arXiv subjects

T. A. Kaplan

Publications and source records attributed to T. A. Kaplan.

9 recordsLinked to original sources

arXiv2011

Canted-spin-caused electric dipoles: a local symmetry theory

A pair of magnetic atoms with canted spins Sa, Sb can give rise to an electric dipole moment P. Several forms for the behavior of such a moment have appeared in the theoretical literature, some of which have been invoked to explain experimental results found in various multiferroic materials. The forms specifically are P1 ~ R x (Sa x Sb); P2 ~ Sa x Sb, and P3 ~ Sa (R . Sa) - Sb (R . Sb), where R is the relative position of the atoms and Sa, Sb are unit vectors. To unify and generalize these various forms we consider P as the most general quadratic function of the spin components that vanishes whenever Sa and Sb are collinear, i.e. we consider the most general expressions that require spin canting. The study reveals new forms. We generalize to the vector P, Moriya's symmetry considerations regarding the (scalar) Dzyaloshinskii-Moriya energy D. Sa x Sb (which led to restrictions on D). This provides a rigorous symmetry argument which shows that P1 is allowed no matter how high the symmetry of the atoms plus environment, and gives restrictions for all other contributions. The analysis leads to the suggestion of terms omitted in the existing microscopic models, suggests a new mechanism behind the ferroelectricity found in the 'proper screw structure' of CuXO2, X=Fe, Cr, and predicts an unusual antiferroelectric ordering in the antiferromagnetically and ferroelectrically ordered phase of RbFe(MoO4)2.

cond-mat.str-el↗

arXiv2010

Frustrated classical Heisenberg and XY models in 2 dimensions with nearest neighbor exchange: exact solution for the ground state phase diagram

The ground state phase diagram is determined exactly for the frustrated classical Heisenberg model plus nearest-neighbor biquadratic exchange interactions on a 2-dimensional lattice. A square- and a rhombic-symmetry version are considered. There appear ferromagnetic, incommensurate-spiral, "up-up-down-down" (uudd) and canted ferromagnetic states, a non-spiral coplanar state that is an ordered vortex lattice, plus a non-coplanar ordered state (a "conical vortex lattice"). In the rhombic case, which adds biquadratic terms to the Heisenberg model used widely for insulating manganites, the uudd state found is the E-type state observed; this along with accounting essentially for the variety of ground states found in these materials, shows that this model probably contains the long-sought mechanism behind the uudd state.

cond-mat.str-el↗

arXiv2009

Comment on 'Distorted perovskite with $e_g^1$ configuration as a frustrated spin system'

Interesting magnetic structure found experimentally in a series of manganites RMnO$_3$, where R is a rare earth, was explained, ostensibly, by Kimura et al, in terms of a classical Heisenberg model with an assumed set of exchange parameters, nearest-neighbor and next-nearest-neighbor interactions, $J_n$. They calculated a phase diagram as a function of these parameters for the ground state, in which the important "up-up-down-down" or E-phase occurs for finite ratios of the $J_n$. In this Comment we show that this state does not occur for such ratios; the error is traced to an incorrect method for minimizing the energy. The correct phase diagram is given. We also point out that the finite temperature phase diagram presented there is incorrect.

cond-mat.str-el↗

arXiv2009

Frustrated classical Heisenberg model in 1 dimension with added nearest-neighbor biquadratic exchange interactions

The ground state phase diagram is determined for the frustrated classical Heisenberg chain with added nearest-neighbor biquadratic exchange interactions. There appear ferromagnetic, incommensurate-spiral, and up-up-down-down phases; a lock-in transition occurs at the spiral boundary. The model contains an isotropic version of the ANNNI model; it is also closely related to a model proposed for some manganites. The Luttinger-Tisza method is not obviously useful due to the non-linear weak-constraint problem; however the ground state is obtained analytically by the exact cluster method of Lyons and Kaplan. The results are compared to the model of Thorpe and Blume, where the Heisenberg part of the energy is not frustrated.

