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Non-Fermi-liquid types of behavior associated with a magnetic quantum critical point in Sr ( Co 1 - x Ni x ) 2 As 2 single crystals

The compound SrCo 2 As 2 with the body-centered tetragonal ThCr 2 Si 2 structure is known to remain paramagnetic down to a temperature T = 0.05 K, but inelastic neutron scattering studies have shown that both ferromagnetic (FM) and antiferromagnetic (AFM) fluctuations occur in single crystals. Thus it is of interest to study how the magnetism evolves on doping SrCo 2 As 2 . Previous work on polycrystalline samples of Sr (Co 1-x Ni x ) 2 As 2 indicated the development of AFM order for 0 < x ≲ 0.3. Here we studied single crystals of Sr(Co 1-x Ni x ) 2 As 2 for 0 < x ≤ 1 and confirmed the occurrence of AFM order which we deduce to have a c -axis helix structure. We also find evidence for an unusual composition-induced magnetic quantum critical point at x ≈ 0.3 where non-Fermi-liquid types of behavior were revealed by heat capacity and electrical resisitivity measurements at low T. Electron-doped Sr (Co 1-x Ni x ) 2 As 2 single crystals with compositions x = 0 to 0.9 were grown out of self-flux and SrNi 2 As 2 single crystals out of Bi flux. The crystals were characterized using single-crystal x-ray diffraction (XRD) at room temperature, and magnetic susceptibility χ (H, T), isothermal magnetization M (H, T), heat capacity Cp (H, T), and electrical resistivity ρ (H, T) measurements versus applied magnetic field H and T. The XRD studies show that the system undergoes a continuous structural crossover from the uncollapsed-tetragonal (ucT) structure to the collapsed tetragonal (cT) structure with increasing Ni doping. The χ(T) data show that SrCo 2 As 2 exhibits an AFM ground state almost immediately upon Ni doping on the Co site. Ab initio electronic-structure calculations for x = 0 and 0.15 indicate that a flat band with a peak in the density of states just above the Fermi energy is responsible for this initial magnetic-ordering behavior on Ni doping. The AFM ordering is observed in the range 0.013 ≤ x ≤ 0.25 with the ordered moments aligned in the ab plane and with a maximum ordering temperature T N = 26.5 K at x = 0.10. The Curie-Weiss-like T dependence of χ in the paramagnetic (PM) state indicates dominant FM interactions. The behavior of the anisotropic susceptibilities below T N suggests a planar helical magnetic ground state with a composition-dependent pitch based on a local-moment molecular-field-theory model, with FM interactions in the ab plane and weaker AFM interactions along the helix c axis. However, the small ordered (saturation) moments ~0.1 μ B per transition metal atom, where μ B is the Bohr magneton, and the values of the Rhodes-Wohlfarth ratio indicate that the magnetism is itinerant. The high-field M (H) isotherms and the low-field χ-1 ( T > T N ) data were successfully analyzed within the framework of Takahashi's theory of FM spin fluctuations. The C p (T) at low T exhibits Fermi-liquid behavior for 0 ≤ x ≤ 0.15 , whereas an evolution to a logarithmic non-Fermi-liquid (NFL) behavior is found for x = 0.2 to 0.3. The logarithmic dependence is suppressed in an applied magnetic field. The low- T ρ ( H = 0 , T ) data show a T 2 dependence for 0 ≤ x ≤ 0.20 and a power-law dependence ρ (H = 0, T) = ρ 0 + AT n with n < 2 for x = 0.20 and 0.30. The exponent n shows a notable field dependence, suggesting both doping- and magnetic-field-tuned quantum critical phenomena. These low- T NFL types of behavior observed in the C p and ρ measurements are most evident near the quantum critical concentration x ≈ 0.3 at which a T = 0 composition-induced transition from the AFM phase to the PM phase occurs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Charge Ordering and Low-Temperature Lattice Distortion in the {beta}'-(BDT-TTF){sub 2}CF{sub 3}CF{sub 2}SO{sub 3} Dime Mott Insulator.

