Many-body Green's function theory for thin ferromagnetic anisotropic Heisenberg films: treatment of the exchange anisotropy

The many-body Green's function theory developed in our previous work for treating the reorientation of the magnetization of thin ferromagnetic films is extended to include the exchange anisotropy. This leads to additional momentum dependencies which require some non-trivial changes in the formalism. The theory is developed for arbitrary spin values S and for multilayers. The effects of the exchange anisotropy and the single-ion anisotropy, which was treated in our earlier work, on the magnetic properties of thin ferromagnetic films are compared. Received 31 October 2002 Published online 7 May 2003     

Many-body Green's function theory for the magnetic reorientation of thin ferromagnetic films

The field-induced reorientation of the magnetization of ferromagnetic films is treated within the framework of many-body Green's function theory by considering all components of the magnetization. We present a new method for the calculation of expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green's functions. This formulation allows a straightforward extension of the monolayer case to thin films with many layers and for arbitrary spin and moreover provides a practicable procedure for numerical computation. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. We utilize the Tyablikov (RPA) decoupling for the exchange interaction terms and the Anderson-Callen decoupling for the anisotropy terms. The dipole coupling is treated in the mean-field approximation, a procedure which we demonstrate to be a sufficiently good approximation for realistic coupling strengths. We apply the new method to monolayers with spin and to multilayer systems with S=1. We compare some of our results to those where mean-field theory (MFT) is applied to all interactions, pointing out some significant differences. Received 19 June 2000 and Received in final form 2 August 2000     

A diatomic network model for electronic states of bulk,surface and thin films

This paper reports our investigations on an exactly solvable network model of solids. General properties of diatomic lattices, in particular the dispersion relations for the energy levels, the structure of the energy bands and the density of states for bulk, surface and thin films are compared with the corresponding properties of the monatomic lattices which we have previously reported. For a thin film of finite thickness, we present a simple but informative method of analyzing Van Hove singularities in the density of states. Effects due to the inclusion of second neighbor interactions are also studied. Calculations are exact and the method has apparent advantages over other methods of discussing similar problems.     

On the application of a single‐crystal κ‐diffractometer and a CCD area detector for studies of thin films

A multipurpose six‐axis κ‐diffractometer, together with the brilliance of the ESRF light source and a CCD area detector, has been explored for studying epitaxial relations and crystallinity in thin film systems. The geometrical flexibility of the six‐axis goniometer allows measurement of a large volume in reciprocal space, providing an in‐depth understanding of sample crystal relationships. By a set of examples of LaAlO₃ thin films deposited by the atomic layer deposition technique, the possibilities of the set‐up are presented. A fast panoramic scan provides determination of the crystal orientation matrices, prior to more thorough inspection of single Bragg nodes. Such information, in addition to a broadening analysis of families of single reflections, is shown to correlate well with the crystallinity, crystallite size, strain and epitaxial relationships in the thin films. The proposed set‐up offers fast and easy sample mounting and alignment, along with crucial information on key features of the thin film structures.     

Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory

ABSTRACT

A new method is proposed for a fast evaluation of high-dimensional integrals of potential energy surfaces (PES) that arise in many areas of quantum dynamics. It decomposes a PES into a canonical low-rank tensor format, reducing its integral into a relatively short sum of products of low-dimensional integrals. The decomposition is achieved by the alternating least squares (ALS) algorithm, requiring only a small number of single-point energy evaluations. Therefore, it eradicates a force-constant evaluation as the hotspot of many quantum dynamics simulations and also possibly lifts the curse of dimensionality. This general method is applied to the anharmonic vibrational zero-point and transition energy calculations of molecules using the second-order diagrammatic vibrational many-body Green's function (XVH2) theory with a harmonic-approximation reference. In this application, high dimensional PES and Green's functions are both subjected to a low-rank decomposition. Evaluating the molecular integrals over a low-rank PES and Green's functions as sums of low-dimensional integrals using the Gauss–Hermite quadrature, this canonical-tensor-decomposition-based XVH2 (CT-XVH2) achieves an accuracy of 0.1 cm^?1 or higher and nearly an order of magnitude speedup as compared with the original algorithm using force constants for water and formaldehyde.     

