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Crystal and Electronic Structure of FeSe at High Pressure and Low Temperature Ravhi S. Kumar,*,† Yi Zhang,*,† Stanislav Sinogeikin,‡ Yuming Xiao,‡ Sathish Kumar,† Paul Chow,‡ Andrew L. Cornelius,† and Changfeng Chen† Department of Physics and Astronomy and HiPSEC, UniVersity of NeVada, Las Vegas, NeVada 89154, and HPCAT, Carnegie Institution of Washington, AdVanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439 ReceiVed: June 30, 2010; ReVised Manuscript ReceiVed: August 20, 2010
We have investigated the high-pressure crystal and electronic structures of superconducting FeSe by highresolution synchrotron powder X-ray diffraction and density functional theory (DFT) calculations at ambient and at low temperatures down to 8 K. Ambient nuclear resonant inelastic X-ray scattering (NRIXS) experiments were performed on FeSe to understand the partial phonon density of states (PDOS) of the high-pressure phases. On the basis of our experimental results and DFT calculations, we demonstrate a pressure-induced distortion of the low-temperature Cmma phase at around 1.6 GPa and the appearance of a high-pressure Pbnm phase. Upon increasing the pressure above 9 GPa, the orthorhombic phase becomes the major phase, and a mixed-phase region exists up to 26 GPa. The pressure-induced structural changes in this system and its connection to Tc enhancement are discussed. 1. Introduction 1
The discovery of superconductivity in FeSe has sparked tremendous interest in iron chalcogenides as they are isomorphic to the FeAs-type high Tc superconductors2-5 but have simpler crystal structure and chemical composition. This should help our understanding of the underlying physics in iron-based superconductors. Recent studies6,7 suggest that superconductivity in FeSe is likely the result of an intricate interplay between their structural, magnetic, and electronic properties, but some key questions remain open. The most pressing among them is a clear structural identification, which is a prerequisite for understanding all other properties. Recent experiments revealed that the structure of FeSe and its superconductivity are more complex than expected. It has been reported that tetragonal (P4/ nmm) FeSe at ambient temperature undergoes a transition to orthorhombic Cmma upon cooling.8 This transition is sensitive to chemical doping and is closely related to the superconductivity.9,10 Remarkably, applied pressure produces a large increase in the superconducting onset temperature of FeSe from 13.5 to 27 K.11 Recent experiments reported further Tc increases up to 37 K under pressures from 8.9 to 22 GPa.12-15 These results are attributed to strong enhancement of antiferromagnetic spin fluctuations near Tc.16 More importantly, the structure of the high-pressure phase is correlated to Tc. It is essential to understand the effect of pressure on this system close to Tc. Recent high-pressure investigations at room temperature (RT) and low temperature (LT) show phase transitions in FeSe from the tetragonal structure.15 At RT, there are two different phase transition sequences reported; one is from tetragonal to hexagonal (P63/mmc) at around 12 GPa, and the other is from tetragonal to orthorhombic (Pbnm).12-14 Since the transition temperature is sensitive to pressure, it is crucial to understand the stability of the high-pressure low-temperature (HPLT) phase * To whom correspondence should be addressed. E-mail: ravhi@ physics.unlv.edu and
[email protected]. † University of Nevada. ‡ Argonne National Laboratory.
and correlate the structural changes under pressure with the observed Tc increase. Here, we report a combined experimental and theoretical study that provides more insight into HPLT structures of FeSe and sheds new light on the pressure-induced structure changes. High-resolution synchrotron powder X-ray diffraction (XRD) is performed under high pressure up to 31 GPa and low temperature down to 8 K with a He pressure medium. Moreover, we further performed nuclear inelastic X-ray scattering experiments and lattice dynamics calculations to understand the phonon density of states of FeSe. The obtained results fully corroborate with the structural assignments and transitions identified by XRD. At HPLT, a sluggish structural transformation from the low-temperature Cmma to orthorhombic Pbnm phase begins as early as 1.6 GPa. Above 9 GPa, the Pbnm orthorhombic phase becomes the major phase with a large volume collapse of 19%. The phase transition becomes complete above 26 GPa. The electronic structures of different FeSe phases and structural properties are explained by DFT calculations. 2. Experimental Methods 2.1. Sample Preparation and Characterization. Polycrystalline samples of FeSe were synthesized using 4N pure starting materials by a solid-state reaction described elsewhere.11 The 57 Fe-enriched (95%) sample was used for nuclear inelastic scattering experiments. XRD patterns were collected at ambient temperature using a PANalytical diffractometer using Cu KR radiation at UNLV. The phase purity was checked by refining the XRD pattern using the Rietveld method. We have inferred well-defined diffraction peaks corresponding to the tetragonal P4/nmm phase. In addition, we noticed peaks corresponding to a secondary hexagonal P63/mmc phase, which was reported previously by other groups.12-15 We obtained the molar percentage of the major tetragonal phase and the secondary NiAs-type hexagonal phase from the refinements as 87 and 13%. The various crystallographic structures at ambient and at low temperatures that will be discussed in the following sections are shown in Figure 1. As the superconducting transition
10.1021/jp1060446 2010 American Chemical Society Published on Web 09/14/2010
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Figure 1. Various crystallographic phases of FeSe; (a) tetragonal (P4/ nmm), (b) hexagonal (P63/mmc), (c) LT orthorhombic (Cmma), and (d) high pressure orthorhombic (Pbnm).
