No Arabic abstract
The ability to control carrier concentration based on the extent of Cu solubility in the $mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ alloy compound (where 0 $leq$ x $leq$ 1) makes $mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ an interesting case study in the field of thermoelectrics. While Cu clearly plays a role in this process, it is unknown exactly how Cu incorporates into the $mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ crystal structure and how this affects the carrier concentration. In this work, we use a combination of resonant energy X-ray diffraction (REXD) experiments and density functional theory (DFT) calculations to elucidate the nature of Cu incorporation into the $mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ structure. REXD across the $mathrm{Cu_k}$ edge facilitates the characterization of Cu incorporation in the $mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ alloy and enables direct quantification of anti-site defects. We find that Cu substitutes for Hg at a 2:1 ratio, wherein Cu annihilates a vacancy and swaps with a Hg atom. DFT calculations confirm this result and further reveal that the incorporation of Cu occurs preferentially on one of the z = 1/4 or z = 3/4 planes before filling the other plane. Furthermore, the amount of $mathrm{Cu_{Hg}}$ anti-site defects quantified by REXD was found to be directly proportional to the experimentally measured hole concentration, indicating that the $mathrm{Cu_{Hg}}$ defects are the driving force for tuning carrier concentration in the $mathrm{Cu_{2x}Hg_{2-x}GeTe_4}$ alloy. The link uncovered here between crystal structure, or more specifically anti-site defects, and carrier concentration can be extended to similar cation-disordered material systems and will aid the development of improved thermoelectric and other functional materials through defect engineering.
We report the study of the skyrmion state near the surface of Cu$_2$OSeO$_3$ using soft resonant elastic x-ray scattering (REXS) at the Cu $L_3$ edge. Within the lateral sampling area of $200 times 200$ $mu$m$^2$, we found a long-range-ordered skyrmion lattice phase as well as the formation of skyrmion domains via the multiple splitting of the diffraction spots. In a recent REXS study of the skyrmion phase of Cu$_2$OSeO$_3$ [Phys. Rev. Lett. 112, 167202 (2014)], Langner et al. reported the observation of the unexpected existence of two distinct skyrmion sublattices that arise from inequivalent Cu sites, and that the rotation and superposition of the two periodic structures leads to a moir{e} pattern. However, we find no energy splitting of the Cu peak in x-ray absorption measurements and, instead, discuss alternative origins of the peak splitting. In particular, we find that for magnetic field directions deviating from the major cubic axes, a multidomain skyrmion lattice state is obtained, which consistently explains the splitting of the magnetic spots into two - and more - peaks.
Resonant X-ray scattering (RXS) is a spectroscopy where both the power of site selective diffraction and the power of local absorption spectroscopy regarding atomic species are combined. By virtue of the dependence on the core level state energy and the three dimensional electronic structure of the intermediate state, this technique is specially suited to study charge, orbital or spin orderings and associated crystal distortions. In the case of charge ordering, we exploit the fact that atoms with closely related site symmetries but with small charge differences exhibit resonances at slightly different energies. The sensitivity of this effect allows for quantitative estimations of the charge disproportion. Opposite to fluorescence or absorption measurements, the power of diffraction relies on the capability of detecting differences that are smaller than the inverse lifetime of the core hole level. To account for the uncertainty of the crystallographic structure and the fact that the charge ordering must be disentangled from the associated atomic displacements, a complete methodology is proposed and applied to the low temperature phase of magnetite. Relative sensitivity on spin, toroidal and orbital ordering is also shown and compared in different transition metal oxide compounds, like V2O3 and GaFeO3.
Resonant magnetic x-ray diffraction experiments were carried out on the stacked triangular lattice antiferromagnet GdPd2Al3. The experiments revealed an expected initial collinear c-axis order at TN1 followed by an additional in-plane order at TN2, while at the same time we found that the ground state is a helically ordered state of a very long incommensurate period of approximately 700A. The distribution of K-domains was highly anisotropic, and the domain with the modulation vector normal to the surface of the crystal was ascendant. Low-field magnetization is discussed on the basis of the observed incommensurate magnetic structure.
We investigated the magnetic structure of the heavy fermion compound CePt$_2$In$_7$ below $T_N~=5.34(2)$ K using magnetic resonant X-ray diffraction at ambient pressure. The magnetic order is characterized by a commensurate propagation vector ${k}_{1/2}~=~left( frac{1}{2} , frac{1}{2}, frac{1}{2}right)$ with spins lying in the basal plane. Our measurements did not reveal the presence of an incommensurate order propagating along the high symmetry directions in reciprocal space but cannot exclude other incommensurate modulations or weak scattering intensities. The observed commensurate order can be described equivalently by either a single-${k}$ structure or by a multi-${k}$ structure. Furthermore we explain how a commensurate-only ordering may explain the broad distribution of internal fields observed in nuclear quadrupolar resonance experiments (Sakai et al. 2011, Phys. Rev. B 83 140408) that was previously attributed to an incommensurate order. We also report powder X-ray diffraction showing that the crystallographic structure of CePt$_2$In$_7$ changes monotonically with pressure up to $P~=~7.3$ GPa at room temperature. The determined bulk modulus $B_0~=~81.1(3)$ GPa is similar to the ones of the Ce-115 family. Broad diffraction peaks confirm the presence of pronounced strain in polycrystalline samples of CePt$_2$In$_7$. We discuss how strain effects can lead to different electronic and magnetic properties between polycrystalline and single crystal samples.
Magnetic spiral structures can exhibit ferroelectric moments as recently demonstrated in various multiferroic materials. In such cases the helicity of the magnetic spiral is directly correlated with the direction of the ferroelectric moment and measurement of the helicity of magnetic structures is of current interest. Soft x-ray resonant diffraction is particularly advantageous because it combines element selectivity with a large magnetic cross-section. We calculate the polarization dependence of the resonant magnetic x-ray cross-section (electric dipole transition) for the basal plane magnetic spiral in hexaferrite Ba0.8Sr1.2Zn2Fe12O22 and deduce its domain population using circular polarized incident radiation. We demonstrate there is a direct correlation between the diffracted radiation and the helicity of the magnetic spiral.