NMR implementations of Gauss sums

I describe the use of NMR experiments which implement Gauss sums as a method for factoring numbers and discuss whether this approach can be computationally useful.     

Orbital and magnetic structure of quasi-1D cobaltites: Ab initio calculations and experiment

The magnetic properties of the orbitally degenerate quasi-one-dimensional cobaltites Sr_xBa_1−xCoO₃ are explained on the basis of a phase separation phenomenon. Noninteracting magnetic particles embedded in a nonferromagnetic matrix develop in the system. Details are given about the electronic and magnetic structure for x=0,0.2$x=0,0.2$ and 0.5. At x=0.5$x=0.5$, the geometry of the CoO₆ trigonally distorted octahedra changes by about 1–2%, but magnetic particles get 3 times bigger, compared to the parent compound, with the corresponding changes in the magnetic properties. The electronic structure of the Co⁴⁺ ion, however, stays roughly unchanged.     

Experimental and theoretical studies on the magnetic property of carbon-doped ZnO

Intrinsic room-temperature ferromagnetism was detected over n-type carbon-doped ZnO prepared through solid-state reaction. Our results of first-principle calculations based on density functional theory revealed that the CZn₄O₁₂ unit is the origin of magnetic moment in the carbon-doped ZnO system. The carbon component has a significant contribution to the net magnetic moment, and any oxygen vacancy present in CZn₄O₁₂ has a negative effect on the magnetic properties of the system. Moreover, both antiferromagnetic and ferromagnetic interactions are predicted among carbon atoms located at different CC distances. The result suggests that the defect density influenced by the distribution of carbon has a significant effect on the magnetic properties of the carbon-doped ZnO system.     

Theoretical study of the magnetic interaction of Cr-doped ZnO with and without vacancies

First-principles density-functional theory (DFT) calculations have been performed to study the magnetic properties of ZnO:Cr with and without vacancies. The results indicate that the doping of Cr in ZnO induces obvious spin polarization around the Fermi level and a total magnetic moment of 3.77μ_B. The ferromagnetism (FM) exchange interaction between Cr atoms is short-ranged and decreases with increasing Cr separation distance. It is suggested that the FM state is not stable with low concentration of Cr. The presence of O vacancies can make the half-metallic FM state of the system more stable, so that higher Curie temperature ferromagnetism may be expected. Nevertheless, Zn vacancies can result in the FM stability decreasing slightly. The calculated formation energy shows that V_Zn+Cr_Zn complex forms spontaneously under O-rich conditions. However, under Zn-rich conditions, the complex of V_O+Cr_Zn forms more easily. Thus, ZnO doped with Cr may exhibit a concentration of vacancies that influence the magnetic properties.     

Stabilization of ferromagnetism in Mn doped ZnO with C co-doping

We present a method for stabilizing ferromagnetism in Mn doped ZnO. We find that Mn doped ZnO show anti-ferromagnetic order in the absence of additional carriers. When Mn doped ZnO is co-doped with C atom at O sites ferromagnetic state gets stabilized. The C doping creates holes which leads to stabilization of ferromagnetic state via hole mediated double exchange mechanism.     

Structural, electronic and magnetic properties of Cr-doped (ZnTe)12 clusters

We have studied the energetics and magnetism in Cr-doped (ZnTe)₁₂ clusters by first principles density functional calculations. Total energy calculations suggest that it is energetically most favourable for Cr atoms to substitute at Zn sites. Both ferromagnetic and anti-ferromagnetic coupling between the Cr atoms exist depending on the Cr-Cr distance in the clusters. The magnetic exchange coupling between Cr atoms is short-ranged.     

The magnetic property of carbon-doped TiO2

Despite carbon and TiO₂ are nonmagnetic, we detected ferromagnetism at room temperature over samples of carbon-doped TiO₂. The materials were prepared by standard solid-state reaction and sintered either in an argon or nitrogen atmosphere. According to Raman results, the samples sintered in nitrogen showed lower D-bond (disordered) and G-bond (graphitic) concentration, plausibly a result of nitrogen incorporation into the carbon-doped TiO₂ materials. All the samples are ferromagnetic at room temperature. With increase of carbon concentration, there is decline of magnetic moment per carbon (in carbide form) due to antiferromagnetic interaction among the carbon atoms. Compared to the sample sintered in argon, the one sintered in nitrogen is lower in magnetic moment due to partial replacement of carbon atoms by nitrogen atoms. We found that the electrons-mediated mechanism is more suitable than the holes-mediated one for the explanation of ferromagnetism of the carbon-doped TiO₂ materials.     

