# Presentation: 146439

## Spin dynamics in cuprate superconductors

**T. E. Mason**
***Spallation Neutron Source Project***

**Harrison Hot Springs**
**Dec. 9, 2000**

**CIAR**
**Superconductivity Program**

## excitations characterized by  ́ ́(Q,)  a measure of absorption at (Q,).
neutron scattering measures:
			S(Q,) ~  ́ ́(Q,) [n()+1].
note:   			Q 0, recover uniform susceptibility.

the proportionality constant involves magnetic moment direction and form factor.

- neutron scattering measures:
- 			S(**Q**,) ~  ́ ́(**Q**,) [n()+1].
- note:   			Q 0, recover uniform susceptibility.
- the proportionality constant involves magnetic moment direction and form factor.

**Neutron Scattering and ****Spin Fluctuations**

## o(Q,) for Metals

- Excitations are electron-hole pairs
- Lindhard susceptibility:
- As T 0 states near F dominate
- Note: NMR relaxation rate:

## Facilities

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

## (La,Nd)2-xSrxCuO4

- 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

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

## 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

- 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

- 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

- 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

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

## Low Energy Excitations in the Metallic State

- For metallic compositions the low energy response has shifted away from the commensurate () position along the (,0) direction.
- The peaks are well defined (>ao/x).

- x=0.075

- x=0.14

- (Yamada et al, 1998)

- 1 meV, 12 K

- 2 meV, 35 K (>Tc)

## 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

- A combination of polarized and unpolarized measurements have permitted a reliable determination of the **Q** and dependence of the magnetic response over a wide range of temperature.

## 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 .

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

******,T Scaling**

-  In the T, 0 limit   o=0.034Å for x=0.14 and 0.06 Å for x=0.17
-  The fact that  and  enter with the same exponent implies:	z = 1where z is the dynamical exponent.  Together with the 1/T2 susceptibility this implies =1.

- The inset shows  ́ ́P/vs T varying with an exponent of 3: for z=1 this implies =0. Ambiguity because of o.

## Quantum Criticality

- Taken together these results reveal that La1.86Sr0.14CuO4 is close to a quantum critical point characterized by exponents z=1, =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, =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?

- The observation that the residual o 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

- 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  ́ ́ for the metallic samples suggests proximity to T=0 QCP.

## 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 YBa2Cu3O7-x

- Low energy, commensurate **[**Q=(), 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 ) 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 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 ) position (b,c) in the superconducting state. From Mook et al. (1998a).

## The () resonance

- Variation of the ) 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

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

## 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

- 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

- 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

- 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  ́ implies sc competes with stripe instability

## Recap

- Absence of low energy spin response along the (,) direction is not expected in simple models with nodal quasiparticles.
- Although statistics limit the bound on low , 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  > 8 meV.
- Minima in inverse lifetime at the incommensurate points.
- (,) 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.