Matrix measures and random walks

In this paper we study the connection between matrix measures and random walks with a tridiagonal block transition matrix. We derive sufficient conditions such that the blocks of the n-step transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure. Several stochastic properties of the processes are characterized by means of this matrix measure. In many cases this measure is supported in the interval [-1, 1]. The results are illustrated by several examples including random walks on a grid and the embedded chain of a queuing system. --Markov chain,block tridiagonal transition matrix,spectral measure,matrix measure,quasi birth and death processes,canonical moments

Absence of ferromagnetism in V-implanted ZnO single crystals

The structural and magnetic properties of V doped ZnO are presented. V ions were introduced into hydrothermal ZnO single crystals by ion implantation with fluences of 1.2*10^16 to 6*10^16 cm^-2. Post-implantation annealing was performed in high vacuum from 823 K to 1023 K. The ZnO host material still partly remains in a crystalline state after irradiation, and is partly recovered by annealing. The V ions show a thermal mobility as revealed by depth profile Auger electron spectroscopy. Synchrotron radiation x-ray diffraction revealed no secondary phase formation which indicates the substitution of V onto Zn site. However in all samples no pronounced ferromagnetism was observed down to 5 K by a superconducting quantum interference device magnetometer.Comment: 13 pages, 4 figs, MMM conference 2007, accepted by J. Appl. Phy

Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3

Combining thermodynamic measurements with theoretical density functional and thermodynamic calculations we demonstrate that the honeycomb lattice iridates A2IrO3 (A = Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S = 1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with Heisenberg interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from \theta = -125 K for Na2IrO3 to \theta = -33 K for Li2IrO3, while the antiferromagnetic ordering temperature remains roughly the same T_N = 15 K for both materials. Using finite-temperature functional renormalization group calculations we show that this evolution of \theta, T_N, the frustration parameter f = \theta/T_N, and the zig-zag magnetic ordering structure suggested for both materials by density functional theory can be captured within this extended HK model. Combining our experimental and theoretical results, we estimate that Na2IrO3 is deep in the magnetically ordered regime of the HK model (\alpha \approx 0.25), while Li2IrO3 appears to be close to a spin-liquid regime (0.6 < \alpha < 0.7).Comment: Version accepted for publication in PRL. Additional DFT and thermodynamic calculations have been included. 6 pages of supplementary material include

Fe-implanted ZnO: Magnetic precipitates versus dilution

Nowadays ferromagnetism is often found in potential diluted magnetic semiconductor systems. However, many authors argue that the observed ferromagnetism stems from ferromagnetic precipitates or spinodal decomposition rather than from carrier mediated magnetic impurities, as required for a diluted magnetic semiconductor. In the present paper we answer this question for Fe-implanted ZnO single crystals comprehensively. Different implantation fluences and temperatures and post-implantation annealing temperatures have been chosen in order to evaluate the structural and magnetic properties over a wide range of parameters. Three different regimes with respect to the Fe concentration and the process temperature are found: 1) Disperse Fe$^{2+}$ and Fe$^{3+}$ at low Fe concentrations and low processing temperatures, 2) FeZn$_2$O$_4$ at very high processing temperatures and 3) an intermediate regime with a co-existence of metallic Fe (Fe$^0$) and ionic Fe (Fe$^{2+}$ and Fe$^{3+}$). Ferromagnetism is only observed in the latter two cases, where inverted ZnFe$_2$O$_4$ and $\alpha$-Fe nanocrystals are the origin of the observed ferromagnetic behavior, respectively. The ionic Fe in the last case could contribute to a carrier mediated coupling. However, their separation is too large to couple ferromagnetically due to the lack of p-type carrier. For comparison investigations of Fe-implanted epitaxial ZnO thin films are presented.Comment: 14 pages, 17 figure

Crystallographically oriented magnetic ZnFe2O4 nanoparticles synthesized by Fe implantation into ZnO

In this paper, a correlation between structural and magnetic properties of Fe implanted ZnO is presented. High fluence Fe^+ implantation into ZnO leads to the formation of superparamagnetic alpha-Fe nanoparticles. High vacuum annealing at 823 K results in the growth of alpha-Fe particles, but the annealing at 1073 K oxidized the majority of the Fe nanoparticles. After a long term annealing at 1073 K, crystallographically oriented ZnFe2O4 nanoparticles were formed inside ZnO with the orientation relationship of ZnFe2O4(111)[110]//ZnO(0001)[1120]. These ZnFe2O4 nanoparticles show a hysteretic behavior upon magnetization reversal at 5 K.Comment: 21 pages, 7 figures, accepted by J. Phys. D: Appl. Phy

Anisotropic Susceptibility of La_2-xSr_xCoO_4 related to the Spin States of Cobalt

We present a study of the magnetic susceptibility of La_2-xSr_xCoO_4 single crystals in a doping range 0.3<=x<=0.8. Our data shows a pronounced magnetic anisotropy for all compounds. This anisotropy is in agreement with a low-spin ground state (S=0) of Co^3+ for x>=0.4 and a high-spin ground state (S=3/2) of Co^2+. We compare our data with a crystal-field model calculation assuming local moments and find a good description of the magnetic behavior for x>=0.5. This includes the pronounced kinks observed in the inverse magnetic susceptibility, which result from the anisotropy and low-energy excited states of Co^2+ and are not related to magnetic ordering or temperature-dependent spin-state transitions

Untersuchungen zur Regulation der Knospenruhe verschiedener Rebsorten durch ökologische und endogene Faktoren

