Our results help in understanding the magnetic interactions in the Mn-based pyrochlore compounds. One of the most fascinating discoveries in the class of transition metal compounds is undoubtedly the observation of high-temperature superconductivity in cuprate.
Transition metals
Why pressure?
Experiments
TM compounds under pressure in this work
The pressure-induced behavior of the Mn-O-Mn bond angle, which is important for the magnetic exchange interactions, is somewhat controversial [27]. It is expected that pressure-induced structural, electronic and vibrational properties of Cd2Re2O7 will contribute to the understanding of the pressure dependence for all temperature-induced transitions.
Organization of the thesis
Here we report the pressure-induced behavior of the structural, electronic, and vibrational properties of CdCr2S4 studied by means of x-ray diffraction, mid-infrared reflectivity, and Raman spectroscopy, respectively, at room temperature. With the aim of elucidating the role of the lattice with respect to the pressure-induced changes of the electronic properties, we investigated the high-pressure structural behavior of two undoped Fe-based compounds, namely BaFe2As2 and the FeSe, which at room temperature was investigated. of synchrotron-based angle-dispersive x-ray powder diffraction.
Macroscopic thermodynamics
Thermodynamic laws
However, in the case of isothermal compression, the thermodynamic potential F(T,V) (i.e. Helmholtz free energy, see Table 2.1) with natural variablesTandVi is preferred. The quantity is the change in a potential energy when a particle is added to a system, all other natural variables of the thermodynamic potential remaining constant.
Thermodynamic parameters
If the number of particles N is not constant, as in the case of an open system, the expression µdN must be added to the differential forms of the thermodynamic potentials. Specifically, Equation 2.25 suggests that the isothermal change of entropy with pressure is of the opposite sign as the coefficient of thermal expansion.
Empirical equations of state of solids
Mie-Gr ¨ uneisen EOS
The quantityγ is identical to the macroscopic or thermodynamic Gr¨uneisen parameterγ defined earlier (Eq.2.29). The value of the parameter γ is of order one and is assumed to be independent of temperature.
Thermal energy F th
Regarding the last point, the quasi-harmonic approach assumes that a change in volume results in a change in vibrational frequencies. The volume-dependent change of the vibration spectrum is characterized by individual mode Gr¨uneisen parametersγiof the quasi-harmonic modesωi[50].
Empirical EOS forms for the ground state
Birch's relation [52] is based on the expansion of the Helmholtz free energyFin power series of isotropic Euler deformationε. where the strainε is related to the volume with ε=−1. 2.50) According to equation 2.8, the isothermal relationship between pressure and volume can be calculated. The main difference between the three forms of EOS is the dependence of the dimensionless B0 on the volume, i.e.
Phase transitions
Classification of phase transitions
First-order phase transitions
When comparing theoretical predictions for a phase transition pressure with experimental results, it should be kept in mind that a theoretical model normally gives the equilibrium transition pressure between two phases (usually for the static lattice case). According to equation 2.11, the difference of entropy and volume per unit mass between two phases 1 and 2 at a phase transition point are.
Pressure-induced structural phase transitions
Upon further compression, Si and Ge adopt denser phases such as hcp and fcc [59]. As a result, it becomes possible to qualitatively understand the systematics of pressure-driven phase transitions of materials.
Overview
Phenomenological phonon Raman scattering
Raman tensor and microscopic description
Due to the limitations in space imposed by the present work, only the basics of the Raman scattering process are briefly introduced.
Raman scattering under pressure
The interrelationship between the structure and the physical properties of transition metal compounds requires a description of the valence electrons that bind the atoms in the solid state. That is, we assume that valence electrons are shared equally by all the same atoms in the solid.
Electronic states of transition metal ions in crystals
Ligand field theory
So far I have discussed the crystal field effect in the case of an octahedral cubic supercharge of the TM ion. The other case is that the ligand states lie at lower energies and will occupy the ground state (as in Fig.4.3).
