We show that the Anomalous Hall Effect (AHE) observed in Colossal Magnetoresistance Manganites is a manifestation of Berry phase effects caused by carrier hopping in a non-trivial spin background. We determine the magnitude and temperature dependence of the Berry phase contribution to the AHE, finding that it increases rapidly in magnitude as the temperature is raised from zero through the magnetic transition temperature Tc, peaks at a temperature Tmax > Tc and decays as a power of T, in agreement with experimental data. We suggest that our theory may be relevant to the anomalous Hall effect in conventional ferromagnets as well. 75.20.Hr, 75.30.Hx, 75.30.Mb The Anomalous Hall Effect(AHE) is a fundamental but incompletely understood aspect of the physics of metallic ferromagnets [1,2]. The Hall effect is the development of a voltage which is transverse to an applied current; the constant of proportionality is the Hall resistivity ρ H . In non-magnetic materials, ρ H is proportional to the magnetic induction B and its sign is determined by the carrier charge. Many ferromagnets however exhibit an anomalous contribution to ρ H which is proportional to the magnetization M , thusThe definition of R s implies a sample with demagnetization factor N ∼ = 1 so that M represents the spin polarization in the material and the physical dipolar magnetic field caused by the ferromagnetically aligned spins cancels. The AHE thus involves a coupling of orbital motion of electrons to the spin polarization and must involve spin-orbit coupling.The conventional theoretical understanding of R s is based on a skew scattering mechanism which is a third order process involving interference between spin-orbit coupling (to first order ) and spin flip scattering ( to second order ) [1,3,4]. In conventional ferromagnets, this theory yields values of R s two orders of magnitude smaller than experimental data [3]. Also, some papers including Ref.[3] use a spin-orbit term involving coupling to the dipole fields produced by the spins which would apparently vanish for demagnetization factor N = 1.Recently, several groups measured the Hall resistivity ρ H of epitaxial films [5] and single crystals [6] of the 'colossal magnetoresistance' (CMR) material La 0.7 Ca 0.3 M nO 3 These materials involve carriers derived from Mn e g symmetry d-levels which may move through the lattice but are strongly ferromagnetically coupled to localized 'core spins' derived from Mn t 2g symmetry orbitals. The coupling is so strong that it may be taken to be infinite: a carrier on site i must have its spin parallel to the core spin on site i. The spin of the mobile carrier is thus quenched, but its amplitude to hop from site i to site j is modulated by a factor involving the relative spin states of core spins on the two sites. This physics is called 'double-exchange' [7].The Hall effect measurements found that in CMR materials ρ H was of the form of Eq.1 with R 0 hole-like and R s electron-like. R s becomes evident above 100K, increases sharply around T c , peaks at a te...

Magnetoresistance-the field-dependent change in the electrical resistance of a ferromagnetic material-finds applications in technologies such as magnetic recording. Near and above the Curie point, T c , corresponding to the onset of magnetic order, scattering of charge carriers by magnetic fluctuations can substantially increase the electrical resistance 1,2 . These fluctuations can be suppressed 3 by a magnetic field, leading to a negative magnetoresistance. Magnetic scattering might also have a role in the 'colossal' magnetoresistance observed in some perovskite manganese oxides 4-6 , but is it not yet clear how to reconcile this behaviour with that of the conventional ferromagnetic materials. Here we show that, in generic models of magnetic scattering, the bulk low-field magnetoresistance (near and above T c ) is determined by a single parameter: the charge-carrier density. In agreement with experiment 3,7,8 , the low-field magnetoresistance scales with the square of the ratio of the field-induced magnetization to the saturation magnetization. The scaling factor is C Ϸ x ؊ 2=3 , where x is the number of charge carriers per magnetic unit cell. Data from very different ferromagnetic metals and doped semiconductors are in broad quantitative agreement with this relationship, with the notable exception of the perovskite manganese oxides (in which dynamic lattice distortions complicate and enhance 4,9-12 the effects of pure magnetic scattering). Our results might facilitate searches for new materials with large bulk magnetoresistive properties.'Colossal' magnetoresistance (CMR) in some manganese oxides (such as the perovskite La 1−x Sr x MnO 3 and the pyrochlore Tl 2 Mn 2 O 7 ) has been found to accompany a transition from a metallic ferromagnetic low-temperature phase to a paramagnetic high-temperature phase 4 . The implication is that magnetic scattering of itinerant carriers from enhanced fluctuations near T c has an important role. This prompts one to ask what are the principal differences from the behaviour in more familiar metallic ferromagnets such as Ni and Fe, other perovskite ferromagnets (for example, La 1−x Ca x CoO 3 ), or doped magnetic semiconductors (for example, Ge 1−x Mn x Te and Eu 1−x Gd x Te). The size of the magnetoresistance differs by at least an order of magnitude among these compounds, and each material might seem to demand a separate analysis, because the magnetic mechanisms can be very different. In the perovskite manganites and cobaltites as well as traditional ferromagnets such as Fe and Ni, the magnetic exchange itself arises from hopping of the conduction electrons (either the local 'double exchange' or the longer-range RKKY coupling), whereas in the Mn pyrochlores and magnetic semiconductors such as EuSe and CdCr 2 Se 4 the magnetic coupling is mediated at least partly by bound electrons (superexchange). We argue that, provided that the transport remains metallic, the detailed model for the magnetism matters much less than a simple trend with carrier density.Scattering from magnetic ...

We discuss magnetotransport in a low density electron gas coupled to spin fluctuations near and above a ferromagnetic transition. Provided the density is low enough (n < ∼ 1/ξ 3 (T ), with ξ(T ) the ferromagnetic correlation length), spin polarons form in an intermediate temperature regime above Tc. Both in the spin polaron regime, and in the itinerant regime nearer Tc, the magnetoresistance is large. We propose that this provides a good model for "colossal" magnetoresistance in the pyrochlore Tl2−xScxMn2O7, fundamentally different from the mechanism in the perovskite manganites such as La1−xSrxMnO3.

We suggest and implement a new Monte Carlo strategy for correlated models involving fermions strongly coupled to classical degrees of freedom, with accurate handling of quenched disorder as well. Current methods iteratively diagonalise the full Hamiltonian for a system of N sites with computation time τN ∼ N 4 . This limits achievable sizes to N ∼ 100. In our method the energy cost of a Monte Carlo update is computed from the Hamiltonian of a cluster, of size Nc, constructed around the reference site, and embedded in the larger system. As MC steps sweep over the system, the cluster Hamiltonian also moves, being reconstructed at each site where an update is attempted. In this method τN,N c ∼ N N 3 c . Our results are obviously exact when Nc = N , and converge quickly to this asymptote with increasing Nc. The accuracy improves in systems where the effective disorder seen by the fermions is large. We provide results of preliminary calculations on the Holstein model and the Double Exchange model. The 'locality' of the energy cost, as evidenced by our results, suggests that several important but inaccessible problems can now be handled with control.

The magnetic properties of the transition metal monoxides MnO and NiO are investigated at equilibrium and under pressure via several advanced first-principles methods coupled with Heisenberg Hamiltonian Monte Carlo. The comparative first-principles analysis involves two promising beyond-local density functionals approaches, namely the hybrid density functional theory and the recently developed variational pseudo-self-interaction correction method, implemented with both plane-wave and atomic-orbital basis sets. The advanced functionals deliver a very satisfying rendition, curing the main drawbacks of the local functionals and improving over many other previous theoretical predictions. Furthermore, and most importantly, they convincingly demonstrate a degree of internal consistency, despite differences emerging due to methodological details (e.g., plane waves versus atomic orbitals).