# Presentation: 666116

## Spin structure and dynamics in the half-doped cobaltate La1.5Sr0.5CoO4

_*Collaboration*_
- J. Tranquada			*BNL*
- G. Gu				*BNL*
- R. Erwin				*NIST CNR*
- S.-H. Lee				*NIST CNR*
- Y. Moritomo			*CIRSE Nagoya Univ.*

- Igor A. Zaliznyak
*Brookhaven National Laboratory*

## Outline

- Crystal structure of La1.5Sr0.5CoO4 and electronic properties of Co2+/Co3+ ions in it
- Charge and spin order at half-doping
- neutron-scattering signatures of charge and spin order
- sample dependence of the short-range order
- Spin-freezing transition: critical slowing down of the spin dynamics
- Low-energy excitations in La1.5Sr0.5CoO4
- magnons
- RIP:optic phonon, magnetic continuum?
- Summary

## Crystal structure of the layered perovskite cobaltate around half-doping

- La1.5Sr0.5CoO4 always (at all T)
- remains in “high-temperature tetragonal” (HTT) phase
- Space group* I4/mmm*, lattice spacings
- a≈3.83 Ǻ, c≈12.5 Ǻ

## La1.5Sr0.5CoO4: bulk properties.

- Resistivity: activation behavior,
- Ea ~ 6000 K

- Susceptibilivity: anisotropic,
- spin-glass-like behavior

- T~30 K

*Moritomo et al (1997)*

- J~250-450 K
- D~400-900 K

## Charge and orbital order at half-doping

- Possible checkerboard fillings of the **e****g** levels on a square lattice

- In-plane “zig-zag”
- (3*x*2-*r*2) / (3*y*2-*r*2)

- Out of plane
- (3*z*2-*r*2)

- In-plane
- (*x*2-*y*2)

## Electronic structure of Co2+/Co3+ ions in La1.5Sr0.5CoO4

**Co****2+**** **(3d7)

- S=3/2

**e****g**

**t****2g**

**Co****3+**** **(3d6)

- S=0

- S=1

- S=2

**e****g**

**t****2g**

## Charge order in La1.5Sr0.5CoO4: neutron diffuse elastic scattering

*Short-range “charge glass” order, I. Zaliznyak, et. al., PRL (2000), PRB (2001)*

## Spin-entropy driven melting of the charge order in La1.5Sr0.5CoO4: neutron diffuse elastic scattering

*Melting of the short-range “charge glass” order, I. Zaliznyak, et. al., PRB (2001)*

- x=0.011(1) lu, z=0.0068(4) lu

## Charge order and a spin system

**Co****2+** form a square-lattice AFM with almost critical frustration, **J****1****~2J****2**

**Co****2+**
- S=3/2

- 2D

**Co****3+**
- S=1
- or
- S=2

*S **z *= 0

*S **z *= ±1

- D

- Strong single-ion anisotropy D~500 K quenches **Co****3+** spin at low T

*S **z *= ±1/2

*S **z *= ±3/2

## Spin order in La1.5Sr0.5CoO4: magnetic elastic neutron scattering 

- Spin order in La1.5Sr0.5CoO4: magnetic elastic neutron scattering

- Q=(0.258(1),0,1), in I4/mmm

- c=0.85(5)c

- m

- m

- m

- m

*Q = (h,h,1)*
*T=10K*

*Q = (0.258,0.258,l)*
*T=6K*

_*Lattice-Lorentzian scattering function*_
*I. A. Zaliznyak and S.-H. Lee in “Modern Techniques for Characterizing Magnetic Materials”, ed. Y. Zhu (Kluwer)*

## Magnetic elastic scattering from the frozen spin structure in La1.5Sr0.5CoO4.

- Lattice-Lorentzian scattering from a damped spin spiral in the a-b plane gives perfect fit to the measured intensity

- Intensity map, calculated
- from the fit

- Al(111)

- Al(200)

- Al(111)

- Al(200)

- T=6 K

## Universal or sample-dependent?

* **Sample #1, by *
*Y. Moritomo, m**≈**0.5g*

* **Sample #2, by *
*G. Gu, m**≈**6g*

## Charge-order scattering from big new sample #2

- c = 0.2c(fixed)

- Al(111)

- Al(200)

- x=0.011(1) lu, z=0.0068(4) lu, zLa/Sr=0.0010(1) lu

## Magnetic scattering from two samples

*T=8K*

*Q = (0.256,0.256,1)*

## Melting of the frozen spin order.

- ab15 a  2
- c0.9c

- 6K

- 38K

- 50K

- BT2&BT4, Ef=14.7 meV, 60’-20’-20’-100’.

## Temperature evolution of the magnetic scattering: raw data.

- BT2&BT4, Ef=14.7 meV, 60’-20’-20’-100’.

- SPINS, Ef=3.7 meV, 40’-60’-60’-240’.

- ~40K?

- ~30K?

- ~40K?

*Where is the spin-ordering transition?*

## Slowing down of the spin fluctuations: is there a criticality?

*Although the critical behavior* E~(T-Tc), =3.0(3) *is not ruled out,*
- log(E) *is surprisingly linear in* log(T):     E~T *with*  ~8 *(!?). *

- log(E)~log(T) ?

- log(E)~log(T) ?

## Spin dynamics: acoustic magnons

## RIP: scattering at higher energy: phonon, magnetic continuum?

*phonon*

*magnetic continuum?*

## RIP, dynamics in La1.5Sr0.5CoO4: acoustic magnons, optic phonon, magnetic continuum?

## Summary

- A short-range checkerboard charge order yields a peculiar spin system in  La1.5Sr0.5CoO4
- A short-range, *incommensurate spin order* results from the frustration and the lattice distortion
- the incommensurability and the correlation length are slightly sample dependent
- Static spin ordering: a *spin-freezing *transition at Ts ≈ 30 K
- relaxation rate vanishes
- correlation length saturates
- Dynamics at low E is dominated by a well-defined, strong band of acoustic magnons
- crosses an optic phonon at 15 meV – interaction?
- Continuum magnetic scattering at 20 meV < E < 30 meV?

## Exchange modulation by superlattice distortion

- Heisenberg spin Hamiltonian

- Superlattice distortion

- Modulated-exchange Hamiltonian

*(**eg**)*

- +

- =

## Spin-spiral ground state better adapts to distortion

- Harmonics at *nQ**c* are generated in spin distribution,

- As a result, the MF ground state energy of a spin spiral is lowered

- To the leading order,

-  In the presence of a superlattice distortion in the crystal antiferromagnetism may loose to a competing near-by spiral state

*I. A. Zaliznyak, Phys. Rev. B (2003).*