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The anomalous Hall effect (AHE) is a topology-related transport phenomenon being of potential interest in spintronics, because this effect enables the efficient probe of magnetic orders (i.e., data readout in memory devices). It is well known that AHE spontaneously occurs in ferromagnets or antiferromagnets with magnetization. While recent studies reveal electric-field induced AHE (via linear magnetoelectric coupling), an AHE originating from nonlinear magnetoelectric coupling remains largely unexplored. Here, by symmetry analysis, we establish the phenomenological theory regarding the spontaneous and electric-field driven AHE in magnets. We show that a large variety of magnetic point groups host an AHE that is driven by uni-axial, bi-axial, or tri-axial electric field and that comes from nonlinear magnetoelectric coupling. Such electric-field driven anomalous Hall conductivities are reversible by reversing the magnetic orders. Furthermore, our first-principles calculations suggest Cr2O3 and CoF2 as candidates hosting the aforementioned AHE. Our work emphasizes the important role of nonlinear magnetoelectric coupling in creating exotic transport phenomena, and offers alternative avenues for the probe of magnetic orders., Comment: 6 pages, 1 table, and 2 figures

The longitudinal nonreciprocal charge transport (NCT) in crystalline materials is a highly non-trivial phenomenon, motivating the design of next generation two-terminal rectification devices (e.g., semiconductor diodes beyond PN junctions). The practical application of such devices is built upon crystalline materials whose longitudinal NCT occurs at room temperature and under low magnetic field. However, materials of this type are rather rare and elusive, and theory guiding the discovery of these materials is lacking. Here, we develop such a theory within the framework of semiclassical Boltzmann transport theory. By symmetry analysis, we classify the complete 122 magnetic point groups with respect to the longitudinal NCT phenomenon. The symmetry-adapted Hamiltonian analysis further uncovers a previously overlooked mechanism for this phenomenon. Our theory guides the first-principles prediction of longitudinal NCT in multiferroic \epsilon-Fe2O3 semiconductor that possibly occurs at room temperature, without the application of external magnetic field. These findings advance our fundamental understandings of longitudinal NCT in crystalline materials, and aid the corresponding materials discoveries., Comment: 6 pages, 2 figures

The realization of magnetic skyrmions in two-dimensional (2D) magnets holds great promise for both fundamental research and device applications. Despite recent progress, two-dimensional skyrmion hosts are still limited, due to the fact that most 2D magnets are centrosymmetric and thus lack Dzyaloshinskii-Moriya interaction (DMI). We show here, using a general analysis based on symmetry, that Bloch-type skyrmions can, in fact, be stabilized in 2D magnets, due to the interplay between in-plane component (dx) of second nearest-neighbor DMI and magnetic anisotropy. Its validity is demonstrated in the Cr2Ge2Te6 monolayer, which is also verified by recent experiments. Our work gives a clear direction for experimental studies of 2D magnetic materials to stabilize skyrmions and should greatly enrich the research on magnetic skyrmions in 2D lattices.

Ferroelectricity in the complementary metal-oxide semiconductor (CMOS)-compatible hafnia (HfO$_2$) is crucial for the fabrication of high-integration nonvolatile memory devices. However, the capture of ferroelectricity in HfO$_2$ requires the stabilization of thermodynamically-metastable orthorhombic or rhombohedral phases, which entails the introduction of defects (e.g., dopants and vacancies) and pays the price of crystal imperfections, causing unpleasant wake-up and fatigue effects. Here, we report a theoretical strategy on the realization of robust ferroelectricity in HfO$_2$-based ferroelectrics by designing a series of epitaxial (HfO$_2$)$_1$/(CeO$_2$)$_1$ superlattices. The advantages of the designated ferroelectric superlattices are defects free, and most importantly, on the base of the thermodynamically stable monoclinic phase of HfO$_2$. Consequently, this allows the creation of superior ferroelectric properties with an electric polarization $>$25 $\mu$C/cm$^2$ and an ultralow polarization-switching energy barrier at $\sim$2.5 meV/atom. Our work may open an entirely new route towards the fabrication of high-performance HfO$_2$ based ferroelectric devices.

