Theory of Half-metallic Ferrimagnetism in Double Perovskites

We present a comprehensive theory of the temperature- and disorder-dependence of half-metallic ferrimagnetism in the double perovskite Sr$_2$FeMoO$_6$ (SFMO) with $T_c$ above room temperature. We show that the magnetization $M(T)$ and conduction electron polarization $P(T)$ are both proportional to the magnetization $M_S(T)$ of localized Fe spins. We derive and validate an effective spin Hamiltonian, amenable to large-scale three-dimensional simulations. We show how $M(T)$ and $T_c$ are affected by disorder, ubiquitous in these materials. We suggest a way to enhance $T_c$ in SFMO without sacrificing polarization

Theory of High Tc_c Ferrimagnetism in a Multi-orbital Mott Insulator

We propose a model for the multi-orbital material Sr$_2$CrOsO$_6$ (SCOO), an insulator with remarkable magnetic properties and the highest $T_c \simeq 725$ K among {\em all} perovskites with a net moment. We derive a new criterion for the Mott transition $(\widetilde{U}_{1} \widetilde{U}_{2})^{1/2}>2.5W$ using slave rotor mean field theory, where $W$ is the bandwidth and $\widetilde{U}_{1(2)}$ are the effective Coulomb interactions on Cr(Os) including Hund's coupling. We show that SCOO is a Mott insulator, where the large Cr $\widetilde{U}_{1}$ compensates for the small Os $\widetilde{U}_{2}$. The spin sector is described by a frustrated antiferromagnetic Heisenberg model that naturally explains the net moment arising from canting and also the observed non-monotonic magnetization $M(T)$. We predict characteristic magnetic structure factor peaks that can be probed by neutron experiments

Probabilistic Hierarchical Forecasting with Deep Poisson Mixtures

Hierarchical forecasting problems arise when time series have a natural group structure, and predictions at multiple levels of aggregation and disaggregation across the groups are needed. In such problems, it is often desired to satisfy the aggregation constraints in a given hierarchy, referred to as hierarchical coherence in the literature. Maintaining hierarchical coherence while producing accurate forecasts can be a challenging problem, especially in the case of probabilistic forecasting. We present a novel method capable of accurate and coherent probabilistic forecasts for hierarchical time series. We call it Deep Poisson Mixture Network (DPMN). It relies on the combination of neural networks and a statistical model for the joint distribution of the hierarchical multivariate time series structure. By construction, the model guarantees hierarchical coherence and provides simple rules for aggregation and disaggregation of the predictive distributions. We perform an extensive empirical evaluation comparing the DPMN to other state-of-the-art methods which produce hierarchically coherent probabilistic forecasts on multiple public datasets. Compared to existing coherent probabilistic models, we obtained a relative improvement in the overall Continuous Ranked Probability Score (CRPS) of 11.8% on Australian domestic tourism data, and 8.1% on the Favorita grocery sales dataset.Comment: Probabilistic Hierarchical Forecasting, Neural Networks, Poisson Mixtures, Preprint submitted to IJ