Spin q , Twistor and Spin c

Spin ^q structures induce (Spin ^q style) twistor spaces, which possess canonical Spin ^c structures. Such structures produce Dirac operators. Their indices for the even dimensional case, and the adiabatic limit of their reduced η-invariants for the odd dimensional case, are discussed. Received: 3 October 1995 / Accepted: 2 March 1997     

Spin phase

The existence of a complementary quantity in the Weyl sense for the third component of spin is discussed. This is called the spin phase and the possibilities of measuring this quantity are considered. Connections between the spin phase and the indeterminacy of the direction for the spin are shown. On leave from the Institute of Physics, Nicolas Copernicus University, Torun, Poland.     

The Spin

It is shown that the spin is naturally introduced into classical mechanics if the latter is formulated as dynamics of the phase space density. It is shown that the uncertainty principle, as the amendment in this dynamics, restricts possible spins, and in particular equation for the particle with the spin ħ/2 is derived. Also equation for the charge with this spin is derived when electromagnetic field is included. In one example it is shown that the modulus of the spin changes with the gradient of the magnetic field.     

Spin glasses

Recent developments in the theory of spin glasses are discussed. There has been considerable progress, due to Parisi, Sompolinsky, and others, towards understanding the infinite range (mean field) model of Sherrington and Kirkpatrick. Relaxation times diverge in the thermodynamic limit, and this nonergodic behavior is now understood to be the cause of earlier difficulties. There has been less progress in the study of more realistic models with short-range interactions, but numerical studies have shown rather clearly the absence of a finite temperature transition in two dimensions. There is probably no transition ind=3 either, though the evidence is less clearcut, which makes it difficult to understand the sharpness of the freezing observed experimentally. Well below the freezing temperature ESR and torque measurements have been fairly well explained by a theory of Henley, Sompolinsky, and Halperin, in which an important ingredient is anisotropy due to the Dzyloshinsky-Moriya interaction proposed by Fert and Levy.     

量子自旋液体候选材料的缪子自旋弛豫研究

量子自旋液体是一种新奇的磁性物态。由于极强的量子涨落，直至零温都不会出现长程序。量子自旋液体的基态不能用序参量描述，并且缺少对称性破缺，因此该物态的实现打破朗道理论的范式。对于量子自旋液体的研究有助于理解高温超导的机理，并且可以被应用在量子计算和量子信息中。目前，尽管理论上有了长足的发展，但仍旧没有任何一个材料被证实为量子自旋液体。因此，探测和确认一个真正的量子自旋液体材料是当前的研究重点。缪子自旋弛豫是一个对磁场极为敏感的实验技术，被广泛应用于量子自旋液体候选材料的研究中。该技术可以观测基态中是否存在磁有序，测量系统中的涨落频率，这两点都是表征量子自旋液体的重要性质。本文简要介绍了量子自旋液体态和缪子自旋弛豫技术，回顾了近期在不同体系的量子自旋液体候选材料中的实验结果，特别是缪子自旋弛豫的成果。这些体系包括一维反铁磁海森堡链（苯甲酸铜），三角格子（YbMgGaO4，NaYbO2 和TbInO3），笼目格[ZnCu3(OH)6Cl2 和 m3Sb3Zn2O14]，蜂窝状格子（Na2IrO3 和 α-RuCl3），以及烧绿石结构（Tb2Ti2O7，Pr2Ir2O7 和Ce2Zr2O7）。     

Recent STAR Spin Results and Spin Measurements at RHIC

The STAR experiment provides measurements of single and double-spin asymmetries in longitudinally and transversely polarized p + p collisions at \(\sqrt s \) = 200 and 510 GeV to deepen our understanding on the proton spin structure and dynamics of parton interactions over a wide range of collision energy, momentum and rapidity of the various produced probes. Polarized processes with W^± production allow us to study the spin-flavor structure of the proton. Recent results obtained by STAR on the double longitudinal asymmetry, A_LL, of pion and jet production at \(\sqrt s \) = 200 and 510 GeV, the single longitudinal, A_L, and transverse, A_N, asymmetry of W^± production at \(\sqrt s \) = 510 GeV are overviewed. STAR results on azimuthal single transverse asymmetry of pion in p^↑ + (p, Au) and jet + π^± in p^↑ + p collisions are discussed. The proposed Forward Calorimeter System (FCS) and Forward Tracking System (FTS) upgrades at STAR would significantly improve the capabilities of existing detectors for measurements of observables such as asymmetries of pion, jet, Drell-Yan pairs produced at forward rapidities.     

Spin Waves in a Surface-Diluted Quant um Spin system

A theoretical investigation of the effects of surface dilution on spin waves in a semi-infinite transverse Ising model (TIM) is presented. Within the framework of the double-time Green's function theory, the loctl density of spin-wave states is obtained by the application of the cluster-Bethe-lattice (CBL) method. Numerical calculations of paramagnetic phases reveal that surface dilution will lead to appearance of the localized spin-wave states whose frequencies are bulk independent while the corresponding density of states is a function of the exchange interactions. Increase of the bulk exchange interactions between the surface and the bulk spins tends to diminish the localized spin-wave states. Dependence of the local density of states on the concentration p of the magnetic atoms is similar with that in a three-dimensional infinite TIM which has been discussed in our previous paper.     

Representation of Spin Group Spin（p, q）

The representation η（P, q） of spin group Spin（p, q） in any dimensional space is given by induction, and the relation between two representations, which are obtained in two kinds of inductions from Spin（p, q） to Spin（p ＋ 1, q ＋ 1） are studied.     

Quantum Communication in Spin Chain with Multiple Spin Exchange Interaction

The transmission of quantum states in the anisotropic Heisenberg XXZ chain model with three-spin exchange interaction is studied. The average fidelity is used to evaluate the state transfer. It is found that quantum communication can be enhanced by the anisotropic coupling and multiple spin interaction. Such spin model can reduce the time required for the perfect state transmission where the fidelity is unity. The maximally entangled Bell states can be generated and separated from the whole quantum systems.     

Spin transfer torques

This tutorial article introduces the physics of spin transfer torques in magnetic devices. Our intention is that it be accessible to beginning graduate students. We provide an elementary discussion of the mechanism of spin transfer torque and review the theoretical and experimental progress in this field. This article is meant to set the stage for the articles which follow in this volume of the Journal of Magnetism and Magnetic Materials, which focus in more depth on particularly interesting aspects of spin-torque physics and highlight unanswered questions that might be productive topics for future research.