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

1
Spin structure and dynamics in the half-doped
cobaltate La1.5Sr0.5CoO4
Igor A. Zaliznyak Brookhaven National Laboratory

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

2
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
• RIPoptic phonon, magnetic continuum?
• Summary

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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 a3.83 ?, c12.5 ?
4
La1.5Sr0.5CoO4 bulk properties.
Moritomo et al (1997)
Resistivity activation behavior, Ea 6000 K
Susceptibilivity anisotropic, spin-glass-like
behavior
T30 K
J250-450 K D400-900 K
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Charge and orbital order at half-doping
Possible checkerboard fillings of the eg levels
on a square lattice
Out of plane (3z2-r2)
In-plane (x2-y2)
In-plane zig-zag (3x2-r2) / (3y2-r2)
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Electronic structure of Co2/Co3 ions in
La1.5Sr0.5CoO4
Co2 (3d7)
S3/2
eg
t2g
Co3 (3d6)
S0
S1
S2
eg
t2g
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Charge order in La1.5Sr0.5CoO4 neutron diffuse
elastic scattering
Short-range charge glass order, I. Zaliznyak,
et. al., PRL (2000), PRB (2001)
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Spin-entropy driven melting of the charge order
in La1.5Sr0.5CoO4 neutron diffuse elastic
scattering
?x0.011(1) lu, ?z0.0068(4) lu
Melting of the short-range charge glass order,
I. Zaliznyak, et. al., PRB (2001)
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Charge order and a spin system
Strong single-ion anisotropy D500 K quenches
Co3 spin at low T
S z 3/2
Co2 S3/2
2D
S z 1/2
Co3 S1 or S2
S z 1
D
S z 0
Co2 form a square-lattice AFM with almost
critical frustration, J12J2
10
Spin order in La1.5Sr0.5CoO4 magnetic elastic
neutron scattering
Q(0.258(1),0,1), in I4/mmm
Q (h,h,1) T10K
m
m
m
m
Q (0.258,0.258,l) T6K
?c0.85(5)c
Lattice-Lorentzian scattering function I. A.
Zaliznyak and S.-H. Lee in Modern Techniques for
Characterizing Magnetic Materials, ed. Y. Zhu
(Kluwer)
11
Magnetic elastic scattering from the frozen spin
structure in La1.5Sr0.5CoO4.
Intensity map, calculated from the fit
T6 K
Al(200)
Al(111)
Al(111)
Al(200)
Lattice-Lorentzian scattering from a damped spin
spiral in the a-b plane gives perfect fit to the
measured intensity
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Universal or sample-dependent?
Sample 2, by G. Gu, m6g
Sample 1, by Y. Moritomo, m0.5g
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Charge-order scattering from big new sample 2
?x0.011(1) lu, ?z0.0068(4) lu,
?zLa/Sr0.0010(1) lu
?c 0.2c(fixed)
Al(111)
Al(200)
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Magnetic scattering from two samples
T8K
Q (0.256,0.256,1)
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Melting of the frozen spin order.
BT2BT4, Ef14.7 meV, 60-20-20-100.
50K
38K
?ab?15 a 2 ?c?0.9c
6K
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Temperature evolution of the magnetic scattering
raw data.
BT2BT4, Ef14.7 meV, 60-20-20-100.
SPINS, Ef3.7 meV, 40-60-60-240.
40K?
40K?
30K?
Where is the spin-ordering transition?
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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) ?ET? with ?
8 (!?).
log(?E)log(T) ?
log(?E)log(T) ?
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Spin dynamics acoustic magnons
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RIP scattering at higher energy phonon,
magnetic continuum?
phonon
magnetic continuum?
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RIP, dynamics in La1.5Sr0.5CoO4 acoustic
magnons, optic phonon, magnetic continuum?
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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 lt E lt 30
  meV?

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Exchange modulation by superlattice distortion
Heisenberg spin Hamiltonian

Superlattice distortion
(eg)

Modulated-exchange Hamiltonian
23
Spin-spiral ground state better adapts to
distortion
Harmonics at nQc are generated in spin
distribution,
To the leading order,
As a result, the MF ground state energy of a spin
spiral is lowered

• 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).