Motivated by the importance of non-collinear and non-coplanar magnetic phases in determining various electrical properties of magnetic materials, we investigate the phase diagrams of the extended Hubbard model on anisotropic triangular lattice. We make use of a mean-field scheme that treats collinear, non-collinear and non-coplanar phases on equal footing. In addition to the ferromagnetic and 120 • antiferromagnetic phases, we find the four-sublattice flux, the 3Q non-coplanar and the non-collinear charge-ordered states to be stable at specific values of filling fraction n. Inter-site Coulomb repulsion leads to intriguing spin-charge ordered phases. Most notable of these are the collinear and non-collinear magnetic states at n = 2/3, which occur together with a pinball-liquid-like charge order. Our results demonstrate that the elementary single-orbital extended Hubbard model on a triangular lattice hosts unconventional spin-charge ordered phases, which have been reported in more complex and material-specific electronic Hamiltonians relevant to layered triangular systems.

We present a combined experimental and theoretical study to understand the magnetism and magnetocaloric behavior of the double perovskite Nd2NiMnO6. The magnetic susceptibility data confirms a ferromagnetic transition with K. An additional feature at T  =  25 K, indicative of antiferromagnetic correlations, is present. A positive magnetocaloric effect (MCE) near and a negative MCE around T  =  25 K is inferred from the temperature dependence of the change in magnetic entropy at low magnetic fields. The negative MCE peak is suppressed on the application of a magnetic field and can be made to switch to a conventional positive MCE upon increasing magnetic field. We understand and reproduce these features in Monte Carlo simulations of a phenomenological Heisenberg model for Nd2NiMnO6. The validity of the model is tested using density functional theory calculations. We argue that this simple understanding of the experimental observations in terms of two antiferromagnetically coupled sublattices allows these results to be useful across a broader class of magnetocaloric materials.

Motivated by the magnetically-driven high-temperature ferroelectric behavior of CuO and the subsequent theoretical efforts to understand this intriguing phenomenon, we study a spin model on a two-dimensional square lattice which possesses some of the key features of the models proposed for CuO. The model consists of Heisenberg couplings between nearest and next-nearest neighbor spins, and biquadratic couplings between nearest neighbors. We use a combination of variational calculations and classical Monte Carlo simulations to study this model at zero and finite temperatures. We show that even an arbitrarily weak biquadratic coupling plays a crucial role in selecting the magnetic ground state. More importantly, a non-collinear magnetic state, characterized by a finite spin current, is stable at finite temperatures. The interesting aspect is that the present model neither includes an inversion-symmetry-breaking term nor the effects of lattice distortions in the Hamiltonian. We conclude that non-collinear magnetism at high temperatures, as observed in CuO, can be explained via pure spin Hamiltonians. We find that the spiral phase is inhomogeneous, and is stabilized by entropic effects. Our study demonstrates that higher order interaction terms are of crucial importance if the stronger interactions together with the lattice geometry contemplate to generate a near degeneracy of magnetic states. The conclusions presented in this work are of particular relevance to the non-collinear magnetism and ferroelectricity observed at high temperatures in cupric oxide.

We present an effective Hamiltonian based real-space approach for studying the weak-coupling Bardeen-Cooper-Schrieffer (BCS) to the strong-coupling Bose-Einstein condensate (BEC) crossover in the two-dimensional attractive Hubbard model at finite temperatures. We introduce and justify an effective classical Hamiltonian to describe the thermal fluctuations of the relevant auxiliary fields. Our results for Tc and phase diagrams compare very well with those obtained from more sophisticated and cpu-intensive numerical methods. We demonstrate that the method works in the presence of disorder and is useful for a real-space description of the effect of disorder on superconductivity. From a combined analysis of the superconducting order parameter, the distribution of auxiliary fields and the quasiparticle density of states, we identify the regions of metallic, insulating, superconducting and pseudogapped behavior. Our finding of the importance of phase fluctuations for the pseudogap behavior is consistent with the conclusions drawn from recent experiments on NbN superconductors. The method can be generalized to study superconductors with non-trivial order parameter symmetries by identifying the relevant auxiliary variables.

We present a comprehensive experimental study of magnetization {\color {blue} ($2 < T < 300$~K, $1 < H < 8$~T)} and magnetocaloric effect in double perovskite materials $R_2$NiMnO$_6$ with $R =$ Pr, Nd, Sm, Gd, Tb, and Dy. While a paramagnetic to ferromagnetic transition, with T$_{\rm C}$ in the range $\sim 100 - 200~$K, is a common feature that can be attributed to the ordering of Mn$^{4+}$ and Ni$^{2+}$ magnetic moments, qualitatively distinct behavior depending on the choice of $R$ is observed at low temperatures. These low-temperature anomalies in magnetization are also manifest in the change in magnetic entropy, $-\Delta S_{M}$, whose sign depends on the choice of $R$. In order to understand these results, we present theoretical analysis based on mean-field approximation and Monte Carlo simulations on a minimal spin model. The model correctly captures the key features of the experimental observations.