arXiv subjects

Burkhard Schmidt

Publications and source records attributed to Burkhard Schmidt.

51 records · Page 3Linked to original sources

arXiv2014

Maximum tunneling velocities in symmetric double well potentials

We consider coherent tunneling of one-dimensional model systems in non-cyclic or cyclic symmetric double well potentials. Generic potentials are constructed which allow for analytical estimates of the quantum dynamics in the non-relativistic deep tunneling regime, in terms of the tunneling distance, barrier height and mass (or moment of inertia). For cyclic systems, the results may be scaled to agree well with periodic potentials for which semi-analytical results in terms of Mathieu functions exist. Starting from a wavepacket which is initially localized in one of the potential wells, the subsequent periodic tunneling is associated with tunneling velocities. These velocities (or angular velocities) are evaluated as the ratio of the flux densities versus the probability densities. The maximum velocities are found under the top of the barrier where they scale as the square root of the ratio of barrier height and mass (or moment of inertia), independent of the tunneling distance. They are applied exemplarily to several prototypical molecular models of non-cyclic and cyclic tunneling, including ammonia inversion, Cope rearrangment of semibullvalene, torsions of molecular fragments, and rotational tunneling in strong laser fields. Typical maximum velocities and angular velocities are in the order of a few km/s and from 10 to 100 THz for our non-cyclic and cyclic systems, respectively, much faster than time-averaged velocities. Even for the more extreme case of an electron tunneling through a barrier of height of one Hartree, the velocity is only about one percent of the speed of light. Estimates of the corresponding time scales for passing through {the narrow domain just} below the potential barrier are in the domain from 2 to 40 fs, much shorter than the tunneling times.

physics.chem-ph↗

arXiv2014

Quantum fluctuations in anisotropic triangular lattices with ferro- and antiferromagnetic exchange

The Heisenberg model on a triangular lattice is a prime example for a geometrically frustrated spin system. However most experimentally accessible compounds have spatially anisotropic exchange interactions. As a function of this anisotropy, ground states with different magnetic properties can be realized. Motivated by recent experimental findings on Cs$_{2}$CuCl$_{4-x}$Br$_{x}$, we discuss the full phase diagram of the anisotropic model with two exchange constants $J_{1}$ and $J_{2}$, including possible ferromagnetic exchange. Furthermore a comparison with the related square lattice model is carried out. We discuss the zero-temperature phase diagram, ordering vector, ground-state energy, and ordered moment on a classical level and investigate the effect of quantum fluctuations within the framework of spin-wave theory. The field dependence of the ordered moment is shown to be nonmonotonic with field and control parameter.

cond-mat.str-el↗

arXiv2013

Topology of surfaces for molecular Stark energy, alignment and orientation generated by combined permanent and induced electric dipole interactions

We show that combined permanent and induced electric dipole interactions of polar and polarizable molecules with collinear electric fields lead to a sui generis topology of the corresponding Stark energy surfaces and of other observables - such as alignment and orientation cosines - in the plane spanned by the permanent and induced dipole interaction parameters. We find that the loci of the intersections of the surfaces can be traced analytically and that the eigenstates as well as the number of their intersections can be characterized by a single integer index. The value of the index, distinctive for a particular ratio of the interaction parameters, brings out a close kinship with the eigenproperties obtained previously for a class of Stark states via the apparatus of supersymmetric quantum mechanics.

physics.chem-ph↗

arXiv2011

"Centrifugal fragmentation" in the photodissociation of H2+ in intense laser fields

By means of quantum-dynamical and classical trajectory calculations of H2+ photodissociation in strong laser fields, it is shown that for certain combinations of pulse durations and intensities the rotational dynamics can lead to centrifugal fragmentation. In that case, the photofragments exhibit characteristic angular distributions. The classical calculations provide a transparent physical picture of this mechanism which is also very well established in collisions between atomic nuclei or liquid droplets: non-rotating systems are stable, whereas rotating systems fragment due to the decrease of the fragmentation barrier with increasing angular momentum.

physics.atm-clus↗

arXiv2011

Staggered moment dependence on field-tuned quantum fluctuations in 2D frustrated antiferromagnets

We propose an efficient method to identify the degree of frustration in quasi-2D antiferromagnets described by the J_1-J_2 Heisenberg model. The frustration ratio J_2/J_1 is usually obtained from analysis of susceptibility, specific heat and saturation field. We show that the non-monotonic field dependence of the staggered moment caused by the suppression of quantum fluctuations in a field depends strongly on the frustration ratio. This gives a powerful criterion to determine J_2/J_1 using a combination of exact diagonalization (ED) method for finite clusters and spin wave analysis. We apply this method to the quasi-2D compound Cu(pz)_2(ClO_4)_2 and show that it leads to an intermediate ratio J_2/J_1 ~ 0.2 for the frustration. We also explain the observed anomalous increase of transition temperature in applied fields as an effect of reduced quantum fluctuations.

