Table of contents

We propose a mixed-space approach using the accurate force constants calculated by the direct approach in real space and the dipole–dipole interactions calculated by linear response theory in reciprocal space, making the accurate prediction of phonon frequencies for polar materials possible using the direct approach as well as linear response theory. As examples, by using the present approach, we predict the first-principles phonon properties of the polar materials α-Al₂O₃, MgO, c-SiC, and h-BN, which are in excellent agreement with available experimental data.

FeSe is employed as reference material to elucidate the observed high T_c superconducting behaviour of the related layered iron pnictides. The structural and ensuing semimetallic band structural forms are here rather unusual, with the resulting ground state details extremely sensitive to the precise shape of the Fe–X coordination unit. The superconductivity is presented as coming from a combination of resonant valence bond and excitonic insulator physics, and incorporating boson–fermion degeneracy. Although sourced in a very different fashion, the latter leads to some similarities with the high temperature superconducting (HTSC) cuprates. The excitonic insulator behaviour sees spin density wave, charge density wave/periodic structural distortion, and superconductive instabilities all vie for ground state status. The conflict leads to a very sensitive and complex set of properties, frequently mirroring HTSC cuprate behaviour. The delicate balance between ground states is made particularly difficult to unravel by the micro-inhomogeneity of structural form which it can engender. It is pointed out that several other notable superconductors, layered in form, semimetallic with indirect overlap and possessing homopolar bonding, would look to fall into the same general category, β-ZrNCl and MgB₂ and the high pressure forms of several elements, like sulfur, phosphorus, lithium and calcium, being cases in point.

The advent of high transverse field muon spin rotation (TF-μSR) has led to recent μSR investigations of the magnetic field response of cuprates above the superconducting transition temperature T_c. Here the results of such experiments on hole-doped cuprates are reviewed. Although these investigations are currently ongoing, it is clear that the effects of high field on the internal magnetic field distribution of these materials is dependent upon competition between superconductivity and magnetism. In La_{2 − x}Sr_xCuO₄ the response to the external field above T_c is dominated by heterogeneous spin magnetism. However, the magnetism that dominates the observed inhomogeneous line broadening below x ∼ 0.19 is overwhelmed by the emergence of a completely different kind of magnetism in the heavily overdoped regime. The origin of the magnetism above x ∼ 0.19 is probably related to intrinsic disorder, but the systematic evolution of the magnetism with doping changes in the doping range beyond the superconducting 'dome'. In contrast, the width of the internal field distribution of underdoped Y Ba₂Cu₃O_y above T_c is observed to track T_c and the density of superconducting carriers. This observation suggests that the magnetic response above T_c is not dominated by electronic moments, but rather inhomogeneous fluctuating superconductivity. The spatially inhomogeneous response of Y Ba₂Cu₃O_y to the applied field may be a means of minimizing energy, rather than being caused by intrinsic disorder.

In this review, we present a summary of experimental studies of magnetism in Fe-based superconductors. The doping dependent phase diagram shows strong similarities to the generic phase diagram of the cuprates. Parent compounds exhibit magnetic order together with a structural phase transition, both of which are progressively suppressed with doping, allowing superconductivity to emerge. The stripe-like spin arrangement of Fe moments in the magnetically ordered state shows identical in-plane structure for the RFeAsO (R = rare earth) and AFe₂As₂ (A = Sr, Ca, Ba, Eu and K) parent compounds, notably different than the spin configuration of the cuprates. Interestingly, Fe_{1 + y}Te orders with a different spin order despite having very similar Fermi surface topology. Studies of the spin dynamics of the parent compounds show that the interactions are best characterized as anisotropic three-dimensional interactions. Despite the room temperature tetragonal structure, analysis of the low temperature spin waves under the assumption of a Heisenberg Hamiltonian indicates strong in-plane anisotropy with a significant next-nearest-neighbor interaction. For the superconducting state, a resonance, localized in both wavevector and energy, is observed in the spin excitation spectrum as for the cuprates. This resonance is observed at a wavevector compatible with a Fermi surface nesting instability independent of the magnetic ordering of the relevant parent compound. The resonance energy (E_r) scales with the superconducting transition temperature (T_C) as E_r ∼ 4.9k_BT_C, which is consistent with the canonical value of ∼ 5k_BT_C observed for the cuprates. Moreover, the relationship between the resonance energy and the superconducting gap, Δ, is similar to that observed for many unconventional superconductors (E_r/2Δ ∼ 0.64).

