Neutron Powder Diffraction Measurements Research Articles

Structural and magnetic properties of LaVO3 - Absence of anomalous diamagnetism

The novel magnetic and structural properties of LaVO3 have been studied in a comprehensive manner using X-ray and neutron powder diffraction, thermogravimetric analysis, X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, electrical transport, and dc magnetization. The lattice parameters have been found to be larger than previously reported, indicating the possibility of a novel phase. For vanadium ions, the valence state is found to be in accordance with the expected value (+3), the effect of larger lattice parameters is also present in the X-ray absorption spectroscopy measurement. Magnetic transition due to the antiferromagnetic ordering of the vanadium sublattice is observed at 142 K (TN). It undergoes a transition to a monoclinic crystal structure below 140 K (Tt). Negative magnetization (anomalous diamagnetism), which has been reported in earlier studies on the magnetic properties of LaVO3, is not observed in the present study. In the M − H isotherms, the ferromagnetic component of vanadium spins is absent. Below TN, the estimated magnetic structure of vanadium sublattice from powder neutron diffraction measurements is C-type antiferromagnetic, which persists in the entire low temperature region. The observed novel structural phase gives rise to pure C-type antiferromagnetic arrangement without weak ferromagnetic component. Theoretical calculations have been carried out to understand the nature of the magnetic ground state.

Entropy Engineering and Tunable Magnetic Order in the Spinel High-Entropy Oxide.

Spinel oxides are an ideal setting to explore the interplay between configurational entropy, site selectivity, and magnetism in high-entropy oxides (HEOs). In this work, we characterize the magnetic properties of the spinel (Cr, Mn, Fe, Co, Ni)3O4 and study the evolution of its magnetism as a function of nonmagnetic gallium substitution. Across the range of compositions studied here, from 0 to 40% Ga, magnetic susceptibility and powder neutron diffraction measurements show that ferrimagnetic order is robust in the spinel HEO. However, we also find that the ferrimagnetic order is highly tunable, with the ordering temperature, saturated and sublattice moments, and magnetic hardness all varying significantly as a function of Ga concentration. Through X-ray absorption and magnetic circular dichroism, we are able to correlate this magnetic tunability with strong site selectivity between the various cations and the tetrahedral and octahedral sites in the spinel structure. In particular, we find that while Ni and Cr are largely unaffected by the substitution with Ga, the occupancies of Mn, Co, and Fe are each significantly redistributed. Ga substitution also requires an overall reduction in the transition metal valence, and this is entirely accommodated by Mn. Finally, we show that while site selectivity has an overall suppressing effect on the configurational entropy, over a certain range of compositions, Ga substitution yields a striking increase in the configurational entropy and may confer additional stabilization. Spinel oxides can be tuned seamlessly from the low-entropy to the high-entropy regime, making this an ideal platform for entropy engineering.

A High-Entropy Multicationic Substituted Lithium Argyrodite Superionic Solid Electrolyte

Bulk-type solid-state batteries (SSBs) constitute a promising next-generation technology for electrochemical energy storage. However, in order for SSBs to become competitive with mature battery technologies, (electro)chemically stable, superionic solid electrolytes are much needed. Multicomponent or high-entropy lithium argyrodites have recently attracted attention for their favorable material characteristics. In the present work, we report on increasing the configurational entropy of the Li6+aP1–xMxS5I solid electrolyte system and examine how this affects the structure-conductivity/stability relationships. Using electrochemical impedance spectroscopy and 7Li pulsed field gradient nuclear magnetic resonance (NMR) spectroscopy, multicationic substitution is demonstrated to result in a very low activation energy for Li diffusion of ∼0.2 eV and a high room-temperature ionic conductivity of ∼13 mS cm–1 (for Li6.5[P0.25Si0.25Ge0.25Sb0.25]S5I). The transport properties are rationalized from a structural perspective by means of complementary neutron powder diffraction and magic-angle spinning NMR spectroscopy measurements. The Li6.5[P0.25Si0.25Ge0.25Sb0.25]S5I solid electrolyte was also tested in high-loading SSB cells with a Ni-rich layered oxide cathode and found by X-ray photoelectron spectroscopy to suffer from interfacial side reactions during cycling. Overall, the results of this study indicate that optimization of conductivity is equally important to optimization of stability, and compositionally complex lithium argyrodites represent a new playground for a rational design of (potentially advanced) superionic solid electrolytes.

Influence of Tb substitution on the structural and magnetic properties of BiFeO3 multiferroic

The effect of Tb substitution on crystal structure and magnetism in the series Bi1-xTbxFeO3 (x = 0.05, 0.10, 0.15, & 0.2) have been investigated using X-ray diffraction, neutron powder diffraction, Raman scattering and magnetization measurements. In this series, a structural transition from hexagonal (R3c) in x = 0.05 to coexisting hexagonal (R3c) and orthorhombic (Pnma) structures, is observed for compounds with x > 0.05. The magnetization studies indicate an enhancement in the ferromagnetic moment from 0.15 µB (x = 0.05) to 0.7µB (x = 0.2) at 5 K indicating a progressive increase in the canting of the AFM spins in the doped compounds. The magnetic structure of both the hexagonal and the orthorhombic phases are primarily G-type AFM structure at temperatures below 300 K. However, a canting is observed for the spins in the hexagonal phase of compositions with higher Tb content. The structural transition and the canted behaviour of the G-type AFM structure, are attributed to chemical pressure (equivalent of ∼ 5GPa) effects arising from the substitution of Bi3+ ions by Tb3+ ions (x ≤ 0.20), with lower ionic radii, leading to reduction in volume (ΔV/V ∼ 0.9 %). These observations are in agreement with earlier published DFT studies on the effect of external pressure on BiFeO3. An anomalous increase in ε’ is observed around 650 K for all the samples in the vicinity of the Néel temperature (TN ∼ 643 K) of BFO indicating magnetoelectric coupling.

