, J i exchange interactions are indicated

HoMn 2 O 5 (26 K) and DyMn 2 O 5 (2 K) in the (a, b) plane. The unit cells are doubled along the a axis, The CM structures of TbMn 2 O 5 (27 K) ,

, The rare earth elements with weights and electrons distribution. From Wikipedia, p.21

21 2.5 (a) Dependence of the electric polarization of the RMn 2 O 5 compounds at ambient pressure as a function of the ionic radii of R 3+. Data from Ref, vol.48, p.70 ,

, Magnetic and electric phase diagram of the RMn 2 O 5 compounds. Here, PM, ICM, CM, PE, and FE are abbreviated forms used to denote paramagnetic, incommensurate magnetic, commensurate magnetic, paraelectric, and ferroelectric states

Dielectric constant ? along b open circles, left scale and specific heat C p /T closed circles, right scale of (a) TbMn 2 O 5 and (b) DyMn 2 O 5 [14], p.23 ,

23 2.9 (a) A schematic representation of the magnetic structure of the ICM phase of YMn 2 O 5. Magnetic exchange pathways are also indicated. (b) Symbols: electrical polarization of YMn 2 O 5 , as calculated from Equation (2.1). Solid line: experimental values of the electrical polarization, Temperature dependence of the electric polarization for RMn, vol.2 ,

URL : https://hal.archives-ouvertes.fr/hal-00495682

, Projection in the (a, b) plane of the magnetic moments along c represented by + and ? symbols. The gray lines represent the AFM chains coupled through the J 3 exchange interactions (represented as red and blue ellipses: red for FM order, p.25

R means the low temperature R 3+ ordering, which is stabilized at the same propagation wave vector as the Mn ordering. The values of ? x (? z ) range, The phase transitions of the RMn 2 O 5 compounds and the corresponding magnetic propagation wave vectors presented on the right side, vol.42, pp.77-81 ,

13 (a) The highly reversible 180° flipping of electric polarization P along the b axis in TbMn 2 O 5 by applying magnetic field along the a axis at 3 K. [9] (b) repeated variation of P along the b axis (red circles) in GdMn 2 O 5 at 2 K by applying reversible magnetic fields along the a axis (light blue lines), vol.27 ,

17 (a) Temperature dependence of the polarization P a and P b of TmMn 2 O 5 during heating under zero magnetic field. The inset shows the crystal structure of TmMn 2 O 5. (b) Magnetic field dependence of P a and P b at 4.2 K, Temperature dependence of dielectric constant ? b and electric polarization P b parallel to the b axis under various magnetic fields in HoMn 2 O 5 ((a) ,

, Temperature profile of the (A) low temperature and (B) high temperature ? b and (C) P b of TbMn 2 O 5 under isotropic pressures (warming only), p.31

, Temperature profile of the (A) low temperature and (B) high temperature ? b and (C) P b of DyMn 2 O 5 under isotropic pressures (warming only), p.31

diagram for DyMn 2 O 5. The pressure separated X phase was found to be paraelectric ,

22 (a) Dielectric constant ? b (b) ferroelectric polarization P b of GdMn 2 O 5 at different pressures, Dielectric constant ? b and ferroelectric polarization of YMn 2 O 5 at 5 K as a function of pressure ,

, Transmission spectra of TbMn 2 O 5 : (a) thin sample, (b) thicker sample, oscillations are averaged out in model curves. e and h are electric and magnetic fields of light. Transmission spectra of YMn 2 O 5 with H ? a and (c) e ? b, (d) e ? c, p.33

Dielectric constant ? of TbMn 2 O 5 from fits of infrared spectra (lower curve) in comparison with high frequency measurements ,

Schematic of the standard X-ray tube with power increased by rotating the anode. [93] (b) schematic representation of the X-ray spectrum ,

, Schematic diagram of diffraction of the X-rays by a crystal (Bragg law)

Schematic of a standard ?-2? X-ray diffractometer ,

they are spheres.) and the Ewald sphere (formation of a cone of diffracted X-rays) in the Debye-Scherrer method, The relationships between the reciprocal lattice ,