We report measurements of magnetoresistance in single-layer graphene as a function of gate voltage (carrier density) at 250 mK. By examining signatures of weak localization (WL) and universal conductance fluctuations (UCF), we find a consistent picture of phase coherence loss due to electron–electron interactions. The gate dependence of the elastic scattering terms suggests that the effect of trigonal warping, i.e. the nonlinearity of the dispersion curves, may be strong at high carrier densities, while intra-valley scattering may dominate close to the Dirac point. In addition, a decrease in UCF amplitude with decreasing carrier density can be explained by a corresponding loss of phase coherence.

The crystal structure of the ferroelectric Cd₂Nb₂O₇ (CNO) has been determined down to T = 98 K using synchrotron radiation. Low temperature structure refinement is conducted in space group Ima 2, starting from the crystal structure previously determined by ab initio methods. Symmetry mode analysis indicates that the primary order parameter is of T_2u symmetry with the largest displacement amplitude at the Nb(2) position. The associated phase transition temperature is obtained as T_c = 194 K by extrapolation. Long exposure x-ray diffraction scans confirm the presence of anisotropic diffuse scattering intensity in layers normal to ⟨110⟩_cub over the entire temperature range. The diffuse scattering intensity significantly decays below T = 198 K. The refined thermal parameters indicate that the disorder responsible for the diffuse scattering is primarily associated with Nb.

We determine the phase diagram of the phase field crystal model in three dimensions by using numerical free energy minimization methods. Previously published results, based on single mode approximations, have indicated that in addition to the uniform (liquid) phase, there would be regions of stability of body-centered cubic, hexagonal and stripe phases. We find that in addition to these, there are also regions of stability of face-centered cubic and hexagonal close packed structures in this model.

The first-principles spin polarization method is used to investigate the magnetic properties of graphite boron nitride (g-BN) sheet induced by Fe doping. We find that a nitrogen or boron atom substituted by Fe can induce a magnetic moment. From standard Mulliken population analysis, we also find that the magnetic moment is mainly dominated by Fe 3d states. Using Heisenberg exchange coupling theory, we study the exchange coupling mechanisms by constructing two-Fe centers in g-BN. The results show the presence of relatively strong exchange coupling for two-Fe substituted two-B atoms and the coupling is ferromagnetic. For the case of two-Fe substituted two-N atoms, the coupling is antiferromagnetic and the exchange coupling is very weak. The paper enriches recent molecular magnetic investigations.

A map of a quantum Heisenberg spin chain into an extended Bose–Hubbard-like Hamiltonian is set up. Within this framework, the spectrum of the corresponding Bose–Hubbard chain, on a periodic one-dimensional lattice containing two, four, and six bosons shows interesting detailed band structures. These fine structures are studied using numerical diagonalization, and nondegenerate and degenerate perturbation theory. We also focus our attention on the effect of the anisotropy and Heisenberg exchange energy on the detailed band structures. The signature of the quantum breather is also set up by the square of the amplitudes of the corresponding eigenvectors in real space.

In order to clarify the effect of hydrogen vacancies on the stability and structure of sodium alanate, NaAlH₄, with and without Ti substitution for Al, first-principles electronic structure calculations were carried out. The relative thermodynamic stability of the Ti dopant and the H vacancy in a supercell was obtained. For the Ti-doped Na₁₆Al₁₆H₆₄ supercell calculations, it was preferable to perform the initial substitution with a cluster of TiAlH_n. We showed that substitution of a Ti atom for an Al atom in Na₁₆Al₁₅TiH₆₃ with H vacancies increases the stability of the structure. A density of states analysis revealed weakening of the bond strength corresponding to increase in the bond length.

