Results from the arable crop rotation study at Oak Park 2000 - 2007

An organic rotation trial was established at Oak Park in 2000. The crop sequence in the seven year rotation was: two years grass-clover, winter wheat, potatoes, winter oats, lupins and spring barley. The grass-clover, which supplies nitrogen to the system, also provides vegetation which of late is cut and mixed with cereal straw to produce compost. The compost replaced sheep manure which was available up to 2007. Manure was applied to potato plots prior to cultivation for the period 2002 to 2007 and to barley plots from 2005 to 2007. The average yield of crops over the period of the rotation was: winter wheat 5.9 t/ha, potatoes 32.7 t/ha, winter oats 5.8 t/ha, lupins 2.4 t/ha and spring barley 4.5 t/ha. Triticale, which was grown in one of the plots designated for winter wheat, had an average yield of 7.5 t/ha. Lupins have been unsatisfactory due to uncompetitiveness with weeds and lateness of maturity

H I observations of the peculiar galaxy NGC 660

The authors present observations of H I emission from the peculiar galaxy NGC 660. H I was detected in the companion galaxy UGC 01195 as well. Sixteen hours of observations were obtained with the VLA telescope of the National Radio Astronomy Observatory during December 1986 and March 1987

Magnetoelectric polarizability: A microscopic perspective

We extend a field theoretic approach for the investigation of the electronic charge-current density response of crystalline systems to arbitrary applied electromagnetic fields. The approach leads to the introduction of microscopic polarization and magnetization fields, as well as free charge and current densities, the dynamics of which are described by a lattice gauge theory. The spatial averages of such quantities constitute the fields of macroscopic electrodynamics. We implement this formalism to study the orbital electronic response of a class of insulators to applied uniform dc electric and magnetic fields at zero temperature. To first-order in the applied fields, the free charge and current densities vanish; thus the response of the system is characterized by the first-order modifications to the microscopic polarization and magnetization fields. Associated with the dipole moment of the microscopic polarization (magnetization) field is a macroscopic polarization (magnetization), for which we extract various response tensors. We focus on the orbital magnetoelectric polarizability (OMP) tensor, and find the accepted expression as derived from the "modern theory of polarization and magnetization." Since our results are based on the spatial averages of microscopic fields, we can identify the distinct contributions to the OMP tensor from the perspective of this microscopic theory, and we establish the general framework in which extensions to finite frequency can be made.Comment: 24 page

From magnetoelectric response to optical activity

We apply a microscopic theory of polarization and magnetization to crystalline insulators at zero temperature and consider the orbital electronic contribution of the linear response to spatially varying, time-dependent electromagnetic fields. The charge and current density expectation values generally depend on both the microscopic polarization and magnetization fields, and on the microscopic free charge and current densities. But contributions from the latter vanish in linear response for the class of insulators we consider. Thus we need only consider the former, which can be decomposed into "site" polarization and magnetization fields, from which "site multipole moments" can be constructed. Macroscopic polarization and magnetization fields follow, and we identify the relevant contributions to them; for electromagnetic fields varying little over a lattice constant these are the electric and magnetic dipole moments per unit volume, and the electric quadrupole moment per unit volume. A description of optical activity and related magneto-optical phenomena follows from the response of these macroscopic quantities to the electromagnetic field and, while in this paper we work within the independent particle and frozen-ion approximations, both optical rotary dispersion and circular dichroism can be described with this strategy. Earlier expressions describing the magnetoelectric effect are recovered as the zero frequency limit of our more general equations. Since our site quantities are introduced with the use of Wannier functions, the site multipole moments and their macroscopic analogs are generally gauge dependent. However, the resulting macroscopic charge and current densities, together with the optical effects to which they lead, are gauge invariant, as would be physically expected.Comment: 24 pages. Minor typographical errors in Eq. 5, 14, 15 of the earlier version are correcte

Z2=0\mathbb{Z}_{2}=0 is topological too

The electronic ground state of a three-dimensional (3D) band insulator with time-reversal ($\Theta$) symmetry or time-reversal times a discrete translation ($\Theta T_{1/2}$) symmetry is classified by a $\mathbb{Z}_{2}$-valued topological invariant and characterized by quantized magnetoelectric response. Here we demonstrate by explicit calculation in model $\mathbb{Z}_{2}$ topological insulator thin-films that whereas the magnetoelectric response is localized at the surface in the $\Theta$ symmetry (non-magnetic) case, it is non-universally partitioned between surface and interior contributions in the $\Theta T_{1/2}$ (anti-ferromagnetic) case, while remaining quantized. Within our model the magnetic field induced polarization arises entirely from an anomalous ${\cal N}=0$ Landau level subspace within which the projected Hamiltonian is a generalized Su-Schrieffer-Heeger model whose topological properties are consistent with those of the starting 3D model.Comment: 6+13 pages, 4 figures, comments welcom

Reconciling magnetoelectric response and time-reversal symmetry in non-magnetic Z2\mathbb{Z}_2 topological insulators

A delicate tension complicates the relationship between the topological magnetoelectric effect in three-dimensional $\mathbb{Z}_2$ topological insulators (TIs) and time-reversal symmetry (TRS). TRS underlies a particular $\mathbb{Z}_2$ topological classification of the electronic ground state of a bulk insulator and the associated quantization of the magnetoelectric coefficient calculated using linear response theory, but according to standard symmetry arguments simultaneously forbids any physically meaningful magnetoelectric response. This tension between theories of magnetoelectric response in bulk and finite-sized materials originates from the distinct approaches required to introduce notions of polarization and orbital magnetization in those fundamentally different environments. In this work we argue for a modified interpretation of the bulk linear response calculations in non-magnetic TIs that is more plainly consistent with TRS, and use this interpretation to discuss the effect's observation - still absent over a decade after its prediction. Our analysis is reinforced by microscopic bulk and thin film calculations carried out using a simplified but still realistic model for the well established V$_2$VI$_3$ (V $=$ (Sb,Bi) and VI $=$ (Se,Te)) family of non-magnetic $\mathbb{Z}_2$ TIs. We conclude that the topological magnetoelectric effect in non-magnetic $\mathbb{Z}_2$ TIs is activated by magnetic surface dopants, and that the charge density response to magnetic fields and the orbital magnetization response to electric fields in a given sample are controlled in part by the configuration of those dopants.Comment: 30 pages, 5 figure