Orbital magnetoelectric coupling at finite electric field

We extend the band theory of linear orbital magnetoelectric coupling to treat crystals under finite electric fields. Previous work established that the orbital magnetoelectric response of a generic insulator at zero field comprises three contributions that were denoted as local circulation, itinerant circulation, and Chern-Simons. We find that the expression for each of them is modified by the presence of a dc electric field. Remarkably, the sum of the three correction terms vanishes, so that the total coupling is still given by the same formula as at zero field. This conclusion is confirmed by numerical tests on a tight-binding model, for which we calculate the field-induced change in the linear magnetoelectric coefficient.Comment: 4 pages, 2 figure

Wannier-based calculation of the orbital magnetization in crystals

We present a first-principles scheme that allows the orbital magnetization of a magnetic crystal to be evaluated accurately and efficiently even in the presence of complex Fermi surfaces. Starting from an initial electronic-structure calculation with a coarse ab initio k-point mesh, maximally localized Wannier functions are constructed and used to interpolate the necessary k-space quantities on a fine mesh, in parallel to a previously-developed formalism for the anomalous Hall conductivity [X.Wang, J. Yates, I. Souza, and D. Vanderbilt, Phys. Rev. B 74, 195118 (2006)]. We formulate our new approach in a manifestly gauge-invariant manner, expressing the orbital magnetization in terms of traces over matrices in Wannier space. Since only a few (e.g., of the order of 20) Wannier functions are typically needed to describe the occupied and partially occupied bands, these Wannier matrices are small, which makes the interpolation itself very efficient. The method has been used to calculate the orbital magnetization of bcc Fe, hcp Co, and fcc Ni. Unlike an approximate calculation based on integrating orbital currents inside atomic spheres, our results nicely reproduce the experimentally measured ordering of the orbital magnetization in these three materials.Comment: 13 pages, 3 figures, 4 table

Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals

We derive a multi-band formulation of the orbital magnetization in a normal periodic insulator (i.e., one in which the Chern invariant, or in 2d the Chern number, vanishes). Following the approach used recently to develop the single-band formalism [T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Phys. Rev. Lett. {\bf 95}, 137205 (2005)], we work in the Wannier representation and find that the magnetization is comprised of two contributions, an obvious one associated with the internal circulation of bulk-like Wannier functions in the interior and an unexpected one arising from net currents carried by Wannier functions near the surface. Unlike the single-band case, where each of these contributions is separately gauge-invariant, in the multi-band formulation only the \emph{sum} of both terms is gauge-invariant. Our final expression for the orbital magnetization can be rewritten as a bulk property in terms of Bloch functions, making it simple to implement in modern code packages. The reciprocal-space expression is evaluated for 2d model systems and the results are verified by comparing to the magnetization computed for finite samples cut from the bulk. Finally, while our formal proof is limited to normal insulators, we also present a heuristic extension to Chern insulators (having nonzero Chern invariant) and to metals. The validity of this extension is again tested by comparing to the magnetization of finite samples cut from the bulk for 2d model systems. We find excellent agreement, thus providing strong empirical evidence in favor of the validity of the heuristic formula.Comment: 14 pages, 8 figures. Fixed a typo in appendix

Orbital magnetization in periodic insulators

Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation of bulk-like Wannier functions in the interior, and an unexpected one arising from net currents carried by Wannier functions near the surface. Each contribution can be expressed as a bulk property in terms of Bloch functions in a gauge-invariant way. Our expression is verified by comparing numerical tight-binding calculations for finite and periodic samples.Comment: submitted to PRL; signs corrected in Eqs. (11), (12), (19), and (20

Variability of reflectance measurements with sensor altitude and canopy type

Data were acquired on canopies of mature corn planted in 76 cm rows, mature soybeans planted in 96 cm rows with 71 percent soil cover, and mature soybeans planed in 76 cm rows with 100 percent soil cover. A LANDSAT band radiometer with a 15 degree field of view was used at ten altitudes ranging from 0.2 m to 10 m above the canopy. At each altitude, measurements were taken at 15 cm intervals also a 2.0 m transect perpendicular to the crop row direction. Reflectance data were plotted as a function of altitude and horizontal position to verify that the variance of measurements at low altitudes was attributable to row effects which disappear at higher altitudes where the sensor integrate across several rows. The coefficient of variation of reflectance decreased exponentially as the sensor was elevated. Systematic sampling (at odd multiples of 0.5 times the row spacing interval) required fewer measurements than simple random sampling over row crop canopies