To investigate an amorphous structure of Ge₂Sb₂Te₅ that satisfies the 8-N rule (so-called 'ideal glass'), we perform alternative melt-quench simulations on Si₂As₂Se₅ and replace atoms in the final structure with Ge–Sb–Te. The resulting structures have salient features of the 8-N rule such as the tetrahedral configuration for all Ge atoms and the localized Te lone pairs at the valence top. In addition, the average Ge–Te and Sb–Te distances are in good agreement with experiment. The energetic stability of the ideal glass supports the existence of this amorphous structure that is distinct from the melt-quenched glass. From the analysis of electronic structures and optical dielectric constants, it is concluded that the electronic character of the melt-quenched amorphous Ge₂Sb₂Te₅ lies in between the resonant p-bonding of the crystalline phase and the covalent bonding of the ideal glass.

Experiments carried out on the intermetallic superconducting material MgB₂ have shown anomalous magnetic field dependence of upper critical field, small angle neutron scattering form factor, specific heat, critical current etc. Similarly, scanning tunnelling microscopy (STM) experiments on vortex structures have shown unusually large vortex core size and two different magnetic and spatial field scales. Also, whereas the specific heat measurements and isotope shift experiments have shown Bardeen–Cooper–Schrieffer-like (BCS-like) behaviour, the temperature dependences of the penetration depth experiments have shown non-BCS-like behaviour. These anomalous behaviours have been attributed to the multiband superconductivity of this material and the nature of the local spatial behaviour of the magnetic induction and the order parameter components having two length scales. We report an analytical investigation of the effect of two length scales on the temperature and the applied magnetic field dependence of several properties of MgB₂, such as, the penetration depth, single vortex and vortex lattice structure, vortex core radius, reversible magnetization, critical current, small angle neutron scattering form factor and the shear modulus of the vortex lattice within the framework of two-order parameter Ginzburg–Landau theory. We solve the corresponding nonlinear Ginzburg–Landau equations numerically exactly using an iterative method for arbitrary applied field H_c1 < H < H_c2, the Ginzburg–Landau parameter and vortex lattice symmetry. This enables us to compute the local spatial behaviour of the magnetic induction and the order parameters accurately for arbitrary applied field and a wide range of temperature. Comparison of the analytical results with experiments on MgB₂ gives very good agreement.

In this work we present a detailed computational study of the structural and elastic properties of cubic Al_xGa_yIn_{1 − x − y}N alloys in the framework of the Keating valence force field model, for which we perform an accurate parametrization based on state-of-the-art density functional theory calculations. When analysing structural properties, we focus on the concentration dependence of the lattice constant, as well as on the distribution of the nearest and the next nearest neighbour distances. Where possible, we compare our results with experiment and calculations performed within other computational schemes. We also present a detailed study of the elastic constants for Al_xGa_yIn_{1 − x − y}N alloy over the whole concentration range. Moreover, we include the accurate quadratic parametrization for the dependence of the alloy elastic constants on the composition. Finally, we examine the sensitivity of the obtained results to computational procedures commonly employed in the Keating model for studies of alloys.

We present the spin dynamics of isolated donor electrons in phosphorus-doped silicon at low temperature and in a high magnetic field. We performed a steady-state electron spin resonance (ESR) on the sample with a dopant concentration of 6.5 × 10¹⁶ cm ^{− 3} in a high field of 2.87 T (80 GHz) and at temperatures from 48 down to 1.8 K. As the temperature decreases below 16 K, the resonance spectral line changes from the usual derivative form characteristic of absorptions. Very long spin–lattice relaxation time T₁ at low temperature gives rise to rapid passage effects and results in a dramatic change in the line shape and intensity as a function of temperature. We show that the numerical analysis based on the passage effects well explains the observed spectral changes with temperature. The spin–lattice relaxation time T₁ is derived by numerical fit to the experimental data. We discuss the dynamic nuclear polarization of ³¹P nuclear spins which shows up as asymmetric intensities of the hyperfine-split ESR resonance lines.