temperature of FeSe is sensitive to the Se and Fe concentration,17 the composition of the samples was checked by energydispersive X-ray (EDX) analysis. The EDX experiments yielded the composition of Fe close to 1.01 and that of Se close to 0.99, which agreed well with the XRD refinement results shown in Table 1. The refined cell parameters and atomic position parameter (z parameter, 0.2691 for Se) agreed well with the reported literature.17 No other impurity phases were observed in the XRD spectra. In the rest of the paper, we have used FeSe instead of denoting the composition. A physical property measurement system (PPMS) from Quantum Design was used to measure the superconducting transition temperature of the samples. DC magnetization measurements for as-synthesized powder samples showed a superconducting onset temperature of around 7 K. The ambient XRD refinement and magnetization plots are shown in Figure 2. 2.2. High-Pressure X-ray Diffraction and Nuclear Inelastic Scattering. High-pressure XRD measurements were performed at the ID-B beamline of Sector16, HPCAT, at the Advanced Photon Source. The powdered sample was loaded in a 150 µm hole of a rhenium gasket in a symmetric-type membrane diamond anvil cell (DAC) with ruby grains for pressure measurement. The culet size of the diamonds was 300 µm, and the gaskets were indented to 50 µm before drilling. He and Ne pressure transmitting media were loaded using the gas loading system available at Sector13-GSECARS, APS, for LT and RT experiments, respectively. A Mar 345 imaging plate was used in the experiments to obtain high-quality powder diffraction patterns. The distance between the sample and the detector and the inclination angle of the imaging plate were calibrated using a CeO2 standard. We have used monochromatic X-ray with wavelengths of λ ) 0.34468 and 0.40662 Å for ambient and LT XRD experiments. For LT experiments, the DAC was cooled down in a continuous He flow type cryostat, and the pressure in the cell was measured in situ with the ruby fluorescence technique.18 Two temperature sensors were placed near the sample to control the temperature to 8 K throughout the measurements with an accuracy of (1 K. The collected XRD patterns were integrated using Fit2D software, and structural analysis was carried using JADE and LHPM Rietica/GSAS Rietveld packages.19,20 Isotopically 57Fe-enriched FeSe samples were loaded in a panoramic-type DAC with a silicone fluid
Kumar et al. pressure medium for nuclear inelastic X-ray scattering. The culet size of the diamonds was 450 µm, and the sample was loaded in a 150 µm hole of a Be gasket. The experiments were performed at ID-D station of HPCAT at ambient temperature. The incident photon energy was tuned to 14.413 keV, the nuclear resonance energy of 57Fe. The delayed signal was measured from avalanche photodiodes positioned at 90° from the direction of the beam. Data were collected in scans of the incident photon energy from -80 to +80 meV from the resonant energy with a monochromator resolution of 2.0 meV. The data analysis was performed using the PHOENIX software package.21 2.3. Theoretical Calculations. To explain the experimental results and understand the underlying physics, we have performed density functional theory (DFT) calculations using the projector augmented waves (PAW) method22 as implemented in VASP.23 The generalized gradient approximation (GGA)24 is used for the exchange-correction potential. We used a plane wave basis set with a cutoff energy of 400 eV and 12 × 12 × 8, 8 × 8 × 8, and 12 × 12 × 8 Monkhorst-Pack25 k-point grids for the tetragonal, orthorhombic Pbnm, and hexagonal structures shown in Figure 2a-d. The unit cell and atomic coordination are fully relaxed. Since the Cmma phase is a slight distortion of the P4/nmm phase and the energy difference between them is smaller than 10 meV/atom, we chose the P4/ nmm structure instead of Cmma in our calculations. The total energy convergence with respect to the k-point grid and cufoff energy is less than 0.5 meV/atom. We also performed calculations using the experimental lattice constants for comparison and found little difference in total energies obtained using the GGA equilibrium and the experimental unit cell. The phonon density of states was calculated using the PHONON package.26 3. Results and Discussion 3.1. High-Pressure Phases of FeSe. We have plotted the evolution of XRD patterns at different pressures at RT in Figure 3a up to 33 GPa. The diffraction patterns remain unchanged up to 11 GPa. Above 11 GPa, we noticed a sudden decrease in intensity of the major diffraction lines (011) and (111) of the P4/nmm phase and an increase in intensity of the diffraction line at 2θ ) 7.4°. The changes observed in the diffraction patterns at these pressures indicated a structural transition. We have used the orthorhombic Pbnm and hexagonal structure models based on previous reports12-15 for fitting the highpressure phase with Rietveld refinements above 11 GPa. The scale, structural, and profile parameters were refined. We made two observations based on the XRD patterns and the Rietveld refinements shown in Figure 3a and b. First, At RT, it is noticed that the transformation of the tetragonal phase to the highpressure phase is rapid, and no mixed-phase region is found from 11 to 33 GPa. Second, even though the refined cell volume of the possible high-pressure orthorhombic and hexagonal phases are nearly equal after the phase transition, the lower Rwp observed for the orthorhombic phase indicates that the Pbnm phase is more favorable at ambient temperature above 11 GPa. Theoretical calculations presented further confirm the experimental results. The key structural parameters such as cell parameters for each phase, atomic position parameters, Se-Se and Fe-Se bond distances, and Se-Fe-Se bond angles are presented for various pressures in Table 1. We have designated the R phase as P4/nmm, the β phase as P63/mmc (NiAs type), and the γ phase as Pbnm at RT. As the P4/nmm phase transforms to Cmma orthorhombic upon cooling below 70 K, we have designated the Cmma phase as the R phase at LT for further discussions. At RT, both of the Se-Se bond lengths decrease with pressure. However, we have noticed that the
