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The Fe electronic structure and magnetism in (i) monoclinic Ca$_2$FeReO$_6$ with a metal-insulator transition at $T_{MI} \sim 140$ K and (ii) quasi-cubic half-metallic Ba$_2$FeReO$_6$ ceramic double perovskites are probed by soft x-ray absorption spectroscopy (XAS) and magnetic circular dichroism (XMCD). These materials show distinct Fe $L_{2,3}$ XAS and XMCD spectra, which are primarily associated with their different average Fe oxidation states (close to Fe$^{3+}$ for Ca$_2$FeReO$_6$ and intermediate between Fe$^{2+}$ and Fe$^{3+}$ for Ba$_2$FeReO$_6$) despite being related by an isoelectronic (Ca$^{2+}$/Ba$^{2+}$) substitution. For Ca$_2$FeReO$_6$, the powder-averaged Fe spin moment along the field direction ($B = 5$ T), as probed by the XMCD experiment, is strongly reduced in comparison with the spontaneous Fe moment previously obtained by neutron diffraction, consistent with a scenario where the magnetic moments are constrained to remain within an easy plane. For $B=1$ T, the unsaturated XMCD signal is reduced below $T_{MI}$ consistent with a magnetic transition to an easy-axis state that further reduces the powder-averaged magnetization in the field direction. For Ba$_2$FeReO$_6$, the field-aligned Fe spins are larger than for Ca$_2$FeReO$_6$ ($B=5$ T) and the temperature dependence of the Fe magnetic moment is consistent with the magnetic ordering transition at $T_C^{Ba} = 305$ K. Our results illustrate the dramatic influence of the specific spin-orbital configuration of Re $5d$ electrons on the Fe $3d$ local magnetism of these Fe/Re double perovskites., Comment: 7 pages, 3 figures

A spacetime domain can be progressively meshed by tent shaped objects. Numerical methods for solving hyperbolic systems using such tent meshes to advance in time have been proposed previously. Such schemes have the ability to advance in time by different amounts at different spatial locations. This paper explores a technique by which standard discretizations, including explicit time stepping, can be used within tent-shaped spacetime domains. The technique transforms the equations within a spacetime tent to a domain where space and time are separable. After detailing techniques based on this mapping, several examples including the acoustic wave equation and the Euler system are considered.

Discontinuous Petrov Galerkin (DPG) methods are made easily implementable using `broken' test spaces, i.e., spaces of functions with no continuity constraints across mesh element interfaces. Broken spaces derivable from a standard exact sequence of first order (unbroken) Sobolev spaces are of particular interest. A characterization of interface spaces that connect the broken spaces to their unbroken counterparts is provided. Stability of certain formulations using the broken spaces can be derived from the stability of analogues that use unbroken spaces. This technique is used to provide a complete error analysis of DPG methods for Maxwell equations with perfect electric boundary conditions. The technique also permits considerable simplifications of previous analyses of DPG methods for other equations. Reliability and efficiency estimates for an error indicator also follow. Finally, the equivalence of stability for various formulations of the same Maxwell problem is proved, including the strong form, the ultraweak form, and a spectrum of forms in between.

Simulation of wave propagation through complex media relies on proper understanding of the properties of numerical methods when the wavenumber is real and complex. Numerical methods of the Hybrid Discontinuous Galerkin (HDG) type are considered for simulating waves that satisfy the Helmholtz and Maxwell equations. It is shown that these methods, when wrongly used, give rise to singular systems for complex wavenumbers. A sufficient condition on the HDG stabilization parameter for guaranteeing unique solvability of the numerical HDG system, both for Helmholtz and Maxwell systems, is obtained for complex wavenumbers. For real wavenumbers, results from a dispersion analysis are presented. An asymptotic expansion of the dispersion relation, as the number of mesh elements per wave increase, reveal that some choices of the stabilization parameter are better than others. To summarize the findings, there are values of the HDG stabilization parameter that will cause the HDG method to fail for complex wavenumbers. However, this failure is remedied if the real part of the stabilization parameter has the opposite sign of the imaginary part of the wavenumber. When the wavenumber is real, values of the stabilization parameter that asymptotically minimize the HDG wavenumber errors are found on the imaginary axis. Finally, a dispersion analysis of the mixed hybrid Raviart-Thomas method showed that its wavenumber errors are an order smaller than those of the HDG method.

This paper presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree.

We consider the numerical approximation of the spectrum of a second-order elliptic eigenvalue problem by the hybridizable discontinuous Galerkin (HDG) method. We show for problems with smooth eigenfunctions that the approximate eigenvalues and eigenfunctions converge at the rate 2k+1 and k+1, respectively. Here k is the degree of the polynomials used to approximate the solution, its flux, and the numerical traces. Our numerical studies show that a Rayleigh quotient-like formula applied to certain locally postprocessed approximations can yield eigenvalues that converge faster at the rate 2k + 2 for the HDG method as well as for the Brezzi-Douglas-Marini (BDM) method. We also derive and study a condensed nonlinear eigenproblem for the numerical traces obtained by eliminating all the other variables.