We present single-crystal x-ray diffraction measurements, optical investigations, and electronic structure calculations for the organic charge-transfer salt beta'-(BEDT-TTF)(2)CF3CF2SO3 synthesized by electrocrystallization. Electronic structure calculations confirm the quasi-one-dimensional behavior of the compound and optical conductivity measurements reveal the dimer-Mott insulating nature of the system. The splitting of the charge-sensitive nu(2) mode in Raman spectra demonstrates the onset of an interlayer charge-ordered phase below 25 K, also suggested by the crystal structure considerations. This transition is accompanied by clear signatures of a lattice distortion in the BEDT-TTF donor layer, as shown by a splitting of the vibrational nu(3) mode in infrared spectra. At the same time, the sharp redshift of the nu(1) mode involving the BEDT-TTF ethylene groups strongly suggests a significant modification of the hydrogen-type bonding present between the BEDT-TTF donor layer and the CF3CF2SO3- anion layer. These observations point to a subtle interplay of charge and lattice degrees of freedom at the phase transition.

Olejniczak, I.↗

Ferromagnetic cluster-glass phase in Ca(Co 1-x Ir x ) 2-y As 2 crystals

In this study, single crystals of Ca(Co 1-x Ir x ) 2-y As 2 with 0≤x≤0.35 and 0.10≤y≤0.14 have been grown using the self-flux technique and characterized by single-crystal x-ray diffraction (XRD), energy-dispersive x-ray spectroscopy, magnetization M, and magnetic susceptibility χ measurements versus temperature T, magnetic field H, and time t, and heat-capacity C p (H,T) measurements. The XRD refinements reveal that all the Ir-substituted crystals crystallize in a collapsed-tetragonal structure as does the parent CaCo 2-y As 2 compound. A small 3.3% Ir substitution for Co in CaCo 1.86 As 2 drastically lowers the A-type antiferromagnetic (AFM) transition temperature T N from 52 to 23 K with a significant enhancement of the Sommerfeld electronic heat-capacity coefficient. The A-type AFM structure consists of ab-plane layers of spins ferromagnetically aligned along the c axis with AFM alignment of the spins in adjacent layers along this axis. The positive Weiss temperatures obtained from Curie-Weiss fits to the χ(T>T N ) data indicate that the dominant magnetic interactions are ferromagnetic (FM) for all x. A magnetic phase boundary is inferred to be present between x=0.14 and x=0.17 from a discontinuity in the x dependencies of the effective moment and Weiss temperature in the Curie-Weiss fits. FM fluctuations that strongly increase with increasing x are also revealed from the χ(T) data. Furthermore, the magnetic ground state for x≥0.17 is a spin glass as indicated by hysteresis in χ(T) between field-cooled and zero-field-cooled measurements and from the relaxation of M in a small field that exhibits a stretched-exponential time dependence. The spin glass has a small FM component to the ordering and is hence inferred to be comprised of small FM clusters. The competing AFM and FM interactions along with crystallographic disorder associated with Ir substitution are inferred to be responsible for the development of a FM cluster-glass phase. A logarithmic T dependence of Cp at low T for x=0.14 is consistent with the presence of significant FM quantum fluctuations. This composition is near the T=0 boundary at x≈0.16 between the A-type AFM phase containing ferromagnetically-aligned layers of spins and the FM cluster-glass phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nature of the ferromagnetic-antiferromagnetic transition in Y 1- x La x TiO 3

In this work, we explore the magnetically ordered ground state of the isovalently substituted Mott insulator Y 1- x La x TiO 3 for x≤ 0.3 via single-crystal growth, magnetometry, neutron diffraction, x-ray magnetic circular dichroism, muon spin rotation, and small-angle neutron scattering (SANS). We find that the decrease in the magnetic transition temperature on approaching the ferromagnetic-antiferromagnetic phase boundary at the La concentration xc ≈ 0.3 is accompanied by a strong suppression of both bulk and local ordered magnetic moments, along with a volume wise separation into magnetically ordered and paramagnetic regions. The thermal phase transition does not show conventional second-order behavior since neither a clear signature of dynamic critical behavior nor a power-law divergence of the magnetic correlation length is found for the studied substitution range; this finding becomes increasingly obvious with increasing La substitution. We find no evidence for a spin-glass phase. Finally, from SANS and magnetometry measurements, we discern a crossover from easy-axis to easy-plane magnetocrystalline anisotropy with increasing La substitution. These results indicate complex changes in magnetic structure upon approaching the phase boundary.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Suppression of antiferromagnetic order and strong ferromagnetic spin fluctuations in Ca(Co 1-x Ni x ) 2-y As 2 single crystals