Das Kältebedürfnis der Sorten Riesling und Spätburgunder wurde untersucht. Durch Kältebehandlung einjähriger Rebsprosse wurde die kritische Austriebszeit daraus hergestellter Stecklinge verkürzt; außerdem nahm der Prozentsatz ausgetriebener Knospen im Verlauf der Ruhephase von Oktober bis März zu. Die Knospenruhe von Riesling war größer als die von Spätburgunder. Nach der Befriedigung des Kältebedürfnisses wurden 3 Austriebsphasen beobachtet:Von November bis Dezember nahm die Dormanz rapide ab.Von Dezember bis Januar blieb die Dormanz im wesentlichen unverändert niedrig.Von Februar bis März wurde der Austrieb erneut stimuliert.Die quantitative Bestimmung von ABS der Knospenproben aus diesen Perioden ergab, daß die 1. Phase mit einer Abnahme der ABS-Kurve in Abhängigkeit von der Kältebehandlung im November korrelierte. Der ABS-Gehalt stieg ab August steil an und erreichte im November ein Maximum. Die darauffolgende kälteinduzierte Inaktivierung freier ABS korrespondierte mit einer Zunahme glykosidisch gebundener ABS. Von Dezember bis März blieb der Gehalt freier ABS in den Knospen mehr oder weniger konstant. Eine Entblätterung der Weinreben Ende August führte zu einer geringeren Austriebshemmung als 3 oder 5 Wochen später. Der Einfluß der Tageslängen auf die Synthese von ABS in den Blättern wird diskutiert. Die obere Schwelle der induktiven Temperatur wurde bei + 5 °C festgesetzt. Das Kältebedürfnis wurde durch Lagerung von nicht induzierten einjährigen Sprossen während unterschiedlicher Perioden bei + 4,0 und -5 °C ermittelt. Der Austrieb wurde in Abhängigkeit von der Länge der Kühlperiode in der niedrigsten Temperaturstufe am stärksten aktiviert. Die Stimulation verhielt sich jedoch zur Temperaturbehandlung nicht proportional.Das Kältebedürfnis wurde als Produkt der „relativen Temperatur" und der „Zeit in Stunden unter +5 °C" (∆ t · h) ausgedrückt. Die physiologische Wirkung der niederen Temperatur auf den Austrieb hängt von ihrer Differenz zum Schwellenwert und von ihrer Einwirkungsdauer ab. Es wurden Versuche zur Synchronisierung dieser ökologischen Faktoren durchgeführt, um das sortenspezifische Kältebedürfnis exakt zu bestimmen.Investigations on the regulation of bud dormancy of different Vitis vinifera varieties by oecological and endogenous factorsThe chilling requirement of the varieties "Riesling" and "Spätburgunder" was investigated. The critical time of bud burst of cuttings from one yearold shoots was shortened by means of chilling treatment. In addition, the percentage of burst buds increased in the course of dormancy from October to March. Compared with "Spätburgunder", the dormancy of "Riesling" was deeper. When the chilling requirement was satisfied, three phases of bud burst were observed:From November to December dormancy decreased rapidly.From December to January dormancy was not altered markedly.From February to March the rate of bud burst was stimulated again.Quantitative determination of ABA from buds sampled in the same periods indicated that the first phase was correlated to the descending of ABA-curve in November. This process coincided with low temperature conditions. The level of ABA was low in August, and increased from August towards a maximum in November. Corresponding to the inactivation of the free ABA the level of ABA-glycosides changed. From December to March the ABA content in the buds remained more or less constant. Defoliation of vines at the end of August resulted in a lower inhibition of the bud burst than defoliation 3 or 5 weeks later. The influence of day length an the synthesis of ABA in the leaves is discussed.The upper threshold for inductive temperature was assumed at +5 °C. The chilling requirement was registered by storage of one year-old shoots, cut before induction, for different periods at +4, 0, and -5 °C. According to same length of chilling period the bud burst was stimulated most at the lowest temperature. The stimulation, however, was not proportional to the temperature treatment. The chilling requirement has been expressed as a product of "relative temperature" and "number of hours below +5 °C" (∆ t · h). The physiological effect of low temperature an bud burst depends an its difference from the temperature threshold and the duration of chilling. Attempts were made to synchronize these oecological factors for exact determination of variety specific chilling requirement

The spin state transition in LaCoO3_{3}; revising a revision

Using soft x-ray absorption spectroscopy and magnetic circular dichroism at the Co-$L_{2,3}$ edge we reveal that the spin state transition in LaCoO$_{3}$ can be well described by a low-spin ground state and a triply-degenerate high-spin first excited state. From the temperature dependence of the spectral lineshapes we find that LaCoO$_{3}$ at finite temperatures is an inhomogeneous mixed-spin-state system. Crucial is that the magnetic circular dichroism signal in the paramagnetic state carries a large orbital momentum. This directly shows that the currently accepted low-/intermediate-spin picture is at variance. Parameters derived from these spectroscopies fully explain existing magnetic susceptibility, electron spin resonance and inelastic neutron data

Ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice: A variational study based on entangled-plaquette states

We study, on the basis of the general entangled-plaquette variational ansatz, the ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice. Our numerical estimates are in good agreement with available exact results and comparable, for large system sizes, to those computed via the best alternative numerical approaches, or by means of variational schemes based on specific (i.e., incorporating problem dependent terms) trial wave functions. The extrapolation to the thermodynamic limit of our results for lattices comprising up to N=324 spins yields an upper bound of the ground-state energy per site (in units of the exchange coupling) of $-0.5458(2)$ [$-0.4074(1)$ for the XX model], while the estimated infinite-lattice order parameter is $0.3178(5)$ (i.e., approximately 64% of the classical value).Comment: 8 pages, 3 tables, 2 figure