Effects of oxygen vacancy location on the electronic structure and spin density of Co-doped rutile TiO2 dilute magnetic semiconductors

According to density functional theory （DFT） using the plane wave base and pseudo-potential, we investigate the effects of the specific location of oxygen vacancy （Vo） in a （Ti,Co）06 distorted octahedron on the spin density and magnetic properties of Co-doped rutile Ti02 dilute magnetic semiconductors. Our calculations suggest that the Vo location has a significant influence on the magnetic moment of individual Co cations. In the case where two Co atoms are separated far away from each other, when the Vo is located at the equatorial site of a Co-contained octahedron, the ground state of the two Co cations is d6（t3g↑, t23g ↓） without any magnetic moment. However, if the Vo is located at the apical site, these two Co sites have different ground states and magnetic moments. The spin densities are also observed to be modified by the exchange coupling between the Co cations and the location of Vo. Some positive spin polarization is induced around the adjacent O ions.     

Effects of oxygen vacancy location on the electronic structure and spin density of Co-doped rutile TiO₂ dilute magnetic semiconductors

According to density functional theory (DFT) using the plane wave base and pseudo-potential, we investigate the effects of the specific location of oxygen vacancy (VO) in a (Ti,Co)O 6 distorted octahedron on the spin density and magnetic properties of Co-doped rutile TiO2 dilute magnetic semiconductors. Our calculations suggest that the V O location has a significant influence on the magnetic moment of individual Co cations. In the case where two Co atoms are separated far away from each other, when the V O is located at the equatorial site of a Co-contained octahedron, the ground state of the two Co cations is d6 (t3 2g ↑, t 3 2g ↓) without any magnetic moment. However, if the V O is located at the apical site, these two Co sites have different ground states and magnetic moments. The spin densities are also observed to be modified by the exchange coupling between the Co cations and the location of V O . Some positive spin polarization is induced around the adjacent O ions.     

氧空位对Co掺杂TiO2稀磁半导体中杂质 分布和磁交换的影响

本文使用基于密度泛函理论的第一性原理方法研究了Co掺杂TiO₂稀磁半导体中氧空位对体系能量和磁性的影响. 通过对总能量的计算发现当引入氧空位后近邻杂质体系能量高于均匀掺杂体系, 同时氧空位易在Co近邻位置富集. 进而发现氧空位的存在及其占位可以影响Co离子间的磁交换, 近邻Co离子体系下氧空位的引入使Co离子间的铁磁耦合减弱; 非近邻Co离子体系下, 底面氧空位使Co离子间呈反铁磁耦合而顶点氧空位使Co离子间呈铁磁耦合. 总之, 氧空位的存在对Co掺杂TiO₂材料的能量及磁性都有较大影响.     

Direct N-alkylation of amines with alcohols using AlCl3 as a Lewis acid

A substitution reaction of amines with alcohols for N-alkylated amines has been developed using inexpensive AlCl_3 without any ligand or additive.Either aromatic or aliphatic amines and primary or secondary alcohols perform the AlCl_3-mediated reaction smoothly to afford various N-alkylated amines in satisfactory yields.     

An electron spin resonance study of Eu doping effect in La4/3Srs/3Mn2O7 single crystal

The effect of Eu3＋ ion doping in the La sites of single-crystal La4/3Srs/3Mn2O7 was investigated. Electron spin resonance （ESR） was applied to La4/3Sr5/3Mn2O7 and （Lao.8Euo.2）4/3Sr5/3Mn2O7 single crystals. A phase separation and phase transitions were observed from the ESR spectra data. Between 350 K and 300 K, both paramagnetic resonance （PMR） and anisotropic ferromagnetic resonance （FMR） lines were observed in the ab plane and the c axis direction, suggesting a coexistence of the paramagnetic （PM） phase and the ferromagnetic （FM） phase. The magnetization measurement reveals a spin-glass-like behavior in single-crystal （Lao.8Euo.2）4/3 Sr5/3Mn2O7 below the temperature of spin freezing Tf （- 29.5 K）.     

Robust univariate spline models for interpolating interval data

We consider spline interpolation problems where information about the approximated function is given by means of interval estimates for the function values over ranges of x-values instead of specific knots. We propose two robust univariate spline models formulated as convex semi-infinite optimization problems. We present simplified equivalent formulations of both models as finite explicit convex optimization problems for splines of degrees up to 3. This makes it possible to use existing convex optimization algorithms and software.     

Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called ‘scaled matrices’ associated with quadratic forms involved. The main result claims that if the condition number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer’s fixed point of a mapping) with a special structure. Thus, a broader question than the open “Question 11” in Hiriart-Urruty (SIAM Rev. 49, 225–273, 2007) is addressed in this paper.