Erratum: Axisymmetric and nonaxisymmetric toroidal vesicle membranes [Acta Phys. Sin. (Overseas Edn), 2, 8811 (1993)]

Xie, Yan; Ouyang, Zhen

doi:10.1088/1004-423x/3/3/009

Cited by 8 publications

(8 citation statements)

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“…After the PSS was revealed as a relativistic symmetry, numerous efforts have been dedicated to tracing the relativistic origin of PSS and its breaking mechanism in a quantitative way. These investigations include the one-dimensional Woods-Saxon potential [33], the spherical Woods-Saxon [34][35][36][37][38], Coulomb [39][40][41], harmonic oscillator [42][43][44][45][46][47][48][49], anharmonic oscillator [50], Hulthén [51,52], Morse [53][54][55][56][57], Rosen-Morse [58,59], Eckart [60,61], Pöschl-Teller [62][63][64][65], diatomic molecular [66], Manning-Rosen [67][68][69], Mie-type [70,71], and Yukawa [72] potentials, as well as the deformed harmonic oscillator [73][74][75][76][77][78], anharmonic o...…”

Section: Introductionmentioning

confidence: 99%

Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations

et al. 2013

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The origin of pseudospin symmetry (PSS) and its breaking mechanism are explored by combining supersymmetry (SUSY) quantum mechanics, perturbation theory, and the similarity renormalization group (SRG) method. The Schrödinger equation is taken as an example, corresponding to the lowest-order approximation in transforming a Dirac equation into a diagonal form by using the SRG. It is shown that while the spin-symmetry-conserving term appears in the single-particle Hamiltonian H, the PSS-conserving term appears naturally in its SUSY partner HamiltonianH.The eigenstates of Hamiltonians H andH are exactly one-to-one identical except for the so-called intruder states. In such a way, the origin of PSS deeply hidden in H can be traced in its SUSY partner HamiltonianH. The perturbative nature of PSS in the present potential without spin-orbit term is demonstrated by the perturbation calculations, and the PSS-breaking term can be regarded as a very small perturbation on the exact PSS limits. A general tendency that the pseudospinorbit splittings become smaller with increasing single-particle energies can also be interpreted in an explicit way.

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Section: Introductionmentioning

confidence: 99%

Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations

et al. 2013

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“…The structures Ti(30)/Au (20) (5), where x is 0 (single magnetic tunnel junction -SMTJ) or 2 nm (double magnetic tunnel junction -DMTJ), were fabricated on natural oxidized single crystal Si square substrates (1 × 1 cm 2 ) with an electron-beam deposition system in vacuum 10 -7 Torr. The layers' thickness is shown in nanometers.…”

Section: Methodsmentioning

confidence: 99%

Magnetic anisotropy and domain structure in spin-valves based on MTJ

Samardak¹,

Sukovatitsina²,

Ognev³

et al. 2011

J. Phys.: Conf. Ser.

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Abstract. We have studied the crystal structure, surface morphology, magnetic anisotropy, domain structure and tunnel magnetoresistance of spin-valves with a single and double MgO barrier layers. We have demonstrated the domain structure for soft and hard magnetic layers and observed significant changes after low temperature annealing. We have carried out magnetoresistance measurements using current-in-plane (CIP) four-probe technique and discovered a substantial difference in the values of TMR ratio for single and double MTJ spinvalves. It is shown that domain structure and magnetization reversal are the same for both systems, but otherwise the behavior of tunnel magnetoresistance is different, because of second MgO barrier effects on the system conductivity. The ability to manipulate the magnetization direction in MTJ systems using temperature annealing is demonstrated. It makes these structures possible for new applications in nanoelectronics as magnetic recording media and high sensitive sensors. 1.IntroductionThe multicomponent magnetic systems are new class of spintronic materials having unique combination of magnetic and electrical properties for prospective nanoelectronic applications as a nonvolatile magnetoresistance memory (MRAM), spin-valve sensors and microwave spin-current generators [1][2][3]. The spin-valves based on magnetic tunnel junctions are very interesting objects for investigation, because of they combine all remarkable properties of both devices: high magnetic field sensitivity and high value of magnetoresistance [4,5]. The classical spin-valve is based on two ferromagnets with different coercive forces separated by a thin metal spacer [5]. The relative magnetization orientation of the two ferromagnetic layers strongly modulates the charge flow through the structure. Using this property of the spin-valve, external magnetic field acting on the magnetic moments of the ferromagnetic layers can be sensed electrically. Spin-valves with insulating interlayers, such as Al 2 O 3 [6] or MgO [7], are called magnetic tunnel junctions (MTJs) and designed to have two stable parallel and anti-parallel states, can also serve as non-volatile solid-state memory elements [8]. These applications, as read head sensors in hard magnetic disks and memory cells in MRAM are perfect examples of a fast transformation of a fundamental physics discovery [9][10][11] in to large scale practical devices. This makes spintronic nanostructures not only of fundamental interest, 1To whom any correspondence should be addressed. Published under licence by IOP Publishing Ltd

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“…The radial equation (29) has an irregular singularity at ρ = ∞. Furthermore, it has a singularity at ρ = 0.…”

Section: Solutions Of Dirac Equation With the New Rnho Potentialmentioning

confidence: 99%

“…Guo et al have solved the Dirac equation with the RNHO potential (see (1)) under the condition of pseudospin symmetry and several particular cases are also discussed [28]. Recently, we have proposed a new RNHO potential, which is replaced the term (sin −2 θ cos 2 θ) by (sin −2 θ cos θ) in (2), and solved the Klein-Gordon equation and Dirac equation with equal scalar and vector potentials, and obtained energy spectrum of bound states and wave functions [29]. Considering that there has been a wide interest in relativistic potentials involving mixtures of vector and scalar potentials with opposite signs, the interest lies on attempts to explain the pseudospin symmetry.…”

Section: Introductionmentioning

confidence: 99%