Theoretic 3-D study of the high-frequency magnetic moment dynamics in thin ferromagnetic films with in-plane uniaxial anisotropy by considering eddy-current generation

In the present paper, theoretic investigations of polarisation vector precession trajectories represented by a macro spin in ferromagnetic films with in-plane uniaxial anisotropy were realised. For this purpose, the Landau–Lifschitz–Gilbert differential equation (LLG) in combination with the Maxwell equations were solved for three dimensions by considering a linear progression of the magnetisation or polarisation with an external field. The frequency and time dependent polarisation trajectories illustrate how a magnetic moment precesses if effective damping and eddy-currents impacts its motion. For computation, typical parameter values like the saturation polarisation J_s=μ₀·M_s=1.4 T and in-plane uniaxial anisotropy μ₀·H_u=4.5 mT were employed. The main focus of simulation was on the variation of the effective damping parameter α_eff between 0.01 and 0.05 and ferromagnetic film thickness t_m between 200 nm and 1200 nm. The frequency-dependent calculations were carried out between 50 MHz and 6 GHz. The time-dependent simulations were done for a duration between 5 and 30 ns.     

Raman micro‐spectroscopy for quantitative thickness measurement of nanometer thin polymer films

The sensitivity of far‐field Raman micro‐spectroscopy was investigated to determine quantitatively the actual thickness of organic thin films. It is shown that the thickness of organic films can be quantitatively determined down to 3 nm with an error margin of 20% and down to 1.5 nm with an error margin of 100%. Raman imaging of thin‐film surfaces with a far‐field optical microscope establishes the distribution of a polymer with a lateral resolution of ~400 nm and the homogeneity of the film. Raman images are presented for spin‐coated thin films of polysulfone (PSU) with average thicknesses between 3 and 50 nm. In films with an average thickness of 43 nm, the variation in thickness was around 5% for PSU. In films with an average thickness of 3 nm for PSU, the detected thickness variation was 100%. Raman imaging was performed in minutes for a surface area of 900 µm². The results illustrate the ability of far‐field Raman microscopy as a sensitive method to quantitatively determine the thickness of thin films down to the nanometer range. Copyright © 2015 John Wiley & Sons, Ltd.     

Thermal conductivity of thermoelectric Al‐substituted ZnO thin films

ZnO:Al thin films with a low electrical resistivity were grown by magnetron sputtering on sapphire substrates. The cross‐plane thermal conductivity (κ = 4.5 ± 1.3 W/mK) at room temperature is almost one order of magnitude lower than for bulk materials. The thermoelectric figure of merit ZT at elevated temperatures was estimated from in‐plane power factor and the cross‐plane thermal conductivity at room temperature. It is expected that the thermal conductivity drops with increasing temperature and is lower in‐plane than cross‐plane. Consequently, the thin film ZT is at least three times higher than for bulk samples at intermediate temperatures. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

低维纳米材料量子热输运与自旋热电性质 ——非平衡格林函数方法的应用

低维材料不断涌现的新奇性质吸引着科学研究者的目光. 除了电子的量子输运行为之外, 人们也陆续发现和确认了热输运中显著的量子行为, 如 热导低温量子化、声子子带、尺寸效应、瓶颈效应等. 这些小尺度体系的热输运性质可以很好地用非平衡格林函数来描述. 本文首先介绍了量子热输运的特性、声子非平衡格林函数方法及其在低维纳米材料中的研究进展; 其次回顾了近年来在 一系列低维材料中发现的热-自旋输运现象. 这些自旋热学现象展现了全新的热电转换机制, 有助于设计新型的热电转换器件, 同时也给出了用热产生自旋流的新途径; 最后介绍了线性响应理论以及在此理论框架下结合声子、电子非平衡格林函数方法进行的一些有益的探索. 量子热输运的研究对热效应基础研究以及声子学器件、能量转换器件的发展有着不可替代的重要作用.     

Calculations of ferromagnetic surface dynamics using the Green's functions theory and matching procedure

A Heisenberg model is employed to study the spin fluctuation dynamics on a (001) ferromagnetic surface using a new theoretical formalism. The solution of the full magnetic problem arising from the absence of magnetic translation symmetry in one dimension due to the presence of a magnetic surface is presented. The calculations are described using simultaneously a closed form of the spin-wave Green's function and the matching procedure in the random-phase approximation. Analytic expressions for the Green's functions are also derived in a low-temperature spin-wave approximation. The theoretical approach determines the bulk and evanescent spin fluctuation fields in the two dimensional plane normal to the surface. The results are used to calculate the localised modes of magnons associated with the surface. Numerical examples of the modes are given and they are found to exhibit various effects due to the interplay between the bulk and surface modes. It is shown that there may be surface spin-waves that decay in amplitude with distance into the bulk domain. Also the bulk spin fluctuations field as well as the magnons localised at the surface depend on the nature of the bulk-surface coupling exchange. The unstable surface magnetic configurations are illustrated and discussed. The results derived from the dynamic correlation functions between a pair of spin operators at any two sites are employed to evaluate the spin deviation in the ferromagnet due to localised surface modes obtained by the matching procedure as a function of temperature. Received 21 April 2002 / Received in final form 25 October 2002 Published online 14 March 2003     

