长程阻错的统计物理理论

一个无序自旋玻璃系统可能有许许多多能量最小态或基态构型．有些格点的自旋可能在所有这些基态中都只取同一个值（这种情况称为自旋凝固）．也有另外一种情况出现，即某些格点在一部分基态中自旋取向上而在其余的基态中自旋向下；这样的格点称为未凝固的格点．本文的工作表明，2个或多个未凝固的格点，虽然每个格点的自旋都随着基态的不同而改变，但是有可能某一些特定的自旋取向组合不会出现于任何一基态构型中．这种现象称为长程阻错．本文提出一个新的长程阻错序参量R来定量刻划这种现象，并将这一统计物理理论用于图的最小覆盖和K—SAT等组合优化问题．     

Magnetic properties of 2D nano-islands I: Ising spin model

An Ising spin effective field theory (EFT) is developed as a framework for a detailed analysis of the magnetic properties of two-dimensional (2D) nano-islands on a nonmagnetic substrate with an out of plane magnetization. The Hamiltonian with nearest neighbor exchange interactions and single-atom magnetic anisotropy defines the ground state. The calculation yields the single site spin correlations, the magnetizations, and the isothermal susceptibilities for the core and periphery domains, and the island core phase diagrams. The choice of a spin S=1 for the atoms permits the analysis of the effects of spin fluctuations via the single site spin correlations. In particular we investigate the effects due to the different anisotropies and reduced dimensionalities for the core and periphery domains. The present model calculations are developed for different 2D nano-islands lattices. Detailed theoretical results are presented for the square and hexagonal lattices, with numerical applications for the 2D Co nano-islands on Pt. The derived transition temperature for the hexagonal lattice nano-islands is in good agreement with the experimental data for Co nano-islands on Pt. Though both the core and the periphery domains have the same order-disorder transition temperature, the magnetization of each domain attains this transition differently. The temperature behavior of the spin correlations is also fundamentally different for the periphery and core sites, which entails distinctly different isothermal susceptibilities, and yields statistically averaged nano-islands susceptibilities that do not correspond to a second order phase transition. The experimental susceptibility results for 2D Co nano-islands on Pt can be interpreted within our EFT Ising model without reference to a transition from a blocking state of the particle to a superparamagnetic behavior. The results for the different lattices are formally comparable, and demonstrate the robustness and general character of the model.     

Intrinsic magnetism induced by vacancy in GaN

We performed total energy electronic-structure calculations based on DFT that clarify the intrinsic magnetism of undoped GaN. The magnetism is due to Ga, instead of N, vacancies. The origin of magnetism arises from the unpaired 2p electrons of N surrounding Ga vacancy. At a vacancy concentration of 5.6%, the ferromagnetic state is 181 meV lower than the antiferromagnetic state. Our findings are helpful to gain a more novel understanding of structural and spin properties of Ga vacancy in wurtzite GaN and also provide a possible way to generate magnetic GaN by introducing Ga vacancies instead of doping with transition-metal atoms.     

Long-range frustration in a spin-glass model of the vertex-cover problem

In a spin-glass system on a random graph, some vertices have their spins changing among different configurations of a ground-state domain. Long-range frustrations may exist among these unfrozen vertices in the sense that certain combinations of spin values for these vertices may never appear in any configuration of this domain. We present a mean field theory to tackle such long-range frustrations and apply it to the NP-hard minimum vertex-cover (hard-core gas condensation) problem. Our analytical results on the ground-state energy density and on the fraction of frozen vertices are in good agreement with known numerical and mathematical results.     

Applications of the coherent state representation in the theory of magnetism: II. Helical spin configurations

In a previous paper, the coherent state representation of spin wave states was used to derive the low temperature expansion for the free energy of the Heisenberg model of a ferromagnet. In this paper, the same formalism is applied to anisotropic systems which are usually described semiclassically. The coherent state parameters are shown to be ideally suited for describing certain of the resulting helical spin configurations. The coherent state approach emphasizes the analogy of these states to superfluid boson systems. A model spin Hamiltonian appropriate to Erbium is chosen and discussed in this light. In particular, the transition in a transverse magnetic field from the ground state cone configuration to a fan configuration, the stability and possible metastability of these states and the fluctuations about them are investigated. Numerical estimates show at least qualitative agreement with experiment.     