CaCo 2–y As 2 is a unique itinerant system having strong magnetic frustration. Here, we report the effect of electron doping on the physical properties resulting from Ni substitutions for Co. The single crystals of Ca(Co 1–x Ni x ) 2–y As 2 were characterized by single-crystal x-ray diffraction, energy-dispersive x-ray spectroscopy, magnetization M versus temperature T, magnetic field H, time t, and heat capacity C p (H, T) measurements. The A-type antiferromagnetic (AFM) transition temperature T N = 52 K for x = 0 decreases to 22 K with only 3% Ni substitution and is completely suppressed for x > 0.16. For 0.11 ≤ x ≤ 0.52 strong ferromagnetic (FM) fluctuations develop as revealed by magnetic susceptibility χ(T) = M(T) / H measurements. For x = 0.11 and 0.16 competing AFM and FM interactions result in a reentrant spin-glass behavior below T N , as evidenced by the observations of thermomagnetic hysteresis and magnetic relaxation. Enhanced FM fluctuations are also found for the x = 0.21 and 0.31 crystals, where χ c increases significantly at low T. A large χ anisotropy in these compositions where χ c is up to a factor of two larger than χ ab suggests that the FM spin fluctuations are quasi-1D in nature. Weak ferromagnetic contributions to the magnetization are found at T = 2 K for x = 0.11 –0.31. Heat-capacity Cp(T) measurements reveal the presence of FM quantum spin fluctuations for 0.11 ≤ x ≤ 0.52, where a logarithmic T dependence of Cp(T) / T is observed at low T. Here, the suppression of AFM order by the development of strong FM fluctuations in Ca(Co 1–x Ni x ) 2–y As 2 crystals suggests the presence of a FM quantum-critical point at x ≈ 0.20. Our density-functional theory (DFT) calculations confirm that FM fluctuations are enhanced by Ni substitutions for Co in CaCo 2–y As 2 . The Sommerfeld electronic heat-capacity coefficient is enhanced for x = 0, 0.21, and 0.42 by about a factor of two compared to DFT calculations of the density of states (DOS) at the Fermi energy, suggesting an enhancement of the DOS from electron-phonon and/or electron-electron interactions. The crystals with x > 0.52 do not exhibit FM spin fluctuations or magnetic order at T ≥ 1.8 K, which was found from the DFT calculations to arise from a Stoner transition. Superconductivity is not observed above 1.8 K for any of the compositions. Neutron-diffraction studies of crystals with x = 0.11 and 0.16 in the crossover regime (0.1 ≲ x ≲ 0.2) show no evidence of A-type ordering as observed in the parent compound with x = 0. Furthermore, no other common magnetic structures, such as ferromagnetic (FM), helical stacking of in-plane FM layers, or in-plane AFM structure, are found with an ordered moment greater than the uncertainty of 0.05 μ B per transition-metal atom.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Structural and vibrational behavior of 2 H -NbSe 2 at high pressures

In this work, the high-pressure structural and vibrational properties of a layered transition metal dichalcogenide 2 H -NbSe 2 were investigated using single-crystal x-ray diffraction and Raman spectroscopy, demonstrating its structural stability up to 35 GPa. The lattice compressibility changes character from being highly anisotropic at low pressures to largely isotropic at high pressures. Concomitantly, the interatomic bonds demonstrate highly anisotropic compression behavior with the Se-Se interlayer bonds compressing by >20%, while the intramolecular Se-Se distance shows a nonmonotonic pressure dependence with a maximum at-12 GPa. The nearest-neighbor central force lattice vibrational model yields pressure dependencies of the interatomic forces in qualitative agreement with bond length compression, providing insight into the vibrational properties of 2 H -NbSe 2 at high pressures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Anticollinear order and degeneracy lifting in square lattice antiferromagnet LaSrCrO 4

