# Presentation: 134954

## Novel Dynamic Scaling Regime in Hole-Doped La2CuO4

*Los Alamos National Laboratory*

**Collaborators**:
- Wei Bao	            	        Los Alamos National Laboratory
- Emilio Lorenzo	        CNRS, Grenoble, France
- Yiming Qiu	        National Institute of Standards and Technology
- Seunghun Lee	        National Institute of Standards and Technology
- Sungil Park	        National Institute of Standards and Technology
- John Sarrao	        Los Alamos National Laboratory

- Novel Dynamic Scaling Regime in Hole-Doped La2CuO4

##  Magnetic and transport properties of hole doped La2CuO4 (Sr, Ba, Li)

-  Magnetic and transport properties of hole doped La2CuO4 (Sr, Ba, Li)
- Theoretical phase diagram of 2D Heisenberg antiferromagnet (HAF)

-  S(**q**,ω) peaks sharply at (π*,*π) in Cu-O plane and flat out of the plane
-  S(**q**,ω) crosses over from ω/T scaling at high temperatures
-      to **a novel low temperature regime characterized by a constant**
**     ****energy scale**
-  The observed crossover possibly corresponds to the theoretically
-      expected **quantum critical  to quantum disordered crossover **for 2D
-      Heisenberg antiferromagnet

**Introduction**

**Spin dynamics of 2D paramagnetic state of La****2****Cu****1-y****Li****y****O****4****  at T<<J**

**Summary**

**Outline**

##  La2CuO4: insulator, 3D AF order below TN≈325 K

- Tetragonal:      (ππ0)
- Orthorhombic:  (100) and (001)

-  La2CuO4: insulator, 3D AF order below *T**N*≈325 K

*Shirane et al., PRL ****59**** 1613 (1987)*

## La2-xSrxCuO4

- La2Cu1-xLixO4

**Suppress N****é****el order by holes**

*Chou et al., PRL ****71****, 2323 (1993)*

-  The 3D long range AF order in La2CuO4 can be suppressed
-      by 2-3% hole doping using Sr or Li, thus allowing experimental investigation
-      of the quantum spin dynamics of the 2D paramagnetic state of hole-doped
-      La2CuO4 in a wide temperature range Tsf<T<<J/kB~1000 K

*Sarrao et al. PRB ****54**** 12014(1996);  Heffner et al., Physica  B (2002) Sasagawa et al., PRB ****66****, 184512 (2002)*

- PM

- PM

## Theoretical phase diagram

**Theoretical phase diagram**

-  A crossover from the quantum critical (QC) regime, where the energy scale
-      is *k**B**T*, to the quantum disordered (QD) regime, where the energy scale is
-      constant, is predicted for y>yc of 2D Heisenberg antiferromagnet
-       *Sachdev, Science ****288****, 475 (2000); Chakravarty, et al., PRL ****60****, 1057 (1988)*

- ξ0~(y-yc)-ν

- ξT=

##  Quantum critical ω/T scaling

** ****Quantum critical ****ω****/T** **scaling**

- The ω/T scaling has been observed in Sr and Ba doped La2CuO4 as
-       a consequence of quantum criticality
*       ** **Aeppli, Science(1997); Keimer, PRL (1991);  Hayden, PRL(1991)*

*Keimer et al., PRL ****67****, 1930 (1991)*

**Direct observation of quantum critical to quantum disordered crossover in Li doped La****2****CuO****4**

## Transport properties

**Transport properties**

*Boebinger et al., PRL 77, 5417 (1996)*

- La2-xSrxCuO4

- La2Cu1-xLixO4

- Sr doping creates a more mobile holes
-     than Li doping

*Sarrao et al., PRB ****54****,12014 (1996)*

## Incommensurate magnetic correlations

**Incommensurate magnetic correlations**

*Yamada, PRB ****57****,6165 (1998)*

- La2-xSrxCuO4

-  Incommensurate dynamic magnetic correlations
-      in La2-xSrxCuO4        *S.-W. Cheong et al., PRL ****67****,1791 (1991)*

*2**δ*

- (π,π)

## Commensurate magnetic correlations 

**Commensurate magnetic correlations **

-  Commensurate dynamic magnetic correlations in LaCu1-xLixO4

- La2Cu1-xLixO4

*Bao et.al., PRL ****84****, 3978 (2000)*

##  Phase diagram of La2Cu1-xLixO4

*Sarrao et al. PRB ****54**** 12014(1996);  Heffner et al., Physica  B (2002);  Sasagawa et al., PRB ****66****, 184512 (2002)*

