO

• Superconductivity suppresses the low energy
  response (below 8 meV) and enhances the higher
  energy response
• The extent of the suppression is
  sample/composition dependent
• Data shown is for x0.16, further from QCP than
  x0.14 sample - more metallic, better sc

26
Changes Induced by Superconductivity are
Significant

• Suppression at low T is complete
• Consistent with x0.15 (Yamada et al)
• Higher energy response shows different Q
  dependence in sc state
• Response at incommensurate point is sharper

27
Momentum Dependence

• Analysis of the momentum dependence of the
  inelastic response reveals that
• magnetic gap does not vary with Q - 6.7 meV
• inverse lifetime or broadening of the gap is
  momentum dependent with a minimum at the
  incommensurate wavevector
• the incommensurate peak in the real part of the
  susceptibility is reduced by superconductivity

28
Recap - Superconductivity

• The wavevector independence of the spin gap is in
  contrast to the nodal structure seen in the
  charge channel for high Tc cuprates
• this deviation of the behavior of spin and charge
  may be taken as evidence of spin-charge
  separation
• at the very least it implies simple
  (non-interacting) models of the effects of d-wave
  superconductivity on the susceptibility are
  inadequate

• Suppression of c implies sc competes with stripe
  instability

29
Recap

• Absence of low energy spin response along the
  (p,p) direction is not expected in simple models
  with nodal quasiparticles.
• Although statistics limit the bound on low w, low
  T signal the very strong effects at higher
  energies, including Q-independence of spin gap
  are well established and visible, even in the raw
  data.
• Enhancement and sharpening in Q for w gt 8 meV.
• Minima in inverse lifetime at the incommensurate
  points.
• (p,p) resonance observed in other cuprates,
  notably Y123, not found in single layer La214,
  appears above Tc for underdoped Y123.
• Incommensurate spin fluctuations seem to be
  common feature at least for underdoped
  compositions.