, The fraction of the diffracted intensity contributing from a surface layer of depth t to the total diffracted intensity of a sample of semi-infinite thickness, p.44

, Top view of the X-ray diffraction set-up. A: X-ray beam, p.47

Schematic representation of the gasket treatments ,

48 3.11 The fluorescent curve measured under different pressure. Dots: the measured data. Lines: the fitted curve through Equation (3.18) ,

, The scattering of a plane wave of neutrons by a single scatterer, p.51

Geometry for a scattering experiment ,

The form factor f (Q) for the scattering of X-rays and for the nuclear and magnetic scattering of neutrons ,

The D1B instrument (ILL, Grenoble) ,

The D20 instrument (ILL, Grenoble) ,

the standard anvil and gasket configuration and the standard and encapsulated gasket designs (right) ,

The information deduced from the powder diffraction data ,

The menu of the FullProf Suite, p.61 ,

The synthesis process of PrMn 2 O 5 powder sample ,

allowed Bragg reflections: blue ticks). The difference between the experimental and calculated profiles is displayed at the bottom of the graph of the crystal structure of ,

, The raw MAR image of CeO 2 and the starting values of the calibration from Dioptas 67

, The MAR image of CeO 2 with masks and the refined values of the calibration from Dioptas

The masks can exclude the obvious diffraction peaks from the diamond and some of the preferred orientations diffraction dots, The MAR image of CeO 2 with masks and the integrated data from the Dioptas ,

X-ray diffraction of CuBe gasket. (b) The refined X-ray diffraction of standard CeO 2 with and without the peaks of the gasket ,

, The X-ray diffraction patterns of RMn 2 O 5 (R = Pr, Nd and Sm) under different pressures, p.69

, The X-ray diffraction patterns of RMn 2 O 5 (R = Gd, Tb and Dy) under different pressures, p.70

, The X-ray diffraction patterns of PrMn 2 O 5 and TbMn 2 O 5 at some selected pressure, p.71

The experimental data are in red, the calculated profile in black, and their difference in blue. The green ticks refer to the nuclear reflections. The peaks of the gasket have been excluded ,

, RMn 2 O 5 with respect to their ambient pressure values. The error bars are of the size of the symbols. a i0 : unit cell parameters at ambient pressure, p.73

, Unit cell parameters ((a i ? a i0 )/a i0 ) of GdMn 2 O 5 and DyMn 2 O 5 with respect to their ambient pressure values calculated by DFT. a i0 : unit cell parameters at ambient pressure, p.73

Dy) with respect to their initial pressure values, of R 3+ (left), of Mn 4+ (middle) and of Mn 3+ (right). The error bars are within the width of the points ,

, Comparison of pressure evolution of the ionic displacements |u| of Gd 3+ and Dy 3+ by X-ray experiments and DFT calculations

14 (a) A magnified representation of Mn 4+ O 6 octahedra and Mn 3+ O 5 pyramid involved in the super-exchange J 3 and J 4. (b) Structure of RMn 2 O 5 in the (a, b) plane in Pm space group within CM magnetic phase (q = ( 1 2 , 0, 0)). Inequivalent super-exchange interactions J 3 and J 4 are indicated ,

The circles are for the DyMn 2 O 5 compound and the crosses for the GdMn 2 O 5 one. left) Mn 4+-O4 and Mn 3+-O4 distances (Å), right) cos 2 ?, ? being the Mn 4+-O4-Mn 3+ angle. (AFM) refers to the geometrical parameters between the atoms involved in AFM ordered Mn 4+-Mn 3+ ions, while (FM) refers to the parameters between the FM ordered ones ,

The circles are for the DyMn 2 O 5 compound and the crosses for the GdMn 2 O 5 one. left)Mn 4+-O3 and Mn 3+-O3 distances (Å), right) sin ?, ? 1 and ? 2 being the two inequivalent Mn 4+-O3-Mn 3+ angles, Variation of the structural parameters involved in the J 4 amplitudes as a function of the applied pressure ,