In semiconductor spintronics, the generation of highly spin-polarized carriers and the efficient probe of spin order (due to strong ferromagnetism) -- at or above room temperature -- are crucial because it allows for the design of spin-based semiconductor devices. Usually, such goals were fulfilled in room-temperature ferromagnetic semiconductors, being rare materials in nature. While room-temperature antiferromagnetic semiconductors are plentiful, the possibility for creating highly spin-polarized carriers and strong ferromagnetism in these materials remain to be unraveled. Here, we explore such a possibility by first-principles simulations, working with CaTcO$_3$ and NaOsO$_3$ perovskites -- being room-temperature antiferromagnetic semiconductors. We find that doping them by electrons or holes results in these materials to be highly spin-polarized, carrying enormous ferromagnetic moments. Doping electrons with moderate carrier density can yield strong ferromagnetism in them, with the ferromagnetic moments being comparable to that in typical ferromagnetic semiconductors. Our work thus indicates the merit of perovskite antiferromagnetic semiconductors in spintronics -- for a possible replacement of ferromagnetic semiconductors.

The anti-symmetric and anisotropic symmetric exchange interactions between two magnetic dipole moments - responsible for intriguing magnetic textures (e.g., magnetic skyrmions) - have been discovered since last century, while their electric analogues were either hidden for a long time or still not known. As a matter of fact, it is only recently that the anti-symmetric exchange interactions between electric dipoles was proved to exist (with materials hosting such an interaction being still rare) and the existence of anisotropic symmetric exchange interaction between electric dipoles remains to be revealed. Here, by symmetry analysis and first-principles calculations, we identify a candidate material in which our aforementioned exchange interactions between electric dipoles are perceptible. More precisely, we find that various phases of hafnia showcase non-collinear alignment of electric dipoles, which is interpreted by our phenomenological theories. This gives evidence that hafnia simultaneously accommodates anti-symmetric and anisotropic symmetric exchange interactions between electric dipoles. Our findings can hopefully deepen the current knowledge of electromagnetism in ferroelectrics, magnets and multiferroics, and have a potential to guide the discovery of novel states of matter (e.g., electric skyrmions) in hafnia and related materials., Comment: 6 pages, 3 figures

The microscopic origin of the electric Dzyaloshinskii-Moriya interaction (eDMI) is unveiled and discussed by analytical analysis and first-principles based calculations. As similar to the magnetic Dzyaloshinskii-Moriya interaction (mDMI), eDMI also originates from electron-mediated effect and more specifically from certain electron hoppings that are being activated due to certain local inversion symmetry breaking. However, the eDMI energy is found to be at least a third-order interaction in atomic displacements instead of bilinear in magnetic dipole moments for mDMI. Furthermore, the eDMI energy form is presented, and we find that novel electrical topological defects (namely, chiral electric bobbers) can arise from this eDMI. Thus unraveling the microscopic origin of eDMI has the potential to lead to, and explain, the discovery of novel polar topological phases., Comment: 37 pages, 14 figures, 9 tables; Physical Review B accepted, see https://journals.aps.org/prb/accepted/89076K2fDde14e0d07313d31c483a35cd4d84b767

Centrosymmetric antiferromagnetic semiconductors, although abundant in nature, seem less promising than ferromagnets and ferroelectrics for practical applications in semiconductor spintronics. As a matter of fact, the lack of spontaneous polarization and magnetization hinders the efficient utilization of electronic spin in these materials. Here, we propose a paradigm to harness electronic spin in centrosymmetric antiferromagnets via Zeeman spin splittings of electronic energy levels -- termed as spin Zeeman effect -- which is controlled by electric field.By symmetry analysis, we identify twenty-one centrosymmetric antiferromagnetic point groups that accommodate such a spin Zeeman effect. We further predict by first-principles that two antiferromagnetic semiconductors, Fe$_2$TeO$_6$ and SrFe$_2$S$_2$O, are excellent candidates showcasing Zeeman splittings as large as $\sim$55 and $\sim$30 meV, respectively, induced by an electric field of 6 MV/cm. Moreover, the electronic spin magnetization associated to the splitting energy levels can be switched by reversing the electric field. Our work thus sheds light on the electric-field control of electronic spin in antiferromagnets, which broadens the scope of application of centrosymmetric antiferromagnetic semiconductors.

Ferroelectric materials are characterized by a spontaneous polar distortion. The behavior of such distortions in the presence of free charge is the key to the physics of metallized ferroelectrics in particular, and of structurally-polar metals more generally. Using first-principles simulations, here we show that a polar distortion resists metallization and the attendant suppression of long-range dipolar interactions in the vast majority of a sample of 11 representative ferroelectrics. We identify a meta-screening effect, occurring in the doped compounds as a consequence of the charge rearrangements associated to electrostatic screening, as the main factor determining the survival of a non-centrosymmetric phase. Our findings advance greatly our understanding of the essentials of structurally-polar metals, and offer guidelines on the behavior of ferroelectrics upon field-effect charge injection or proximity to conductive device elements., Comment: 13 pages, 9 figures

