Calculating magnetic interactions in organic electrides

Abstract

We present our calculation results for organic magnetic electrides. In order to identify the 'cavity' electrons, we use maximally-localized Wannier functions and 'empty atom' technique. The estimation of magnetic coupling is then performed based on magnetic force linear response theory. Both short-and long-range magnetic interactions are calculated with a single self-consistent calculation of a primitive cell. With this scheme we investigate four different organic electrides whose magnetic properties have been partly unknown or under debate. Our calculation results unveil the nature of magnetic moment and their interactions, and justify or defy the validity of preassumed spin models. Our work not only provides useful insight to understand magnetic electrides but also suggests a new paradigm to study the related materials.

Cloaking the underlying long-range order of randomly perturbed lattices

“…Since the characteristic function is uniformly continuous at the origin, and sincef (0) = 1, the perturbed point pattern is hyperuniform if and only if the original point pattern is hyperuniform. Hyperuniformity is preserved even if the moments of the perturbations do not exist, but in that case the class of hyperuniformity changes (that is, the asymptotic behavior of the structure factor at the origin) [8,31].…”

“…A common way to introduce disorder into an otherwise ordered system, such as a perfect crystal or quasicrystal, is to randomly perturb the particle positions of that system [1][2][3][4]. A perturbed lattice is a point pattern (process) in d-dimensional Euclidean space R d obtained by displacing each point in a Bravais lattice [5] according to some stochastic rule [1,[6][7][8]. Perturbed lattices have been intensively studied in a broad range of contexts, from statistical physics and cosmology [9,10] to crystallography lattices [1,2] or to probability theory, including distributions of zeros of random entire functions [11] and number rigidity [12][13][14].…”

“…A typical stochastic rule is the Gaussian distribution [12], in which case the model is also called an Einstein pattern [20]. Alternatively, the distributions can have heavy tails like the Cauchy or the Pareto distributions [8].…”

“…Perturbed lattices with i.i.d. displacements are always hyperuniform, but the hyperuniformity class depends on whether the first and second moments of the perturbations exist [6,8]. If both exist, then the perturbed lattice is class I hyperuniform with σ 2 (R) ∼ R d−1 , that is, the number variance grows like the surface area of the observation window.…”

“…In what follows, we will compute both Λ and τ to thoroughly characterize the degree of order and disorder in hyperuniform perturbed lattices. Currently, perturbed lattices with weak or no correlations are among the rare examples of amorphous hyperuniform point patterns that can be easily simulated with a million particles per sample [8,14,52,53]. However, in general, the resulting point patterns are not fully amorphous in the sense that their structure factor exhibits Bragg peaks, which are 'inherited' from the original lattice.…”