We study the renormalization group flow of the interactions in the two-dimensional t-t ′ Hubbard model near half filling in a N -patch representation of the whole Fermi surface. Starting from weak to intermediate couplings the flows are to strong coupling with different character depending on the choice of parameters. In a large parameter region elastic Umklapp scatterings drive an instability which on parts of the Fermi surface exhibits the key signatures of an insulating spin liquid (ISL), as proposed by Furukawa et al., rather than a conventional symmetry-broken state. The ISL is characterized by both strong d-wave pairing and antiferromagnetic correlations, however it is insulating due to the vanishing local charge compressibility and a spin liquid because of the spin gap arising from the pairing correlations. We find that the ISL is a consequence of a Fermi surface close to the saddle points at the Brillouin zone boundaries which provides an intrinsic and mutually reinforcing coupling between pairing and Umklapp channels.

The Kondo lattice Hamiltonian with ferromagnetic Hund's coupling as a model for manganites is investigated. The classical limit for the spin of the (localized) $t_{2g}$ electrons is analyzed on lattices of dimension 1,2,3 and $\infty$ using several numerical methods. The phase diagram at low temperature is presented. A regime is identified where phase separation occurs between hole undoped antiferromagnetic and hole-rich ferromagnetic regions. Experimental consequences of this novel regime are discussed. Regions of incommensurate spin correlations have also been found. Estimations of the critical temperature in 3D are compatible with experiments.Comment: Accepted in Phys. Rev. Letter

Controlling ferromagnetism by an external electric field has been a great challenge in materials physics, for example towards the development of low-power-consumption spintronics devices. To achieve an efficient mutual control of electricity and magnetism, the use of multiferroics--materials that show both ferroelectric and ferromagnetic/antiferromagnetic order--is one of the most promising approaches. Here, we show that GdFeO(3), one of the most orthodox perovskite oxides, is not only a weak ferromagnet but also possesses a ferroelectric ground state, in which the ferroelectric polarization is generated by the striction through the exchange interaction between the Gd and Fe spins. Furthermore, in this compound, ferroelectric polarization and magnetization are successfully controlled by magnetic and electric fields, respectively. This unprecedented mutual controllability of electricity and magnetism is attributed to the unique feature of composite domain wall clamping of the respective domain walls for electric and magnetic orders. This domain wall feature generally determines the efficiency of the mutual controllability and thus could have an important role towards the application of multiferroics to practical devices.