Electronic topological transition and phase transition in rhodium and iridium based inter metallic compounds

Of the Rh₃Y, Rh₃La, Ir₃Y and Ir₃La inter-metallic compounds, the compound Rh₃Y exists in hexagonal structure, Ir₃Y and Ir₃La exist in rhombohedral structure, whereas the compound Rh₃La exists in both hexagonal and rhombohedral structures. Based on our tight binding-linear muffin tin orbital (TB-LMTO) study of other rhodium and iridium-based Rh₃X and Ir₃X (where X=Ti, Zr, Hf, V, Nb, Ta and Sc) inter-metallic compounds of AuCu₃ type cubic structure, an attempt is made to examine whether the compounds Rh₃Y, Rh₃La, Ir₃Y and Ir₃La will undergo a structural phase transition to cubic structure from their experimentally reported structures. From our study, it is observed that the compounds Rh₃Y and Rh₃La undergo a structural phase transition to cubic phase at 4.5 and 10.1 GPa, respectively, from their experimentally reported hexagonal and rhombohedral phases. Further it is predicted that both the compounds Ir₃Y and Ir₃La can exist in the cubic phase itself at ambient condition, in contrary to the experimental observation. From the band structure outputs that have been plotted for the compounds under compression, it is observed that the compounds Rh₃La, Ir₃Y and Ir₃La undergo the Lifshitz type of transition which may change the Fermi surface topology and hence the physical properties of these compounds.     

Fcc-hcp phase coexistence in Al at high pressures: Explanation in terms of density of states

The density of states (DOS) of fcc and hcp structures of Al has been calculated for normal and high pressures. It has been found that the DOS of both structures, near the Fermi level, is similar over a range of compressed volumes close to the fcc-hcp transition volume (V/V₀∼0.53). This similarity is the reason for the reported coexistence of fcc-hcp phases over a wide range of pressures near the fcc-hcp phase transition. All calculations have been performed using the FP-LAPW method with GGA.     

First‐principles study of the electronic structure and the associated magnetism of carbon‐doped TiO2

Based on first‐principles calculations, the electronic structure and the associated magnetism of carbon‐doped rutile TiO₂ have been investigated in the frame of the generalized gradient approximation (GGA). We find that the carbon substitutional oxygen ions can induce a magnetic moment of about 2.0µ_B/C, but the carbon substitutional titanium cannot provide any magnetism. Graphics of the spin density show that the magnetism is from the structure distortion around the carbon substitutional oxygen ions in the (110) plane of primitive TiO₂. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

First principle study on phase stability and electronic structure of YCu

The phase stability and electronic structure of YCu were studied by self-consistent full-potential linearized augmented plane wave method (FP_LAPW) on the basis of the density functional theory (DFT). The calculated equilibrium volumes are 41.963 and 173.21 Å³$173.21{\text{Å}}^3$ for B2 and B27 structures respectively, which are in good agreement with the experimental values. The total energy of the B27 phase is about 0.03 eV lower than that of the B2 phase. The formation energies are −1.173 and −1.204 eV$-1.204\text{eV}$ for B2 and B27 structures respectively. The density of state at the Fermi energy, N(EF)$N(E_F)$, is 1.08 states/eV$1.08\text{states}/\text{eV}$ for B2 phase and 0.92 states/eV$0.92\text{states}/\text{eV}$ for B27 phase, respectively. These results indicate that the B27 phase is the thermodynamic ground state equilibrium phase of YCu at low temperatures, as observed experimentally. However, our calculations also predict that a pressure-induced B27 to B2 phase transition exists in YCu.     

Pressure induced phase transition in ZnS

The phase transition of ZnS from the zincblende (ZB) structure to the rocksalt (RS) structure is investigated by the ab initio plane-wave pseudopotential density functional theory method. It is found that the pressures for transition from the ZB structure to the RS structure are 17.5 GPa from total energy-volume data and 15.4 GPa from equal enthalpies, consistent with the experimental data. From the high pressure elastic constants obtained, we find that the ZB structure ZnS is unstable when the applied pressure is larger than 17 GPa. Moreover, the dependence of the normalized primitive cell volume V/V₀ on pressure P can also be successfully obtained.     

Oxygen vacancy induced ferromagnetism in rutile TiO2–x

First‐principles LDA + U calculations have been performed to study the effects of oxygen vacancies (V_O) on the electronic structure and magnetism in undoped rutile TiO_2–x . Instead of treated as an adjustive parameter, the value of U was determined by constrained‐density‐functional calculations. The calculated electronic structure reveals that the valence electrons released by V_O would occupy mainly the neighboring Ti:3d orbital which then becomes spin‐polarized due to intra‐atomic exchange interaction, thereby giving rise to the half‐metallic ferromagnetism. The magnetization induced by V_O in rutile TiO_2–x is almost proportional to the V_O concentration (x) for x > 0.0625, and becomes 0 for x ≤ 0.0417. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Carrier-mediated ferromagnetism in N co-doped (Zn, Mn)O-based diluted magnetic semiconductors

Mn-doped ZnO is anti-ferromagnetic spin glass state, however, it becomes half-metallic ferromagnets upon hole doping. In this Letter we report a theoretical study of (Zn, Mn)O system codoped with N, and show that this codoping can change the ground state from anti-ferromagnetic to ferromagnetic. We have carried out the first-principles electronic structure calculations and report total energy to estimate whether the ferromagnetic state was stable or not. Our approach is based on the spin-polarized relativistic Korringa–Kohn–Rostoker (SPR–KKR) density functional theoretical (DFT) method, within the coherent potential approximation (CPA). Self-consistent electronic structure calculations were performed within the local density approximation, using the Vosko–Wilk–Nusair parameterization of the exchange-correlation energy functional. Our results for energy difference between ferromagnetic sate and spin glass state as well as their dependence on concentrations were presented and discussed.     

