Green's function theory of quasi-two-dimensional spin-half Heisenberg ferromagnets: stacked square versus stacked kagom\'e lattice

We consider the thermodynamic properties of the quasi-two-dimensional spin-half Heisenberg ferromagnet on the stacked square and the stacked kagom\'e lattices by using the spin-rotation-invariant Green's function method. We calculate the critical temperature $T_C$, the uniform static susceptibility $\chi$, the correlation lengths $\xi_\nu$ and the magnetization $M$ and investigate the short-range order above $T_C$. We find that $T_C$ and $M$ at $T>0$ are smaller for the stacked kagom\'e lattice which we attribute to frustration effects becoming relevant at finite temperatures.Comment: shortened version as published in PR

Frustrated spin ladder with alternating spin-1 and spin-1/2 rungs

We study the impact of the diagonal frustrating couplings on the quantum phase diagram of a two-leg ladder composed of alternating spin-1 and spin-1/2 rungs. As the coupling strength is increased the system successively exhibits two gapped paramagnetic phases (a rung-singlet and a Haldane-like non-degenerate states) and two ferrimagnetic phases with different ferromagnetic moments per rung. The first two states are similar to the phases studied in the frustrated spin-1/2 ladder, whereas the magnetic phases appear as a result of the mixed-spin structure of the model. A detailed characterization of these phases is presented using density-matrix renormalization-group calculations, exact diagonalizations of periodic clusters, and an effective Hamiltonian approach inspired by the analysis of numerical data. The present theoretical study was motivated by the recent synthesis of the quasi-one-dimensional ferrimagnetic material Fe$^{II}$Fe$^{III}$ (trans-1,4-cyclohexanedicarboxylate) exhibiting a similar ladder structure.Comment: 10 pages, 8 figure

Large Negative Electronic Compressibility of LaAlO3-SrTiO3 Interfaces with Ultrathin LaAlO3 Layers

A two-dimensional electron liquid is formed at the n-type interface between SrTiO3 and LaAlO3. Here we report on Kelvin probe microscopy measurements of the electronic compressibility of this electron system. The electronic compressibility is found to be negative for carrier densities of \approx10^13/cm^2. At even smaller densities, a metal-to-insulator transition occurs. These local measurements corroborate earlier measurements of the electronic compressibility of LaAlO3-SrTiO3 interfaces obtained by measuring the capacitance of macroscopic metal-LaAlO3-SrTiO3 capacitors

Excitation of the electric pygmy dipole resonance by inelastic electron scattering

To complete earlier studies of the properties of the electric pygmy dipole resonance (PDR) obtained in various nuclear reactions, the excitation of the 1$^-$ states in $^{140}$Ce by $(e,e')$ scattering for momentum transfers $q=0.1-1.2$~fm$^{-1}$ is calculated within the plane-wave and distorted-wave Born approximations. The excited states of the nucleus are described within the Quasiparticle Random Phase Approximation (QRPA), but also within the Quasiparticle-Phonon Model (QPM) by accounting for the coupling to complex configurations. It is demonstrated that the excitation mechanism of the PDR states in $(e,e')$ reactions is predominantly of transversal nature for scattering angles $\theta_e \approx 90^o-180^o$. Being thus mediated by the convection and spin nuclear currents, the $(e,e')$ like the $(\gamma,\gamma')$ reaction, may provide additional information to the one obtained from Coulomb- and hadronic excitations of the PDR in $(p,p')$, $(\alpha,\alpha')$, and heavy-ion scattering reactions. The calculations predict that the $(e,e')$ cross sections for the strongest individual PDR states are in general about three orders of magnitude smaller as compared to the one of the lowest $2^+_1$ state for the studied kinematics, but that they may become dominant at extreme backward angles.Comment: Prepared for the special issue of EPJA on the topic "Giant, Pygmy, Pairing Resonances and related topics" dedicated to the memory of Pier Francesco Bortigno

Absence of long-range order in a spin-half Heisenberg antiferromagnet on the stacked kagome lattice