Crystal and Electronic Structure of FeSe
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TABLE 1: Refined Atomic Parameters for FeSe at RT (variable coordinates x, y, and z, isotropic thermal parameters, site occupancies) at Selected Pressures from Synchrotron X-ray Data along with Cell Parameters, Bond Lengths, and Agreement Factors, Rp, Rwp, and χ2 pressure ambient Fe
Se
1.4 GPa
1.9 GPa
2.6 GPa
structure
R (P4/nmm)
β (P63/mmc)
R (P4/nmm)
β (P633/mmc)
R (P4/nmm)
β (P63/mmc)
R (P4/nmm)
β (P63/mmc)
x y z Biso (Å2) occ. x y z Biso (Å2) occ. a (Å) b (Å) c (Å) volume (Å3) Fe-Fe (Å) Fe-Se (Å) Se1-Se1 (Å) Se1-Se2 (Å) Se-Fe-Se (°)
1/4 -1/4 0 3.3(4) 1.01(2) 1/4 1/4 0.2877(3) 0.40(2) 0.99(3) 3.7685(1) 3.7685(1) 5.5194(1) 78.38(4) 2.6647(3) 2.3999(7) 3.7684(9) 3.6871(7) 110.48(6) 114.95(8) 3.28 3.99 2.1
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.6361(9) 3.6361(9) 5.907(2) 67.64(2)
1/4 -1/4 0 4.1(4) 1 1/4 1/4 0.2901(6) 1.1(2) 1 3.7665(9) 3.7665(9) 5.4359(4) 77.12(1) 2.6637(9) 2.4567(2) 3.7670(3) 3.5072(5) 108.16(5) 114.79(4)
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5996(1) 3.5996(1) 5.9071(9) 66.28(5)
1/4 -1/4 0 4.2(2) 1 1/4 1/4 0.2916(6) 1.3(1) 1 3.7526(3) 3.7526(3) 5.3915(4) 75.92(4) 2.6535(3) 2.4481(2) 3.7526(6) 3.4767(7) 107.74(2) 114.76(2)
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5941(8) 3.5941(8) 5.8736(1) 65.71(1)
1/4 -1/4 0 3.7(4) 1 1/4 1/4 0.2924(3) 0.74(1) 1 3.7401(5) 3.7401(5) 5.3397(4) 74.69(6) 2.6446(9) 2.4362(2) 3.7402(2) 3.4503(1) 107.89(3) 114.77(4)
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5839(6) 3.5839(6) 5.8302(5) 64.85(5)
Rp (%) Rwp (%) GOF (χ2)
3.19 4.36 2.5
3.54 4.76 3.4
1.96 2.8 2.1
pressure 3.4 GPa R (P4/nmm)
structure Fe
Se
x y z Biso (Å2) occ. x y z Biso (Å2) occ. a (Å) b (Å) c (Å) volume (Å3) Fe-Fe (Å) Fe-Se (Å) Se1-Se1 (Å) Se1-Se2 (Å) Se-Fe-Se (°) Rp (%) Rwp (%) GOF (χ2)
1/4 -1/4 0 4.5(8) 1 1/4 1/4 0.2989(5) 0.42(3) 1 3.7218(7) 3.7218(7) 5.2940(1) 73.33(4) 2.6316(7) 2.4446(5) 3.7217(3) 3.3816(4) 106.99(7) 114.70(5) 1.6 2.13 2.1
4 GPa R (P4/nmm)
β (P63/mmc) 0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5652(2) 3.5652(2) 5.7855(3) 63.68(6)
4.8 GPa β (P63/mmc)
1/4 -1/4 0 4.2(2) 1 1/4 1/4 0.2915(6) 1.3(1) 1 3.7105(3) 3.7105(3) 5.2748(1) 72.62(4) 2.6238(1) 2.4248(3) 3.7106(3) 3.3934(1) 107.55(5) 114.74(3) 1.7 2.49 2.4
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5561(5) 3.5561(5) 5.7487(9) 62.96(1)
R (P4/nmm)
β (P63/mmc)
1/4 -1/4 0 4.3(4) 1 1/4 1/4 0.3002(7) 0.33(9) 1 3.6928(5) 3.6928(5) 5.2250(7) 71.25(5) 2.6112(1) 2.4230(2) 3.6928(4) 3.3429(3) 107.11(4) 114.71(9) 1.7 2.55 2.8
0 0 0 1 1/3 2/3 1/4 0.0058(10) 1 3.5348(7) 3.5348(7) 5.6898(4) 61.57(1)
pressure 6 GPa structure Fe x y z Biso (Å2) occ. Se x y z Biso (Å2) occ. a (Å) b (Å) c (Å) volume (Å3) Fe-Fe (Å) Fe-Se (Å) Se1-Se1 (Å) Se1-Se2 (Å) Se-Fe-Se (°) Rp (%) Rwp (%) GOF (χ2)
R (P4/nmm) 1/4 -1/4 0 3.3(4) 1 1/4 1/4 0.3126(3) 0.56(6) 1 3.6733(3) 3.6733(3) 5.1809(5) 69.90(8) 2.5975(4) 2.4447(8) 3.6734(7) 3.2501(4) 105.5(9) 114.6(2) 2.02 2.95 3.3
7.2 GPa
β (P63/mmc) 0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5209(9) 3.5209(9) 5.6053(7) 60.18(1)
R (P4/nmm)
β (P63/mmc)
1/4 ′0 -1/4 0 0 0 3.4(2) 0.6 1 1 1/4 1/3 1/4 2/3 0.3170(6) 1/4 1.3(1) 0.6 1 1 3.6543(9) 3.4985(5) 3.6543(9) 3.4985(5) 5.1461(8) 5.5576(6) 68.72(5) 58.91(1) 2.5842(8) 2.4439(9) 3.6547(2) 3.2071(7) 105.1(5) 114.5(6) 3.54 4.76 3.4
8.5 GPa R (P4/nmm) 1/4 -1/4 0 3.5(3) 1 1/4 1/4 0.3188(7) 0.77(8) 1 3.6357(9) 5.6357(9) 5.1123(5) 67.58(1) 2.5712(5) 2.4412(8) 3.6362(9) 3.1688(4) 104.2(9) 114.5(5) 2.69 3.61 2.3
11 GPa
β (P63/mmc) 0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.4822(8) 3.4822(8) 5.5069(5) 57.83(2)
R (P4/nmm) 1/4 -1/4 0 3.3(3) 1 1/4 1/4 0.3058(7) 0.94(8) 1 3.6103(1) 3.6103(1) 5.0447(6) 65.75(5) 2.5527(8) 2.3748(4) 3.6101(5) 3.2181(9) 106.8(3) 114.6(9) 2.09 2.97 2.5
β (P63/mmc) 0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.4474(1) 3.4474(1) 5.4534(7) 56.12(9)
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TABLE 1: Continued pressure 13 GPa
15 GPa
17 GPa
19 GPa
structure Fe
Se
x y z Biso (Å2) occ. x y z Biso (Å2) occ. a (Å) b (Å) c (Å) volume (Å3) Rp (%) Rwp (%) GOF (χ2)
21 GPa
22 GPa
24 GPa
27 GPa
30 GPa
33 GPa
0.283(2) 0.039(1) 1/4 2.4(2) 1 0.589(2) 0.269(2) 1/4 3.1(1) 1 5.694(9) 5.291(7) 3.422(9) 103.1(2) 2.64 3.61 4.8
0.272(6) 0.039(3) 1/4 4.4(1) 1 0.589(9) 0.271(7) 1/4 3.2(9) 1 5.883(8) 5.225(6) 3.325(4) 102.2(4) 2.1 2.64 3.4
0.268(3) 0.034(3) 1/4 4.3(4) 1 0.591(7) 0.273(8) 1/4 2.6(1) 1 5.830(2) 5.175(9) 3.330(8) 100.5(2) 2.45 3.76 5.5
0.263(2) 0.042(6) 1/4 4.1(2) 1 0.594(3) 0.271(6) 1/4 1.5(2) 1 5.805(6) 5.192(9) 3.309(7) 99.7(8) 2.51 3.74 5.8
γ (Pbnm) 0.2252(2) 0.0419(9) 3.3(3) 1 0.6134(7) 0.2550(2) 1/4 2.5(1) 1 5.8313(7) 5.4223(7) 3.4417(5) 108.82(8) 2.76 3.66 4
0.2184(8) 0.0335(6) 1/4 2.2(6) 1 0.5995(2) 0.2389(6) 1/4 1.1(7) 1 5.8258(8) 5.4148(7) 3.4174(5) 107.80(7) 2.31 2.87 2.1
0.2143(5) 0.0155(8) 1/4 2.2(1) 1 0.5807(9) 0.2375(7) 2.5(2) 1 5.7614(1) 5.4128(8) 3.4119(9) 106.40(2) 2.21 2.87 3.2
0.2162(5) 0.0255(8) 1/4 2.6(2) 1 0.5877(3) 0.2393(4) 1/4 1.7(4) 1 5.7581(9) 5.3501(9) 3.4194(3) 105.34(5) 1.56 2.24 2.2
