Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

Multiferroic magnetoelectric composite systems such as ferromagnetic-ferroelectric heterostructures have recently attracted an ever-increasing interest and provoked a great number of research activities, driven by profound physics from coupling between ferroelectric and magnetic orders, as well as potential applications in novel multifunctional devices, such as sensors, transducers, memories, and spintronics. In this Review, we try to summarize what remarkable progress in multiferroic magnetoelectric composite systems has been achieved in most recent few years, with emphasis on thin films; and to describe unsolved issues and new device applications which can be controlled both electrically and magnetically.

Recent Progress in Multiferroic Magnetoelectric Composites: from Bulk to Thin Films

Kamihara and coworkers' report of superconductivity at ${T}_{c}=26\text{ }\text{ }\mathrm{K}$ in fluorine-doped LaFeAsO inspired a worldwide effort to understand the nature of the superconductivity in this new class of compounds. These iron pnictide and chalcogenide (FePn/Ch) superconductors have Fe electrons at the Fermi surface, plus an unusual Fermiology that can change rapidly with doping, which lead to normal and superconducting state properties very different from those in standard electron-phonon coupled ``conventional'' superconductors. Clearly, superconductivity and magnetism or magnetic fluctuations are intimately related in the FePn/Ch, and even coexist in some. Open questions, including the superconducting nodal structure in a number of compounds, abound and are often dependent on improved sample quality for their solution. With ${T}_{c}$ values up to 56 K, the six distinct Fe-containing superconducting structures exhibit complex but often comparable behaviors. The search for correlations and explanations in this fascinating field of research would benefit from an organization of the large, seemingly disparate data set. This review provides an overview, using numerous references, with a focus on the materials and their superconductivity.

Superconductivity in iron compounds

Multiferroics, defined for those multifunctional materials in which two or more kinds of fundamental ferroicities coexist, have become one of the hottest topics of condensed matter physics and materials science in recent years. The coexistence of several order parameters in multiferroics brings out novel physical phenomena and offers possibilities for new device functions. The revival of research activities on multiferroics is evidenced by some novel discoveries and concepts, both experimentally and theoretically. In this review, we outline some of the progressive milestones in this stimulating field, especially for those single-phase multiferroics where magnetism and ferroelectricity coexist. First, we highlight the physical concepts of multiferroicity and the current challenges to integrate the magnetism and ferroelectricity into a single-phase system. Subsequently, we summarize various strategies used to combine the two types of order. Special attention is paid to three novel mechanisms for multiferroicity generation: (1) the ferroelectricity induced by the spin orders such as spiral and E-phase antiferromagnetic spin orders, which break the spatial inversion symmetry; (2) the ferroelectricity originating from the charge-ordered states; and (3) the ferrotoroidic system. Then, we address the elementary excitations such as electromagnons, and the application potentials of multiferroics. Finally, open questions and future research opportunities are proposed.

Multiferroicity: the coupling between magnetic and polarization orders

Multiferroics, defined for those multifunctional materials in which two or more kinds of fundamental ferroicities coexist, have become one of the hottest topics of condensed matter physics and materials science in recent years. The coexistence of several order parameters in multiferroics brings out novel physical phenomena and offers possibilities for new device functions. The revival of research activities on multiferroics is evidenced by some novel discoveries and concepts, both experimentally and theoretically. In this review article, we outline some of the progressive milestones in this stimulating field, specially for those single phase multiferroics where magnetism and ferroelectricity coexist. Firstly, we will highlight the physical concepts of multiferroicity and the current challenges to integrate the magnetism and ferroelectricity into a single-phase system. Subsequently, we will summarize various strategies used to combine the two types of orders. Special attentions to three novel mechanisms for multiferroicity generation: (1) the ferroelectricity induced by the spin orders such as spiral and E-phase antiferromagnetic spin orders, which break the spatial inversion symmetry, (2) the ferroelectricity originating from the charge ordered states, and (3) the ferrotoroidic system, will be paid. Then, we will address the elementary excitations such as electromagnons, and application potentials of multiferroics. Finally, open questions and opportunities will be prospected.

Multiferroicity, The coupling between magnetic and polarization

The magnetic field response of the transport properties of novel materials and then the large magnetoresistance effects are of broad importance in both science and application. We report large transverse magnetoreistance (the magnetoresistant ratio ~ 1.3 × 105% in 2 K and 9 T field, and 4.3 × 106% in 0.4 K and 32 T field, without saturation) and field-induced metal-semiconductor-like transition, in NbSb2 single crystal. Magnetoresistance is significantly suppressed but the metal-semiconductor-like transition persists when the current is along the ac-plane. The sign reversal of the Hall resistivity and Seebeck coefficient in the field, plus the electronic structure reveal the coexistence of a small number of holes with very high mobility and a large number of electrons with low mobility. The large MR is attributed to the change of the Fermi surface induced by the magnetic field which is related to the Dirac-like point, in addition to orbital MR expected for high mobility metals.

/pdf/anisotropic-giant-magnetoresistance-in-nbsb2-44r23j7jaz.pdf

Anisotropic giant magnetoresistance in NbSb2.

Here, we present a systematic study of both the temperature and frequency dependence of the optical response in TaAs, a material that has recently been realized to host the Weyl semimetal state. Our study reveals that the optical conductivity of TaAs features a narrow Drude response alongside a conspicuous linear dependence on frequency. The weight of the Drude peak decreases upon cooling, following a T2 temperature dependence, in good agreement with theoretical predictions. Two linear components with distinct slopes dominate the low-temperature optical conductivity. A comparison between our experimental results and theoretical calculations suggests that the linear conductivity below ~230 cm–1 arises purely from interband transitions near the Weyl points, providing rich information about the Weyl semimetal state in TaAs.

Optical spectroscopy of the Weyl semimetal TaAs

We report two-dimensional quantum transport in SrMnBi${}_{2}$ single crystals. The linear energy dispersion leads to unusual nonsaturated linear magnetoresistance since all Dirac fermions occupy the lowest Landau level in the quantum limit. The transverse magnetoresistance exhibits a crossover at a critical field ${B}^{*}$ from semiclassical weak-field ${B}^{2}$ dependence to the high-field linear-field dependence. With an increase in temperature, the critical field ${B}^{*}$ increases and the temperature dependence of ${B}^{*}$ satisfies the quadratic behavior which is attributed to the Landau-level splitting of the linear energy dispersion. The effective magnetoresistant mobility ${\ensuremath{\mu}}_{\text{MR}}\ensuremath{\sim}3400$ cm${}^{2}$/V s is derived. Angular-dependent magnetoresistance and quantum oscillations suggest dominant two-dimensional (2D) Fermi surfaces. Our results illustrate the dominant 2D Dirac fermion states in SrMnBi${}_{2}$ and imply that bulk crystals with Bi square nets can be used to study low-dimensional electronic transport commonly found in 2D materials such as graphene.

Kefeng Wang

Papers

Multiferroicity: the coupling between magnetic and polarization orders

Multiferroicity, The coupling between magnetic and polarization

Anisotropic giant magnetoresistance in NbSb2.

Optical spectroscopy of the Weyl semimetal TaAs

Quantum Transport of Two-dimensional Dirac Fermions in SrMnBi(2)