This paper introduces five notions, including π-algebras, π-ideals, Hopf π-algebras, π-modules and Hopf π-modules, verifies the fundamental isomorphism theorem of π-algebras and studies some algebraic properties of Hopf π-algebras as well.

Hopf π- Algebras

Recent advances in the theory and experimental realization of ferromagnetic semiconductors give hope that a new generation of microelectronic devices based on the spin degree of freedom of the electron can be developed. This review focuses primarily on promising candidate materials (such as GaN, GaP and ZnO) in which there is already a technology base and a fairly good understanding of the basic electrical and optical properties. The introduction of Mn into these and other materials under the right conditions is found to produce ferromagnetism near or above room temperature. There are a number of other potential dopant ions that could be employed (such as Fe, Ni, Co, Cr) as suggested by theory [see, for example, Sato and Katayama-Yoshida, Jpn. J. Appl. Phys., Part 2 39, L555 (2000)]. Growth of these ferromagnetic materials by thin film techniques, such as molecular beam epitaxy or pulsed laser deposition, provides excellent control of the dopant concentration and the ability to grow single-phase layers. T...

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Wide band gap ferromagnetic semiconductors and oxides

By Vyjayanthi Chari and Andrew Pressley: 651 pp., £22.95 (US$34.95), isbn 0 521 55884 0 (Cambridge University Press, 1994).

A guide to quantum groups

Existing semiconductor electronic and photonic devices utilize the charge on electrons and holes in order to perform their specific functionality such as signal processing or light emission. The relatively new field of semiconductor spintronics seeks, in addition, to exploit the spin of charge carriers in new generations of transistors, lasers and integrated magnetic sensors. The ability to control of spin injection, transport and detection leads to the potential for new classes of ultra-low power, high speed memory, logic and photonic devices. The utility of such devices depends on the availability of materials with practical (>300 K) magnetic ordering temperatures. In this paper, we summarize recent progress in dilute magnetic semiconductors (DMS) such as (Ga, Mn)N, (Ga, Mn)P, (Zn, Mn)O and (Zn, Mn)SiGeN2 exhibiting room temperature ferromagnetism, the origins of the magnetism and its potential applications in novel devices such as spin-polarized light emitters and spin field effect transistors.

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Advances in wide bandgap materials for semiconductor spintronics

GaMnN thin films were synthesized using gas-source molecular-beam epitaxy. Mn concentrations between 3 and 12 at. % were investigated. No evidence of second-phase formation was observed by powder x-ray diffraction or high-resolution cross section transmission electron microscopy in films with 9% or less Mn. The films were n type as determined by capacitance–voltage or Hall analysis. Magnetic characterization performed using a squid magnetometer showed evidence of ferromagnetic ordering at room temperature for all samples. In agreement with theoretical predictions, material with 3% Mn showed the highest degree of ordering per Mn atom. At 320 K, the samples show a nonzero magnetization indicating a TC above room temperature.

Magnetic properties of n-GaMnN thin films

The magnetization of Ga1−xMnxN (x<0.1) crystals was measured as a function of the magnetic field and temperature. Paramagnetic behavior typical of spin S=5/2 expected for Mn2+ (d5) magnetic centers was observed in the temperature range of 2 K<T<300 K. On the other hand, antiferromagnetic coupling between Mn ions was clearly visible. The nearest neighbor (NN) coupling constant JNN/kB=−1.9 K was estimated from the temperature dependence of the magnetization.

Paramagnetism and antiferromagnetic d–d coupling in GaMnN magnetic semiconductor

Ammonothermal synthesis of GaN doped with transition metal ions (Mn, Fe, Cr)

In this work, we present measurements of the dynamics of photoexcited carriers in GaInN/GaN quantum wells (QWs) grown on ammonothermal GaN, especially thermalization and recombination rates Emission properties were measured by time-resolved photoluminescence (PL) and electroluminescence spectroscopy Due to the use of high quality homoepitaxial material, we were able to obtain very valuable data on carrier thermalization The temperature dependence of the QW energy observed in PL shows characteristic S-shape with a step of about 10 meV Such a behavior (related to thermalization and localization at potential fluctuations) is often reported for QWs; but in our samples, the effect is smaller than in heteroepitaxial InGaN/GaN QWs due to lower potential fluctuation in our material Absorption properties were studied by photocurrent spectroscopy measurements A comparison of emission and absorption spectra revealed a shift in energy of about 60 meV Contrary to PL, the QW energy observed in absorption decreas

Dynamics of thermalization in GaInN/GaN quantum wells grown on ammonothermal GaN

Tulczyjew triple for physical systems with configuration manifold equipped with Lie group structure is constructed and discussed. The case of systems invariant with respect to group acton is considered together with appropriate reduction of the Tulczyjew triple. The theory is applied to free rigid-body dynamics.

The Tulczyjew triple in mechanics on a Lie group

Tulczyjew triple for physical systems with configuration manifold equipped with a Lie group structure is constructed and discussed. Systems invariant with respect to group and subgroup actions are considered together with appropriate reductions of the Tulczyjew triple. The theory is applied to free and constrained rigid-body dynamics.

https://www.aimsciences.org/article/exportPdf?id=f99a85e7-24da-4dfe-ab47-734648f89d17

Marcin Zając

Papers

Paramagnetism and antiferromagnetic d–d coupling in GaMnN magnetic semiconductor

Ammonothermal synthesis of GaN doped with transition metal ions (Mn, Fe, Cr)

Dynamics of thermalization in GaInN/GaN quantum wells grown on ammonothermal GaN

The Tulczyjew triple in mechanics on a Lie group

The Tulczyjew triple in mechanics on a Lie group