序参量守恒的反铁磁分子晶体的非线性集体激发

采用双子格模型和相干态表示，考虑磁－声子耦合作用和磁子间的相互作用，研究了序参量守恒的一维反铁磁分子晶体ＣｅＡｓ在外磁场存在下的非线性集体激发特性，并求了孤立子能量、质量和自旋的空间组态，给出在一维序参量守恒的反铁磁分子晶体ＣｅＡｓ中出现的非线性磁子局域特性。     

Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron

The observation of hysteresis effects in single molecule magnets like Mn12-acetate has initiated ideas of future applications in storage technology. The appearance of a hysteresis loop in such compounds is an outcome of their magnetic anisotropy. In this Letter we report that magnetic hysteresis occurs in a spin system without any anisotropy, specifically where spins mounted on the vertices of an icosahedron are coupled by antiferromagnetic isotropic nearest-neighbor Heisenberg interaction giving rise to geometric frustration. At T = 0 this system undergoes a first-order metamagnetic phase transition at a critical field Bc between two distinct families of ground state configurations. The metastable phase of the system is characterized by a temperature and field dependent survival probability distribution.     

Competing spin phases in geometrically frustrated magnetic molecules

We identify a class of zero-dimensional classical and quantum Heisenberg spin systems exhibiting anomalous behavior in an external magnetic field B similar to that found for the geometrically frustrated kagome lattice of classical spins. Our calculations for the isotropic Heisenberg model show the emergence of a pronounced minimum in the differential susceptibility dM/dB at B(sat)/3 as the temperature T is raised from 0 K for structures based on corner-sharing triangles, specifically the octahedron, cuboctahedron, and icosidodecahedron. As the first experimental evidence we note that the giant Keplerate magnetic molecule {Mo(72)Fe(30)} (Fe(3+) ions on the 30 vertices of an icosidodecahedron) exhibits this behavior. For low T when B approximately B(sat)/3 two competing families of spin configurations exist of which one behaves magnetically "stiff" leading to a reduction of dM/dB.     

Field-induced transitions and spatial chaos in the classical XY spin chain

We study the lowest-lying excitation of a classical ferromagnetic XY spin chain, in the presence of a symmetry breaking magnetic field. Extremizing the energy of this system leads to a two-dimensional nonlinear map, whose allowed phase space shrinks with increasing field in a nontrivial manner. The orbits of the map represent the set of extremum energy spin configurations. For each field, we compute the energy of the members of this set and find the lowest energy among them, excluding the obvious ground state configuration with all spins parallel along the field direction. This state turns out to be the unstable fixed point of the map. We show that up to a certain (primary) critical field, a separatrixlike 2pi soliton configuration is the lowest-energy excitation, with an energy very close to the ground state energy. For any field beyond this critical field, the soliton disappears and lowest excitation is a librational configuration corresponding to the outermost orbit in the phase plot at that field. Further, its energy is found to be much higher than the ground state energy, leading to a sharp jump in the difference in energy between the former and the latter at this field. With further increase in the field, sharp jumps in the excitation energy arise at certain secondary critical fields as well. We show that these appear when the corresponding spin configurations become commensurate. This complex behavior of the energy is interpreted and its effect on the magnetization and static susceptibility of the system is also studied.     

Quantum competitions between the effects of the interlayer exchange couplings and the magnetically structural symmetry in a four-layer ferrimagnetic superlattice

The magnon energy spectra, the sublayer magnetization and the quantum fluctuations in a ferrimagnetic superlattice consisting of four different magnetic sublayers are studied by employing the linear spin-wave approach and Green's function technique. The effects of the interlayer exchange couplings and the spin quantum numbers on the sublayer magnetization and the quantum fluctuations of the systems are discussed for three different spin configurations. The roles of quantum competitions among the interlayer exchange couplings and the symmetry of the different spin configurations have been understood. The magnetizations of some sublayers increase monotonously, while those of others can exhibit their maximum, and the quantum fluctuations of the whole superlattice system can show a minimum when one of the antiferromagnetic interlayer exchange couplings increases. This is due to the quantum competition/transmission of effects of the interlayer exchange couplings. When the spin quantum number of sublayers varies, the system goes through from a quantum region of small spin numbers to a classical region of large spin numbers. The quantum fluctuations of the system exhibit a maximum as a function of the spin quantum number of a sublayer, which is related with higher symmetry of the system. It belongs to the type III Shubnikov group of magnetic groups. This magnetically structural symmetry consists of not only the symmetry of space group, but also the symmetry of the direction and strength of spins.     