Structural phase transition of boron nitride compound

The full-potential band-structure scheme based on the linear combination of overlapping nonorthogonal local-orbital (FPLO) is used. The crystal potential and density are represented as a lattice sum of local overlapping nonspherical contributions. The energetic transitions of BN of zinc-blende and wurtzite structures are calculated using the band structure scheme. The energy gap at ambient pressure is found to be indirect for the two structures. The structural properties of two structures of BN are (obtained from the total energy calculations) and the total density of states are calculated. The phase transition parameter of BN is investigated. The ionicity character of BN has been calculated to test the validity of our recent models. The results are in reasonable agreement with experimental and other theoretical results.     

First-principles study of electronic structure, chemical bonding, and optical properties of cubic SrHfO3

Electronic structure and optical properties of SrHfO₃ are calculated using the full potential linearized augmented plane wave plus local orbitals method. The calculated equilibrium lattice is in reasonable agreement with the experimental data. From the density of states (DOS) as well as charge density studies, we find that the bonding between Sr and HfO₃ is mainly ionic and that HfO₃ entities bond covalently. The complex dielectric functions are calculated, which are in good agreement with the available experimental results. The effect of the spin-orbit coupling on the optical properties is also investigated and found to be quite small.     

Coupling of Magnetization and Structural Distortions in Multiferroic BiFeO3： an Ab Initio Density Functional Theory Study

The coupling between magnetism and structural distortions in BiFeO3 （BFO） is investigated using density functional theory by considering the spin-orbit effect. Computational results show that the resulting magnetization M is rotated by reversal of sense of rotation of the oxygen octahedra in the double cell. The resulting magnetization is determined by the antiferrodistortive （AFD） distortions and ferroelectric （FE） displacements. This work clarifies the previous view that magnetism is only coupled with, and determined by, FE displacements. The excellent ferroelectricity is attributed significantly to the anomaly of Born effective charge of Bi, which is caused by the stereochemically active long pair of Bi 6s.     

Magnetic phase diagram in a quasi-two-dimensional electron gas

Using spin density functional theory within the framework of the local spin density approximation with Perdew-Zunger type exchange-correlation energy, ferromagnetism in a quasi-two-dimensional electron gas (Q-2DEG) is studied. The electronic and magnetic structures of a thin film are calculated as a function of film thickness and electron density. Ferromagnetism in the Q-2DEG is found to appear at a higher electron density than in the three-dimensional electron gas. Unless a film is very thin, with decreasing electron density, a magnetic phase transition occurs from a spin-unpolarized fluid to a Wigner film with surface magnetism, in which the spin polarization localizes only in the neighborhood of surfaces. Further decreasing density induces another transition to a fully spin-polarized ferromagnetic Wigner film.     

First-Principles Studies on Properties of Boron-Related Impurities in c-BN

We investigate, by first-principles calculations, the pressure dependence of formation enthalpies and defective geometry and bulk modulus of boron-related impurities （VB, Cs, NB, and OB） with different charged states in cubic boron nitride （c-BN） using a supercell approach. It is found that the nitrogen atoms surrounding the defect relax inward in the case of CB, while the nitrogen atoms relax outward in the other cases. These boron-related impurities become much more stable and have larger concentration with increasing pressure. The impurity CB^＋1 is found to have the lowest formation enthalpy, make the material exhibit semiconductor characters and have the bulk modulus higher than ideal c-BN and than those in the cases of other impurities. Our results suggest that the hardness of c-BN may be strengthened when a carbon atom substitutes at a B site.     

A theoretical study of Fe adsorption along Bi-nanolines on the H/Si(0 0 1) surface

We have investigated the energetic stability and equilibrium geometry of the adsorption of transition metal Fe atoms near the self-organized Bi lines on hydrogen passivated Si(0 0 1) surface. Our total energy results show that there is an attractive interaction between Fe adatoms along the Bi-nanolines. For the energetically most stable configuration, the Fe adatoms are seven-fold coordinated, occupying the subsurface interstitial sites aside the Bi-nanolines. With increased coverage, Fe atoms are predicted to form two parallel lines, symmetrically on both sides of the Bi line. Within our local spin-density functional calculations, we find that for the most stable geometries the Fe adatoms exhibit an antiferromagnetic coupling.