Response of an artificially blown clarinet to different blowing pressure profiles

Using an artificial mouth with an accurate pressure control, the onset of the pressure oscillations inside the mouthpiece of a simplified clarinet is studied experimentally. Two time profiles are used for the blowing pressure: in a first set of experiments the pressure is increased at constant rates, then decreased at the same rate. In a second set of experiments the pressure rises at a constant rate and is then kept constant for an arbitrary period of time. In both cases the experiments are repeated for different increase rates. Numerical simulations using a simplified clarinet model blown with a constantly increasing mouth pressure are compared to the oscillating pressure obtained inside the mouthpiece. Both show that the beginning of the oscillations appears at a higher pressure values than the theoretical static threshold pressure, a manifestation of bifurcation delay. Experiments performed using an interrupted increase in mouth pressure show that the beginning of the oscillation occurs close to the stop in the increase of the pressure. Experimental results also highlight that the speed of the onset transient of the sound is roughly the same, independently of the duration of the increase phase of the blowing pressure.Comment: 14 page

p-Type doping of II-VI heterostructures from surface states: application to ferromagnetic Cd1−x_{1-x}Mnx_xTe quantum wells

We present a study of p-type doping of CdTe and Cd$_{1-x}$Mn$_x$Te quantum wells from surface states. We show that this method is as efficient as usual modulation doping with nitrogen acceptors, and leads to hole densities exceeding $2 \times 10^{11}$ cm$^{-2}$. Surface doping was successfully applied to obtain carrier-induced ferromagnetism in a Cd$_{1-x}$Mn$_x$Te quantum well. The observed temperature dependence of photoluminescence spectra, and the critical temperature, correspond well to those previously reported for ferromagnetic quantum wells doped with nitrogen.Comment: 4 figure

Microphotoluminescence study of disorder in ferromagnetic (Cd,Mn)Te quantum well

Microphotoluminescence mapping experiments were performed on a modulation doped (Cd,Mn)Te quantum well exhibiting carrier induced ferromagnetism. The zero field splitting that reveals the presence of a spontaneous magnetization in the low-temperature phase, is measured locally; its fluctuations are compared to those of the spin content and of the carrier density, also measured spectroscopically in the same run. We show that the fluctuations of the carrier density are the main mechanism responsible for the fluctuations of the spontaneous magnetization in the ferromagnetic phase, while those of the Mn spin density have no detectable effect at this scale of observation.Comment: 4 pages, 3 figure

Excitonic giant Zeeman effect in GaN:Mn^3+

We describe a direct observation of the excitonic giant Zeeman splitting in (Ga,Mn)N, a wide-gap III-V diluted magnetic semiconductor. Reflectivity and absorption spectra measured at low temperatures display the A and B excitons, with a shift under magnetic field due to s,p-d exchange interactions. Using an excitonic model, we determine the difference of exchange integrals between Mn^3+ and free carriers in GaN, N_0(alpha-beta)=-1.2 +/- 0.2 eV. Assuming a reasonable value of alpha, this implies a positive sign of beta which corresponds to a rarely observed ferromagnetic interaction between the magnetic ions and the holes.Comment: 4 pages, 4 figure

Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

Carrier-induced ferromagnetism in p-Zn1-xMnxTe

We present a systematic study of the ferromagnetic transition induced by the holes in nitrogen doped Zn1-xMnxTe epitaxial layers, with particular emphasis on the values of the Curie-Weiss temperature as a function of the carrier and spin concentrations. The data are obtained from thorough analyses of the results of magnetization, magnetoresistance and spin-dependent Hall effect measurements. The experimental findings compare favorably, without adjustable parameters, with the prediction of the Rudermann-Kittel-Kasuya-Yosida (RKKY) model or its continuous-medium limit, that is, the Zener model, provided that the presence of the competing antiferromagnetic spin-spin superexchange interaction is taken into account, and the complex structure of the valence band is properly incorporated into the calculation of the spin susceptibility of the hole liquid. In general terms, the findings demonstrate how the interplay between the ferromagnetic RKKY interaction, carrier localization, and intrinsic antiferromagnetic superexchange affects the ordering temperature and the saturation value of magnetization in magnetically and electrostatically disordered systems.Comment: 14 pages, 10 figure

Ferromagnetic (Ga,Mn)N epilayers versus antiferromagnetic GaMn3_3N clusters

Mn-doped wurtzite GaN epilayers have been grown by nitrogen plasma-assisted molecular beam epitaxy. Correlated SIMS, structural and magnetic measurements show that the incorporation of Mn strongly depends on the conditions of the growth. Hysteresis loops which persist at high temperature do not appear to be correlated to the presence of Mn. Samples with up to 2% Mn are purely substitutional Ga$_{1-x}$Mn$_x$N epilayers, and exhibit paramagnetic properties. At higher Mn contents, precipitates are formed which are identified as GaMn$_3$N clusters by x-ray diffraction and absorption: this induces a decrease of the paramagnetic magnetisation. Samples co-doped with enough Mg exhibit a new feature: a ferromagnetic component is observed up to $T_c\sim175$ K, which cannot be related to superparamagnetism of unresolved magnetic precipitates.Comment: Revised versio

Influence of s,p-d and s-p exchange couplings on exciton splitting in (Zn,Mn)O

This work presents results of near-band gap magnetooptical studies on (Zn,Mn)O epitaxial layers. We observe excitonic transitions in reflectivity and photoluminescence, that shift towards higher energies when the Mn concentration increases and split nonlinearly under the magnetic field. Excitonic shifts are determined by the s,p-d exchange coupling to magnetic ions, by the electron-hole s-p exchange, and the spin-orbit interactions. A quantitative description of the magnetoreflectivity findings indicates that the free excitons A and B are associated with the Gamma_7 and Gamma_9 valence bands, respectively, the order reversed as compared to wurtzite GaN. Furthermore, our results show that the magnitude of the giant exciton splittings, specific to dilute magnetic semiconductors, is unusual: the magnetoreflectivity data is described by an effective exchange energy N_0(beta-alpha)=+0.2+/-0.1 eV, what points to small and positive N_0 beta. It is shown that both the increase of the gap with x and the small positive value of the exchange energy N_0 beta corroborate recent theory describing the exchange splitting of the valence band in a non-perturbative way, suitable for the case of a strong p-d hybridization.Comment: 8 pages, 8 figure

Inverse problem and Bertrand's theorem

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical equation. This permit a particulary compact and elegant proof of Bertrand's theorem.Comment: 11 pages, 3 figure