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Commencing from the centrosymmetric MnRMnSbO$_6$ compound, we explore the realm of magnetic polar double-double perovskite oxides characterized by significant ferroelectric polarization. Employing symmetry operations, first-principles methodologies, and Monte Carlo simulations, our investigation delves into the structural, magnetic, ferroelectric, and electronic attributes of the polar LaFeMnNiO$_6$ and LaTiMnNiO$_6$ compounds. The structural analysis uncovers that the paraelectric-ferroelectric phase transition is intricately linked to the Fe/Ti-displacement of square planar Fe/TiO$_4$. Notably, the magnetic LaFeMnNiO$_6$ and LaTiMnNiO$_6$ compounds demonstrate robust ferroelectric polarizations, measuring 20.0 $\mu$C/cm$^2$ and 21.8 $\mu$C/cm$^2$, respectively, accompanied by minimalist forbidden energy gaps of 1.40 eV and 1.18 eV using the GGA+U method. Furthermore, we pinpoint elevated magnetic transition temperatures for these compounds. Additionally, our study scrutinizes the energies associated with diverse spin configurations and identifies potential minimum decomposition pathways into stable oxides. This comprehensive analysis ensures the meticulous formation of the LaFeMnNiO$_6$ and LaTiMnNiO$_6$ compounds.

Cubic perovskite-structure ABO$_3$ and A$_{1-x}$A$^{\prime}$$_x$BO$_3$-type oxides have been investigated extensively while their hexagonal-structure versions have received minimal attention, even though they are multiferroic and can form heterostructures with the manifold hexagonal two-dimensional materials. Hexagonal ferrites of the form RFeO$_3$, where R is yttrium or a rare-earth element such as Lu, Yb, etc., feature coupled ferroelectricity (FE) and weak-ferromagnetism (wFM), exhibiting linear magnetoelectricity. Their only drawback is weak ferromagnetism. In this paper, we employ density-functional-theory (DFT) calculations on hexagonal LuFeO$_3$ ($h$-LFO), targeting its magnetic ordering by electron doping,anticipating spin-disproportionation of the Fe sublattices. Indeed, we show that spin-disproportionation in heavily-electron-doped versions Lu$_{1-x}$Hf$_x$FeO$_3$ ($h$-LHFO), especially for x=1/3 and 1/2, leads to robust out-of-plane collinear ferrimagnetism that is stable at room temperature. Furthermore, the robust ferroelectricity of $h$-LFO persists via a Jahn-Teller metal-to-insulator transition. Finally, we construct a $h$-LHFO/$h$-2D heterostructure, where $h$-2D stands for the FE/FM monolayer MnSTe, and demonstrate strong magnetoelectric coupling, namely manipulation of magnetic skyrmions in MnSTe by an external electric field through the $h$-LHFO polarization, opening up a new realm for magnetoelectric applications.

We employed first-principles density functional theory calculations guided by group-theoretical analysis and demonstrated the control of insulator-metal-insulator transition, polarization and two sublattice magnetization in (LaFeO$_3$)$_1$/(CaFeO$_3$)$_1$ superlattice via. multi structural mode coupling i.e., 'multimode coupling'. We have discovered a polar A-type charge disproportionation mode, Q$_{ACD}$ (analogous to the A-type antiferromagnetic ordering), and found that it couples with the trilinear coupling, $Q_{Tri}$ mode (common in $Pnma$ perovskite oxides and involves three structural modes), and lowers the symmetry further. By tuning the strength of the coupling between the participating modes, the polar metallic phase, polar zero bandgap semiconducting, and polar insulating phases can be obtained. Here, $Q_{Tri}$ switches the polarization direction, whereas, Q$_{ACD}$ can trigger insulator-metal-insulator transition along with the polarization switching. The mechanism is true for any transition metal superlattices constituted with $Pnma$ building blocks and with partially filled $e_g$ or $t_{2g}$ electron(s) at the transition metal sites.

This work investigates the origins of cation ordering of double perovskites using first-principles theory computations combined with machine learning (ML) and causal relations. We have considered various oxidation states of A, A', B, and B' from the family of transition metal ions to construct a diverse compositional space. A conventional framework employing traditional ML classification algorithms such as Random Forest (RF) coupled with appropriate features including geometry-driven and key structural modes leads to highly accurate prediction (~98%) of A-site cation ordering. We have evaluated the accuracy of ML models by entailing analyses of decision paths, assignments of probabilistic confidence bound, and finally introducing a direct non-Gaussian acyclic structural equation model to investigate causality. Our study suggests that the structural modes are the most important features for classifying layered, columnar and rock-salt ordering. For clear layered ordering, the charge difference between the A and A' is the most important feature which in turn depends on the B, B' charge separation. Based on the outputs from ML models, we have designed functional forms with these features to derive energy differences forming clear layered ordering. The trilinear coupling between tilt, rotation, and A-site antiferroelectric displacement in Landau free-energy expansion becomes the necessary condition behind the formation of A-site cation ordering.