Spin state configuration
Two cases can be distinguished: if the π states of the ligand lie at higher energies than the TM states, they will be unoccupied. The realization of either high- or low-spin configurations will also affect the ionic radius of the TM ions in question; the ionic radius of the HS state is larger than the ionic radius of the LS state.
Jahn-Teller effect and orbital ordering
The splitting of the energy levels caused by the Jahn-Teller effect can also be rationalized in terms of the crystal field. However, the Jahn-Teller splittings in both gandt2g states are smaller compared to the crystal field splitting ∆CF, so that we are dealing with relatively small deformations of the coordination octahedron.
Exchange interactions in transition metal compounds
- The Hubbard model
- Charge transfer and Mott-Hubbard insulators
- Magnetic properties
- Double exchange interaction
- Charge ordering
In the second limit ∆U, a sufficiently small U leads to the metallic ground state (region D in Fig. 4.7, d-band metals) due to the overlap of the lower and upper Hubbard bands [Fig. 4.6(a)]. In the center of the Brillouin zone (|kkk|=0), the magnon frequency ωmagnon(kkk) has a finite value.
Superconductivity
From eq.4.8 it is clear that the sign of the pressure dependence of Tcis is controlled by the change in both N(EF)(electronic term) and the change in the phonon frequency. Normally, the application of pressure results in an increase in the phonon frequency due to the stiffening of the lattice, but on the other hand reduces N(EF) due to the broadening of the electronic bands.
Overview
The diamond anvil cell
Ruby luminescence for pressure measurement
The 3d levels of free Cr3+ ions are separated under the cubic and trigonal crystal fields. Measuring ruby luminescence for pressure calibration is more or less a routine procedure.
Pressure media
A narrowing of the R lines with increasing pressure is evident from the decrease in intensity to the minimum between the lines. The peak profile of the R lines is a Lorentzian function; width corresponds to the intrinsic lifetime of the excited states.
Experimental setups
- Low-temperature measurements: Cryostat
- Raman measurements under high pressure
- Mid-infrared reflectivity
- X-ray diffraction
Typical exposure times are 1-45 s, depending on the scattering cross section and the thickness of the sample. First, the path length of the X-ray beam in the diamond is 50 times longer than in the sample.
Introduction
It is evident from the above discussion that observations of the pressure-induced behavior of ReO3 are partially inconsistent. Although the cubic Pm3m phase is Raman inactive, the other reported high-pressure phases are expected to show Raman activity (Table 6.1).
Experiments
The high compactness of this phase is achieved through the paired rotations of the corner-bonded ReO6 octahedra. Our initial motivation was to study ReO3 by pressure Raman spectroscopy to characterize the vibrational properties of the observed high-pressure phases, as well as to elucidate the discrepancy in the number and sequence of pressure-induced structural phase transitions.
Structure under pressure
The open circles indicate the measured spectra, the red line represents the best refinement, and the blue line indicates the difference between the measured and the refined pattern.
Si oil)
Structural considerations
This effect is demonstrated in the Raman spectra of the tetragonal P4/mbm phase (see next section). Assuming no deformation of the octahedra, the volume gradually decreases as the rotation angle increases.
High-pressure Raman results
Here I should remind that the choice of PTM affects the pressure-induced structural paths of ReO3. The most prominent features are attributed to the two low-frequency Raman modes Eg and A1g of the tetragonal P4/mbm phase.
The transformation from Pm3m to the P4/mbm structure takes place exclusively by coupled anti-phase rotations of ReO6. However, ReO3 can be considered an exceptional case due to the large frequency regime where soft-phonon theory can be applied.
Introduction
Here we investigate the evolution of the structural and vibrational properties of LaTiO3 under high pressure. We can observe that there is an increase in the mid-infrared reflectivity starting above.
Experimental details
The Pbnm-I phase, PTr=11.5 GPa for the Pbnm-II phase and PTr=33 GPa for the tetragonal I4/mcm high-pressure phase.
