A new method of computing multipolar exchange interaction in spin-orbit coupled systems is developed using multipolar tensor expansion of the density matrix in local density approximation+U electronic structure calculation. Within the mean field approximation, exchange constants can be mapped into a series of total energy calculations by the pair-flip approximation technique. The application to uranium dioxide shows an antiferromagnetic superexchange coupling in dipoles but a ferromagnetic one in quadrupoles which is very different from past studies. Further calculation of the spin-lattice interaction indicates it is of the same order with the superexchange and characterizes the overall behavior of the quadrupolar part as a competition between them.

Weyl semimetals (WSMs), a new type of topological condensed matter, are currently attracting great interest due to their unusual electronic states and intriguing transport properties such as chiral anomaly induced negative magnetoresistance, a semi-quantized anomalous Hall effect and the debated chiral magnetic effect. These systems are close cousins of topological insulators (TIs) which are known for their disorder tolerant surface states. Similarly, WSMs exhibit unique topologically protected Fermi arcs surface states. Here we analyze electron-phonon scattering, a primary source of resistivity in metals at finite temperatures, as a function of the shape of the Fermi arc where we find that the impact on surface transport is significantly dependent on the arc curvature and disappears in the limit of a straight arc. Next, we discuss the effect of strong surface disorder on the resistivity by numerically simulating a tight binding model with the presence of quenched surface vacancies using the Coherent Potential Approximation (CPA) and Kubo-Greenwood formalism. We find that the limit of a straight arc geometry is remarkably disorder tolerant, producing surface conductivity that is a factor of 50 larger of a comparable set up with surface states of TI. Finally, a simulation of the effects of surface vacancies on TaAs is presented, illustrating the disorder tolerance of the topological surface states in a recently discovered WSM material.

We introduce a theoretical framework for computaions of anisotropic multipolar exchange interactions found in many spin-orbit coupled magnetic systems and propose a method to extract these coupling constants using a density functional total energy calculation. This method is developed using a multipolar expansion of local density matrices for correlated orbitals that are responsible for magnetic degrees of freedom. Within the mean-field approximation, we show that each coupling constant can be recovered from a series of total energy calculations via what we call the "pair-flip" technique. This technique flips the relative phase of a pair of multipoles and computes corresponding total energy cost associated with the given exchange constant. To test it, we apply our method to Uranium Dioxide, which is a system known to have pseudospin J = 1 superexchange induced dipolar, and superexchange plus spin-lattice induced quadrupolar orderings. Our calculation reveals that the superexchange and spin-lattice contributions to the quadrupolar exchange interactions are about the same order with ferro-and antiferro-magnetic contributions, respectively. This highlights a competition rather than a cooperation between them. Our method could be a promising tool to explore magnetic properties of rare-earth compounds and hidden-order materials.

Applying linear response and the magnetic force theorem in correlated density functional theory, the inter-sublattice exchange constants of antiferromagnetic Eu are calculated and found to vanish near the pressure of Pc=82 GPa, just where magnetic order is observed experimentally to be lost. The Eu 4f 7 moment remains unchanged at high pressure, again in agreement with spectroscopic measurements, leaving the picture of perfect frustration of interatomic Ruderman-Kittel-Kasuya-Yoshida couplings in a broad metallic background, leaving a state of electrons strongly exchange coupled to arbitrarily oriented, possibly quasistatic local moments. This strongly frustrated state gives way to superconductivity at Tc=1.7K, observed experimentally. These phenomena, and free energy considerations related to correlations, suggest an unusual phase of matter that is discussed within the scenarios of the Doniach Kondo lattice phase diagram, the metallic spin glass class, and itinerant spin liquid or spin gas systems.