Spin-wave resonance as a tool for probing surface anisotropies in ferromagnetic thin films: Application to the study of (Ga,Mn)As

In this paper we provide a concise review of present achievements in the study of spin-wave resonance (SWR) in ferromagnetic semiconductor (Ga,Mn)As thin films. The theoretical treatment of the experimental SWR data obtained so far concentrates specifically on the spherical surface pinning (SSP) model, in which the surface spin pinning energy is expressed by configuration angles (the out-of-plane polar angle $?$ and the in-plane azimuthal angle $\phi$) defining the direction of surface magnetization in the considered thin film. The model is based on a series expansion of the surface spin pinning energy; the terms in the series represent the respective pinning contributions from the cubic anisotropy as well as uniaxial anisotropies. Comparing theory with the reported experimental studies of SWR in thin films of the ferromagnetic semiconductor (Ga,Mn)As, we find that besides the first-order cubic anisotropy, higher-order cubic anisotropies (in the second and third orders) as well as uniaxial anisotropies (perpendicular in the first and second orders, and in-plane diagonal) occur on the surface of this material. We use our results to plot a 3D hypersurface visualizing the angle dependence of the surface spin pinning energy in configurational space. An advantage of this spatial representation is that the shape of the obtained hypersurface allows us to predict new SWR effects that have not yet been observed experimentally. Prospective experimental studies for the verification of this surface pinning model would bring new insight into the surface anisotropy phenomenon in (Ga,Mn)As thin films and help complete the knowledge in this field, the shortage of which in the literature available to date is becoming bothersome.     

Mapping of the electronic work function anisotropy of RF sputtered molybdenum thin film electrodes for piezoelectric devices

Amplitude modulated Kelvin probe force microscopy was performed on molybdenum (Mo)-thin films deposited on Si(001) substrates by RF magnetron sputtering. Evolution of film microstructure from amorphous to crystalline was observed with increasing RF power from 25 W to 200 W. Spatial mapping of work function across the film surface revealed that the Mo-thin film deposited at 200 W possesses an average work function ~4.94 ± 0.06 eV while higher values were observed at lower RF powers. The genesis of distinct periodic changes in work function is attributed to the formation of the surface dipole layer associated with the adsorbates of different polarities (O₂⁻/OH⁻ or H⁺). A phenomenological model is also presented to elucidate their effect.     

Densification of sol–gel silica thin films induced by hard X‐rays generated by synchrotron radiation

In this article the effects induced by exposure of sol–gel thin films to hard X‐rays have been studied. Thin films of silica and hybrid organic–inorganic silica have been prepared via dip‐coating and the materials were exposed immediately after preparation to an intense source of light of several keV generated by a synchrotron source. The samples were exposed to increasing doses and the effects of the radiation have been evaluated by Fourier transform infrared spectroscopy, spectroscopic ellipsometry and atomic force microscopy. The X‐ray beam induces a significant densification on the silica films without producing any degradation such as cracks, flaws or delamination at the interface. The densification is accompanied by a decrease in thickness and an increase in refractive index both in the pure silica and in the hybrid films. The effect on the hybrid material is to induce densification through reaction of silanol groups but also removal of the organic groups, which are covalently bonded to silicon via Si—C bonds. At the highest exposure dose the removal of the organic groups is complete and the film becomes pure silica. Hard X‐rays can be used as an efficient and direct writing tool to pattern coating layers of different types of compositions.     

Interference effects in the UV(VUV)‐excited luminescence spectroscopy of thin dielectric films

The problem of exciting UV and VUV light interference affecting experimental photoluminescence excitation spectra is analysed for the case of thin transparent films containing arbitrarily distributed emission centres. A numerical technique and supplied software aimed at modelling the phenomenon and correcting the distorted spectra are proposed. Successful restoration results of the experimental synchrotron data for ion‐implanted silica films show that the suggested method has high potential.     

Metal‐assisted chemical etching of CIGS thin films for grain size analysis

Grain size of the CIGS absorber is an important monitoring factor in the CIGS solar cell manufacturing. Electron backscatter diffraction (EBSD) analysis is commonly used to perform CIGS grain size analysis in the scanning electron microscope (SEM). Although direct quantification on SEM image using the average grain intercept (AGI) method is faster and simpler than EBSD, it is hardly applicable on CIGS thin films. The challenge is that, not like polycrystalline silicon, to define grain boundaries by selective chemical etching is not easily realizable for the multi‐component CIGS alloy. In this Letter, we present direct quantification of CIGS thin film grain size using the AGI method by developing metal‐assisted wet chemical etching process to define CIGS grain boundaries. The calculated value is similar to EBSD result.