Se1-Se2 bond length is highly compressible in comparison to the Se1-Se1 bond length. Further, the Fe-Se bond distance changes gradually with pressure upon approaching the phase transition pressure. The Se1-Fe-Se1 bond angle remains between 114.5 and 114.75° up to 8 GPa, while the Se2-Fe-Se2 angle decreases rapidly with pressure. The bond length and bond angle changes observed are consistent with those of Gabrino et al.13 As the low-temperature structural data are important for understanding and correlating the effect of pressure on Tc, we further focused on the Cmma structure, which is a distorted form of the ambient tetragonal phase. The diffraction patterns at selected pressures at 8 K are shown in Figure 4. The hexagonal P63/mmc phase observed at RT with the tetragonal phase was still found as a secondary phase in the diffraction patterns collected at 1.3 GPa and 8 K. We have performed a two-phase refinement to understand the phase composition by including the hexagonal phase. The refinement showed a molar phase fraction of around 3% for the hexagonal phase. The diffraction patterns obtained at 8 K as a function of pressure up to 31 GPa are shown in Figure 2a. Upon increasing pressure above 9 GPa, we have observed major changes in the diffraction patterns, indicative of a structural phase transition. In contrast to the RT results, a mixed-phase region with diffraction lines representing
0.2764(6) 0.0375(8) 1/4 4.4(2) 1 0.5959(5) 0.2645(3) 1/4 1.4(8) 5.754(6) 5.340(5) 3.412(3) 104.8(7) 1.78 2.20 2.4
0.279(2) 0.038(2) 1/4 2.9(6) 1 0.590(2) 0.280(2) 1/4 3.1(3) 1 5.753(9) 5.293(8) 3.414(3) 103.9(9) 2.81 3.96 4.1
the Cmma phase denoted by the markers (Figure 4) was observed up to 23 GPa. Above 31 GPa, we observed peaks corresponding only to the high-pressure phase. The refinements show unequivocally that the structure is orthorhombic Pbnm, which is consistent with other reports.13,15 Our attempts to fit the high-pressure phase with hexagonal symmetry did not succeed. Upon analyzing the low-pressure region, we have noticed that the doublet peak corresponding to the (021) and (201) reflections of the Cmma phase (inset of Figure 4) starts to split into a three-peak structure as early as 1.6 GPa. It is evident from our experiments that the distortion increases with pressure, and the third peak labeled by a dotted line shown in inset of Figure 4 shifts toward lower angle with increasing pressure. The diffraction peak emerging at this pressure does not correspond to either the Cmma or NiAs-type P63/mmc used in the refinements. Upon monitoring the pressure evolution of the X-ray diffraction patterns, it can be clearly noticed that this peak becomes a major line in the Pbnm phase above 9 GPa. In order to understand the diffraction profile, we have incorporated the Pbnm phase in the refinements above 1.6 GPa. We have used the cell parameters from DFT simulation for the Pbnm phase, and we were able to fit the XRD pattern above 1.6 GPa well after including the orthorhombic Pbnm phase and show the refinement plot obtained at 3.9 GPa in Figure 2a. The cell
Figure 2. Rietveld refinement of the XRD pattern collected at room temperature. The peaks were indexed with the tetragonal P4/nmm space group. The star symbols indicate the secondary NiAs-type P63/mmc phase. The refinement factors are 3.28, 3.99, and 2.1% for Rp, Rwp, and χ2 respectively. The inset shows the zero-field cooled DC magnetization measurement as a function of temperature performed on the sample.
Crystal and Electronic Structure of FeSe
Figure 3. (a) XRD patterns collected at various pressures at RT for FeSe. The high-pressure Pbnm phase labeled as II appears above 11 GPa. Region I represents the tetragonal phase. (b) Rietveld refinement plots for the tetragonal and orthorhombic structures. The solid line is the simulation, and the markers represent the experimental spectra. The difference line and phase markers are shown below. The wavelength used for RT experiments is 0.34468 Å. The detailed structural parameters such as cell parametersa and atomic positions are provided in Table 1.
parameters for the Pbnm phase obtained at 1.6 GPa are a ) 5.1887(5) Å, b ) 5.6834(5) Å, and 3.6892(6) Å with cell volume V ) 108.79(5) Å3. These values are in agreement with theoretical simulations. As the phase contribution from Pbnm is very small up to 7 GPa, the atomic position parameters were not incorporated in the refinement. Around 8.1 GPa, we have used the atomic position parameters obtained from theory as reference and refined them. The refined positions of Fe atoms are 0.2001(2), 0.0149(5), and 0.25; Se positions are 0.5693(9), 0.2279(6), and 0.25. The Rietveld refinement profiles are shown for three different pressures of 1.3, 4.9, and 31 GPa in Figure 5. The key structural parameters at different pressures at 8 K are listed in Table 2. Above 8 GPa, the phase fraction of Pbnm increases to 38%, and at around 18 GPa, the phase fraction is found to be 84%. We found that the Cmma phase remained at 7.6% up to 26 GPa, indicating the existence of a mixed-phase region. Above 26 GPa, the Cmma phase completely transformed to Pbnm. At 9 GPa, we estimated a volume collapse of about 19% from Cmma to Pbnm. From 1.6 to 9 GPa, the cell parameters of the Cmma phase decreased gradually. However, the large compressibility found along the c axis in comparison with that along a and b indicates anisotropy in the lattice compression. The pressure evolution of the Fe-Se-Fe angles shows a rapid decrease at around 1.6 GPa, and these angles further decrease more slowly at higher pressures. The variation of the unit cell volume with theoretical calculations is presented
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Figure 4. X-ray diffraction patterns collected at various pressures up to 31 GPa at 8 K. The solid star symbols indicate the presence of Cmma diffraction peaks at 18 and 21 GPa. The inset shows the evolution of the diffraction line corresponding to the Pbnm phase.