Neutron diffraction, susceptibility and magnetization measurements (for R = Er only) were performed on iron borates RFe₃(BO₃)₄ (R = Pr, Er) to investigate details of the crystallographic structure, the low temperature magnetic structures and transitions and to study the role of the rare earth anisotropy. PrFe₃(BO₃)₄, which crystallizes in the spacegroup R32, becomes antiferromagnetic at T_N = 32 K, with τ = [0 0 3/2], while ErFe₃(BO₃)₄, which keeps the P3₁21 symmetry over the whole studied temperature range 1.5 K < T < 520 K, becomes antiferromagnetic below T_N = 40 K, with τ = [0 0 1/2]. Both magnetic propagation vectors lead to a doubling of the crystallographic unit cell in the c-direction. Due to the strong polarization of the Fe-sublattice, the magnetic ordering of the rare earth sublattices appears simultaneously at T_N. The moment directions are determined by the rare earth anisotropy: easy-axis along c for PrFe₃(BO₃)₄ and easy-plane a–b for ErFe₃(BO₃)₄. There are no spin reorientations present in either of the two compounds but there is the appearance below 10 K of a minority phase in the Er-compound adopting a 120° arrangement of the Er-moments.

We have investigated the structural, electronic, and magnetic properties of Mn₃Cu_{1 − x}Ge_xN (x = 0, 0.125, 0.25) using first-principles density-functional theory within the generalized gradient approximation (GGA) + U schemes. The crystal structure of the compounds is a tetragonal crystal for x = 0 while it is a cubic crystal for x = 0.125, 0.25. The unit cell volume increases as the Ge doping increases. Our GGA + U calculations give a metallic ground state from x = 0 to 0.25 in agreement with experiments. The magnetic structure for x = 0 is found to be the ferromagnetic state while for x = 0.125, 0.25 it is the Γ^5g-type antiferromagnetic state. From the density of states (DOS), the coupling between Ge 4p and Mn 3d is the main reason for magnetic transition in Mn₃Cu_{1 − x}Ge_xN.

Polarized neutron diffraction has been used to study the magnetization distribution in two isostructural inter-metallic compounds NiMnSb and PdMnSb. Band structure calculations have predicted that whereas the former should be a half metallic ferromagnet the latter should not. Measurements made at 5 K on different crystals show that disorder can occur between the A (Mn) and B (Sb) sites in both alloys and in the case of NiMnSb, by partial occupation of the void D sites by Ni. In all the crystals most of the moment was found on the Mn atoms in the A sites; in NiMnSb it is due to spin only but in PdMnSb there is evidence for a significant orbital contribution (g = 2.22). The magnitudes of the moments associated with each atom are in fair agreement with the theoretical values; however, the distribution of magnetization around the Mn atoms is found to have nearly spherical symmetry (40% e_g) rather than the 50% e_g character expected from the band structure.

Epitaxial orthorhombic La_0.5Lu_0.5Ni_0.5Mn_0.5O₃ (LLNMO) thin films deposited on Nb:SrTiO₃ (NSTO) substrates are prepared by pulsed laser deposition and their ferroelectricity and magnetism are investigated using various techniques. It is revealed that the as-prepared thin films are ferromagnetic (FM) insulators. The FM transition occurring at ∼ 125 K is evidenced by the well defined hysteresis at low temperature, with a saturated magnetic moment as high as 1.8 µ_B/f.u. at ∼ 5 K. A reversible ferroelectric polarization of ∼ 0.2 µC cm ^{− 2} below ∼ 140 K is also observed. The magnetism can be understood by the FM ordering associated with a partially ordered major Ni^{2 +} –Mn^{4 +} plus minor Mn^{3 +} –Ni^{3 +} configuration, while the ferroelectricity is argued to originate from the A-site disordering of La^{3 +} and Lu^{3 +} .