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Comparisons with the experimental results

The experimental properties of high-T$ _{c}$ cuprates and manganites have been analyzed by means of the Hubbard, p-d, t-t'-U and Kondo Heisenberg models in Refs. [118,119,120,46,82,121,98,45,73,93,107,83].

In particular, the following properties have been studied:

  1. Incommensurate magnetism in $ LSCO$, $ LBCO$ and $ YBCO$ [122,123,124,125] in Refs. [118,119,46,82]

  2. Specific Heat and Entropy in $ LSCO$, $ LBCO$ and $ YBCO$ [126,127,128,129,130] in Ref. [120]

  3. Spin susceptibility in $ LSCO$ and $ YBCO$ [74,74,131,74,75] in Refs. [46,121,73]

  4. Band structure and Fermi surface in $ LSCO$ [132,133,134,135,136,137,138,139,140,141,142]in Refs. [121,98,93,83]

  5. Entropy in $ LSCO$ [143] in Ref. [121]

  6. Crossing points [144,145,146,147,148,149,150,151]in Ref. [45]

  7. Softening of spin-wave dispersion in manganites [108,109,110] in Ref. [107]

There is experimental evidence that in some hole-doped high-T$ _{c}$ cuprates, as $ LSCO$, the Fermi level is close to the van Hove singularity for values of doping close to those where the superconducting phase is suppressed [131]. We have shown that many experimentally observed features in the overdoped region of $ LSCO$ (i.e., a strongly pronounced peak in the entropy [127,128,130], in the linear coefficient of the specific heat [126,130] and in the uniform static spin magnetic susceptibility [131], a change of sign for the Hall coefficient [152], an abrupt change in the shape of the Fermi surface [132,133,134], etc. etc.) can be easily described by the relative position of the van Hove singularity with respect to the Fermi level (i.e., within a van Hove scenario). In fact, the crossing naturally produces an enhancement of the density of states and the change of the Fermi surface nature.

Within the framework of the 2D t-t'-U model, we have computed the structure of the energy bands, the shape of the Fermi surface and the relative position of the van Hove singularity in order to find a value of the t' parameter, one per each cuprate family, which could give a good agreement between our data and the experimental ones for all three quantities at the same time. The comparison with the experimental data [132,133,134,135,136,137,138,139,140,141,142]has shown that the t-t'-U model is capable to describe both $ LSCO$ and $ NCCO$, that share the property to be 1-layer cuprates. On the contrary, it does not seem the case for $ YBCO$ that is a 2-layer cuprate.

We have also shown that the shape of the Fermi Surface and the incommensurate spin fluctuations are connected, i.e. that ARPES and neutron scattering experiments are intimately related. For $ LSCO$, in particular, the nature, shape and bending of the Fermi surface have been quite well reproduced together with the position and the relative weight of the incommensurate peaks in the spin susceptibility [122,123,124].

We also predicted that commensurate magnetism should be recovered in the nearness of the critical doping. Moreover, the linear behavior of the incommensurability amplitude, observed in the low-doping region, agrees exceptionally well with the experimental data [122,123,124].

It has already been experimentally observed that there is a linear relation between the incommensurability amplitude and the critical temperature up to the optimal doping level [153]. Our theoretical results confirm this behavior. Recalling that in $ LSCO$ the commensurate-incommensurate transition is observed at the same value of doping where superconductivity starts, at least for $ LSCO$, a scenario that relates the superconducting phase to the presence of incommensurate magnetism emerges.

One feature present in a large variety of systems is a characteristic crossing point in the specific heat curves versus $ T$ [144,145,146,147,148,149,150,151]. We obtained several characteristic crossing points for the response functions when reported as functions of some thermodynamics variable. These peculiar features, already evidenced by Vollhardt [154], marked turning points where different response functions evolve from a non-interacting behavior to an unconventional dependence of the conjugate variables.

The results obtained for the uniform static susceptibility of the two-layer Hubbard model have been analyzed in relation to those experimentally observed in $ YBCO$[74,75] and others double-layered materials with a overall qualitative agreement.

In Pr$ _{0.63}$Sr$ _{0.37}$MnO$ _{3}$ there is a tendency to the planar $ x^{2}-y^{2}$ ferrotype orbital ordering [108,110]. That means that orbital fluctuations mostly renormalize exchange bonds in two dimensions. Let us note that magnons in ($ \pi$, $ \pi$, $ \pi$) direction are sensible to all three spatial directions of the exchange bonds and thus, their dispersion remains unaffected by orbital fluctuations and softening of the spectrum in this direction is purely due to the AFM spin fluctuations. In our approach we attribute softening phenomena to the effect of the suppression of the FM ordering only by the AFM superexchange interaction and thus on the direction ($ \pi$, $ \pi$, $ \pi$) we estimate ordering correctly.

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avella 2002-06-10