Recent advances in the synthesis of polar molecular materials have produced practical alternatives to ferroelectric ceramics, opening up exciting new avenues for their incorporation into modern electronic devices. However, in order to realize the full potential of polar polymer and molecular crystals for modern technological applications, it is paramount to assemble and evaluate all the available data for such compounds, identifying descriptors that could be associated with an emergence of ferroelectricity. In this work, we utilized data-driven approaches to judiciously shortlist candidate materials from a wide chemical space that could possess ferroelectric functionalities. An importance-sampling based method was utilized to address the challenge of having a limited amount of available data on already known organic ferroelectrics. Sets of molecular- and crystal-level descriptors were combined with a Random Forest Regression algorithm in order to predict spontaneous polarization of the shortlisted compounds. First-principles simulations were performed to further validate the predictions obtained from the machine learning model.

Here we follow, both experimentally and theoretically, the development of magnetism in Tb clusters from the atomic limit, adding one atom at a time. The exchange interaction is, surprisingly, observed to drastically increase compared to that of bulk, and to exhibit irregular oscillations as a function of the interatomic distance. From electronic structure theory we find that the theoretical magnetic moments oscillate with cluster size in exact agreement with experimental data. Unlike the bulk, the oscillation is not caused by the RKKY mechanism. Instead, the inter-atomic exchange is shown to be driven by a competition between wave-function overlap of the 5d shell and the on-site exchange interaction, which leads to a competition between ferromagnetic double-exchange and antiferromagnetic super-exchange. This understanding opens up new ways to tune the magnetic properties of rare-earth based magnets with nano-sized building blocks.

Discovering materials that display a linear magnetoelectric effect at room temperature is challenge. Such materials could facilitate novel devices based on the electric-field control of magnetism. Here we present simple, chemically intuitive design rules to identify a new class of bulk magnetoelectric materials based on the 'bicolor' layering of $Pnma$ ferrite perovskites, e.g., LaFeO$_3$/ LnFeO$_3$ superlattices for which Ln = lanthanide cation. We use first-principles density-functional theory calculations to confirm these ideas. Additionally, we elucidate the origin of this effect and show it is a general consequence of the layering of any bicolor, $Pnma$ perovskite superlattice in which the number of constituent layers are odd (leading to a form of hybrid improper ferroelectricity) and Goodenough- Kanamori rules. Here, the polar distortions induce both weak ferromagnetism and a linear magnetoelectric effect. Our calculations suggest that the effect is 2-3 times greater in magnitude than that observed for the prototypical magnetoelectric material, Cr$_2$O$_3$. We use a simple mean field model to show that the considered materials order magnetically above room temperature.

A population-based study of a quantitative trait, e.g. Blood Pressure(BP) may be seriously compromised when the trait is subject to the effects of a treatment. Without appropriate corrections this can lead to considerable reduction of statistical power. Here we demonestrate this in the scenario of QTL mapping through Single-Marker Analysis. The data are simulated from a normal mixtrure for different values of allele frequencies, separation between normal populations and Linkage Disequilibrium, and several methods of correction are compared to check which can best compensate for the loss of power if treatment effects are ignored. In one of these methods, underlying BPs are approximated by subtracting an estimate of mean value of medicine effect from obsereved BPs in treated subjects. We domonestrate the efficacy of this method throughout different choices of parameters. Finally to account for quantitative traits that follow non-normal distributions, data are simulated from lognormal mixtures similarly and Kruskal-Wallis test is used to obtain estimates of powers for different methods of analysis.

One of the primary objectives in molecular nano-spintronics is to manipulate the spin states of organic molecules with a d-electron center, by suitable external means. In this letter, we demonstrate by first principles density functional calculations, as well as second order perturbation thoery, that a strain induced change of the spin state, from S=1 $\to$ S=2, takes place for an iron porphyrin (FeP) molecule deposited at a divacancy site in a graphene lattice. The process is reversible in a sense that the application of tensile or compressive strains in the graphene lattice can stabilize FeP in different spin states, each with a unique saturation moment and easy axis orientation. The effect is brought about by a change in Fe-N bond length in FeP, which influences the molecular level diagram as well as the interaction between the C atoms of the graphene layer and the molecular orbitals of FeP., Comment: 5 pages, 3 figures

The search for materials displaying a large magnetoelectric effect has occupied researchers for many decades. The rewards could include not only advanced electronics technologies, but also fundamental insights concerning the dielectric and magnetic properties of condensed matter. In this article, we focus on the magnetoelectric effect in transition metal oxides and review the manner in which first-principles calculations have helped guide the search for (and increasingly, predicted) new materials and shed light on the microscopic mechanisms responsible for magnetoelectric phenomena., Comment: 24 pages, 12 figures