Structure under pressure
Although the relative volume change in the transition from Pbnm-I to Pbnm-II is small [
High-pressure Raman results
- Raman scattering at room temperature
- Raman scattering at low temperatures
The Pbnm-I to Pbnm-II transition is accompanied by an abrupt decrease in the frequency of the broad and asymmetric Ag(3) state [Fig.7.9(b)], as well as an overall Raman intensity increase. On the other hand, and for higher phonon frequencies (ωph>150 cm−1), the contribution from the electron-phonon scattering rate will dominate the Raman scattering cross section.
Discussion
From equation 7.5 it becomes clear that for a pressure-induced bandwidth-controlled insulator-to-metal transition at constant temperature, and if no structural transition occurs, the Raman intensity will increase due to the subsequent reduction of the effective mass ∗ . Another important observation is the "adjustment" of the Ti-O bond length after the Pbnm-I to Pbnm-II transition.
Introduction
This discrepancy mainly arises from the pressure-induced change of the Mn-O-Mn bond angle. Although the ferromagnetic behavior of the Y3+ and Lu3+ compounds (TCurie'15 K) can be explained with the superexchange picture, for the In3+ and Tl3+ compounds (TCurie'150 K) one must take into account an electronic term, namely the strong hybridization between the Tl(6s)/ In(5s)-O(2p) orbitals with the unoccupied Mn(bv) states.
Experiments
This electronic separation weakens the strength of the ferromagnetic coupling, leading to a reduction of TCurie under pressure. The Y2Mn2O7 compound is the simplest of the Mn pyrochlores, with only one magnetic ion (Mn4+).
Structure under pressure
The equation of state (EOS) data of Y2Mn2O7[Fig.8.3(a)] were fitted to a third-order Birch-Murnaghan equation of state. The position parameter of oxygen increases slightly with increasing pressure [Fig.8.3(b)] and all cation-oxygen bond lengths decrease with application of pressure [Fig.8.3(c)].
High-pressure Raman results
This increase in the Raman intensity of the Egmode under pressure corresponds to the intensity increase of the extra Bragg peak in the XRD patterns with pressure increase [Fig.8.2(b)]. The change in the Raman frequency of the overtone exhibits a sublinear behavior upon pressure increase throughout the investigated pressure range [Fig.8.4(b), Table8.2].
High-pressure mid-infrared reflectivity
The rest of the observed Raman modes show regular behavior of their frequencies, slopes and intensities under pressure. Another point worth noting is the decrease in the reflectance value with increasing pressure (Fig. 8.5).
Discussion
However, I must emphasize here that this remains an approximate approach to the interpretation of structural properties. In the case of Tl2Mn2O7, the situation is more complicated due to the ambiguous behavior of the Mn-O-Mn superexchange bond angle and electrical resistivity under pressure.
Introduction
The cubic crystal structure of Cd2Re2O7 (Figure 9.1) can be described by two interpenetrating networks: one of corner-shared ReO(1)6 octahedra, which is the "backbone" of the structure, and the other of Cd4O(2) tetrahedra of the non-participating oxygen atoms in the formation of the ReO6 octahedra, denoted as O(2) in Fig.9.1. So far, high-pressure studies of Cd2Re2O7 have been dedicated to transport and superconducting properties.
Experimental details
Structure under pressure
Now looking at the monoclinic high-pressure phase that appears in the XRD patterns above 20 GPa (Fig. 9.3), this corresponds to a monoclinic deformation of the initial cubic cell. These Bragg peaks correspond to the (111) and (222) crystalline planes of the monoclinic phase, respectively, implying some kind of preferential orientation for the pressure-induced amorphization.
High-pressure Raman results
The higher number of observed Raman modes indicates a lower structural symmetry of the high-pressure phase. However, after the cubic to monoclinic transition, some Raman modes corresponding to the cubic pyrochlore phase can still be observed [Fig.9.6(b)].
High-pressure mid-infrared reflectivity
The mode Gr¨uneisen parametersγ are derived from the relation γ=(BTr/ωTr)·(∂ ω/∂P)(see equation 2.42 in Chapter 2), where the bulk moduliBTr=170 GPa (for the cubic phase) and BTr=188 GPa (for the monoclinic high-pressure phase) was used. Taking into account our XRD study, these almost characteristic Raman spectra indicate a loss of local order for the high-pressure monoclinic crystalline phase of Cd2Re2O7, i.e.
