spin dynamics in cuprate superconductors
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CIAR Superconductivity Program. Spin dynamics in cuprate superconductors. T. E. Mason Spallation Neutron Source Project. Harrison Hot Springs Dec. 9, 2000. Neutron Scattering and Spin Fluctuations. excitations characterized by c ´´( Q , w ) è a measure of absorption at ( Q , w ).

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spin dynamics in cuprate superconductors

Superconductivity Program

Spin dynamics in cuprate superconductors

T. E. Mason

Spallation Neutron Source Project

Harrison Hot Springs

Dec. 9, 2000

neutron scattering and spin fluctuations
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.
c o q w for metals
co(Q,w) for Metals
  • Excitations are electron-hole pairs
  • Lindhard susceptibility:
  • As T è0 states near eF dominate
  • Note: NMR relaxation rate:
  • Neutron scattering measurements were carried out using TAS6 (RITA) at Risø, IN20 at the ILL , and MARI at ISIS.
la nd 2 x sr x cuo 4
  • 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 Tc=39 K for x~0.15)

Vaknin et al (1987)

paramagnetic critical scattering
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))
la 2 cuo 4 spin wave response
La2CuO4 Spin Wave Response
  • The magnetic excitations of undoped La2CuO4 are well described by (renormalized) classical spin wave theory for the 2D spin 1/2 Heisenberg antiferromagnet

(Hayden et al, 1991)

(Hayden et al, 1990)

stripe ordering
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 x=1/8.
effect of doping
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
energy integrated response
Energy Integrated Response
  • The correlation length extracted from S(Q) decreases from 6.2 Å in La2CuO4 (T=295 K) to 3.7 Å (=ao) in La1.86Sr0.14CuO4 (17 K) however the bulk of the spin fluctuations are still AF in nature.
local susceptibility
Local Susceptibility
  • A new energy scale (~25 meV) is present in the metallic sample
low energy excitations in the metallic state

0.5 (

, 0)

Low Energy Excitations in the Metallic State



  • 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 (x>ao/Öx).

(Yamada et al, 1998)

1 meV, 12 K

2 meV, 35 K (>Tc)

normal state energy dependence
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.
increased energy temperature have similar effects
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.
temperature dependence
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.
w t scaling
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,wè0 limit kèko=0.034Å for x=0.14 and 0.06 Å for x=0.17
  • 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 h=1.

The inset shows c´´P/w vs T varying with an exponent of 3: for z=1 this implies h=0. Ambiguity because of ko.

quantum criticality
Quantum Criticality
  • Taken together these results reveal that La1.86Sr0.14CuO4 is close to a quantum critical point characterized by exponents z=1, h=0. These exponents are consistent with expectations for the QCP associated with 2D insulating magnets (Sachdev and Ye, 1992; Chubukov et al, 1994).
  • Alternatively z=1, h=1 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.
link to commensurate stripe instability
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 x=1/8: 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.
recap normal state
Recap - Normal State
  • Insulator, Antiferromagnet
    • spin waves
  • La2CuO4 (x=0)
  • Insulator, MFL
    • broad, commensurate response
  • La2-x(Ba,Sr)xCuO4 (x=0.05)
  • Metal incommensurate response
  • La2-xSrxCuO4 (x=0.14, 0.17)

Temperature and energy dependence of c´´ for the metallic samples suggests proximity to T=0 QCP.

yba 2 cu 3 o 6 x spin dynamics
YBa2Cu3O6+x 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)
superconducting yba 2 cu 3 o 7 x
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).
incommensurate fluctuations in yba 2 cu 3 o 7 x
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).
the p p resonance
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)
the resonance in underdoped y123
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).
superconductivity in lsco
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 x=0.16, further from QCP than x=0.14 sample - more metallic, better sc
changes induced by superconductivity are significant
Changes Induced by Superconductivity are Significant
  • Suppression at low T is complete
    • Consistent with x=0.15 (Yamada et al)
  • Higher energy response shows different Q dependence in sc state
    • Response at incommensurate point is sharper
momentum dependence
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
recap superconductivity
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
  • 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 > 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.