Electrical spin injection and detection in Germanium using three terminal geometry

In this letter, we report on successful electrical spin injection and detection in \textit{n}-type germanium-on-insulator (GOI) using a Co/Py/Al$_{2}$O$_{3}$ spin injector and 3-terminal non-local measurements. We observe an enhanced spin accumulation signal of the order of 1 meV consistent with the sequential tunneling process via interface states in the vicinity of the Al$_{2}$O$_{3}$/Ge interface. This spin signal is further observable up to 220 K. Moreover, the presence of a strong \textit{inverted} Hanle effect points at the influence of random fields arising from interface roughness on the injected spins.Comment: 4 pages, 3 figure

Electrical and thermal spin accumulation in germanium

In this letter, we first show electrical spin injection in the germanium conduction band at room temperature and modulate the spin signal by applying a gate voltage to the channel. The corresponding signal modulation agrees well with the predictions of spin diffusion models. Then by setting a temperature gradient between germanium and the ferromagnet, we create a thermal spin accumulation in germanium without any tunnel charge current. We show that temperature gradients yield larger spin accumulations than pure electrical spin injection but, due to competing microscopic effects, the thermal spin accumulation in germanium remains surprisingly almost unchanged under the application of a gate voltage to the channel.Comment: 7 pages, 3 figure

Crossover from spin accumulation into interface states to spin injection in the germanium conduction band

Electrical spin injection into semiconductors paves the way for exploring new phenomena in the area of spin physics and new generations of spintronic devices. However the exact role of interface states in spin injection mechanism from a magnetic tunnel junction into a semiconductor is still under debate. In this letter, we demonstrate a clear transition from spin accumulation into interface states to spin injection in the conduction band of $n$-Ge. We observe spin signal amplification at low temperature due to spin accumulation into interface states followed by a clear transition towards spin injection in the conduction band from 200 K up to room temperature. In this regime, the spin signal is reduced down to a value compatible with spin diffusion model. More interestingly, we demonstrate in this regime a significant modulation of the spin signal by spin pumping generated by ferromagnetic resonance and also by applying a back-gate voltage which are clear manifestations of spin current and accumulation in the germanium conduction band.Comment: 5 pages, 4 figure

Spin-pumping into surface states of topological insulator {\alpha}-Sn, spin to charge conversion at room temperature

We present experimental results on the conversion of a spin current into a charge current by spin pumping into the Dirac cone with helical spin polarization of the elemental topological insulator (TI) {\alpha}-Sn[1-3]. By angle-resolved photoelectron spectroscopy (ARPES) we first confirm that the Dirac cone at the surface of {\alpha}-Sn (0 0 1) layers subsists after covering with Ag. Then we show that resonant spin pumping at room temperature from Fe through Ag into {\alpha}-Sn layers induces a lateral charge current that can be ascribed to the Inverse Edelstein Effect[4-5]. Our observation of an Inverse Edelstein Effect length[5-6] much longer than for Rashba interfaces[5-10] demonstrates the potential of the TI for conversion between spin and charge in spintronic devices. By comparing our results with data on the relaxation time of TI free surface states from time-resolved ARPES, we can anticipate the ultimate potential of TI for spin to charge conversion and the conditions to reach it.Comment: 14 pages, 5 figure

Bridging knowing and proving in mathematics An essay from a didactical perspective

Text of a talk at the conference "Explanation and Proof in Mathematics: Philosophical and Educational Perspective" held in Essen in November 2006International audienceThe learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which they can apply in significant problem situations, and which is amenable to falsification and argumentation. They can validate what they claim to be true but using means generally not conforming to mathematical standards. Here, I analyze how this situation underlies the epistemological and didactical complexities of teaching mathematical proof. I show that the evolution of the learners' understanding of what counts as proof in mathematics implies an evolution of their knowing of mathematical concepts. The key didactical point is not to persuade learners to accept a new formalism but to have them understand how mathematical proof and statements are tightly related within a common framework; that is, a mathematical theory. I address this aim by modeling the learners' way of knowing in terms of a dynamic, homeostatic system. I discuss the roles of different semiotic systems, of the types of actions the learners perform and of the controls they implement in constructing or validating knowledge. Particularly with modern technological aids, this model provides a basis designing didactical situations to help learners bridge the gap between pragmatics and theory