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We discuss how x-ray Compton scattering spectra can be used for investigating the evolution of electronic states in cathode materials of Li batteries under the lithiation/delithiation process. In particular, our analysis of the Compton spectra taken from polycrystalline LixCoO2 samples shows that the spectra are dominated by the contribution of the O-2p redox orbital. We identify a distinct signature of d-orbital delocalization, which is tied directly to the conductivity of the material, providing a descriptor based on Compton spectra for monitoring the lithiation range with improved conductivity and kinetics for electrochemical operation. Our study demonstrates that Compton scattering spectroscopy can provide a window for probing complex electronic mechanisms underlying the charging and discharging processes in Li-battery materials., Comment: 12 pages, 2 figures, and 1 table

Non-destructive determination of lithium distribution in a working battery is key for addressing both efficiency and safety issues. Although various techniques have been developed to map the lithium distribution in electrodes, these methods are mostly applicable to test cells. Here we propose the use of high-energy x-ray Compton scattering spectroscopy to measure the local lithium concentration in closed electrochemical cells. A combination of experimental measurements and parallel first-principles computations is used to show that the shape parameter S of the Compton profile is linearly proportional to lithium concentration and thus provides a viable descriptor for this important quantity. The merits and applicability of our method are demonstrated with illustrative examples of LixMn2O4 cathodes and a working commercial lithium coin battery CR2032., Comment: 14 pages, 5 figures

Bonding characteristics of liquid boron at 2500K are studied by using high resolution Compton scattering. An excellent agreement is found between the measurements and the corresponding Car-Parinello molecular dynamics simulations. Covalent bond pairs are clearly shown to dominate in liquid boron along with the coexistence of diffuse pairs. Our study reveals the complex bonding pattern of liquid boron, and gives insight into the unusual properties of this high temperature liquid.

We present an incisive spectroscopic technique for directly probing redox orbitals based on bulk electron momentum density measurements via high-resolution x-ray Compton scattering. Application of our method to spinel LixMn2O4, a lithium ion battery cathode material, is discussed. The orbital involved in the lithium insertion and extraction process is shown to mainly be the oxygen 2p orbital. Moreover, the manganese 3d states are shown to experience spatial delocalization involving 0.16 electrons per Mn site during the battery operation. Our analysis provides a clear understanding of the fundamental redox process involved in the working of a lithium ion battery., Comment: 24 pages, 3 figures

We have observed the bulk Fermi surface (FS) in an overdoped ($x$=0.3) single crystal of La$_{2-x}$Sr$_x$CuO$_4$ by using Compton scattering. A two-dimensional (2D) momentum density reconstruction from measured Compton profiles yields a clear FS signature in the third Brillouin zone along [100]. The quantitative agreement between density functional theory (DFT) calculations and momentum density experiment suggests that Fermi-liquid physics is restored in the overdoped regime. In particular the predicted FS topology is found to be in good accord with the corresponding experimental data. We find similar quantitative agreement between the measured 2D angular correlation of positron annihilation radiation (2D-ACAR) spectra and the DFT based computations. However, 2D-ACAR does not give such a clear signature of the FS in the extended momentum space in either the theory or the experiment., Comment: 9 pages, 8 figures

Metallic liquid silicon at 1787K is investigated using x-ray Compton scattering. An excellent agreement is found between the measurements and the corresponding Car-Parrinello molecular dynamics simulations. Our results show persistence of covalent bonding in liquid silicon and provide support for the occurrence of theoretically predicted liquid-liquid phase transition in supercooled liquid states. The population of covalent bond pairs in liquid silicon is estimated to be 17% via a maximally-localized Wannier function analysis. Compton scattering is shown to be a sensitive probe of bonding effects in the liquid state., Comment: 5pages, 3 postscript figures

We report on a new method to determine the degree of bulk spin polarization in single crystal Co$_{(1-x)}$Fe$_x$S$_2$ by modeling magnetic Compton scattering with {\it ab initio} calculations. Spin-dependent Compton profiles were measured for CoS$_2$ and Co$_{0.9}$Fe$_{0.1}$S$_2$. The {\it ab initio} calculations were then refined by rigidly shifting the bands to provide the best fit between the calculated and experimental directional profiles for each sample. The bulk spin polarizations, $P$, corresponding to the spin-polarized density of states at the Fermi level, were then extracted from the {\it refined} calculations. The values were found to be $P=-72 \pm 6 %$ and $P=18 \pm 7%$ for CoS$_2$ and Co$_{0.9}$Fe$_{0.1}$S$_2$ respectively. Furthermore, determinations of $P$ weighted by the Fermi velocity ($v_F$ or $v_F^2$) were obtained, permitting a rigorous comparison with other experimental data and highlighting the experimental dependence of $P$ on $v_F$.

We report high-resolution, bulk Compton scattering measurements unveiling the Fermi surface of an optimally-doped iron-arsenide superconductor, Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$. Our measurements are in agreement with first-principles calculations of the electronic structure, revealing both the $X$-centered electron pockets and the $\Gamma$-centered hole pockets. Moreover, our data are consistent with the strong three-dimensionality of one of these sheets that has been predicted by electronic structure calculations at the local-density-approximation-minimum As position. Complementary calculations of the noninteracting susceptibility, $\chi_0({\bf q}, \omega)$, suggest that the broad peak that develops due to interband Fermi-surface nesting, and which has motivated several theories of superconductivity in this class of material, survives the measured three dimensionality of the Fermi surface in this family.