Discussion
A possible explanation for the driving force behind the cubic-to-monoclinic structural transition could therefore be a pressure-induced charge ordering of the Re5+ cation towards the more stable Re4+ and Re6+ valence configurations, which will subsequently result in a disproportionation of the ReO6 octahedra, i.e. a pressure-induced charge order can also explain the loss of the mid-infrared oscillator strength that accompanies the structural modification [Fig. 9.7(a) and 9.7(b)], a situation reminiscent of the heavily studied Mn-based perovskites [252].
Introduction
At ambient conditions, CdCr2S4 crystallizes in the cubic spinel structure (space group SGFd3m, Z=8, see Fig.10.1). The spinel structure (Fig. 10.1) can be considered as built of distorted Cr4S4 cubes which share a Cr site.
Experimental details
Here we report the pressure-induced behavior of the structural, electronic and vibrational properties of CdCr2S4, studied by X-ray diffraction, mid-infrared reflectivity and Raman spectroscopy, respectively. The degree of the trigonal distortion is determined by the value of the fractional coordinate of the S anions.
Structure under pressure
On the other hand, the Cd-S bond length of the CdS4tetrahedra retains a single value in the tetragonal structure (Table 10.1). This is proven in fig. 10.4(d) by the behavior of the two separated Cr-S bond lengths under pressure.
High-pressure Raman results
The different colors of the Raman spectra indicate the different phases (black for cubic, red for tetragonal, blue for orthorhombic and green for amorphous). Notice the two soft states of the tetragonal phase (red-line spectra), which are the result of splitting of e.g. The Raman mode of the cubicFd3mphase (black-line spectra).
High-pressure mid-infrared reflectivity
I4 1/amd+ Orthorhombic phase Amorphous phase. b) Reflectivity value at 0.5 eV as a function of pressure.
Discussion
I would like to add at this point some thoughts about the effect of the cubic-to-tetragonal structural transition on the magnetic properties. In CdCr2S4, another effect associated with the cubic-to-tetragonal transition could be an enhancement of the antiferromagnetic interactions over the ferromagnetic ones under pressure due to the decrease in the Cr-Cr distance.
Introduction
However, controversial results have been reported regarding the pressure dependence of the magneto-structure transition temperature (Fig. 11.2) and the pressure region of the superconducting phase, while a pressure-induced superconducting transition is not always observed. The disappearance of the superconducting phase coincides with a structural phase transformation, with the tetragonal FeSe adopting a defective NiAs-type structure (SGP63/mmc, Z=2).
Experimental details
BaFe 2 As 2 under pressure
The pressure-induced variation of selected interatomic structural parameters, namely (c) the Fe–Fe and Fe–As bond distances and (d) the As–Fe–As bond angles are also plotted.
FeSe under pressure
In Fig.11.7(a) we can observe that the tetragonal-to-hexagonal structural transition is accompanied by a significant relative volume decrease with respect to the volume of the tetragonal phase, namely 16%. Another pressure-induced effect worth noting is the pressure change of the hexagonal/axial ratio [black circles in Fig.11.7(b)].
Discussion
Until now I have only dealt with the structural aspects of the Fe-based superconductors, and they Regarding the electronic properties of these compounds, all the undoped Fe-based compounds exhibit very similar electronic structures.
Conclusions
This caused some confusion about the mechanism responsible for the magnetic properties of the Mn-based pyrochlore compounds. However, the pressure-induced behavior of Y2Mn2O7 resolves the role of the lattice in the magnetic interactions of these compounds.
Outlook
Kracher, Decoupling of superconducting and magnetic/structural phase transitions in electron-doped BaFe2As2, Phys. Han-fland, High pressure studies of perovskite Re16O3 and Re18O3 isotopes (oral), European High Pressure Research Group (EHPRG) 2008, Valencia, Spain.