A ferroelectric crystal exhibits a stable and switchable electrical polarization that is manifested in the form of cooperative atomic displacements. A ferromagnetic crystal exhibits a stable and switchable magnetization that arises through the quantum mechanical phenomenon of exchange. There are very few 'multiferroic' materials that exhibit both of these properties, but the 'magnetoelectric' coupling of magnetic and electrical properties is a more general and widespread phenomenon. Although work in this area can be traced back to pioneering research in the 1950s and 1960s, there has been a recent resurgence of interest driven by long-term technological aspirations.

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Multiferroic and magnetoelectric materials

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

The surprising discovery of high-temperature superconductivity in a material containing a strong magnet—iron—has led to thousands of publications. By placing all the data in context, it becomes clear what we know and where we are headed.

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High-temperature superconductivity in iron-based materials

Journal of Physics Condensed Matter: Preface

We have found a remarkable increase (up to 60%) of the dielectric constant with the onset of magnetic order at $42\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ in the metastable orthorhombic structures of $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_{3}$ and $\mathrm{Ho}\mathrm{Mn}{\mathrm{O}}_{3}$ that proves the existence of a strong magnetodielectric coupling in the compounds. Magnetic, dielectric, and thermodynamic properties show distinct anomalies at the onset of the incommensurate magnetic order and thermal hysteresis effects are observed around the lock-in transition temperature at which the incommensurate magnetic order locks into a temperature independent wave vector. The ${\mathrm{Mn}}^{3+}$ spins and ${\mathrm{Ho}}^{3+}$ moments both contribute to the magnetodielectric coupling. A large magnetodielectric effect was observed in $\mathrm{Ho}\mathrm{Mn}{\mathrm{O}}_{3}$ at low temperature where the dielectric constant can be tuned by an external magnetic field resulting in a decrease of up to 8% at $7\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. By comparing data for $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_{3}$ and $\mathrm{Ho}\mathrm{Mn}{\mathrm{O}}_{3}$ the contributions to the coupling between the dielectric response and Mn and Ho magnetic moments are separated.

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Large Magnetodielectric Effects in Orthorhombic HoMnO3 and YMnO3

The newly-discovered homologous series HgBa 2 Ca n −1 Cu n O 2 n +2+δ [Hg-12 ( n -1) n ] with n = 1, 2, 3,… possesses the highest superconducting transition-temperature ( T c ) to date. Unfortunately, because of the complexity of its compound chemistry, it remains a challenge to prepare samples with pure or nearly-pure Hg-12 ( n -1) n for both scientific and applied studies. In the present investigation, we report the successful development of a controlled vapor/solid reaction process for the synthesis of samples with up to 75 to 90% Hg-1212 and 65 to 75% Hg-1223 by volume, which display sharp superconducting transitions up to 135 K. Detailed steps of the process are presented and discussed.

Synthesis of the high-temperature superconductors HgBa2CaCu2O6+δ and HgBa2Ca2Cu3O8+δ

The newest homologous series of superconducting Fe-pnictides, LiFeAs (Li111) and NaFeAs (Na111) have been synthesized and investigated. Both crystallize with the layered tetragonal anti-PbFCl-type structure in P4 / nmm space group. Polycrystalline samples and single crystals of Li111 and Na111 display superconducting transitions at ∼18 K and 12–25 K, respectively. No magnetic order has been found in either compound, although a weak magnetic background is clearly in evidence. The origin of the carriers and the stoichiometric compositions of Li111 and Na111 were explored.

The synthesis and characterization of LiFeAs and NaFeAs

A review of high pressure studies on Fe-pnictide superconductors is given. The pressure effects on the magnetic and superconducting transitions are discussed for different classes of doped and undoped FeAs-compounds: ROFeAs (R = rare-earth), AeFe2As2 (Ae = Ca, Sr, Ba), and AFeAs (A = Li, Na). Pressure tends to decrease the magnetic transition temperature in the undoped or only slightly doped compounds. The superconducting Tc increases with low pressure for underdoped FeAs-pnictides, remains approximately constant for optimal doping, and decreases linearly in the overdoped range. The undoped LaOFeAs and AeFe2As2 become superconducting under pressure although non-hydrostatic pressure condition seems to play a role in CaFe2As2. The superconductivity in the (undoped) AFeAs is explained as a chemical pressure effect due to the volume contraction caused by the small ionic size of the A-elements. The binary FeSe shows the largest pressure coefficient of Tc in the Se-deficient superconducting phase.

High pressure studies on Fe-pnictide superconductors

Positron-annihilation lifetime and Doppler broadening energy spectra have been measured in high-temperature superconductors $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+\ensuremath{\delta}}$ as a function of temperature between 10 and 293 K. The observed positron lifetime and Doppler boradening $S$ parameter show an onset increase near the superconducting critical temperature (${T}_{c}=90$ K). This variation does not exist in a similar nonsuperconducting sample that contains a saturated oxygen vacancy content. These results give evidence that the oxygen vacancy and electronic structure change play an important role for high-${T}_{c}$ superconductivity.

C. W. Chu

Papers

Large Magnetodielectric Effects in Orthorhombic HoMnO3 and YMnO3

Synthesis of the high-temperature superconductors HgBa2CaCu2O6+δ and HgBa2Ca2Cu3O8+δ

The synthesis and characterization of LiFeAs and NaFeAs

High pressure studies on Fe-pnictide superconductors

Positron annihilation in the high-temperature superconductor YBa2Cu3O6+ delta.