Figure 5. Rietveld refinement profiles for FeSe at 8 K and 1.3, 4.9, and 31 GPa. At 1.3 GPa, Cmma and P63/mmc phases are included in the refinement. At 4.9 GPa Cmma, P63/mmc, and Pbnm phases are included. The 31 GPa diffraction pattern represents the Pbnm phase. The markers represent the experimental spectra, and solid lines are calculated spectra. The phase markers and difference lines are shown below. The corresponding structural parameters are listed in Table 2.
in Figure 6a. The changes observed in the cell parameters and z(Se) are shown as Figure 6b and c. Earlier studies on iron
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TABLE 2: Refined Atomic Parameters for FeSe at 8 K (variable coordinates x, y, and z, isotropic thermal parameters, site occupancies) at Selected Pressures from Synchrotron X-ray Data along with Cell Parameters, Bond Lengths, and Agreement Factors, Rp, Rwp, and χ2 pressure 1.3 GPa structure Fe
Se
x y z Biso (Å2) occ. x y z Biso (Å2) occ. a (Å) b (Å) c (Å) volume (Å3) Fe-Fe (Å) Fe-Se (Å) Se-Se plane (Å) Fe-Se-Fe (°)
molar phase fraction (%) Rp (%) Rwp (%) GOF (χ2)
R (Cmmm)
1.6 GPa
β (P63/mmc)
3/4 0 0 1.1(5) 1 1/2 1/4 0.2629(8) 2.8(7) 1 5.2659(3) 5.2925(5) 5.3283(7) 148.50(2) 2.6327(7) × 2 2.6465(6) × 2 2.3336(5) × 4 3.7330(6) × 4 3.6586(9) × 2 106.22(9) 69.07(9) 68.63(9) 96.94 1.71 2.42 2.2
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5879(8) 3.5879(8) 5.8592(8) 65.32(7)
R (Cmmm)
β (P63/mmc)
3/4 0 0 2.5(1) 1 1/2 1/4 0.2795(9) 0.96(2) 1 5.2878(9) 5.2410(7) 5.3412(9) 148.02(6) 2.6205(4) 2.6439(4) 2.3859(9) 3.7225(7) 3.5403(7) 102.53(2) 67.29(8) 66.61(9)
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5626(4) 3.5626(4) 5.8546(5) 64.35(6)
γ (Pbnm)
2.1 GPa R (Cmmm)
β (P63/mmc)
γ (Pbnm)
3/4 0 0 2.5(1) 1 1/2 1/4 0.2759(8) 1.5(3) 1 5.2646(8) 5.2426(9) 5.2941(8) 146.12(9) 2.6213(4) 2.6323(5) 2.3632(3) 3.7148(9) 3.5433(6) 103.63(9) 67.69(9) 67.37(9)
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5568(8) 3.5568(8) 5.8144(7) 63.70(2)
5.185(7) 5.6817(8) 3.6898(5) 108.70(5
5.1887(5) 5.6834(5) 3.6892(6) 108.79(5)
3.06 3.54 4.76 3.4
2.26 3.61 3.5
pressure 2.3 GPa structure Fe x y z Biso (Å2) occ. Se x y z Biso (Å2) occ. a (Å) b (Å) c (Å) volume (Å3) Fe-Fe (Å) Fe-Se (Å) Se-Se plane (Å) Fe-Se-Fe (°)
molar phase fraction (%) Rp (%) Rwp (%) GOF (χ2)
2.8 GPa
3.2 GPa
R (Cmmm) β (P63/mmc) γ (Pbnm) R (Cmmm) β (P63/mmc) γ (Pbnm) R (Cmmm) β (P63/mmc) γ (Pbnm) 3/4 0 0 2.4(9) 1 1/2 1/4 0.2768(8) 1.5(2) 1 5.2487(7) 5.2383(9) 5.2761(5) 145.06(7) 2.6244(4) 2.6191(4) 2.3601(9) 3.7077(2) 3.5256(8) 103.54(9) 67.56(9) 67.40(7)
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5472(9) 3.5472(9) 5.8157(5) 63.37(4)
4.59 7.9 4.1
5.1476(3) 5.6840(2) 3.6915(9) 108.01(5)
3/4 0 0 2.5(4) 1 1/2 1/4 0.2769(5) 1.6(9) 1 5.2464(9) 5.2233(9) 5.2565(7) 144.06(7) 2.6232(9) 2.6116(4) 2.3545(9) 3.7016(7) 3.5185(5) 103.63(7) 67.70(3) 67.36(5)
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5430(4) 3.5430(4) 5.7726(5) 62.75(3)
5.37 7.5 4.0
5.2902(5) 5.5143(5) 3.6853(6) 107.50(4)
3/4 0 0 2.8(7) 1 1/2 1/4 0.2778(6) 1.6(2) 1 5.2136(4) 5.2391(6) 5.2412(8) 143.16(5) 2.6195(4) 2.6068(4) 2.3525(9) 3.6956(8) 3.5050(3) 103.52(9) 67.66(9) 67.29(7) 4.12 6.77 3.3
0 0 0 0.6 1 1/3 2/3 1/4 0.6 1 3.5350(5) 3.5350(5) 5.7691(7) 62.43(6)
5.2834(7) 5.5141(8) 3.6766(5) 107.11(5)
Crystal and Electronic Structure of FeSe
J. Phys. Chem. B, Vol. 114, No. 39, 2010 12603
TABLE 2: Continued Pressure 3.9 GPa structure Fe x
4.9 GPa
5.5 GPa
R (Cmmm) β (P63/mmc) γ (Pbnm) R (Cmmm) β (P63/mmc) γ (Pbnm) R (Cmmm) β (P63/mmc) γ (Pbnm) 3/4
0
3/4
0
3/4
0
y
0
0
0
0
0
0
z
0
0
0
0
0
0
Biso (Å2)
2.1(6)
0.6
2.9(7)
0.6
2.2(2)
0.6
occ.
1
1
1
1
1
1
Se x
1/2
1/3
1/2
1/3
1/2
1/3
y
1/4
2/3
1/4
2/3
1/4
2/3
z
0.2854(8)
1/4
0.2851(7)
1/4
0.2913(2)
1/4
Biso (Å2)
1.6(4)
0.6
1.1(7)
0.6
0.82(5)
0.6
occ.