** ****Phase diagram of La****2****Cu****1-x****Li****x****O****4**

-  Cold neutron inelastic scattering study of the quantum spin dynamics
-     of 2D paramagnetic state of La2Cu1-xLixO4 (x=0.04, 0.06 and 0.1)

- PM

## The scattering cross section is proportional to the Fourier transformed dynamic spin correlation function, 

- The scattering cross section is proportional to the ***Fourier transformed***** *****dynamic spin correlation function***,

***Fluctuation-Dissipation theorem***:

**Magnetic neutron scattering**

## SPINS cold neutron triple axis spectrometer at NCNR

**SPINS cold neutron triple axis spectrometer at NCNR**

**Notes:**
Many experiments carried out on cold neutron triple axis spectrometer SPINS. 
Shown here with a high field low temperature cryogenic system the instrument probes dynamics processes in solids on the ps time scale and the nm length scale 

##  Resolution-limited in plane peak at q=(100)=(π,π)

-  Resolution-limited in plane peak at q=(100)=(π,π)
-  In-plane correlation length, ξ,  ≥40Å; mean distance of Li, d, ≈15  Å
-  Flat along out-of-plane (k) direction; 2D dynamic spin correlations

**Spatial spin correlations**

- La2Cu0.94Li0.06O4

## Spin excitation spectra S(ω,q)

**Spin excitation spectra S****(****ω****,q)**
** **

- a

-  Low energy magnetic neutron scattering intensity first enhanced,
-     then suppressed upon cooling

**q**=(100)=(π,π)

- La2Cu0.94Li0.06O4

## ω/T scaling at high T

-  Data taken above 50 K fall onto a single ω/T scaling curve

- La2Cu0.94Li0.06O4

## Departure from ω/T scaling at low T

**Departure from ****ω****/T**** scaling at low T**

- La2Cu0.94Li0.06O4

-  ω/T scaling becomes invalid below 50 K

## Constant energy scale at low T

-  Energy scale, Γ, saturates to a finite value at low temperatures

- La2Cu0.94Li0.06O4

## Temperature dependence of χπ, I(ω~0)

-  Different scaling regimes below and above Tx ≈50K

- La2Cu0.94Li0.06O4

## Scaling plot: La2Cu0.94Li0.06O4

**Scaling plot: La****2****Cu****0.94****Li****0.06****O****4**

-  T>50K: ω/T quantum critical scaling regime
-  T<50K: a novel regime with a constant energy scale

## Scaling plot: La2Cu0.9Li0.1O4

**Scaling plot: La****2****Cu****0.9****Li****0.1****O****4**

-  T>30K: ω/T quantum critical scaling regime
-  T<30K: a novel regime with a constant energy scale

## The novel low temperature regime

- La2Cu0.94Li0.06O4

- The observed crossover is not related to the spin glass transition
- The low temperature regime may be the QD regime of 2D Heisenberg  AF
-  Gapless χ"(ω): possible role of spin-charge scattering
*     *
*    **Sachdev et al., PRB ****51****, 14874 (1995); Liu and Su, Phys. Lett. ****200****, 393 (1995).*

##  A crossover from ω/T scaling to a novel constant energy  

**Experimental phase diagram La****2****Cu****1-y****Li****y****O****4**

-  A crossover from ω/T scaling to a novel constant energy
-      scale  regime upon cooling in all samples with *T**x* =35, 50
-      and 30 K for y=0.04, 0.06 and 0.1

##  First observation of a crossover in spin dynamics from the quantum

-      critical ω/T scaling to a new low temperature regime with a constant
-      energy scaling upon cooling in La2Cu1-yLiyO4 (y=0.04, 0.06 and 0.1)
-  Gapless χ"(ω): possible coupling between doped holes and spin
-                              dynamics in doped cuprates
- Magnetic phase separation: the 2D (π,π)-correlated spin component not
-                                                  frozen

**Summary**

-                   *W. Bao Y. Chen et al., Phys. Rev. Lett. ****91, ****127005 (2003)*
* **W. Bao et al., Phys. Rev. Lett.  ****84****,3978 (2000)*