In this work, we report the static and dynamic magnetic properties of LaSrCrO 4 , a seemingly canonical spin-3/2 square-lattice antiferromagnet that exhibits frustration between magnetic layers—owing to their AB stacking—and offers a rare testbed to investigate accidental-degeneracy lifting in magnetism. Neutron diffraction experiments on single-crystal samples uncover a remarkable anticollinear magnetic order below T N = 170 K characterized by a Néel arrangement of the spins within each layer and an orthogonal arrangement between adjacent layers. To understand the origin of this unusual magnetic structure, we analyze the spin-wave excitation spectrum by means of inelastic neutron scattering and bulk measurements. A spectral gap of 0.5 meV, along with a spin-flop transition at 3.2 T, reflect the energy scale associated with the degeneracy-lifting. A minimal model to explain these observations requires both a positive biquadratic interlayer exchange and dipolar interactions, both of which are on the order of 10 –4 meV, only a few parts per million of the dominant exchange interaction J 1 ≈11 meV. These results provide direct evidence for the selection of a noncollinear magnetic structure by the combined effect of two distinct degeneracy lifting interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Absence of precursor incommensurate charge order in electronic nematic Ba 0.35 Sr 0.65 Ni 2 As 2

Recent discoveries of charge order and electronic nematic order in the iron-based superconductors and cuprates have pointed towards the possibility of nematic and charge fluctuations playing a role in the enhancement of superconductivity. The Ba 1–x Sr x Ni 2 As 2 system, closely related in structure to the BaFe 2 As 2 system, has recently been shown to exhibit both types of ordering without the presence of any magnetic order. We report single-crystal x-ray diffraction experiments on Ba 0.35 Sr 0.65 Ni 2 As 2 , providing evidence that the previously reported incommensurate charge order with wave-vector (0, 0.28, 0) tet in the tetragonal state of BaNi 2 As 2 vanishes by 65% Sr substitution together with nematic order. Furthermore, our measurements suggest that the nematic and incommensurate charge orders are closely tied in the tetragonal state and show that the (0, 0.33, 0) tri charge ordering in the triclinic phase of BaNi 2 As 2 evolves to become (0, 0.5, 0) tri charge ordering at x = 0.65 before vanishing at x = 0.71.

36 MATERIALS SCIENCE↗

Structural evolution of iodine on approach to the monatomic state

Here, we applied single-crystal x-ray diffraction and Raman spectroscopy in a diamond-anvil cell up to 36 GPa and first-principles theoretical calculations to study the molecular dissociation of solid iodine at high pressure. Unlike previously reported, we find that the familiar Cmce molecular phase transforms to a Cmc2 1 molecular structure at 16 GPa, and then to an incommensurate polymeric Fmmm⁡(00⁢$\gamma$)⁢s⁢00 structure, which can be viewed as a mixture of molecular I 2 and zigzag chains of three iodine atoms, at 20 GPa. The available data are consistent with metallization of iodine at the boundary between the commensurate Cmc⁢2 1 structure and the incommensurate Fmmm⁡(00⁢$\gamma$)s⁢00 structure at 20 GPa.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

K 2 Co 2 TeO 6 : A layered magnet with a S = 1 2 Co 2 + honeycomb lattice

Recent observations of Kitaev interactions in d 7 electron configurations have generated research interest in Co 2+ based honeycomb magnets. Here, we report the synthesis of a K 2 Co 2 TeO 6 single crystal. X-ray diffraction and electron microscopy experiments show that K 2 Co 2 TeO 6 crystallizes in a $P$6 3 /$mcm$ space group with undistorted honeycomb layers of Co 2+ ions. Anisotropic magnetic and thermodynamic characterizations demonstrate an effective S = $\frac{1}{2}$ state of Co 2+ at low temperature, competing magnetic phases, and weak magnetic transitions that can be suppressed by applying fields. Moreover, the interlayer K disorder level is tunable by thermal treatments, and it affects the magnetic features obviously. In conclusion, our findings provide a new and promising platform for studying Kitaev physics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Hidden anomalies in topological t – PtBi 2 – x probed by second harmonic generation