磁原胞与化学原胞不一致的磁性晶体的磁结构

本文发展了一个讨论磁原胞与化学原胞不一致的磁性晶体的自旋位形的宏观方法。引进一个有限羣,其元素乃是分布于一个磁原胞内的空间羣的元素。该羣的对称元素作用于次晶格的自旋密度上,使热力势保持不变。利用这原理可以建立热力势按次晶格自旋密度的展式。由热力势取极小条件决定磁性晶体的自旋位形。应用这个方法具体地讨论了四类磁性晶体的自旋位形,对每一类情况得到了与中子衍射实验一致的结果。利用本方法在某些情况下,也可以得到螺旋形的自旋位形。     

Magnetic anisotropy of elongated thin ferromagnetic nano-islands for artificial spin ice arrays

The energetics of thin elongated ferromagnetic nano-islands is considered for some different shapes, aspect ratios and applied magnetic field directions. These nano-island particles are important for artificial spin ice materials. For low temperature, the magnetic internal energy of an individual particle is evaluated numerically as a function of the direction of a particle's net magnetization. This leads to estimations of effective anisotropy constants for (1)?the easy axis along the particle's long direction, and (2)?the hard axis along the particle's thin direction. A spin relaxation algorithm together with fast Fourier transform for the demagnetization field is used to solve the micromagnetics problem for a thin system. The magnetic hysteresis is also found. The results indicate some possibilities for controlling the equilibrium and dynamics in spin ice materials by using different island geometries.     

Information storage capacity of discrete spin systems

Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper bound on the amount of information that can be stored reliably in a given volume of discrete spin systems which are supported by gapped local Hamiltonians. However, all the previously known systems were far below this theoretical bound, and it remained open whether there exists a gapped spin system that saturates this bound. Here, we present a construction of spin systems which saturate this theoretical limit asymptotically by borrowing an idea from fractal properties arising in the Sierpinski triangle. Our construction provides not only the best classical error-correcting code which is physically realizable as the energy ground space of gapped frustration-free Hamiltonians, but also a new research avenue for correlated spin phases with fractal spin configurations.     

Dipole-dipole minimum energy configuration for Platonic,Archimedean and Catalan solid structures

Several magnetic materials consisting of dipoles owe their properties to the specific nature of the dipole-dipole interaction. In the present work, we study systems of dipoles where the particles are arranged on various types of three-dimensional structures. However, these solids are not arbitrary. They constitute the well-known Platonic, Archimedean and Catalan solids. We systematically study them in order to fill a gap in the literature that does not contemplate this interaction in the previous solids, despite the fact that they are encountered in many different physical systems. In particular, in the regime of strong dipole moments where a classical treatment is possible, we shall provide not only the minimum energy but also the precise orientations of all their dipoles. We will numerically obtain the minimum energy configuration where all vertices possess the same classic dipole, either electric or magnetic.     

石墨烯纳米片磁有序和自旋逻辑器件第一原理研究

尺寸效应和拓扑阻挫能够在有限石墨烯纳米片段中形成磁有序,本文对能够产生大自旋或电子自旋反铁磁耦合的石墨烯有限片段进行合理分类,提出几种能够作为基本逻辑门的特殊结构并对其进行第一原理电子结构计算,为设计高密度超快自旋器件提供了有效方案和理论依据.计算结果证明：基于有限石墨烯片段的逻辑门结构能够在室温下进行错误率较低的可纠错运算.     

磁性薄膜自旋重取向行为的Monte Carlo模拟

利用Monte Carlo方法模拟了二维简单立方结构磁性薄膜的自旋重取向行为，重点研究了各向异性和偶极相互作用对系统自旋取向的影响．通过计算，获得了系统的相图以及系统组态、磁分量、比热等随偶极相互作用和温度的变化规律．模拟结果表明，在一定的参数范围内，随着温度的升高，系统的自旋取向将由垂直向平行方向转变。     

Magnetic properties of 2D nano-islands II: Ising spin model with out-of-plane magnetic field

