Publisher Summary The chapter presents a study on the applications of the recursion method to the electronic structure from the atomic perspective. The recursion method is an efficient technique for obtaining the spectral properties of any operator that, when defined on a countable basis, is relatively sparse. The developments in a number of areas of solid state theory are discussed, with particular emphasis on the following: (1) the practical details of recursion-type calculations and (2) the impact of the results of such calculations. In each case the achievements of alternative approaches are compared and the limitations of each technique are discussed. The chapter begins with a brief critical examination of the physical assumptions that must be made before recursion-type calculations become relevant and feasible in the context of the electronic structure of solids. The chapter also introduces key concepts, such as the local density of states and some quantities related to it. Several schemes, including the recursion method, for calculating the local density of states are introduced, and are compared from the practical standpoint of (1) the form of the ingredients, (2) the ease and efficiency of obtaining results, and (3) the accuracy and reliability of such results. The chapter explains the physics of a series of systems where Bloch's theorem and its implications become increasingly irrelevant. The electronic structure and phonon spectra of ideal transition metal and semiconductor surfaces are discussed. The chapter presents an analysis on the changes induced by ordered overlayers.

Applications of the Recursion Method to the Electronic Structure from an Atomic Point of View

Within the RPA approach forT=0, the excitations of the Heisenberg spin glass system Eu
 x
 Sr1−x
S are studied by numerical methods, using a continued fraction algorithm. Both the density of statesg(E) and also the spectral functionS(q,E) are calculated for systems with (16)3 sites, withx=0.4, 0.5, and 0.6 (spin glass phase), and also forx≧0.7 (ferromagnetic phase). Forq-vectors within the (1,1,1) plane,S(q,E) shows magnon peaks even in the spin glass phase, over the whole range ofq. However, these peaks are quite broad, and there is considerable intensity at small energies even for largeq, leading to a finite intercept ofg(E) forE→0. Over a large temperature range, the specific heat is approximately linear inT forx≲0.7.

Excitations in Heisenberg Spin Glasses

Structure and magnetic order of Cr-rich Rb2Cr1-xMnxCl4 crystals

Low-temperature neutron diffraction measurements were performed on single crystals of Rb2Cr1-xMnxCl4 (0<or=x<or=1). From these experiments a concentration versus temperature magnetic phase diagram is obtained. Three concentration ranges with different magnetic behaviour are found. In the same range as the Jahn-Teller-induced superstructure occurs, 0<or=x<or=0.41, a somewhat canted ferromagnetic structure exists. An antiferromagnetic order is found in the range 0.59<or=x<or=1. The T versus x dependence of the phase boundaries and the magnitudes of the magnetic moments are discussed with respect to percolation behaviour. Within the percolation limits xF=0.41 for ferromagnetic and xAF=0.59 for antiferromagnetic ordering no magnetic long-range order is observed. This finding is consistent with a proposed spin glass phase for intermediate concentrations.

Magnetic phase diagram of Rb2Cr1-xMnxCl4 (0≤x≤1)

We present an investigation of the effect of randomizing exchange coupling strengths in the $S=1/2$ square lattice quasi-two-dimensional quantum Heisenberg antiferromagnet (QHAF) ${(\mathrm{QuinH})}_{2}\mathrm{Cu}{({\mathrm{Cl}}_{x}{\mathrm{Br}}_{1\ensuremath{-}x})}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{H}}_{2}\mathrm{O}$ (QuinH $=$ Quinolinium, ${\mathrm{C}}_{9}{\mathrm{H}}_{8}{\mathrm{N}}^{+}$), with $0\ensuremath{\le}x\ensuremath{\le}1$. Pulsed-field magnetization measurements allow us to estimate an effective in-plane exchange strength $J$ in a regime where exchange fosters short-range order, while the temperature ${T}_{\mathrm{N}}$ at which long-range order (LRO) occurs is found using muon-spin relaxation, allowing us to construct a phase diagram for the series. We evaluate the effectiveness of disorder in suppressing ${T}_{\mathrm{N}}$ and the ordered moment size, and we find an extended disordered phase in the region $0.4\ensuremath{\lesssim}x\ensuremath{\lesssim}0.8$ where no magnetic order occurs. The observed critical substitution levels are accounted for by an energetics-based competition between different local magnetic orders. Furthermore, we demonstrate experimentally that the ground-state disorder is driven by quantum effects of the exchange randomness, which is a feature that has been predicted theoretically and has implications for other disordered quasi-two-dimensional QHAFs.

/pdf/magnetic-order-and-disorder-in-a-quasi-two-dimensional-4qgzojo4a0.pdf

Magnetic order and disorder in a quasi-two-dimensional quantum Heisenberg antiferromagnet with randomized exchange

The magnetic excitations of the dilute two-dimensional ferromagnetic Heisenberg system K2Cu1−x
Zn
 x
 F4 have been studied by inelastic neutron scattering forx = 0, 0.08 and 0.22, atT = 2 K. The dispersion of the frequency and of the linewidth has been obtained for wavevectorsq in the direction of the strongest dispersion,q~(1, 1,0), within the plane containing the strong exchange interaction. In the dilute samples,x = 0.08 and 0.22, the effect of the nonmagnetic impurities on both the frequency and the linewidth has been observed. Excellent agreement is obtained between the experimental results and the predictions of a continued-fraction-computer-simulation of the lineshapes, for the sample withx = 0.08. Forx = 0.22, there is still good agreement, although the experimental frequencies are slightly higher than predicted.

Spin wave excitations in the dilute two-dimensional ferromagnet K 2 Cu 1−x Zn x F 4

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Spin wave excitations in the dilute two-dimensional ferromagnet K 2 Cu 1−x Zn x F 4