cond-mat.str-el↗

arXiv2011

Ordered moment in the anisotropic and frustrated square lattice Heisenberg model

The two-dimensional frustrated next nearest neighbor Heisenberg model on the square lattice is a prime example for a spin system where quantum fluctuations can either destroy or stabilize magnetic order. The phase boundaries and staggered moment dependence on the frustration ratio J_2/J_1 of the exchange constants are fairly well understood both from approximate analytical and numerical methods. In this work we use exact diagonalization for finite clusters for an extensive investigation of the more general J_1a,b-J_2 model which includes a spatial exchange anisotropy between next-neighbor spins. We introduce a systematic way of tiling the square lattice and, for this low symmetry model, define a controlled procedure for the finite size scaling that is compatible with the possible magnetic phases. We obtain ground state energies, structure factors and ordered moments and compare with the results of spin wave calculations. We conclude that J_1a,b exchange anisotropy strongly stabilizes the columnar antiferromagnetic phase for all frustration parameters, in particular in the region of the spin nematic phase of the isotropic model.

cond-mat.str-el↗

arXiv2010

Frustrated local moment models for Fe-pnictide magnetism

The low energy spin excitations of the Fe pnictide parent compounds have been determined by inelastic neutron scattering and interpreted within the local moment J_1a,b-J_2 Heisenberg model with orthorhombic symmetry. This has led to alternative exchange models that strongly differ in the size of anisotropy. Although the compounds are itinerant the localised spin model can explain basic features of the excitations. The inherent frustration of this model leads to quantum fluctuations and possible moment reduction. We investigate this question in detail using spin wave approximation and partly exact diagonalisation Lanczos calculations for finite clusters. We find that the orthorhombic anisotropy stabilizes the columnar AF phase and its moment. For the exchange models proposed from inelastic neutron scattering we can exclude a strong influcence of frustration on the moment size. We also investigate dependence of magnetisation and susceptibility on field and temperature.

cond-mat.str-el↗

arXiv2009

The two-dimensional frustrated Heisenberg model on the orthorhombic lattice

We discuss new high-field magnetization data recently obtained by Tsirlin et al. for layered vanadium phosphates in the framework of the square-lattice model. Our predictions for the saturation fields compare exceptionally well to the experimental findings, and the strong bending of the curves below saturation agrees very well with the experimental field dependence. Furthermore we discuss the remarkably good agreement of the frustrated Heisenberg model on the square lattice in spite of the fact that the compounds described with this model actually have a lower crystallographic symmetry. We present results from our calculations on the thermodynamics of the model on the orthorhombic (i.e., rectangular) lattice, in particular the temperature dependence of the magnetic susceptibility. This analysis also sheds light on the discussion of magnetic frustration and anisotropy of a class of iron pnictide parent compounds, where several alternative suggestions for the magnetic exchange models were proposed.

cond-mat.str-el↗

arXiv2009

Exploring the spin-1/2 frustrated square lattice model with high-field magnetization measurements

We report on high-field magnetization measurements for a number of layered vanadium phosphates that were recently recognized as spin-1/2 frustrated square lattice compounds with ferromagnetic nearest-neighbor couplings (J_1) and antiferromagnetic next-nearest-neighbor couplings (J_2). The saturation fields of the materials lie in the range from 4 to 24 T and show excellent agreement with the previous estimates of the exchange couplings deduced from low-field thermodynamic measurements. The consistency of the high-field data with the regular frustrated square lattice model provides experimental evidence for a weak impact of spatial anisotropy on the nearest-neighbor couplings in layered vanadium phosphates. The variation of the J_2/J_1 ratio within the compound family facilitates the experimental access to the evolution of the magnetization curve upon the change of the frustration magnitude. Our results support the recent theoretical prediction by Thalmeier et al. [Phys. Rev. B, 77, 104441 (2008)] and give evidence for the enhanced bending of the magnetization curves due to the increasing frustration of the underlying spin system.

cond-mat.str-el↗

arXiv2006

Two-dimensional frustrated spin systems in high magnetic fields

We discuss our numerical results on the properties of the S = 1/2 frustrated J1-J2 Heisenberg model on a square lattice as a function of temperature and frustration angle phi = atan(J2/J1) in an applied magnetic field. We cover the full phase diagram of the model in the range -pi <= phi <= pi. The discussion includes the parameter dependence of the saturation field itself, and addresses the instabilities associated with it. We also discuss the magnetocaloric effect of the model and show how it can be used to uniquely determine the effective interaction constants of the compounds which were investigated experimentally.