Two-dimensional spin-uncompensated momentum density distributions, $\rho_{\rm s}^{2D}({\bf p})$s, were reconstructed in magnetite at 12K and 300K from several measured directional magnetic Compton profiles. Mechanical de-twinning was used to overcome severe twinning in the single crystal sample below the Verwey transition. The reconstructed $\rho_{\rm s}^{2D}({\bf p})$ in the first Brillouin zone changes from being negative at 300 K to positive at 12 K. This result provides the first clear evidence that electrons with low momenta in the minority spin bands in magnetite are localized below the Verwey transition temperature., Comment: 13 pages, 4 figures, accepted in Physical Review B

We have studied the [100]-[110] anisotropy of the Compton profile in the bilayer manganite. Quantitative agreement is found between theory and experiment with respect to the anisotropy in the two metallic phases (i.e. the low temperature ferromagnetic and the colossal magnetoresistant phase under a magnetic field of 7 T). Robust signatures of the metal-insulator transition are identified in the momentum density for the paramagnetic phase above the Curie temperature. We interpret our results as providing direct evidence for the transition from the metallic-like to the admixed ionic-covalent bonding accompanying the magnetic transition. The number of electrons involved in this phase transition is estimated from the area enclosed by the Compton profile anisotropy differences. Our study demonstrates the sensitivity of the Compton scattering technique for identifying the number and type of electrons involved in the metal-insulator transition., Comment: 4 pages, 4 figures, accepted for publication in Physical Review Letters

We present a combination of ab initio calculations, magnetic Compton scattering and polarized neutron experiments, which elucidate the density distribution of unpaired electrons in the kagome staircase system Co3V2O8. Ab initio wave functions were used to calculate the spin densities in real and momentum space, which show good agreement with the respective experiments. It has been found that the spin polarized orbitals are equally distributed between the t2g and the eg levels for the spine (s) Co ions, while the eg orbitals of the cross-tie (c) Co ions only represent 30% of the atomic spin density. Furthermore, the results reveal that the magnetic moments of the cross-tie Co ions, which are significantly smaller than those of the spine Co ions in the zero-field ferromagnetic structure, do not saturate by applying an external magnetic field of 2 T along the easy axis a, but that the increasing bulk magnetization originates from induced magnetic moments on the O and V sites. The refined individual magnetic moments are mu(Co_c)=1.54(4) mu_B, mu(Co_s)=2.87(3) mu_B, mu(V)=0.41(4) mu_B, mu(O1)=0.05(5) mu_B, mu(O2)=0.35(5) mu_B, and; mu(O3)=0.36(5) mu_B combining to the same macroscopic magnetization value, which was previously only attributed to the Co ions.

The surprise discovery of superconductivity below 5K in sodium cobalt oxides when hydrated with water has caught the attention of experimentalists and theorists alike. Most explanations for its occurence have focused heavily on the properties of some small elliptically shaped pockets predicted to be the electronically dominant Fermi surface sheet, but direct attempts to look for them have instead cast serious doubts over their existence. Here we present evidence that these pockets do indeed exist, based on bulk measurements of the electron momentum distribution in unhydrated and hydrated sodium cobalt oxides using the technique of x-ray Compton scattering.

The Fermi surface topology of the shape-memory alloy Ni[0.62]Al[0.38] has been determined using Compton scattering. A large area of this Fermi surface can be made to nest with other areas by translation through a vector of ~ 0.18 [1,1,0] (2pi/a), which correponds to the wavevector associated with martensitic precursor phenomena such as phonon softening and diffuse streaking in electron diffraction patterns. This observation is compelling evidence that these phenomena are driven by the enhanced electron-lattice coupling due to the Fermi surface nesting.

We present a novel technique for enhancing Fermi surface (FS) signatures in the 2D distribution obtained after the 3D momentum density in a crystal is projected along a specific direction in momentum space. These results are useful for investigating fermiology via high resolution Compton scattering and positron annihilation spectroscopies. We focus on the particular case of the (110) projection in an fcc crystal where the standard approach based on the use of the Lock-Crisp-West (LCW) folding theorem fails to give a clear FS image due to the strong overlap with FS images obtained through projection from higher Brillouin zones. We show how these superposed FS images can be disentangled by using a selected set of reciprocal lattice vectors in the folding process. The applicability of our partial folding scheme is illustrated by considering Compton spectra from an Al-3at%Li disordered alloy single crystal. For this purpose, high resolution Compton profiles along nine directions in the (110) plane were measured. Corresponding highly accurate theoretical profiles in Al-3at%Li were computed within the local density approximation (LDA)-based Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) first-principles framework. A good level of overall accord between theory and experiment is obtained, some expected discrepancies reflecting electron correlation effects notwithstanding, and the partial folding scheme is shown to yield a clear FS image in the (110) plane in Al-3%Li., Comment: 24 pages, 8 figures, to appear in Phys. Rev. B

We report high-resolution Compton profiles (CP's) of Al along the three principal symmetry directions at a photon energy of 59.38 keV, together with corresponding highly accurate theoretical profiles obtained within the local-density approximation (LDA) based band-theory framework. A good accord between theory and experiment is found with respect to the overall shapes of the CP's, their first and second derivatives, as well as the anisotropies in the CP's defined as differences between pairs of various CP's. There are however discrepancies in that, in comparison to the LDA predictions, the measured profiles are lower at low momenta, show a Fermi cutoff which is broader, and display a tail which is higher at momenta above the Fermi momentum. A number of simple model calculations are carried out in order to gain insight into the nature of the underlying 3D momentum density in Al, and the role of the Fermi surface in inducing fine structure in the CP's. The present results when compared with those on Li show clearly that the size of discrepancies between theoretical and experimental CP's is markedly smaller in Al than in Li. This indicates that, with increasing electron density, the conventional picture of the electron gas becomes more representative of the momentum density and that shortcomings of the LDA framework in describing the electron correlation effects become less important., Comment: 7 pages, 6 figures, regular article