cond-mat.str-el↗

arXiv2007

Scanning-probe spectroscopy of semiconductor donor molecules

Semiconductor devices continue to press into the nanoscale regime, and new applications have emerged for which the quantum properties of dopant atoms act as the functional part of the device, underscoring the necessity to probe the quantum structure of small numbers of dopant atoms in semiconductors[1-3]. Although dopant properties are well-understood with respect to bulk semiconductors, new questions arise in nanosystems. For example, the quantum energy levels of dopants will be affected by the proximity of nanometer-scale electrodes. Moreover, because shallow donors and acceptors are analogous to hydrogen atoms, experiments on small numbers of dopants have the potential to be a testing ground for fundamental questions of atomic and molecular physics, such as the maximum negative ionization of a molecule with a given number of positive ions[4,5]. Electron tunneling spectroscopy through isolated dopants has been observed in transport studies[6,7]. In addition, Geim and coworkers identified resonances due to two closely spaced donors, effectively forming donor molecules[8]. Here we present capacitance spectroscopy measurements of silicon donors in a gallium-arsenide heterostructure using a scanning probe technique[9,10]. In contrast to the work of Geim et al., our data show discernible peaks attributed to successive electrons entering the molecules. Hence this work represents the first addition spectrum measurement of dopant molecules. More generally, to the best of our knowledge, this study is the first example of single-electron capacitance spectroscopy performed directly with a scanning probe tip[9].

cond-mat.mes-hall↗

arXiv2006

Simple microscopic model of the magneto-electric effect in non-collinear magnets

A 2-site 2-electron model with s- and p-states on each site, having constrained average site-spins S_a, S_b, with angle theta between them, simpler than the previous closely-related model of Katsura et al (KNB), is considered. Intra-site Coulomb repulsion and inter-site spin-orbit coupling V_(SO) are included. The ground state has an electric dipole moment pi consistent with the result of KNB, pi proportional to R x (S_a x S_b) = f, R connecting the two sites, and application to a spiral leads to ferroelectric polarization with direction f, also in agreement with the previous result. However, the present result shows the expected behavior pi goes to 0 as V_(SO) goes to 0, unlike the previous one.

cond-mat.other↗

arXiv2005

On Fermion Entanglement

Under the historical definition of entanglement, namely that encountered in Einstein--Podolski--Rosen (EPR)--type experiments, it is shown that a particular Slater determinant is entangled. Thus a definition which holds that any Slater determinant is unentangled, found in the literature, is inconsistent with the historical definition. A generalization of the historical definition that embodies its meaning as quantum correlation of observables, in the spirit of the work of many others, but is much simpler and more physically transparent, is presented.

quant-ph↗

arXiv2005

The Chemical Potential

The definition of the fundamental quantity, the chemical potential, is badly confused in the literature: there are at least three distinct definitions in various books and papers. While they all give the same result in the thermodynamic limit, major differences between them can occur for finite systems, in anomalous cases even for finite systems as large as a cm$^3$. We resolve the situation by arguing that the chemical potential defined as the symbol $μ$ conventionally appearing in the grand canonical density operator is the uniquely correct definition valid for all finite systems, the grand canonical ensemble being the only one of the various ensembles usually discussed (microcanonical, canonical, Gibbs, grand canonical) that is appropriate for statistical thermodynamics, whenever the chemical potential is physically relevant. The zero-temperature limit of this $μ$ was derived by Perdew et al. for finite systems involving electrons, generally allowing for electron-electron interactions; we extend this derivation and, for semiconductors, we also consider the zero-T limit taken after the thermodynamic limit. The enormous finite size corrections (in macroscopic samples, e.g. 1 cm$^3$) for one rather common definition of the c.p., found recently by Shegelski within the standard effective mass model of an ideal intrinsic semiconductor, are discussed. Also, two very-small-system examples are given, including a quantum dot.

cond-mat.stat-mech↗

arXiv2004

Spin swap vs. double occupancy in quantum gates

We propose an approach to realize quantum gates with electron spins localized in a semiconductor that uses double occupancy to advantage. With a fast (non-adiabatic) time control of the tunnelling, the probability of double occupancy is first increased and then brought back exactly to zero. The quantum phase built in this process can be exploited to realize fast quantum operations. We illustrate the idea focusing on the half-swap operation, which is the key two-qubit operation needed to build a CNOT gate.

cond-mat.mes-hall↗