We use first-principles methods to study oxygen-octahedra rotations in ABO3 perovskite oxides. We focus on the short-period, perfectly antiphase or in-phase, tilt patterns that characterize most compounds and control their physical (e.g., conductive, magnetic) properties. Based on an analytical form of the relevant potential energy surface, we discuss the conditions for the stability of polymorphs presenting different tilt patterns, and obtain numerical results for a collection of thirty-five representative materials. Our results reveal the mechanisms responsible for the frequent occurrence of a particular structure that combines antiphase and in-phase rotations, i.e., the orthorhombic Pbnm phase displayed by about half of all perovskite oxides and by many non-oxidic perovskites. The Pbnm phase benefits from the simultaneous occurrence of antiphase and in-phase tilt patterns that compete with each other, but not as strongly as to be mutually exclusive. We also find that secondary antipolar modes, involving the A cations, contribute to weaken the competition between different tilts and play a key role in their coexistence. Our results thus confirm and better explain previous observations for particular compounds. Interestingly, we also find that strain effects, which are known to be a major factor governing phase competition in related (e.g., ferroelectric) perovskite oxides, play no essential role as regards the relative stability of different rotational polymorphs. Further, we discuss why the Pbnm structure stops being the ground state in two opposite limits, for large and small A cations, showing that very different effects become relevant in each case. Our work thus provides a comprehensive discussion on these all-important and abundant materials, which will be useful to better understand existing compounds as well as to identify new strategies for materials engineering.

After decades of searching for robust nanoscale ferroelectricity that could enable integration into the next generation memory and logic devices, hafnia-based thin films have appeared as the ultimate candidate because their ferroelectric (FE) polarization becomes more robust as the size is reduced. This exposes a new kind of ferroelectricity, whose mechanism still needs to be understood. Towards this end, thin films with increased crystal quality are needed. We report the epitaxial growth of Hf0.5Zr0.5O2 (HZO) thin films on (001)-oriented La0.7Sr0.3MnO3/SrTiO3 (STO) substrates. The films, which are under epitaxial compressive strain and are predominantly (111)-oriented, display large FE polarization values up to 34 {\mu}C/cm2 and do not need wake-up cycling. Structural characterization reveals a rhombohedral phase, different from the commonly reported polar orthorhombic phase. This unexpected finding allows us to propose a compelling model for the formation of the FE phase. In addition, these results point towards nanoparticles of simple oxides as a vastly unexplored class of nanoscale ferroelectrics.

Magnetoelectric multiferroic materials, particularly with the perovskite structure, are receiving a lot of attention because of their inherent coupling between electrical polarization and magnetic ordering. However, very few types of direct coupling between polarization and magnetization are known, and it is unclear whether they can be useful to the design of novel spintronic devices exploiting the control of magnetization by electric fields. For instance, the typical bi-quadratic coupling only allows to change the magnitude of the magnetization by an electric field, but it does not permit an electric-field-induced switching of the magnetization. Similarly, the so-called Lifshitz invariants allow an electric-field control of complicated magnetic orderings, but not of the magnetization. Here, we report the discovery of novel direct couplings between polarization and magnetization in epitaxial perovskite films, via the use of first-principles methods and the development of an original Landau-type phenomenological theory. Our results feature penta-linear interactions involving the ferromagnetic and anti-ferromagnetic vectors as well as the polar distortions and oxygen octahedral tilting, and permit a number of striking effects. Examples include a continuous electric-field control of the magnetization magnitude and sign, and the discrete switching of the magnetization magnitude. Thus, the high-order, penta-linear couplings demonstrated in this work may open new paths towards novel magneto-electric effects, as well as, spintronic and magnonic devices., Comment: Work supported by ERC Consolidator grant MINT (Contract No. 615759)

We report a Raman scattering study of six rare earth orthoferrites RFeO3, with R = La, Sm, Eu, Gd, Tb, Dy. The use of extensive polarized Raman scattering of SmFeO3 and first-principles calculations enable the assignment of the observed phonon modes to vibrational symmetries and atomic displacements. The assignment of the spectra and their comparison throughout the whole series allows correlating the phonon modes with the orthorhombic structural distortions of RFeO3 perovskites. In particular, the positions of two specific Ag modes scale linearly with the two FeO6 octahedra tilt angles, allowing the distortion throughout the series. At variance with literature, we find that the two octahedra tilt angles scale differently with the vibration frequencies of their respective Ag modes. This behavior as well as the general relations between the tilt angles, the frequencies of the associated modes and the ionic radii are rationalized in a simple Landau model. The reported Raman spectra and associated phonon-mode assignment provide reference data for structural investigations of the whole series of orthoferrites., Comment: 9 pages, 5 figures