1. 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 l’Etat Solide, Orsay Yakov M. Mukovskii, D. Shulyatev Moscow State Steel and Alloys Institute, Moscow

2. Outline How to explain the shape of the spin wave dispersion curves of metallic manganites La 0.7 (Ca 1-y Sr y ) 0.3 MnO 3 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.

3. Spin Wave Dispersion Curves Both curves show first a parabolic shape at small-q values and then a flatenned shape near the zone boundary.

4. The Spin Wave Dispersion Curve of La 0.7 Pb 0.3 MnO 3 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

5. A Phonon-Magnon Coupling is possible as the magnon branch crosses the LO1 phonon branch around  = 0.3, (N. Furukawa JPSJ 68 (1999) 2522) but a precise study of phonons and magnons near the zone boundary has eliminated this possibility.

6. Lattice defects in the crystal could also explain the ZB softening of the spin wave dispersion curve, specially the short range correlated lattice polarons.

8. The spin wave dispersion curve of these 4 compounds has the same shape including La 0.7 Sr 0.3 MnO 3 where there is no short range correlated lattice polarons.

9. Evolution of the spin wave stiffness constant and of the super exchange integrals of the two systems La 1-x Ca x MnO 3 and La 1-x Sr x MnO 3 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: J a,b always ferromagnetic, between first neighbors in the basal plane and J c, 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, J a,b and J c are determined by the branch similar to that of non doped compound LaMnO 3. When the hole-poor matrix is split into small clusters, J a,b and J c are determined from the highest energy levels and in the metallic phase where they become isotropic, J a,b = J c they are determined by the zone boundary energy.

10. Spin Waves and Charge Segregation Hole-rich droplets in a hole-poor matrix. Hole-rich droplets at the percolation threshold Hole-poor droplets with standing waves embedded in a hole-rich matrix. ? Å Å

11. At the M-I transition, no change in the evolution of the SE couplings J a,b and J c (cf. Oleś and Feiner in the low doping regime) and J a,b = J c in the metallic state. At T M-I there is a step increase of the spin wave stiffness constant, in the Ca- and Sr- compounds.

12. 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 T C 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 T C 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.

13. 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 J 1 and J 4 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 J 1 with the doping rate, while J 4 increases normally.

14. 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

15. 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.