1
1
1
1
1
1
a (Å)
5.1891(4)
3.5152(4)
5.2879(7)
5.1801(9)
3.4959(7)
5.2599(5)
5.1763(8)
3.4801(6)
5.3301(2)
b (Å)
5.2281(5)
3.5152(4)
5.5272(8)
5.1796(9)
3.4959(7)
5.5347(9)
5.1533(9)
3.4801(6)
5.5681(9)
c (Å)
5.1877(7)
5.7388(7)
3.6456(8)
5.1651(7)
5.7382(8)
3.6401(6)
5.1473(8)
5.6793(7)
3.560(1)
volume (Å3)
140.73(7)
61.41(7)
106.55(9)
138.58(8)
60.73(5)
105.97(8)
137.30(5)
59.56(7)
105.65(5)
Fe-Fe (Å)
2.6140(4)
2.5901(5)
2.5881(8)
2.5945(4)
2.5898(4)
2.5766(8)
Fe-Se (Å)
2.3629(9)
2.3499(6)
2.3627(6)
Se-Se
3.6830(6)
3.6626(6)
3.6521(5)
plane (Å)
3.4336(4)
3.4112(8)
3.3635(9)
Fe-Se-Fe (°)
102.40(7)
102.39(8)
101.21(9)
67.16(6)
66.88(9)
66.41(8)
66.59(9)
66.87(9)
66.08(5)
molar phase fraction (%) Rp (%)
5.58
6.14
5.14
Rwp (%)
6.51
7.72
7.2
GOF (χ2)
3.3
4.7
3.8
pressure 7 GPa structure Fe x
8.1 GPa
9 GPa
R (Cmmm) β (P63/mmc) γ (Pbnm) R (Cmmm) β (P63/mmc) γ (Pbnm) R (Cmmm) β (P63/mmc) γ (Pbnm) 3/4
0
3/4
0
0.2001(2)
3/4
0
y
0
0
0
0
0.0149(5)
0
0
0.2042(6) 0.0452(7)
z
0
0
0
0
1/4
0
0
1/4
Biso (Å2)
2.8(3)
0.6
2.4(2)
0.6
2.3(8)
2.8(3)
0.6
2.2(6)
occ.
1
1
1
1
1
1
1
1
Se x
1/2
1/3
1/2
1/3
0.5693(9)
1/2
1/3
0.5551(7)
y
1/4
2/3
1/4
2/3
0.2279(6)
1/4
2/3
0.2457(3)
z
0.2919(7)
1/4
0.2940(3)
1/4
1/4
0.2929(5)
1/4
1/4
Biso (Å2)
0.62(5)
0.6
0.57(6)
0.6
0.63(7)
0.63(8)
0.6
0.62(7)
occ.
1
1
1
1
1
1
1
a (Å)
5.1398(5)
3.408(3)
5.269(5)
5.0985(9)
3.391(1)
5.261(3)
5.0642(6)
3.339(3)
5.304(4)
b (Å)
5.1375(5)
3.408(3)
5.630(5)
5.1285(4)
3.391(1)
5.474(4)
5.0874(6)
3.339(3)
5.364(4)
c (Å)
5.0995(6)
5.906(6)
3.5514(9)
5.0702(5)
5.908(2)
3.628(3)
5.0169(7)
5.953(4)
3.642(6)
volume (Å3)
134.65(7)
59.42(6)
104.99(6)
132.57(5)
58.85(2)
104.5
129.25(9)
57.49(2)
103.65(6)
Fe-Fe (Å)
2.5699(4)
2.5642(6)
2.5321(5)
0.98
40.30
2.5687(4)
2.5492(4)
2.5437(5)
Fe-Se (Å)
2.3487(9)
2.3431(9)
2.3226(8)
Se-Se
3.6335(7)
3.6159(8)
3.5884(7)
plane (Å)
3.3325(6)
3.2958(6)
3.2763(8)
Fe-Se-Fe (°)
101.34(9)
100.98(8)
101.18(5)
66.33(5)
66.34(6)
66.40(8)
66.30(9)
65.90(9)
molar phase fraction (%)
60.26
66.06(9) 1.07
38.67
58.72
Rp (%)
4.60
4.31
3.55
Rwp (%)
6.42
6.41
5.40
GOF (χ2)
3.2
3.1
2.9
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J. Phys. Chem. B, Vol. 114, No. 39, 2010
Kumar et al.
TABLE 2: Continued pressure 18 GPa
Fe
Se
21 GPa
23 GPa
26 GPa
31 GPa
structure
R (Cmmm)
γ (Pbnm)
R (Cmmm)
γ (Pbnm)
R (Cmmm)
γ (Pbnm)
R (Cmmm)
γ (Pbnm)
γ (Pbnm)
x y z Biso (Å2) occ. x y z Biso (Å2) occ. a (Å) b (Å) c (Å) volume (Å3) molar phase fraction (%) Rp (%) Rwp (%) GOF (χ2)
3/4 0 0 0.6 1 1/2 1/4 0.2990(8) 0.6 1 4.891(2) 4.959(9) 5.073(6) 123.07(3) 15.71
0.2001(7) 0.0541(3) 0 3.5(8) 1 0.5618(5) 0.2207(5) 1/4 1.1(8) 1 5.346(2) 5.281(2) 3.538(6) 99.90(6) 84.29
3/4 0 0 0.6 1 1/2 1/4 0.2994(7) 0.6 1 4.926(1) 4.894(7) 4.963(8) 119.68(6) 11.54
0.2062(4) 0.0487(3) 0 2.1(8) 1 0.5640(8) 0.2253(6) 1/4 0.77(5) 1 5.353(5) 5.222(1) 3.530(2) 98.69(4) 88.46
3/4 0 0 0.6 1 1/2 1/4 0.3108(6) 0.6 1 4.934(2) 4.865(6) 4.939(5) 118.58(6) 7.98
0.2116(5) 0.0361(3) 0 2.9(7) 1 0.5752(4) 0.2267(3) 1/4 0.36(9) 1 5.335(7) 5.242(4) 3.505(9) 98.07(9) 92.02
3/4 0 0 0.6 1 1/2 1/4 0.3130(6) 0.6 1 4.861(4) 4.902(7) 4.922(4) 117.32(8) 7.58
0.2062(5) 0.0487(3) 1/4 2.1(8)
0.2344(6) 0.0610(8) 1/4 2.3(4) 1 0.5748(1) 0.22158(1) 1/4 0.9(6) 1 5.318(2) 5.209(2) 3.4385(9) 95.27(5)
2.01 2.65 3.7
3.72 4.44 4.1
arsenide compounds show that the Tc is sensitive to the distortions in the edge-sharing tetrahedral FeAs4 units. Tc reaches a maximum when the FeAs4 units are in an ideal position. While the behavior of FeSe is very similar to that of other iron arsenides where the distortions in the tetrahedaral Fe-Se increase with pressure, differences arise with the effect of pressure on Tc. The rapid Tc increase in FeSe with pressure induced distortions at around 1.6 GPa, and a maximum found at around 34 K at 6.7 GPa implies mainly that the lattice anisotropy, crystallographic, and electronic structures play important roles in the superconducting properties. The effect of the early appearance of the minor Pbnm phase from the Tc changes in this context still needs to be understood. The pressure-volume data of the Cmma phase at LT fitted to a third-
Figure 6. (a) Pressure versus volume data for FeSe at 8 K. The open triangles and squares show the experimental points for Cmma and Pbnm phases, respectively. The closed triangle markers with a solid line and the closed square markers with a solid line represent the theoretical calculations for Cmma and Pbnm phases, respectively. The vertical dotted line at around 9 GPa indicates the transition point above which the Pbnm phase becomes major. The inset (b) shows the variation of cell parameters for the Cmma phase with pressure. The solid triangles, squares, and circles represent a, b, and c, respectively (c) Variation of the z parameter of Se for the Cmma phase with pressure.