The noncentrosymmetric Weyl semimetal PtBi 2–x (t-PtBi 2–x ) exhibits various interesting technologically important physical properties. We report the experimental investigation of PtBi 1.6 via second harmonic generation (SHG), single-crystal x-ray diffraction, magnetic susceptibility, and electrical resistivity measurements. While bulk structural, magnetic, and electrical properties show no phase transitions below room temperature, the temperature dependence of the SHG intensity reveals two anomalies: one at T* ~ 60 K and another at T x ~ 200 K. Quantitative analysis indicates that the SHG signal results from both the buckled Bi1 surface termination with the 3m symmetry and flat Bi2 surface termination with the m symmetry. However, the anomalies are mainly driven by Bi1 on the surface: (1) T* marks the onset of surface states which is also manifested in the c-axis resistivity drop and (2) T x corresponds to the lowest thermal contraction of the structure and enhanced magnetic susceptibility. Furthermore, this study demonstrates that SHG is a powerful technique for probing surface properties even for noncentrosymmetric materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Charge density waves and pinning by lattice anisotropy in 214 cuprates

The detection of static charge density waves (CDWs) in La 2-x ⁢Sr x ⁢CuO 4 (LSCO) with x ~ 0.12 at relatively high temperatures has raised the question of what lattice feature pins the CDWs. Some recent structural studies have concluded that some form of monoclinic distortion, indicated by the appearance of certain weak Bragg peaks (type M peaks) at otherwise forbidden positions, are responsible for CDW pinning. Here, as a test of this idea, we present neutron diffraction results for a single crystal of La 2-x ⁢Ba x CuO 4 (LBCO) with x = 1/8, which is known to undergo two structural transitions on cooling, from high-temperature tetragonal (HTT) to low-temperature orthorhombic (LTO) near 240 K, involving a collective tilt pattern of the corner-sharing CuO 6 octahedra, and from LTO to low-temperature tetragonal (LTT) near 56 K, involving a new tilt pattern and the appearance of intensity at peaks of type T. We observe both type M and type T peaks in the LTT phase, while the type M peaks (but not type T) are still present in the LTO phase. Given that CDW order is observed only in the LTT phase of LBCO, it is apparent that the in-plane Cu-O bond anisotropy associated with the octahedral tilt pattern is responsible for charge pinning. We point out that evidence for a similar, but weaker, bond anisotropy has been observed previously in LSCO and should be responsible for CDW pinning there. In the case of LBCO, the monoclinic distortion may help to explain previously reported magneto-optical evidence for gyrotropic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Physical properties of the Ce 2 M Al 7 Ge 4 heavy-fermion compounds ( M = Co , Ir , Ni , Pd )

Here, we report the synthesis, crystal structure, and characterization by means of single-crystal x-ray diffraction, neutron powder diffraction, and magnetic, thermal, and transport measurements of the new heavy-fermion compounds Ce 2 MAl 7 Ge 4 (M=Co,Ir,Ni,Pd). These compounds crystallize in a noncentrosymmetric tetragonal space group P$\bar{4}$2 1 m, consisting of layers of square nets of Ce atoms separated by Ge-Al and M-Al-Ge blocks. Ce 2 CoAl 7 Ge 4 ,Ce 2 IrAl 7 Ge 4 , and Ce 2 NiAl 7 Ge 4 order magnetically below TM=1.8, 1.6, and 0.8 K, respectively. There is no evidence of magnetic ordering in Ce 2 PdAl 7 Ge 4 down to 0.4 K. Furthermore, the small amount of entropy released in the magnetic state of Ce 2 MAl 7 Ge 4 (M = Co, Ir, Ni) and the reduced specific heat jump at T M suggest a strong Kondo interaction in these materials. Ce 2 PdAl 7 Ge 4 shows non-Fermi liquid behavior, possibly due to the presence of a nearby quantum critical point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic structures and excitations in a multiferroic Y-type hexaferrite BaSrCo 2 Fe 11 AlO 22