An Ising effective field theory model is presented to calculate the magnetic properties of 2D nano-islands on a nonmagnetic substrate, subject to an externally out-of-plane applied magnetic field. The system Hamiltonian contains nearest neighbor exchange interactions, single-atom magnetic anisotropies, and the Zeeman term. The calculations yield, in particular, the single site spin correlations, the magnetizations, and the isothermal susceptibilities, for the core and periphery domains of the nano-island. The choice of a spin S=1 for the atoms of the system permits the analysis of local spin fluctuations via the single site spin correlations. We investigate in this respect the effects due to the different magnetocrystalline anisotropies and reduced dimensionalities, for the core and periphery domains, and in particular the critical influence of the applied magnetic field. Detailed theoretical results are presented for the square and hexagonal lattice symmetries, with numerical applications for the 2D monolayer Co nano-islands on a Pt substrate. It is shown that the remarkable differences between the magnetic properties of the core and periphery domains in zero field are washed out when an out-of-plane field is applied. The applied field also provokes critical discontinuities for the spin correlations and magnetization reversals, for the core and periphery domains, which are especially evident for the hexagonal lattice nano-island in the range of fields of interest. The discontinuities and magnetization reversals occur over elementary temperature widths, and shift to lower temperatures with increasing field. The field-dependant isothermal susceptibilities show new features very different from those for the susceptibilities in zero field. The present Ising model does not show any blocking temperature transition to superparamagnetism.     

Mesoscopic spin clusters, phase separation, and induced order in spin-gap magnets: A review

In many low-dimensional systems with antiferromagnetic interactions, a magnetic order of the Néel type is absent. These systems remain in a quantum-disordered (spin-liquid) state down to zero temperature. The disordered state appears to be stable to weak perturbations when magnetic excitations are separated from the ground state by an energy gap. The stability of the spin-liquid ground state is destroyed upon introduction of impurities or in a sufficiently strong magnetic field. This paper presents a review of the main results of the experimental investigations performed in order to reveal and identify mesoscopic spin clusters formed in the vicinity of impurity ions, to determine the spatial structure of an impurity-induced magnetic order in spin-gap systems, and to examine the low-frequency excitation spectra of field-induced antiferromagnetic phases.     

Anomalous magnetism of the nanocrystalline oxide TiO<Subscript>2</Subscript> surface

The magnetic properties of an oxygen-deficient nanocrystalline undoped titanium dioxide synthesized by the gas-phase, electric-explosion, and chemical method have been studied. The defect state was controlled using reduction treatments in vacuum or in a hydrogen atmosphere. It is shown that the defect state of the surface of nanocrystalline oxides (for example, the existence of vacancies in the anion sublattice and other defects) has a dominant influence on the formation of the magnetic properties of the samples under study. The main contributions to the magnetism of TiO₂ nanoparticles after the reduction treatments are the paramagnetic contribution of the matrix, the paramagnetic Curie–Weiss contribution, and the contribution of the spontaneous magnetic moment provided by the existence of regions with different spin ordering. A heterogeneous magnetic state is found to exist in the TiO₂ nanopowders; for example, at low temperatures, shifted hysteresis loops are observed as a result of a possible set of magnetic states with different spin orders. It is shown that a soft compaction or grinding of nanopowders in an agate mortar lead to substantial increase in the magnetization, sometimes, by a factor of more than two, regardless of the nanopowder synthesis method and the initial phase state of TiO₂ (anatase or rutile structures). This experimental fact proves the key role of the surface defects and the magnetic moment carriers with different spin configurations localized mainly on the nanoparticle surface. The compaction changes the magnetization only in the case when the initial magnetic state has a nonlinear “quasi-superparamagnetic” character of the magnetization curve. As a result of predominant exchange interaction between the nanoparticles with a frustrated character of spin ordering on the nanoparticles surface, the ferromagnetic contribution increases as nanoparticles contact.     

自旋霍尔纳米振荡器的非线性动力学及其应用

自旋霍尔纳米振荡器利用电流产生的自旋轨道力矩驱动磁性薄膜中磁矩进行高频进动,能在微纳尺度下实现全电学调控的相干自旋波和微波信号,是一类新型的纳米自旋电子学器件,在信息存储、处理和通信方面具有广泛的应用前景。基于强自旋轨道矩效应,人们近期在各类铁 磁/非磁重金属构成的双层薄膜结构中,已实现了多种不同自旋波模式的电学激发和调控,并对 其复杂的非线性动力学特性进行了深入的探究。基于这些前期的研究结果与最新的进展,我们在 本综述中对“对三角”结构的纳米间隙型、“蝴蝶结”型、纳米线型、垂直纳米点接触型以及阵 列等具有各类器件结构的自旋霍尔纳米振荡器所体现出来的丰富非线性动力学特性进行了详细讨 论与归纳,并对其在新型低能耗量子磁振子自旋器件和非冯诺依曼架构的自旋型人工神经网络计 算方面的潜在应用也进行了探讨。