3.80 5.31 4.2
0.5640(8) 0.2253(6) 1/4 0.61(8) 5.334(2) 5.210(3) 3.482(2) 96.78(9) 92.42 3.27 4.56 3.9
2.1 2.8 4.8
order Birch-Murnaghan equation show B0 ) 30.9 (3) GPa, with B0′ ) 6.1(9). The low bulk modulus calculated from the experimental data shows that FeSe is highly compressible and is consistent with other reports.13,15 Figure 7 shows the measured and calculated phonon density of states (PDOS) at high pressures. The Fe partial PDOS spectrum shows four prominent regions, the transverse acoustic
Figure 7. Fe partial phonon DOS for FeSe at different pressures up to 27 GPa. The solid lines are theoretical calculations, and the lines with markers represent experimental data. The phonon modes labeled A, B, C, D, and E are explained in the text.
Crystal and Electronic Structure of FeSe
J. Phys. Chem. B, Vol. 114, No. 39, 2010 12605
Figure 8. Enthalpy versus pressure for tetragonal (P4/nmm), orthorhombic (Pbnm), and hexagonal (P63/mmc) phases of FeSe.
(TA) modes below 10 meV (labeled A), longitudinal acoustic (LA) modes (labeled B) around 15 meV, the B1g Raman mode (labeled C), and the optical modes above 30 meV (labeled D and E) in the 3 GPa spectrum. Upon increasing pressure, the intensity of the acoustic modes reduces rapidly due to anisotropic lattice compression inherent to the layered structure. Further above 9 GPa, the intensity of the optical modes increases, indicating a phase transition to the orthorhombic structure. From the experimental data, we have obtained the Lamb-Mossbauer factor fLM ) 0.47(1) and the mean force constant D ) 129 (3) N/m for the ambient tetragonal phase. At around 16 GPa, we have obtained fLM ) 0.69(1) and D ) 191(10) N/m. The calculated PDOS of the tetragonal and orthorhombic Pbnm structures and the increase in intensity of phonon modes at higher energies are generally in agreement with theoretical and experimental results.6,27 Theoretical calculations were performed to understand the changes in PDOS and are discussed further. In order to investigate the phase changes and the transition from Cmma to Pbnm, we first examined the enthalpy for the tetragonal, orthorhombic Pbnm, and hexagonal phases (Figure 8). A possible phase transition point between the tetragonal and orthorhombic Pbnm phases is identified at 10.5 GPa, which is in good agreement with our XRD results. The enthalpy of the hexagonal structure is greater than that of Pbnm by 0.058 eV/ f.u. (where f.u. is a formula unit) at 0 GPa and by 0.136 eV/f.u. at 24 GPa, indicating that the Pbnm phase is more favorable. It should be noted that the secondary hexagonal phase found in experiment could be due to lattice strain since the enthalpy difference at ambient pressure is small. The calculated phase transition from tetragonal to either Pbnm or hexagonal phases leads to a pronounced volume reduction of about 15%, in good agreement with experimental results. The compressed tetragonal cell collapses along the c axis before reaching the transition pressure. The shape difference of PDOS between theory and experiment is likely due to thermal effects as the experiments were done at finite temperature while the DFT calculations were performed at 0 K. The PDOS of the hexagonal phase, however, is not available for comparison due to the calculated imaginary phonon frequencies near the (0.5, 0, 0) point, which suggests that the hexagonal structure is dynamically unstable at LT. Nevertheless, it could be stabilized at RT since some RT XRD refinement12 claimed that the high-pressure phase should be hexagonal. On the basis of the above experimental and theoretical results, we conclude that there exist two LT FeSe phases between 0 and 31 GPa. The low-pressure phase is mainly Cmma, and the high-pressure phase is orthorhombic Pbnm. The observed mixed-phase region at LT is composed of both Cmma and Pbnm phases. We next investigate the electronic structures of tetragonal and Pbnm FeSe. As shown in Figure 9a, the calculated band structure of tetragonal FeSe is in excellent agreement with previous results.6 The parabolic band structures near the Γ and M points result in the discrete cylindrical Fermi surface (FS) shown in Figure 9c. It is clear the electron FS in
Figure 9. Electronic band structure of the (a) tetragonal phase of FeSe at 0 GPa and (b) orthorhombic Pbnm phase of FeSe at 16 GPa. (c-e) Fermi surface of the tetragonal phase of FeSe at 0 and 9 GPa and orthorhombic Pbnm phase of FeSe at 16 GPa.
the zone center overlaps with the hole FS in the corner by a nesting vector q ) (π, π, 0). The FS nesting in FeSe leads to a spin density wave (SDW) phase at LT,6 which was observed in a recent experiment.13 At 9 GPa (Figure 9d), the electron FS is distorted such that its shape is no longer 2D cylindrical. Meanwhile, the hole FS is only slightly distorted. As a result, the FS nesting effect, which is strong at ambient pressure, is suppressed at high pressure. Nevertheless, SDW can still develop with the reduced nesting. In fact, experiment observed a SDW transition at 6 GPa,13 although the corresponding anomaly is not as clear as that at 0 GPa. In a spin fluctuation picture, the superconducting pairing competes with the SDW for the same FS. If the SDW becomes unstable due to the reduced FS nesting, the superconducting phase is likely to appear at an earlier stage. Consequently, for the Cmma phase, higher pressure, which enhances the FS shape mismatch in nesting, would lead to higher Tc.11 The band structure and FS of orthorhombic Pbnm FeSe are plotted in Figure 9b and e, respectively. There is no sign of superconductivity for the high-pressure Pbnm phase when the same spin fluctuation picture is applied since the calculated band structure is drastically different from that of any known ironbased superconductors and the FS is not strongly nested. We believe that the observed Tc increase between 9 and 26 GPa13 is not due to the high-pressure orthorhombic Pbnm phase but to the pressure-induced distortion in the Cmma phase. The Cmma phase gradually diminishes beyond 23 GPa, and the orthorhombic Pbnm persists thereafter. This is consistent with a previous high-pressure experiment12 in which Tc enhancement is observed above 8.9 GPa with an increasing resistivity offset from zero after the transition, with the superconductivity completely disappearing above 29 GPa. Interestingly, our calculations show that the Pbnm phase is metallic at high pressure. This is in contrast to the semiconducting resistivity behavior observed at 29 GPa in a previous experiment.12 We have examined the band structures of P63/mmc and 2 × 2 × 2 (Fe32Se32) and 1 × 1 × 2 (Fe8Se8) Pbnm with one Se vacancy at 29 GPa. They are all metallic for the nonmagnetic and ferromagnetic cases.