cond-mat.str-el↗

arXiv2006

Kondo Lattice Model with Finite Temperature Lanczos Method

We investigate the Kondo Lattice Model on 2D clusters using the Finite Temperature Lanczos Method. The temperature dependence of thermodynamic and correlations functions are systematically studied for various Kondo couplings JK. The ground state value of the total local moment is presented as well. Finally, the phase diagrams of the finite clusters are constructed for periodic and open boundary conditions. For the two boundary conditions, two different regimes are found for small JK/t, depending on the distribution of non-interacting conduction electron states. If there are states within JK around the Fermi level, two energy scales, linear and quadratic in JK, exist. The former is associated with the onsite screening and the latter with the RKKY interaction. If there are no states within JK around the Fermi level, the only energy scale is that of the RKKY interaction. Our results imply that the form of the electron density of states (DOS) plays an important role in the competition between the Kondo screening and the RKKY interaction. The former is stronger if the DOS is larger around the Fermi level, while the latter is less sensitive to the form of the DOS.

cond-mat.str-el↗

arXiv2004

Third-order magnetic susceptibility of the frustrated square-lattice antiferromagnet

We present results from our analysis of the finite-temperature properties of the spin 1/2 $J_{1}$-$J_{2}$ Heisenberg model on a square lattice. The analysis is based on the exact diagonalization of small clusters with 16 and 20 sites utilizing the finite-temperature Lanczos method. In particular, we focus on the temperature dependence of the third-order magnetic susceptibility as a method to resolve the ambiguity of exchange constants. We discuss the entire range of the frustration angle $ϕ=\tan^{-1}(J_{2}/J_{1})$ parameterizing the different possible phases of the model, including the large region in the phase diagram with at least one ferromagnetic exchange constant.

cond-mat.str-el↗

arXiv2004

Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model

The spin 1/2 Heisenberg model on a square lattice with antiferromagnetic nearest- and next-nearest neighbour interactions (the $J_1$--$J_2$ model) has long been studied as a paradigm of a two-dimensional frustrated quantum magnet. Only very recently, however, have the first experimental realisations of such systems been synthesized. The newest material, Pb$_2$VO(PO$_4$)$_2$ seems to have mixed ferro-- and antiferromagnetic exchange couplings. In the light of this, we extend the semiclassical treatment of the $J_1$--$J_2$ model to include ferromagnetic interactions, and present an analysis of the finite temperature properties of the model based on the exact diagonalization of 8, 16 and 20 site clusters. We propose that diffuse neutron scattering can be used to resolve the ambiguity inherent in determining the ratio and sign of $J_1$ and $J_2$ from thermodynamic properties alone, and use a finite temperature Lanczos algorithm to make predictions for the relevant high temperature spin-spin correlation functions. The possibility of a spin-liquid phase occurring for ferromagnetic $J_1$ is also briefly discussed.

cond-mat.str-el↗

arXiv1996

Excitations in Spin Chains and Specific-Heat Anomalies in Yb(4)As(3)

An explanation is given for the observed magnetic-field dependence of the low-temperature specific heat coefficient of Yb(4)As(3). It is based on a recently developed model for that material which can explain the observed heavy-fermion behaviour. According to it the Yb(3+)-ions are positioned in a net of parallel chains with an effective spin coupling of the order of J = 25 K. The magnetic-field dependence can be understood by including a weak magnetic coupling J' between adjacent chains. The data require a ratio J'/J of about 10^{-4}. In that case the experimental results can be reproduced very well by the theory.

cond-mat↗

arXiv1995

Theoretical Model for the Semimetal Yb_4As_3

We present a model which can explain semiquantitatively a number of the unusual properties of \mbox{Yb$_4$As$_3$}. The structural phase transition at $T_{\text{c}}\simeq300\,\mbox{K}$ is described by a band Jahn-Teller effect of correlated electrons and is interpreted as a charge ordering of the Yb ions. The low carrier concentration in the low-temperature phase follows from the strong electron correlations of the 4f-holes on the Yb sites and can be viewed as self-doping of charge-ordered chains. The observed heavy-fermion behaviour is on a scale of $T^\ast\simeq50\,\mbox{K}$ and is due to spinon-like excitations in the Yb$^{3+}$-chains. The appearance of a second low-energy scale around 0.2\,K is due to the Fermi energy of the low-density carriers.

cond-mat↗