Metamagnetism of itinerant electrons in multi-layer ruthenates

The problem of quantum criticality in the context of itinerant ferro- or metamagnetism has received considerable attention [S. A. Grigera et. al., Science 294, 329 (2001); C. Pfleiderer et. al., Nature, 414, 427 (2001)]. It has been proposed that a new kind of quantum criticality is realised in materials such as MnSi or Sr_3Ru_2O_7. We show based on a mean-field theory that the low-temperature behaviour of the n-layer ruthenates Sr_{n+1}Ru_nO_{3n+1} can be understood as a result of a Van Hove singularity (VHS). We consider a single band whose Fermi energy, E_F, is close to the VHS and deduce a complex phase diagram for the magnetism as a function of temperature, magnetic field and E_F. The location of E_F with respect to the VHS depends on the number of layers or can be tuned by pressure. We find that the ferromagnetic quantum phase transition in this case is not of second but of first order, with a metamagnetic quantum critical endpoint at high magnetic field. Despite its simplicity this model describes well the properties of the uniform magnetism in the single, double and triple layer ruthenates. We would like to emphasise that the origin of this behaviour lies in the band structure.Comment: 7 pages, 3 figures, typos corrected and acknowledgement added, to appear in the Europhysics Letter

Thermodynamics of itinerant metamagnetic transitions

Theoretical studies of the metamagnetism and anomalous phase of Sr3Ru2O7 have focused on the role of van Hove singularities, although much experimental evidence points towards quantum criticality having a large effect. We investigate the magnetic and thermodynamic properties of systems where magnetic field tunes through such a peak in the electronic density of states. We study the generic case of a van Hove singularity in 2D. We see that in combination with the requirement of number conservation and interaction effects the peak in the density of states produces several interesting phenomena including raising the critical field of the transition above naive estimates, altering the relationship between temperature and field scales and creating a distinctive double-peak structure in the electronic specific heat. We show that this apparent non-Fermi liquid behaviour can be caused at mean-field level by a peak in the density of states.Comment: 6 pages, 4 figure

Chirality induced anomalous-Hall effect in helical spin crystals

Under pressure, the itinerant helimagnet MnSi displays unusual magnetic properties. We have previously discussed a BCC helical spin crystal as a promising starting point for describing the high pressure phenomenology. This state has topologically nontrivial configurations of the magnetization field. Here we note the consequences for magneto-transport that arise generally from such spin textures. In particular a skyrmion density induced `topological' Hall effect, with unusual field dependence, is described.Comment: 4 pages, 3 figures, to appear in the proceedings of SCES 07 (the international conference on strongly correlated electron systems 2007 in Houston, USA

Wilson's renormalization group applied to 2D lattice electrons in the presence of van Hove singularities

The weak coupling instabilities of a two dimensional Fermi system are investigated for the case of a square lattice using a Wilson renormalization group scheme to one loop order. We focus on a situation where the Fermi surface passes through two saddle points of the single particle dispersion. In the case of perfect nesting, the dominant instability is a spin density wave but d-wave superconductivity as well as charge or spin flux phases are also obtained in certain regions in the space of coupling parameters. The low energy regime in the vicinity of these instabilities can be studied analytically. Although saddle points play a major role (through their large contribution to the single particle density of states), the presence of low energy excitations along the Fermi surface rather than at isolated points is crucial and leads to an asymptotic decoupling of the various instabilities. This suggests a more mean-field like picture of these instabilities, than the one recently established by numerical studies using discretized Fermi surfaces.Comment: gzipped tar file, 31 pages including 10 figures, minor correction of misprint

Solution of the infinite range t-J model

The t-J model with constant t and J between any pair of sites is studied by exploiting the symmetry of the Hamiltonian with respect to site permutations. For a given number of electrons and a given total spin the exchange term simply yields an additive constant. Therefore the real problem is to diagonalize the "t- model", or equivalently the infinite U Hubbard Hamiltonian. Using extensively the properties of the permutation group, we are able to find explicitly both the energy eigenvalues and eigenstates, labeled according to spin quantum numbers and Young diagrams. As a corollary we also obtain the degenerate ground states of the finite $U$ Hubbard model with infinite range hopping -t>0.Comment: 15 pages, 2 figure

