Thermodynamic and magnetic properties of the electron gas in the inhomogeneous magnetic field Hr−1

The nonrelativistic and relativistic energy eigenvalues of the electron in the inhomogeneous magnetic fieldH _z =Hr ⁻¹,r=(x ² +y ²)^1/2 are derived in a form displaying the explicit spin dependence. The possibility of magnetic hydrogen atom formation and the spontaneouse ⁺ e ⁻ pair creation following from these eigenvalues is mentioned. The expressions for pressure, energy, particle number and magnetic moment of an electron gas in this IMF are calculated in the degenerate limit. The possibility of spontaneous magnetisation,i.e., ferromagnetic behaviour, is established. Further, the pressure of the electron gas in the same type of fields is an order of magnitude higher than those in a homogeneous magnetic field and crossed homogeneous electric and magnetic fields for comparable field strengths.     

Photodetachment of H- near an elastic surface in a magnetic field

This paper investigates the photodetachment of the negative hydrogen ion H near an elastic wall in a magnetic field.The magnetic field confines the perpendicular motion of the electron,which results in a real three-dimensional well for the detached electron.The analytical formulas for the cross section of the photodetachment in the threedimensional quantum well are derived based on both the quantum approach and closed-orbit theory.The magnetic field and the elastic surface lead to two completely different modulations to the cross section of the photodetachment.The oscillation amplitude depends on the strength of the magnetic field,the ion-wall distance and the photon polarization as well.Specially,for the circularly polarized photon-induced photodetachment,the cross sections display a suppressed(E E th) 1/2 threshold law with energy E in the vicinity above Landau energy E th,contrasting with the(E E th) 1/2 threshold law in the presence of only the magnetic field.The semiclassical calculation fits the quantum result quite well,although there are still small deviations.The difference is attributed to the failure of semiclassical mechanics.     

Density function study transition metal chromium-doped alkali clusters: the finding of magnetic superatom

The structures, stabilities and magnetic properties of CrX_n (X = Na, Rb and Cs; n up to 9) clusters are studied using density functional theory to search for the stable magnetic superatoms. The geometrical optimisations indicate the ground-state structures of CrX_n evolve toward a close packed structure with an interior Cr atom surrounded by X atoms as the cluster size increase. Their stabilities are analysed by the relative energy, gain in energy (ΔE(n)) and the highest unoccupied molecular orbital and lowest unoccupied molecular orbital gaps. Furthermore, the magnetic moments of CrX_n clusters show an odd–even oscillation. Here, we mainly focus on the CrX₇ (X = Na, Rb and Cs) clusters due to the same valence count as the known stable magnetic superatoms VNa₈, VCs₈ and TiNa₉. Although these clusters all have a filled electronic configuration 1S²1P⁶ and large magnetic moment 5 μ_B, our studies indicate that only CrNa₇ is highly stable compared to its nearest neighbours, while CrRb₇ and CrCs₇ clusters are less stable. This suggests that Cr-doped Na₇ is most appropriate for filled electronic configuration and CrNa₇ is shown to be a stable magnetic superatom. More interesting, we find CrRb₈ and CrCs₈ with the filled electronic configuration 1S²1P⁶ have higher stability and large magnetic moment 6 μ_B in their respective series.     

自旋为1/2的XY模型亚铁磁棱型链的物性和有序-无序竞争

利用不变本征算符法, 计算低温下自旋为1/2的XY模型一维亚铁磁棱型链系统的元激发谱, 讨论在此系统中不同的特殊情形下的元激发能量, 从而给出体系的三个临界磁场强度的解析解H_C1, H_C2, H_peak. 分析不同外磁场下 体系的磁化强度随温度的变化规律, 发现三个临界磁场强度的解析解H_C1, H_C2, H_peak是正确的, 并从三个元激发对磁化强度的贡献进行了说明. 低温下磁化强度随外磁场的变化呈现1/3磁化平台. 体系的磁化率随温度或者外磁场的变化都出现了双峰现象. 这说明双峰源于二聚体分子内电子自旋平行排列的铁磁交换作 用能和二聚体与单基体分子间电子自旋反平行排列的反铁磁交换作用能, 热无序能, 外磁场强度相关的自旋磁矩势能之间的竞争.     