We study the ground state of a spin-half Heisenberg antiferromagnet on the stacked kagome lattice by using a spin-rotation-invariant Green's-function method. Since the pure two-dimensional kagome antiferromagnet is most likely a magnetically disordered quantum spin liquid, we investigate the question whether the coupling of kagome layers in a stacked three-dimensional system may lead to a magnetically ordered ground state. We present spin-spin correlation functions and correlation lengths. For comparison we apply also linear spin wave theory. Our results provide strong evidence that the system remains short-range ordered independent of the sign and the strength of the interlayer coupling

Improved bounds for the crossing numbers of K_m,n and K_n

It has been long--conjectured that the crossing number cr(K_m,n) of the complete bipartite graph K_m,n equals the Zarankiewicz Number Z(m,n):= floor((m-1)/2) floor(m/2) floor((n-1)/2) floor(n/2). Another long--standing conjecture states that the crossing number cr(K_n) of the complete graph K_n equals Z(n):= floor(n/2) floor((n-1)/2) floor((n-2)/2) floor((n-3)/2)/4. In this paper we show the following improved bounds on the asymptotic ratios of these crossing numbers and their conjectured values: (i) for each fixed m >= 9, lim_{n->infty} cr(K_m,n)/Z(m,n) >= 0.83m/(m-1); (ii) lim_{n->infty} cr(K_n,n)/Z(n,n) >= 0.83; and (iii) lim_{n->infty} cr(K_n)/Z(n) >= 0.83. The previous best known lower bounds were 0.8m/(m-1), 0.8, and 0.8, respectively. These improved bounds are obtained as a consequence of the new bound cr(K_{7,n}) >= 2.1796n^2 - 4.5n. To obtain this improved lower bound for cr(K_{7,n}), we use some elementary topological facts on drawings of K_{2,7} to set up a quadratic program on 6! variables whose minimum p satisfies cr(K_{7,n}) >= (p/2)n^2 - 4.5n, and then use state--of--the--art quadratic optimization techniques combined with a bit of invariant theory of permutation groups to show that p >= 4.3593.Comment: LaTeX, 18 pages, 2 figure

Zigzag spin-S chain near ferromagnet-antiferromagnet transition point

The properties of the ferromagnetic frustrated spin-S one-dimensional Heisenberg model in the vicinity of the transition point from the ferromagnetic to the singlet ground state is studied using the perturbation theory (PT) in small parameter characterizing the deviation from the transition point. The critical exponents defining the behavior of the ground state energy and spin correlation functions are determined using scaling estimates of infrared divergencies of the PT. It is shown that the quantum fluctuations for $s=1/2$ are sufficiently strong to change the classical critical exponents, while for spin systems with $s\geq 1$ the critical exponents remain classical. The dimerization in the singlet phase near the transition point is discussed.Comment: 13 pages, 3 figure

Localized-magnon states in strongly frustrated quantum spin lattices

Recent developments concerning localized-magnon eigenstates in strongly frustrated spin lattices and their effect on the low-temperature physics of these systems in high magnetic fields are reviewed. After illustrating the construction and the properties of localized-magnon states we describe the plateau and the jump in the magnetization process caused by these states. Considering appropriate lattice deformations fitting to the localized magnons we discuss a spin-Peierls instability in high magnetic fields related to these states. Last but not least we consider the degeneracy of the localized-magnon eigenstates and the related thermodynamics in high magnetic fields. In particular, we discuss the low-temperature maximum in the isothermal entropy versus field curve and the resulting enhanced magnetocaloric effect, which allows efficient magnetic cooling from quite large temperatures down to very low ones.Comment: 21 pages, 10 figures, invited paper for a special issue of "Low Temperature Physics " dedicated to the 70-th anniversary of creation of concept "antiferromagnetism" in physics of magnetis

How branching can change the conductance of ballistic semiconductor devices

We demonstrate that branching of the electron flow in semiconductor nanostructures can strongly affect macroscopic transport quantities and can significantly change their dependence on external parameters compared to the ideal ballistic case even when the system size is much smaller than the mean free path. In a corner-shaped ballistic device based on a GaAs/AlGaAs two-dimensional electron gas we observe a splitting of the commensurability peaks in the magnetoresistance curve. We show that a model which includes a random disorder potential of the two-dimensional electron gas can account for the random splitting of the peaks that result from the collimation of the electron beam. The shape of the splitting depends on the particular realization of the disorder potential. At the same time magnetic focusing peaks are largely unaffected by the disorder potential.Comment: accepted for publication in Phys. Rev.