Magnetic domain formation in itinerant metamagnets

We examine the effects of long-range dipolar forces on metamagnetic transitions and generalize the theory of Condon domains to the case of an itinerant electron system undergoing a first-order metamagnetic transition. We demonstrate that within a finite range of the applied field, dipolar interactions induce a spatial modulation of the magnetization in the form of stripes or bubbles. Our findings are consistent with recent observations in the bilayer ruthenate Sr$_3$Ru$_2$O$_7$.Comment: 4 pages, 3 figures, minor changes, references adde

Breakdown of the Fermi-liquid regime in the 2D Hubbard model from a two-loop field-theoretical renormalization group approach

We analyze the particle-hole symmetric two-dimensional Hubbard model on a square lattice starting from weak-to-moderate couplings by means of the field-theoretical renormalization group (RG) approach up to two-loop order. This method is essential in order to evaluate the effect of the momentum-resolved anomalous dimension $\eta(\textbf{p})$ which arises in the normal phase of this model on the corresponding low-energy single-particle excitations. As a result, we find important indications pointing to the existence of a non-Fermi liquid (NFL) regime at temperature $T\to 0$ displaying a truncated Fermi surface (FS) for a doping range exactly in between the well-known antiferromagnetic insulating and the $d_{x^2-y^2}$-wave singlet superconducting phases. This NFL evolves as a function of doping into a correlated metal with a large FS before the $d_{x^2-y^2}$-wave pairing susceptibility finally produces the dominant instability in the low-energy limit.Comment: 9 pages, 9 figures; published in Phys. Rev.

Phonon-mediated tuning of instabilities in the Hubbard model at half-filling

We obtain the phase diagram of the half-filled two-dimensional Hubbard model on a square lattice in the presence of Einstein phonons. We find that the interplay between the instantaneous electron-electron repulsion and electron-phonon interaction leads to new phases. In particular, a d$_{x^2-y^2}$-wave superconducting phase emerges when both anisotropic phonons and repulsive Hubbard interaction are present. For large electron-phonon couplings, charge-density-wave and s-wave superconducting regions also appear in the phase diagram, and the widths of these regions are strongly dependent on the phonon frequency, indicating that retardation effects play an important role. Since at half-filling the Fermi surface is nested, spin-density-wave is recovered when the repulsive interaction dominates. We employ a functional multiscale renormalization-group method that includes both electron-electron and electron-phonon interactions, and take retardation effects fully into account.Comment: 8 pages, 5 figure

Electronic instabilities of a Hubbard model approached as a large array of coupled chains: competition between d-wave superconductivity and pseudogap phase

We study the electronic instabilities in a 2D Hubbard model where one of the dimensions has a finite width, so that it can be considered as a large array of coupled chains. The finite transverse size of the system gives rise to a discrete string of Fermi points, with respective electron fields that, due to their mutual interaction, acquire anomalous scaling dimensions depending on the point of the string. Using bosonization methods, we show that the anomalous scaling dimensions vanish when the number of coupled chains goes to infinity, implying the Fermi liquid behavior of a 2D system in that limit. However, when the Fermi level is at the Van Hove singularity arising from the saddle points of the 2D dispersion, backscattering and Cooper-pair scattering lead to the breakdown of the metallic behavior at low energies. These interactions are taken into account through their renormalization group scaling, studying in turn their influence on the nonperturbative bosonization of the model. We show that, at a certain low-energy scale, the anomalous electron dimension diverges at the Fermi points closer to the saddle points of the 2D dispersion. The d-wave superconducting correlations become also large at low energies, but their growth is cut off as the suppression of fermion excitations takes place first, extending progressively along the Fermi points towards the diagonals of the 2D Brillouin zone. We stress that this effect arises from the vanishing of the charge stiffness at the Fermi points, characterizing a critical behavior that is well captured within our nonperturbative approach.Comment: 13 pages, 7 figure