First principles based atomistic modeling of phase stability in PMN-xPT

We have performed molecular dynamics simulations using a shell model potential developed by fitting first principles results to describe the behavior of the relaxor-ferroelectric (1-x)PbMg1/3Nb2/3O3-xPbTiO3 (PMN-xPT) as function of concentration and temperature, using site occupancies within the random site model. In our simulations, PMN is cubic at all temperatures and behaves as a polar glass. As a small amount of Ti is added, a weak polar state develops, but structural disorder dominates, and the symmetry is rhombohedral. As more Ti is added the ground state is clearly polar and the system is ferroelectric, but with easy rotation of the polarization direction. In the high Ti content region, the solid solution adopts ferroelectric behavior similar to PT, with tetragonal symmetry. The ground state sequence with increasing Ti content is R-MB-O-MC-T. The high temperature phase is cubic at all compositions. Our simulations give the slope of the morphotropic phase boundaries, crucial for high temperature applications. We find that the phase diagram PMN-xPT can be understood within the random site model.Comment: 27 pages, 9 figure

Jahn-Teller Distortion and Ferromagnetism in the Dilute Magnetic Semiconductors GaN:Mn

Using first-principles total-energy methods, we investigate Jahn-Teller distortions in III-V dilute magnetic semiconductors, GaAs:Mn and GaN:Mn in the cubic zinc blende structure. The results for an isolated Mn impurity on a Ga site show that there is no appreciable effect in GaAs, whereas, in GaN there is a Jahn-Teller effect in which the symmetry around the impurity changes from T$_{d}$ to D$_{2d}$ or to C$_{2v}$. The large effect in GaN occurs because of the localized d$^4$ character, which is further enhanced by the distortion. The lower symmetry should be detectable experimentally in cubic GaN with low Mn concentration, and should be affected by charge compensation (reductions of holes and conversion of Mn ions to d$^5$ with no Jahn-Teller effect). Jahn-Teller effect is greatly reduced because the symmetry at each Mn site is lowered due to the Mn-Mn interaction. The tendency toward ferromagnetism is found to be stronger in GaN:Mn than in GaAs:Mn and to be only slightly reduced by charge compensation.Comment: 6 pages, 3 figure

First-principles study of (BiScO3){1-x}-(PbTiO3){x} piezoelectric alloys

We report a first-principles study of a class of (BiScO3)_{1-x}-(PbTiO3)_x (BS-PT) alloys recently proposed by Eitel et al. as promising materials for piezoelectric actuator applications. We show that (i) BS-PT displays very large structural distortions and polarizations at the morphotropic phase boundary (MPB) (we obtain a c/a of ~1.05-1.08 and P_tet of ~1.1 C/m^2); (ii) the ferroelectric and piezoelectric properties of BS-PT are dominated by the onset of hybridization between Bi/Pb-6p and O-2p orbitals, a mechanism that is enhanced upon substitution of Pb by Bi; and (iii) the piezoelectric responses of BS-PT and Pb(Zr_{1-x}Ti_x)O3 (PZT) at the MPB are comparable, at least as far as the computed values of the piezoelectric coefficient d_15 are concerned. While our results are generally consistent with experiment, they also suggest that certain intrinsic properties of BS-PT may be even better than has been indicated by experiments to date. We also discuss results for PZT that demonstrate the prominent role played by Pb displacements in its piezoelectric properties.Comment: 6 pages, with 3 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/ji_bi/index.htm

First-principles theory of ferroelectric phase transitions for perovskites: The case of BaTiO3

We carry out a completely first-principles study of the ferroelectric phase transitions in BaTiO$_3$. Our approach takes advantage of two features of these transitions: the structural changes are small, and only low-energy distortions are important. Based on these observations, we make systematically improvable approximations which enable the parameterization of the complicated energy surface. The parameters are determined from first-principles total-energy calculations using ultra-soft pseudopotentials and a preconditioned conjugate-gradient scheme. The resulting effective Hamiltonian is then solved by Monte Carlo simulation. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. We find the transitions to be intermediate between order-disorder and displacive character. We find all three phase transitions to be of first order. The roles of different interactions are discussed.Comment: 33 pages latex file, 9 figure