Classical Electromagnetic Interaction of a Point Charge and a Magnetic Moment: Considerations Related to the Aharonov–Bohm Phase Shift

A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v ² /c ² is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v ² /c ² , does reveal a connection between the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1/c ⁴ and hence is negligible in a 1/c ² analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the magnetic moment. The changing magnetic moment leads to an electric force back at the point charge which (i) is of order 1/c ² , (ii) depends upon the magnetic dipole moment, changing sign with the dipole moment, (iii) is odd in the charge q of the passing charge, and (iv) reverses sign for charges passing on opposite sides of the magnetic moment. Using the insight gained from this relativistic model and the analogy of a point charge outside a conductor, we suggest that a realistic multi-particle magnetic moment involves a changing magnetic moment which keeps the electromagnetic field momentum constant. This means also that the magnetic moment does not allow a significant shift in its internal center of energy. This criterion also implies that the Lorentz forces on the charged particle and on the point charge are equal and opposite and that the center of energy of each moves according to Newton's second law F=Ma where F is exactly the Lorentz force. Finally, we note that the results and suggestion given here are precisely what are needed to explain both the Aharonov–Bohm phase shift and the Aharonov–Casher phase shift as arising from classical electromagnetic forces. Such an explanation reinstates the traditional semiclassical connection between classical and quantum phenomena for magnetic moment systems.     

Dynamos at extreme magnetic Prandtl numbers: insights from shell models

We present a magnetohydrodynamic (MHD) shell model suitable for computation of various energy fluxes of MHD turbulence for very small and very large magnetic Prandtl numbers Pm; such computations are inaccessible to direct numerical simulations. For small Pm, we observe that both kinetic and magnetic energy spectra scale as k^?5/3 in the inertial range, but the dissipative magnetic energy scales as k^?11/3exp?(? k/k_η). Here the kinetic energy at large length scale feeds the large-scale magnetic field that cascades to small-scale magnetic field, which gets dissipated by Joule heating. The large-Pm dynamo has a similar behaviour except that the dissipative kinetic energy scales as k^?13/3. For this case, the large-scale velocity field transfers energy to the large-scale magnetic field, which gets transferred to small-scale velocity and magnetic fields; the energy of the small-scale magnetic field also gets transferred to the small-scale velocity field, and the energy thus accumulated is dissipated by the viscous force.     

Enhanced magnetic coercivity and maximum energy product in double‐perovskite Y2CoMnO6single crystals

We have investigated the influence of different annealing conditions on the magnetic properties on the single crystals of double‐perovskite Y₂CoMnO₆. The ferromagnetic moment along the c‐axis with the large magnetic coercivity and high squareness ratio was observed. Particularly, in the quenched specimen, the magnetic functionality has been greatly improved compared to that of the as‐grown crystal. The magnetic coercivity and maximum energy product have been increased by ～120% and ～50%, respectively, by comprising substantial disorders and defects. Our result renders an efficient route to improve the magnetic functionality in mixed‐valent magnets. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Valley filtering due to orbital magnetic moment in bilayer graphene

We investigate the effect of valley-dependent orbital magnetic moment on the transmission of quasiparticles through biased bilayer graphene npn and pnp junctions in the presence of out-of-plane magnetic field. It is shown that the valley-polarized Zeeman-like energy splitting, due to the interaction of orbital magnetic moment with magnetic field, can suppress the transmission of quasiparticles of one valley while transmitting those of the other valley. This valley-selective transmission property can be exploited for valley filtering. We demonstrate that the npn and pnp junction, respectively, filters off the $K^{\prime }$-valley and K-valley particles, with nearly perfect degree of filtration.     

Neutron Scattering and a.c. Susceptibility Studies on the Geometrically Frustrated Tb2Ti2O7

We have performed neutron scattering and a.c. susceptibility _a.c. studies on polycrystallline Tb₂Ti₂O₇ to investigate the magnetic correlations in this antiferromagnetic pyrochlores. Evidence of changes in the magnetic correlation length has been observed by neutron diffraction in different parts of an applied field/temperature phase diagram. This cooperative paramagnet has been shown to increase its magnetic correlations, from nearest neighbour to 100 Å, in modest fields (<7 T) and temperatures (T>2 K); however, in zero field the system does not order above 15 mK, even with its large moment.     