A remarkable hardening (~ 30 cm-1) of the normal mode of vibration associated with the symmetric stretching of the oxygen octahedra for the Ba2FeReO6 and Sr2CrReO6 double perovskites is observed below the corresponding magnetic ordering temperatures. The very large magnitude of this effect and its absence for the anti-symmetric stretching mode provide evidence against a conventional spin-phonon coupling mechanism. Our observations are consistent with a collective excitation formed by the combination of the vibrational mode with oscillations of local Fe or Cr 3d and Re 5d occupations and spin magnitudes., Comment: 12 pages, 4 figures

We investigated the rare-earth transition metal oxide series, Ln2CuTiO6 (Ln=Y, Dy, Ho, Er and Yb), crystallizing in the hexagonal structure with non-centrosymmetric P63cm space group for possible occurrences of multiferroic properties. Our results show that while these compounds, except Ln=Y, exhibit a low temperature antiferromagnetic transition due to the ordering of the rare-earth moments, the expected ferroelectric transition is frustrated by the large size difference between Cu and Ti at the B-site. Interestingly, this leads these compounds to attain a rare and unique combination of desirable paraelectric properties with high dielectric constants, low losses and weak temperature and frequency dependencies. First-principles calculations establish these exceptional properties result from a combination of two effects. A significant difference in the MO5 polyhedral sizes for M = Cu and M = Ti suppress the expected co-operative tilt pattern of these polyhedra, required for the ferroelectric transition, leading to relatively large values of the dielectric constant for every compound investigated in this series. Additionally, it is shown that the majority contribution to the dielectric constant arises from intermediate-frequency polar vibrational modes, making it relatively stable against any temperature variation. Changes in the temperature stability of the dielectric constant amongst different members of this series are shown to arise from changes in relative contributions from soft polar modes., Comment: Accepted for publication in Phys. Rev. B (21 pages, 2 Table, 8 Figures)

The crystallographic and magnetic properties of La{0.5+delta}A{0.5-delta}Mn{0.5+epsilon}Ru{0.5-epsilon}O{3} (A= Ca, Sr, Ba) were investigated by means of neutron powder diffraction. All studied samples show the orthorhombic perovskite crystal structure, space group Pnma, with regular (Mn,Ru)O{6} octahedra and no chemical ordering of the Mn3+ and Ru4+ ions. Ferromagnetic spin structures were observed below Tc ~ 200-250 K, with an average ordered moment of ~ 1.8-2.0 Bohr magnetons per (Mn,Ru). The observation of long-range ferromagnetism and the absence of orbital ordering are rationalized in terms a strong Mn-Ru hybridization, which may freeze the orbital degree of freedom and broaden the eg valence band, leading to an orbital-glass state with carrier-mediated ferromagnetism.

We have investigated the structure and electronic properties of ferrimagnetic double perovskites, A2FeReO6 (A= Ca, Sr, Ba). The A=Ba phase is cubic (Fm3m) and metallic, while the A=Ca phase is monoclinic (P21/n) and nonmetallic. 57Fe Mossbauer spectroscopy shows that iron is present mainly in the high-spin (S=5/2) Fe3+ state in the Ca compound, while it occurs in an intermediate state between high-spin Fe2+ and Fe3+ in the Ba compound. It is argued that a direct Re t2g - Re t2g interaction is the main cause for the metallic character of the Ba compound; the high covalency of Ca-O bonds and the monoclinic distortion (which lifts the degeneracy of t2g states) seem to disrupt the Re-Re interaction in the case of the Ca compound, making it non-metallic for the same electron count., Comment: 1 eps file

Ceramics of A_{2}FeReO_{6} double-perovskite have been prepared and studied for A=Ba and Ca. Ba_{2}FeReO_{6} has a cubic structure (Fm3m) with $a\approx $8.0854(1) \AA whereas Ca_{2}FeReO_{6} has a distorted monoclinic symmetry with $a\approx 5.396(1) \AA, b\approx 5.522(1) \AA, c\approx 7.688(2) \AA$ and $\beta =90.4^{\circ} (P21/n)$. The barium compound is metallic from 5 K to 385 K, i.e. no metal-insulator transition has been seen up to 385 K, and the calcium compound is semiconducting from 5 K to 385 K. Magnetization measurements show a ferrimagnetic behavior for both materials, with T_{c}=315 K for Ba_{2}FeReO_{6} and above 385 K for Ca_{2}FeReO_{6}. A specific heat measurement on the barium compound gave an electron density of states at the Fermi level, N(E_{F}) equal to 6.1$\times 10^{24} eV^{-1}mole^{-1}$. At 5 K, we observed a negative magnetoresistance of 10 % in a magnetic field of 5 T, but only for Ba_{2}FeReO_{6}. Electrical, thermal and magnetic properties are discussed and compared to the analogous compounds Sr_{2}Fe(Mo,Re)O_{6}., Comment: 5 pages REVTeX, 7 figures included, submitted to PRB