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4. Conclusions In summary, we have demonstrated by a combined experimental and theoretical study that FeSe undergoes a pressureinduced transition from the Cmma to Pbnm phase, which begins to appear as early as 1.6 GPa at 8 K. The Pbnm phase becomes a major phase above 9 GPa. Our experiments and theoretical band structural calculations suggest that the Tc enhancement under pressures may take place via a structural distortion in the Cmma phase that suppresses the Fermi surface nesting and possibly enhances superconductivity in FeSe. Also, the results of the electronic calculations, in accordance with previous experiments, show that the high-pressure Pbnm phase is not superconducting. In addition to pressure-induced structural changes, alternative mechanisms such as spin or magnetic fluctuations need to be taken into account to understand the effect of pressure on this new class of novel superconductors. Acknowledgment. Work at UNLV was supported by DOE under Cooperative Agreement No. DE-FC52-06NA26274. The experiments were performed at HPCAT (Sector 16), Advanced PhotonSource (APS), Argonne National Laboratory. HPCAT is supported by DOE-BES, DOE-NNSA, NSF, and the W.M. Keck Foundation. APS is supported by DOE-BES under Contract No. DE-AC02-06CH11357. References and Notes (1) Hsu, F.-C.; Luo, J.-Y.; Yeh, K.-W.; Chen, T.-K.; Huang, T.-W.; MWu, P.; Lee, Y.-C.; Huang, Y.-L.; Chu, Y.-Y.; Yan, D.-C.; Wu, M.-K. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 14262. (2) Kamihara, Y.; Watanabe, T.; Hirano, M.; Hosono, H. J. Am. Chem. Soc. 2008, 130, 3296. (3) Chen, X. H.; Wu, T.; Wu, G.; Liu, R. H.; Chen, H.; Fang, D. F. Nature 2008, 453, 76110. (4) Ren, Z. A.; Che, G. C.; Dong, X. L.; Yang, J.; Lu, W.; Yi, W.; Shen, X. L.; Li, Z. C.; Sun, L. L.; Zhou, F.; Zhao, Z. X. Europhys. Lett. 2008, 83, 17002. (5) Rotter, M.; Tegel, M.; Johrendt, D. Phys. ReV. Lett. 2008, 101, 107006.
Kumar et al. (6) Subedi, A.; Zhang, L. J.; Singh, D. J.; Du, M. H. Phys. ReV. B 2008, 78, 134514. (7) Lee, K.-W.; Pardo, V.; Pickett, W. E. Phys. ReV. B 2008, 78, 174502. (8) Margadonna, S.; Takabayashi, Y.; McDonald, M. T.; Kasperkiewicz, K.; Mizuguchi, Y.; Takano, Y.; Fitch, A. N.; Suard, E.; Prassides, K. Chem. Commun. 2008, 5607. (9) McQueen, T. M.; Williams, A. J.; Stephens, P. W.; Tao, J.; Zhu, Y.; Ksenofontov, V.; Casper, F.; Felser, C.; Cava, R. J. Phys. ReV. Lett. 2009, 103, 057002. (10) Wang, M. J.; Luo, J. Y.; Huang, T. W.; Chang, H. H.; Chen, T. K.; Hsu, F. C.; Wu, C. T.; Wu, P. M.; Chang, A. M.; Wu, M. K. Phys. ReV. Lett. 2009, 103, 117002. (11) Mizuguchi, Y.; Tomioka, F.; Tsuda, S.; Yamaguchi, T.; Takano, Y. Appl. Phys. Lett. 2008, 93, 152505. (12) Medvedev, S.; McQueen, T. M.; Troyan, I. A.; Palasyuk, T.; Eremets, M. I.; Cava, R. J.; Naghavi, S.; Casper, F.; Ksenofontov, V.; Wortmann, G.; Felser, C. Nat. Mater. 2009, 8, 630. (13) Garbarino, G.; Sow, A.; Lejay, P.; Sulpice, A.; Toulemonde, P.; Mezouar, M.; Nu´n˜ez-Regueiro, M. Europhys. Lett. 2009, 86, 27001. (14) Braithwaite, D.; Salce, B.; Lapertot, G.; Bourdarot, F.; Marin, C.; Aoki, D.; Hanfland, M. J. Phys.: Condens. Matter 2009, 21, 232202. (15) Margadonna, S.; Takabayashi, Y.; Ohishi, Y.; Mizuguchi, Y.; Takano, Y.; Kagayama, T.; Nakagawa, T.; Takata, M.; Prassides, K. Phys. ReV. B 2009, 80, 064506. (16) Imai, T.; Ahilan, K.; Ning, F. L.; McQueen, T. M.; Cava, R. J. Phys. ReV. Lett. 2009, 102, 177005. (17) McQueen, T. M.; Huang, Q.; Ksenofontov, V.; Felser, C.; Xu, Q.; Zandbergen, H.; Hor, Y. S.; Allred, J.; Williams, A. J.; Qu, D.; Checkelsky, J.; Ong, N. P.; Cava, R. J. Phys. ReV. B 2009, 79, 014522. (18) Mao, H. K.; Xu, J.; Bell, P. M. J. Geophys. Res. 1986, 91, 4673. (19) Hunter, B. LHPM-RIETICA. www.rietica.org. (20) Larsen, A. C. Von Freele, R. B., Los Alamos National Laboratory Report, LUAR; Los Alamos National Laboratory: Los Alamos, NM, 1994; Vol. 86. (21) Sturhahn, W. Hyperfine Interact. 2000, 125, 149. (22) Kresser, G.; Joubert, D. Phys. ReV. B 1999, 59, 1758. (23) Kresser, G.; Furthm ¨ uller, J. Phys. ReV. B 1996, 54, 11169. (24) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (25) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (26) Parlinski, K.; Li, Z. Q.; Kawazoe, Y. Phys. ReV. Lett. 1997, 78, 4063. (27) Ksenofontov, V.; Wortmann, G.; Chumakov, A. I.; Gasi, T.; Medvedev, S.; McQueen, T. M.; Cava, R. J.; Felser, C. Phys. ReV. B 2010, 81, 184510.
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