Pressure evolution of (a) temperature dependence of the ferroelectric polarization [66] and (b) the magnetic patterns at 1.5 K subtracted from the 40 K diffraction pattern of YMn 2 O 5 [90] ,

, Magnetic patterns of TbMn 2 O 5 at 1.5 K. The magnetic peak ? 1 Å ?1 indicates the onset of the pressure-induced commensurate (PCM) phase, p.83

, Selected information of Pr 3+ from the output BSR file of BasIreps, p.84

, Selected basic function information of Pr 3+ from the output FP file BasIreps, p.84

The magnetic ordering in the (a, b) plane of PrMn 2 O 5 : (a) the CM1 phase at 20 K; (b) the CM2 phase at 1.5 K ,

, 6 (a) Dielectric constant ? b measurement and (b) dielectric loss measurement of PrMn 2 O 5 single crystal as a function of temperature under various pressures (warming and cooling, p.86

PND diffractograms of PrMn 2 O 5 (a) under 3 GPa, at 6 K, 11 K, 20 K and 30 K (b) under 7 GPa at 6 K, 11 K and 20 K, vol.87 ,

Rietveld refinements of the neutron diffraction data of PrMn 2 O 5 at the lowest temperature, 6 K, and under 3 GPa, 5 GPa and 8 GPa ,

Evolution as a function of pressure of the ratio between the ambient pressure CM3 and the pressure induced PCM phases in PrMn 2 O 5 at 6 K ,

, GPa (a) in the (a, b) plane with the 2 1 (b) and a 2 ? 1 (b ? ) screw axis (glide plane) between Mn 3+ and Mn 4+ , and (b) in the, p.89

, to their ambient pressure values at 6 K. a i0 is a unit cell parameter under ambient pressure at 6 K. Lattice parameters from the refinement of the PND data, p.91

, Magnetic structure of (a) the HT phase at 15 K with the spiral arrangement of Mn ions; (b) the LT phase at 2 K. Magnetic interactions J 3 , J 4 and J 5 are also shown, vol.92

15 PND curves under 2.4 GPa, at 6 K, 14 K, 22 K and 60 K. Reflections of nuclear phase, CM phase and ICM phase are indicated respectively ,

, PND curves under the highest pressure, 6.6 Gpa, at 6 K, 10 K, 18 K, 25 K and 60 K. Reflections of nuclear phase, CM phase and PCM phase are indicated respectively, p.94

, Pressure-temperature phase diagram of DyMn 2 O 5. The lines are a guide to the eye, p.95

For the sake of clarity, the amplitude of the moments of Mn 3+ and Mn 4+ in D 1 model have multiplied by a factor 2, the amplitude of the moments of Dy 3+ in D 2 model have multiplied by a factor 2 and the amplitude of the moments of Dy 3+ in planar model have multiplied by a factor 3 ,

20 (a) Magnetic structure of GdMn 2 O 5 at 1.5 K. The blue (orange) ellipses show the Mn 3+ / Mn 3+ (Gd 3+ / Mn 3+ ) AFM pairs. Stars identify the Gd 3+ / Mn 3+ pair proposed by Lee et al. in their model for a Gd-Mn ES mechanism[50]. (b) Atomic displacements associated with the release of the magnetic frustration at the origin of the two ES mechanisms, leading to the polarization, Schematic 1D chains representing the energy gains for different propagation components k z along the c axis. (a) k z = 1 2 (as for the PCM phase) ,

101 5.23 Temperature evolutions of CM phase at 2.4 GPa (a) at 7, 20 and 32 K and (b) the corresponding amplitude of moments of Gd and Mn ions, Pressure evolutions of the CM phase at 7 K (a) the PND curves at 2.4, 5.0 and 8.4 GPa and (b) the corresponding amplitude of the moments of Gd, vol.100 ,

102 5.25 Magnetic structure of the PCM phase of GdMn 2 O 5 at 32 K, 8.4 GPa. The amplitude of the moments of Gd 3+ are multiplied by a factor 8 for the sake of clarity, p.103 ,

