Spin Waves in Metallic Manganites

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Spin Waves in Metallic Manganites

• Fernande Moussa, Martine Hennion,
• Gaël Biotteau (PhD), Pascale Kober-Lehouelleur
  (PhD)
• Dmitri Reznik, Hamid Moudden
• Laboratoire Léon Brillouin, CEA / CNRS, Saclay
• Loreynne Pinsard-Godart, Alexandre Revcolevschi.
• Laboratoire de Physico-Chimie de lEtat Solide,
  Orsay
• Yakov M. Mukovskii, D. Shulyatev
• Moscow State Steel and Alloys Institute, Moscow

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Outline

• How to explain the shape of the spin wave
  dispersion curves of metallic manganites
• La0.7(Ca1-ySry)0.3MnO3 0 y 1
• Effect of Magnon-Phonon Coupling?
• Effect of Correlated Lattice Polarons?
• Evolution with doping of two kinds of magnetic
  coupling.
• Some arguments to explain this peculiar shape.

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Spin Wave Dispersion Curves

Both curves show first a parabolic shape at
small-q values and then a flatenned shape near
the zone boundary.
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The Spin Wave Dispersion Curve of La0.7Pb0.3MnO3
is the unique case where a double - exchange or
Heisenberg model fits perfectly these
measurements.
Measured spin wave dispersion along all major
symmetry directions at 10 K. Solid lines show the
dispersion relation for a Heisenberg ferromagnet
with nearest-neighbor coupling that best fits the
data. From T. G. Perring et al. PRL 77 (1996)
711 TC 355 K, J1 2.2 meV
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A Phonon-Magnon Coupling is possible as the
magnon branch crosses the LO1 phonon branch
around z 0.3, (N. Furukawa JPSJ 68 (1999)
2522) but a precise study of phonons and magnons
near the zone boundary has eliminated this
possibility.

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Lattice defects in the crystal could also explain
the ZB softening of the spin wave dispersion
curve, specially the short range correlated
lattice polarons.
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The spin wave dispersion curve of these 4
compounds has the same shape including
La0.7Sr0.3MnO3 where there is no short range
correlated lattice polarons.
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Evolution of the spin wave stiffness constant and
of the super exchange integrals of the two
systems La1-xCaxMnO3 and La1-xSrxMnO3 with the
doping rate x.
How to define these magnetic couplings in the
whole doping range? As long as these compounds
are insulating, they are fundamentally
inhomogeneous, it is proved by experiments and
predicted by theories Nagaev, Khomskii,
Dagotto, Moreo, Yunoki. First, small hole-rich
droplets appear, then they percolate but remain
insulating, then, small hole-poor clusters
appear. In each case the two systems are coupled
and form a true ground state and not separated
phases. The spin wave stiffness constant D is
always defined in the parabolic regime, i.e. at
small q-values, and when there are two branches,
we choose the ferromagnetic branch which appears
with doping, which is ferromagnetic and mainly
related to hole-rich domains. Two exchange
integrals can also be defined Ja,b always
ferromagnetic, between first neighbors in the
basal plane and Jc, first AF then F between first
neighbors along the c axis. They are connected to
the hole-poor matrix. When there are two
branches, by continuity, Ja,b and Jc are
determined by the branch similar to that of non
doped compound LaMnO3. When the hole-poor matrix
is split into small clusters, Ja,b and Jc are
determined from the highest energy levels and in
the metallic phase where they become isotropic,
Ja,b Jc they are determined by the zone
boundary energy.
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Spin Waves and Charge Segregation
?
Å
Å
Hole-poor droplets with standing waves embedded
in a hole-rich matrix.
Hole-rich droplets in a hole-poor matrix.
Hole-rich droplets at the percolation threshold
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At the M-I transition, no change in the evolution
of the SE couplings Ja,b and Jc (cf. Oles and
Feiner in the low doping regime) and Ja,b Jc in
the metallic state.
At TM-I there is a step increase of the spin
wave stiffness constant, in the Ca- and Sr-
compounds.
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This continuity versus the doping rate of the
magnetic coupling measured at large q-values
reminds of the hole-poor clusters present in the
FI. While the discontinuity of the magnetic
coupling measured at small q-values, could be the
true signature of the transition to the metallic
state.
To our knowledge, there are two experiments in
favour of such different Mn ions in the Ca-doped
systems i) neutron scattering measurements
around TC that reveal spin fluctuations in
addition to spin waves (J. Lynn 1996) and ii)
muon spin relaxation studies which also suggest
an inhomogeneous distribution of Mn ions (R.H.
Heffner 1997). But both experiments are near TC
and not at low temperature.
An other difficulty with this idea of hole-poor
Mn ions in the metallic phase is that there is
one magnon dispersion curve et no anomalous
damping.
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Recently, a paper of F. Ye, P. Dai and J.
Fernandez-Baca, PRL 96 (2006) 47204, has treated
exactly this subject. To explain the shape of the
spin wave dispersion in the metallic phase of the
perovskite manganites, they propose a Heisenberg
model with SE couplings J1 and J4 between first
and forth neighbors (a and 2a). Their model takes
perfectly into account their measurements. One
can understand that, in the metallic phase, the
magnetic coupling spreads on longer distances.
But what is more difficult to admit in their
case, is the decrease, in the metallic phase, of
J1 with the doping rate, while J4 increases
normally.
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A model based on the modulation of magnetic
exchange bonds by the orbital degree of freedom
has been proposed by Khaliullin (PRB, 61,(2000)
3494 in the metallic state there is no orbital
order. But if orbital fluctuations on two
neighbouring sites are sufficiently slow, a kind
of renormalized SE coupling can be defined,
smaller than the magnetic coupling defined in the
mean metallic lattice and visible around the zone
boundary. It is a possible explanation of the
softening of the spin wave dispersion curve near
the zone boundary
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Conclusion

• We prefer to explain the shape of the SW
  dispersion curves as follows The regular
  increase of the SE couplings through the I-M
  transition reminds the low-doping regime. The SE
  couplings have been always attached to the
  hole-poor medium where a weak orbital order still
  exists. In the metallic state, there is no more
  hole-poor clusters and no orbital order. We can
  imagine however, slow fluctuations favouring a
  very short range orbital order on 2 or 3
  hole-poor neighbouring sites, which evolves
  slowly compared to the frequency of the ZB spin
  waves. It allows to determine a SE integral, in
  the continuity of the low doping regime, weaker
  than the magnetic coupling of the mean metallic
  medium, only visible around the zone boundary.