Here, we have investigated magnetic orders and excitations in a Y-type hexaferrite BaSrCo 2 Fe 11 AlO 22 (BSCoFAO), which was reported to exhibit spin-driven ferroelectricity at room temperature. By means of magnetization, electric polarization, and neutron-diffraction measurements using single-crystal samples, we establish a H-T magnetic phase diagram for magnetic field perpendicular to the c axis (H ⟂c ). This system exhibits an alternating longitudinal conical (ALC) magnetic structure in the ground state, and it turns into a non-co-planar commensurate magnetic order with spin-driven ferroelectricity under H ⟂c . The field-induced ferroelectric phase remains as a metastable state after removing magnetic field below 250 K. This metastability is the key to understanding of magnetic field reversal of the spin-driven electric polarization in this system. Inelastic polarized neutron-scattering measurements in the ALC phase reveal a magnetic excitation at around 7.5 meV, which is attributed to spin components oscillating in a plane perpendicular to the cone axis. This phasonlike excitation is expected to be an electric-field active magnon, i.e., electromagnon excitation, in terms of the magnetostriction mechanism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effect of nickel substitution on magnetism in the layered van der Waals ferromagnet Fe 3 GeTe 2

We have grown a series of nickel-substituted single crystals of the layered ferromagnet (FM) Fe 3 GeTe 2 . The large single-crystalline samples of (Fe 1–x Ni x ) 3 GeTe 2 with x = 0–0.84 were characterized with single-crystal x-ray diffraction, magnetic susceptibility, electrical resistance, and muon spin spectroscopy. We find Fe can be continuously substituted with Ni with only a minor structural variation. In addition, FM order is suppressed from T C = 212K for x = 0 down to T C = 50K for x=0.3, which is accompanied by a strong suppression of saturated and effective moments, and Curie-Weiss temperature. Beyond x=0.3, the FM order is continuously smeared into a FM cluster-glass phase, with a nearly full magnetic volume fraction. Here, we attribute the observed change in the nature of magnetic order to the intrinsically disordered structure of Fe 3 GeTe 2 and subsequent dilution effects from the Ni substitution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Single-crystal investigation of the proposed type-II Weyl semimetal CeAlGe

We present details of materials synthesis, crystal structure, and anisotropic magnetic properties of single crystals of CeAlGe, a proposed type-II Weyl semimetal. Single-crystal x-ray diffraction confirms that CeAlGe forms in a noncentrosymmetric I4 1 md space group, in line with predictions of nontrivial topology. Magnetization, specific heat, and electrical transport measurements were used to confirm antiferromagnetic order below 5 K, with an estimated magnon excitation gap of Δ = 9.11 K from heat capacity and hole-like carrier density of 1.4 × 10 20 cm –3 from Hall effect measurements. The easy magnetic axis is along the [100] crystallographic direction, indicating that the moment lies in the tetragonal ab plane below 7 K. A spin-flop transition to less than 1 μ B /Ce is observed to occur below 30 kOe at 1.8 K in the M(H) (H ∥ a) data. Furthermore, small magnetic fields of 3 and 30 kOe are sufficient to suppress magnetic order when applied along the a and c axes, respectively, resulting in a complex T–H phase diagram for H ∥ a and a simpler one for H ∥ c.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Order-Disorder Transitions in ( Ca x Sr 1 - x ) 3 Rh 4 Sn 13

The classification of structural phase transitions as displacive or order-disorder in character is usually based on spectroscopic data above the transition. Here, we use single crystal x-ray diffraction to investigate structural correlations in the quasiskutterudites, (Ca x Sr 1-x ) 3 Rh 4 Sn 13 , which have a quantum phase transition at x ~ 0.9. Three-dimensional pair distribution functions show that the amplitudes of local atomic displacements are temperature independent below the transition and persist to well above the transition, a signature of order-disorder behavior. The implications for the associated electronic transitions are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