The CIGS thin film surface morphology before and after the wet chemical etching. Grain boundaries are well defined after the processing.     

Downward self‐polarization of lead‐free (K0.5Na0.5)(Mn0.005Nb0.995)O3 ferroelectric thin films on Nb:SrTiO3 substrate

Spontaneously appearing macroscopic polarization (self‐polarization) in ferroelectrics without an electrode or an external electric field would enable the freedom to design many ferroelectric heterostructures and devices. The (K_0.5Na_0.5)(Mn_0.005Nb_0.995)O₃ (KNMN) thin film was grown on Nb:SrTiO₃ single‐crystal substrate and the resultant self‐polarization behavior due to strain relaxation was investigated. The lattice mismatch and difference in TEC between the KNMN thin film and the Nb:SrTiO₃ substrate creates a compressive strain. The compressive strain gradient may be the main cause for the observed downward self‐polarization. The downward self‐polarization of the KNMN thin film can be explained by the strong inhomogeneous compressive strain caused by strain relaxation. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

MOKE hysteresis loop method of determining the anisotropy constants of ferromagnetic thin films: fe on GaAs(1 0 0) with overlayers of Au and Cr

This paper presents a quantitative method used to determine the magnetocrystalline anisotropy constants of thin magnetic films from normalized magnetization data measured on a magneto-optic Kerr effect (MOKE) magnetometer. The method is based on a total magnetic energy density model, and incorporates higher order effects in the detected signal. By way of illustration, the method is used to determine the magnetocrystalline anisotropy constants of epitaxial thin Fe films on GaAs substrates, which have different overlayers. It is shown that a Cr overlayer on a 30 ML thick Fe film reduces the uniaxial contribution to the magnetic anisotropy compared with an Au overlayer.     

Influence of polarity inversion on the electrical properties of Ga‐doped ZnO thin films

This study investigates how polarity inversion influences the relationship between the electrical properties of heavily Ga‐doped ZnO (GZO) films deposited by RF magnetron sputtering and their thickness. The electrical properties observed in very thin films are correlated with a change of polarity from O‐polar to Zn‐polar face upon increasing the film thickness based on results of valence band spectra measured by X‐ray photoelectron spectroscopy. It is found that the electrical properties of very thin GZO films deposited on Zn‐polar ZnO templates are significantly improved compared to those deposited on O‐polar face. A low resistivity of 2.62 × 10^–4 Ω cm, high Hall mobility of 26.9 cm²/V s, and high carrier concentration of 8.87 × 10²⁰ cm^–3 being achieved with 30 nm‐thick GZO films using Zn‐polar ZnO templates on a glass substrate. In contrast, the resistivity of 30 nm‐thick GZO films on bare glass that shows more likely O‐polar is very poor about 1.44 × 10^–3 Ω cm with mobility and carrier concentration are only 11.9 cm²/V s and 3.64 × 10²⁰ cm^–3, respectively. It is therefore proposed that polarity inversion plays an important role in determining the electrical properties of extremely thin GZO films. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Tuning the phase transition of ZnO thin films through lithography: an integrated bottom‐up and top‐down processing

An innovative approach towards the physico‐chemical tailoring of zinc oxide thin films is reported. The films have been deposited by liquid phase using the sol–gel method and then exposed to hard X‐rays, provided by a synchrotron storage ring, for lithography. The use of surfactant and chelating agents in the sol allows easy‐to‐pattern films made by an organic–inorganic matrix to be deposited. The exposure to hard X‐rays strongly affects the nucleation and growth of crystalline ZnO, triggering the formation of two intermediate phases before obtaining a wurtzite‐like structure. At the same time, X‐ray lithography allows for a fast patterning of the coatings enabling microfabrication for sensing and arrays technology.     

Sol-gel technique for the generation of europium-doped mesoporous and dense thin films: A luminescent study

In this paper, a series of europium-activated titania mesoporous and dense thin films were prepared by sol-gel process. Structural characterizations show that high europium ion loadings can be incorporated into titanium dioxide walls without destroying the mesoporous arrangement. However, high europium content locks the titanium dioxide crystallization process. Upon 10% europium ions loading, mesoporous thin films are mainly amorphous, whereas dense ones are still partially crystallized. Eu³⁺ ion luminescence has been investigated by exciting through the semiconductor host lattice. Emission features reveal that europium ions adopt similar environments (nanocrystalline and glassy-like ones) in both dense and mesoporous thin films. Fluctuations of europium emission under continuous UV excitation have been observed. One observes that the effect strongly depends on the thin films’ crystalline character which is strongly related with the texturation and existence at the mesoscopic length scale.