27 Perspective view of the magnetic structure of SmMn 2 O 5 at 6 K. The blue Mn 3+ pyramids and the red Mn 4+ octahedra are represented, vol.104 ,

, Diffractograms and phase ratio of the pressure evolutions of the CM and PCM phases at 15 K

, 29 PND curves of SmMn 2 O 5 at 10.3 Gpa and 32 K. No CM phase is present, p.107

The moments of Sm 3+ are along the c axis. The amplitude of the moments of Sm 3+ are multiplied by a factor 2 for the sake of clarity, Magnetic structure of SmMn 2 O 5 at 32 K, 10.3 GPa ,

, Pressure-temperature phase diagram of SmMn 2 O 5. The lines are a guide to the eye, vol.108

Schematic 1D chains representing the energy gains for different propagation components k z along the c axis. (a) k z = 1 2 (as for the PCM phase). (b) k z = 0 (as for the CM phase of SmMn 2 O 5 at ambient pressure with all the spins along c axis.) ,

, DyMn 2 O 5 at 6.6 GPa, 18 K. The amplitude of the moments of Dy 3+ have multiplied by a factor 3. (c) GdMn 2 O 5 at 8.4 GPa, 32 K. The amplitude of the moments of Gd 3+ have multiplied by a factor 8. (d) SmMn 2 O 5 at 10.3 GPa, 32 K. The moments of Sm 3+ are along the c axis. The amplitude of the moments of Sm 3+ have multiplied by a factor 2, Magnetic structure of the PCM phase of (a) PrMn 2 O 5 at 8 GPa, 6K. (b), p.111

Pressure-temperature phase diagrams of RMn 2 O 5, p.113 ,

,

SmMn 2 O 5 at different pressures with ambient lattice parameters of GdMn 2 O 5 and TbMn 2 O 5 ,

Classification of multiferroics due to different microscopic mechanism of ferroelectricity [19] ,

Atomic positions of DyMn 2 O 5 at 298 K in the Pbam space group, vol.18 ,

The lattice parameters are a = 7.2931 Å, b = 8.5025 Å, c = 5.6743 Å. ? = 90° ,

Magnetic easy axis of the RMn 2 O 5 compounds ,

, Main factors that affect the multiferroic properties of the RMn 2 O 5 family, p.35

41 3.2 B 0 and B ? 0 values of the Rydberg-Vinet EOS equation ,

Tb and Dy) at ambient pressure, room temperature in the Pbam space group, vol.2 ,

Tb and Dy) at ambient pressure, room temperature in the Pbam space group, vol.2, p.71 ,

Tb and Dy) at the highest pressure, room temperature. The position of the oxygens are fixed to the ones of the ambient pressure ,

74 8 GPa in the magnetic space group Pmc ? 2 ? 1 with ? 2 = 2.09, R p = 33, vol.5 ,

90 5.2 Refined parameters of the PCM phase of DyMn 2 O 5 at 18 K, 6.6 GPa with different models. Magnetic moments of Dy 3+ and Mn ions are in µ B and the agreement factors are in % ,

Refined results for the magnetic structure parameters of DyMn 2 O 5 at 18 K, 6.6 GPa with the planar model in P1 space group. ? and ? refer to the polar angle and the azimuthal angle ,

Magnetic moments of Gd 3+ and Mn ions are in µ B and the agreement factors are in % ,

GPa with the planar model in P1 space group with ? 2 = 1.85, R p = 43, 2%, R w p = 27.7%, R ex p = 20.1%, R Br agg = 4.0% and R mag = 27.4 %. ? and ? refer to the polar angle and the azimuthal angle ,

, 2%, R w p = 18.7%, R ex p = 3.4%, R Br agg = 2.9% and R mag = 21.5%. All the moments are along the c direction, GPa, 15 K in the P 2a m space group with ? 2 = 30, vol.7, p.30

, Moments of R 3+ at the highest pressure, ? 8 ± 2 GPa

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