Structural, electronic and magnetic properties of the Mnben Ni(110) c(2×2) surface alloy

Using first-principles total energy method, we study the structural, the electronic and the magnetic properties of the MnNi(110) c(2×2) surface alloy. Paramagnetic, ferromagnetic, and antiferromagnetic surfaces in the top layer and the second layer are considered. It turns out that the substitutional alloy in the outermost layer with ferromagnetic surface is the most stable in all cases. The buckling of the Mn–Ni(110) c(2×2) surface alloy in the top layer is as large as 0.26á(1á=0.1 n13) and the weak rippling is 0.038 AA in the third layer, in excellent agreement with experimental results. It is proved that the magnetism of Mn can stabilize this surface alloy. Electronic structures show a large magnetic splitting for the Mn atom, which is slightly higher than that of Mn–Ni(100) c(2×2) surface alloy (3.41 eV) due to the higher magnetic moment. A large magnetic moment for the Mn atom is predicted to be 3.81 μ_B. We suggest the ferromagnetic order of the Mn moments and the ferromagnetic coupling to the Ni substrate, which confirms the experimental results. The magnetism of Mn is identified as the driving force of the large buckling and the work-function change. The comparison with the other magnetic surface alloys is also presented and some trends are predicted.     

Magnetic behaviour of TbMnFe

Neutron diffraction and M?ssbauer measurements have been carried out on the cubic Laves phase intermetallic TbMnFe. The magnetic moment on the transition metal atom is found to be low, 0.2μ _B, at room temperature. This moment is temperature independent down to 10 K. Magnetic moment on the rare earth atom varies from 2.5μ _B at 296 K to 7.27μ _B at 10 K. M?ssbauer spectra recorded at 298 K and 78 K have magnetic character but there is a large distribution of hyperfine field values. Both these features arise due to magnetic frustration created in the sample due to the competing ferro and antiferromagnetic interactions between the transition metal atoms.     

On the spectrum of the hydrogen atom in an ultrastrong magnetic field

Various approaches to computing the energies of the ground state and excited levels of the hydrogen atom in an ultrastrong magnetic field B that considerably exceeds the field B _a = m _e ² e ³ c/ħ ³ ∼ 10⁹ G are considered. The effects of polarization of vacuum and anomalous magnetic moment of the electron on the position of the atomic levels are discussed. The vacuum polarization effects are negligibly weak for B < 10¹⁵ G but become significant in fields B ≫ 10¹⁶ G, in which these effects qualitatively modify the atomic spectrum in this range. The difference in the behaviors of the even and odd energy levels for B ≫ B _a is analyzed and the formulas for the energies of odd levels as a function of field B are refined.     

Magnetic Moment of the 3/2− Ground State of 185W

Nuclear magnetic resonance measurement have been performed for ¹⁸⁵W oriented at 8 mK in an Fe host. The magnetic hyperfine splitting frequency at an external magnetic field of 0.1 T was determined to be 196.6(2) MHz. With the known hyperfine field of B _hf = −71.4(18) T, the nuclear magnetic moment of ¹⁸⁵W is deduced as μ(¹⁸⁵W) = +0.543(14) μ_N.     

Mn5Ge2.7M0.3 (M=Ga，Al，Sn) 化合物的磁性和磁熵变

研究了Mn₅Ge_2.7M_0.3(M=Ga，Al，Sn)化合物的磁性和磁熵变. x射线衍射实验表明，研究的化合物均呈六角Mn₅Si₃型结构. 三种原子对Ge原子的替代，使得平均Mn原子磁矩下降，但居里温度没有明显的变化. 由于磁矩的降低，导致磁熵变值的下降，在磁场变化为4.0×10⁶A·m^-1时，对应于M=Ga，Al和Sn的样品，最大磁熵变值ΔS^max_Ｍ分别为6.1，6.3和5.3J·kg^-1K^-1，但磁熵变峰值的半高宽ΔＴ_ＦＷＨＭ有所增加. 另外，Mn₅Ge_2.7M_0.3(M=Ga，Al，Sn)化合物在高于居里温度的Arrott曲线上出现了一个不连续点，即样品在一定温度下的顺磁磁化率在某一临界磁场下发生了突变，临界磁场与温度几乎呈正比关系.这可能是由于样品在加一定磁场时3d带的费米能级发生了变化，使得有效电子数的减少所致. 关键词： 居里温度 平均Mn原子磁矩 磁熵变 Arrott图     

A Review of NMR Studies in RCo3 Systems Presenting d-Moment Instability

For the past few years, intermetallic systems with the formula RCo₃, where R is a rare earth, have attracted the attention of the magnetism community. In these systems, the magnetism associated to the Co ions presents a magnetic instability which gives rise to metamagnetic phase transitions observed as a change on the Co magnetic moment for some critical values of the molecular field acting on this sublattice. A number of publications about these systems is concerned with basic magnetic measurements and ⁵⁹Co NMR in compounds such as Y_1–x R _x Co₃, where R = Gd, Nd, Er. The Co ions are distributed among three crystal sites with different symmetries, one of these sites being further split into two magnetic sites, a fact in itself that considerably complicates the NMR spectra. Besides, as we have observed, the linewidths and even the number of lines appearing on the NMR spectra are strongly dependent on some NMR features, such as the radiofrequency power applied to the sample. Adding to this fact, these magnetic peculiarities depend on the compounds stoichiometry; therefore it is no surprise to find conflicting results in the literature. In the present paper a review of the NMR published data will be made, including some new results of our own.     

