The /?Mn2 compounds are characterized by an instability of the Mn moment in a highly frustrated crystallographic structure. Although quite general, this problem has not yet been treated. A model derived from the Hubbard Hamiltonian is proposed. It accounts for the new physics observed: complex ordered phases where magnetic and nonmagnetic sites coexist and unusual dependence on external parameters.PACS numbers: 75.10.-b, 05.50.+q, 75.25.+ZThe very peculiar properties of the RMri2 intermetallic compounds, where R is a rare-earth element, are associated with the instability of the itinerant-electron antiferromagnetism in a frustrated lattice.These compounds crystallize in either the C14 hexagonal (R =Pr, Nd, Sm, Ho, Er, Tm, Lu, or Th) or the C15 cubic (/?=Y, Sm, Gd, Tb, Dy, or Ho) Laves phase structure. The Mn atoms occupy the corners of regular tetrahedra, stacked in a base-to-base and summit-tosummit sequence in the hexagonal structure and in a corner-sharing way in the cubic one. 1 In both cases, due to the topology of the atomic packing the Mn lattice is highly frustrated.On the other hand, the Mn moments in the /?Mn2 series are very close to the magnetic-nonmagnetic (M-NM) instability. Below a critical Mn-Mn distance Mn remains nonmagnetic, i.e., in compounds with R=Sc or a heavy lanthanide like Ho, Er, Tm, and Lu. Above the critical distance, i.e., with light lanthanides, R =Pr, Nd, Sm, and Gd, large moments with antiferromagnetic (AF) interactions are found. 2 Complex magnetic orderings are then observed due to the lattice frustration. They set in at a first-order transition accompanied by a large volume discontinuity 2 which is accounted for by a substantial jump of the Mn moment at the ordering. In the compounds near the critical Mn-Mn spacing the magnetism becomes extremely sensitive to the external parameters such as temperature, pressure, magnetic field, or alloying. A good illustration is given by TbMn2. In the paramagnetic phase this compound exhibits strong short-range order. As the temperature is decreased two close magnetic transitions develop. At low temperature, the magnetic structure can be destabilized by an applied field, leading to magnetic isotherms with large field hysteresis. 3 Application of pressure induces a dramatic decrease of the ordering temperature of the Mn ions, at a rate of 36 K/kbar. 4 The substitution of only 3% of Tb by Sc is enough to destroy the Mn moment. 5 The case of DyMn2 is particularly interesting, as although all the Mn sites are chemically equivalent, only a fraction of them bears a magnetic moment. This mixed phase has been observed by NMR (Ref. 6) and by powder neutron diffraction. 7 Here we study a model which we expect contains the essential features of these systems: instability of the magnetic moment and frustration. The interplay between these two effects leads to the unusual phases and properties observed.In the RMr\2 compounds in which a Mn ordering takes place the Neel temperature is roughly independent of the rare earth R (T N -100 K). *» 2 This shows tha...

We study the electron transport through a magnetic molecular transistor in the Kondo limit using the slave boson technique. We include the electron-phonon coupling and analyze the cases where the spin of the molecule is either S = 1/2 or S = 1. We use the Schrieffer-Wolff transformation to write down a low energy Hamiltonian for the system. In the presence of electron-phonon coupling, and for S = 1, the resulting Kondo Hamiltonian has two active channels. At low temperature, these two channels interfere destructively, leading to a zero conductance.

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We study the BiO m high-r c oxides and compare them to the CuO" systems (m,n =2 or 3). Both are described by a general Hamiltonian and studied by perturbation theory in the hopping energy. It is shown that a common polarization mechanism can give rise to pairing of the O holes added to the antiferromagnetic or disproportionated semiconducting states. The necessary conditions are proximity of the M (Cu or Bi) and O levels, a gap in the electronic spectrum of the system, and important nearestneighbor M-O repulsion.

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We apply the Gutzwiller approach to the attractive Hubbard model in the whole range of filling. The repulsion-attraction transformation of the Hamiltonian is shown to be valid also for this particular mean-field approximation. The physical meaning of the results is discussed.The discovery of high-temperature superconductivity has renewed the interest in the attractive Hubbard model as many proposals involve the concept of negative-U centers with E /L = g q (d, n t, n t )E -Ud,where the relevant parameters are U/t and the filling of the corresponding band. This apparently simple Hamiltonian contains analogous difficulties as the repulsive one to be solved. In the weak-coupling limit, the normal Hartree-Fock approximation yields the usual BCS picture. This result can be inferred from the repulsive case, by means of the repulsion-attraction transformation as has been shown by Mertsching.In the opposite strongcoupling limit, the fermions form local singlet pairs which behave as hard-core bosons and the physics is quite difFerent. The intermediate regime is still strongly discussed, especially in two dimensions, in connection with the superconducting oxides.Here we use Gutzwiller variational wave function and combinatorial approximation to solve Eq. (1), at T=O. Now due to the on-site attraction, simple occupied sites (instead of doubly occupied as in the repulsive case) are reduced. We verify that the repulsion-attraction transformation works also for this mean-field approach and we discuss the physical meaning of the results in this case.Let L, N&, N&, S, D, and E be the number of lattice points, up and down spins, single and doubly occupied and empty sites, respectively: n& =%&/L, n& =X&/L, s =S/L, d =D/L, and e =E!L.A projection operator, which reduces by a factor g the amplitude of the S sites, is defined as p, =1 -(1 -g)(n, t n, t)-(2) le& = / p;leo& =g'leo& where l go& is the ground state of the uncorrelated system ( U =0).Using the Gutzwiller approach, in a similar fashion than for the repulsive Hubbard model, ' one obtains then the variational wave function for the correlated state results: (S) where K is the average energy of the o. spins in the uncorrelated system. Equations (4) and (S) are the same expressions already obtained for the repulsive case, they are then valid for all U. For the paramagnetic half-filled band case: n t =n t = -, ', as q [Eq. (S)] is an even function of U, there is also a metal-insulator transition (as first remarked by Brinkman and Rice' for the repulsive case) for a finite value of the interaction, U, =+8lE l. These results for the particular case of half-filling have already been quoted by Gebhard and Vollhardt. " For an attraction larger than this critical value, all particles form localized pairs, there is no kinetic energy in this approximation, and the ground-state energy for U ( U, is Fg /L = Ud = -l Ul /4. For U ) -8le. l, Es/L = -I-. . I[1 -( U/81-. . 1)]'. This "critical value" indicates a change of behavior: from related but unbounded particles to singlet boson pairs...

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