Magnetic ordering in Ho‐doped Bi2Te3 topological insulator

We investigate the magnetic properties of Ho‐doped Bi₂Te₃ thin films grown by molecular beam epitaxy. Analysis of the polarized X‐ray absorption spectra at the Ho M₅ absorption edge gives an effective 4f magnetic moment which is ～45% of the Hund's rule ground state value. X‐ray magnetic circular dichroism (XMCD) shows no significant anisotropy, which suggests that the reduced spin moment is not due to the crystal field effects, but rather the presence of non‐magnetic or antiferromagnetic Ho sites. Extrapolating the temperature dependence of the XMCD measured in total electron yield and fluorescence yield mode in a field of 7 T gives a Curie–Weiss temperature of ?_CW ≈ –30 K, which suggests antiferromagnetic ordering, in contrast to the paramagnetic behavior observed with SQUID magnetometry. From the anomaly of the XMCD signal at low temperatures, a Néel temperature T_N between 10 K and 25 K is estimated. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Structural and magnetic properties of Fe<Subscript>m</Subscript>Y<Subscript>n</Subscript> (m + n = 7, Y = Ru,Rh, Pd,and Pt) nanoalloys

The structural and magnetic properties of the small binary clusters Fe _m Y _n (with m + n = 7, Y = Ru, Rh, Pd, Pt) were studied through extensive ab initio calculations, by means of the fully unconstrained version of the density-functional method, as implemented in the SIESTA code, within the generalized gradient approximation. The lowest energy state geometries, the chemical ordering, and the electronic and the magnetic structures were calculated. We found that the lowest energy geometrical structures for the pure Ru, Rh, Pd, Pt, and Fe heptamers, are a cube without an apex, a triangular prism capped on a square face, a decahedron, a side capped double square, and a decahedron, respectively. Starting from these geometries of the pure element heptamers, we followed the changes in the geometric structure as a function of the chemical composition. We analyzed all the different chemical arrangements, which depend on the particular geometry, and magnetic moment orientations, in the whole range of compositions. In general, there are important modifications to the magnetic moment of the Y atoms as soon as one of them is substituted by an Fe atom in the cluster. In contrast, under the same circumstances, the Fe magnetic moment takes values larger than 3 μ _B and keeps almost this value, insensitive to the structure, composition and chemical order of the system.     

Spin coupling and magnetic field effects on the finite-size free energy and its non-extensivity for 1-D Ising model with nearest and next-nearest neighbor interactions in nanosystem

The effects of second-neighbor spin coupling interactions and a magnetic field are investigated on the free energies of a finite-size 1-D Ising model. For both ferromagnetic of nearest neighbor (NN) and next-nearest neighbor (NNN) spin coupling interactions, the finite-size free energy first increases and then approaches a constant value for any size of the spin chain. In contrast, when NNN and NN spin coupling interactions are antiferromagnetic and ferromagnetic, respectively, the finite-size free energy gradually decreases by increasing the competition factor and eventually vanishes for large values of it. When a magnetic field is applied, the finite-size free energy decreases with respect to the case of zero magnetic fields for both ferromagnetic and antiferromagnetic spin coupling interactions. Deviation of free energy per size for finite-size systems relative to the infinite system increases when the spin coupling interactions as well as the f parameter (the ratio of the magnetic field to NN spin coupling interaction) increase.     

Passage of relativistic magnetic dipole moments through magnetic fields

We have solved the Dirac equation with an anomalous moment Pauli-coupling exactly for a constant magnetic field and derived the general relativistic formulas for phase changes due to translational motion and spin rotations. We also give transmission and reflection coefficients, spin rotation for tunnelling and barrier penetration. For ultrarelativistic particles the spin rotation angle on the path of lengthL is equal to (2μB L/ħc)[1 +m ² c ⁴/(E²-μ ² B ²)].