Frustration and 120° Magnetic Ordering in the Layered Triangular Antiferromagnets AFe(PO3F)2 (A = K, (NH4)2Cl, NH4, Rb, and Cs)

A new family of oxofluorophoshates, AFe(PO3F)2 (A = K, (NH4)2Cl, NH4, Rb, and Cs), was synthesized via ionothermal methods using PF6 ionic liquids. Single-crystal and powder X-ray diffraction reveal that AFe(PO3F)2 with A = (NH4)2Cl crystallizes in a trigonal structure, while AFe(PO3F)2 with A = NH4, Rb, and Cs crystallizes in a triclinic structure. Dimorphic KFe(PO3F)2 crystallizes in both the trigonal and triclinic forms. The structures of all compounds feature Yavapaiite-like Fe(PO3F)2 slabs, which are characterized by triangular Fe layers, planar in the case of the trigonal structure and undulated in the case of the triclinic one. Magnetization measurements reveal all compounds to order antiferromagnetically at low temperatures. The trigonal phases AFe(PO3F)2 (A = K and (NH4)2Cl) display complex magnetic H–T phase diagrams. The observation of magnetization plateaus at Msat/3 (Msat = saturation magnetization) indicates the existence of the up–up–down (UUD) and V-phases at applied magnetic fields in the magnetically ordered state. Powder neutron diffraction measurements of KFe(PO3F)2 confirm the 120° spin structure at zero fields. Along c, the magnetic moments form a commensurate spiral since the spins in each plane are rotated by 90° with respect to the adjacent one. To our knowledge, this is the first time such a non-centrosymmetric version of the 120° spin structure with a 90° rotation between nearest planes has been reported.

Successive magnetic orderings in the Ising spin chain magnet DyNi5Ge3

In this report, we investigated a new rare-earth-based one-dimensional Ising spin chain magnet $\mathrm{Dy}{\mathrm{Ni}}_{5}{\mathrm{Ge}}_{3}$ by means of magnetization, specific heat, and powder neutron diffraction measurements. Due to the crystalline electrical field splitting, the magnetic Dy ions share an Ising-like ground doublet state. Owning to the local point symmetry, these Ising moments form into two canted magnetic sublattices, which were further confirmed by the angle-dependent magnetization measurement. In zero fields, two successive antiferromagnetic phase transitions were found at temperatures ${T}_{\mathrm{N}1}=6\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{N}2}=5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, respectively. Only part of the moments are statically ordered in this intermediate state between ${T}_{\mathrm{N}1}$ and ${T}_{\mathrm{N}2}$. Powder neutron diffraction experiments at different temperatures were performed as well. An incommensurate magnetic propagation vector of ${\mathbf{k}}_{\mathbf{m}}=(0.5,0.4,0.5)$ was identified. The refined spin configurations through the irreducible representation analysis confirmed that these Ising spins are canted in the crystal $ab$ plane.

Zigzag magnetic order in a novel tellurate compound Na4−δNiTeO6 with S = 1 chains

Na4−δNiTeO6 is a rare example in the transition-metal tellurate family of realizing an S = 1 spin-chain structure. By performing neutron powder diffraction measurements, the ground-state magnetic structure of Na4−δNiTeO6 is determined. These measurements reveal that below TN ∼ 6.8(2) K, the Ni2+ moments form a screwed ferromagnetic (FM) spin-chain structure running along the crystallographic a axis but these FM spin chains are coupled antiferromagnetically along the b and c directions, giving rise to a magnetic propagation vector of k = (0, 1/2, 1/2). This zigzag magnetic order is well supported by first-principles calculations. The moment size of Ni2+ spins is determined to be 2.1(1)μB at 3 K, suggesting a significant quenching of the orbital moment due to the crystalline electric field (CEF) effect. The previously reported metamagnetic transition near HC ∼ 0.1 T can be understood as a field-induced spin-flip transition. The relatively easy tunability of the dimensionality of its magnetism by external parameters makes Na4−δNiTeO6 a promising candidate for further exploring various types of novel spin-chain physics.

The mechanism behind SnO metallization under high pressure

SnO is known to undergo metallization at ∼ 5 GPa while retaining its tetragonal symmetry. However, the mechanism of this metallization remains speculative. We present a combined experimental and computational study including pressure-dependent infrared spectroscopy, resistivity, and neutron powder diffraction measurements. We show that, while the excess charge mobility increases with pressure, the lattice distortion, in terms of the z-position of Sn, is reduced. Both processes follow a similar trend that consists of two stages, a moderate increment up to ∼ 3 GPa followed by a rapid increase at higher pressure. This behavior is discussed in terms of polaron delocalization. The pressure-induced delocalization is dictated by the electron–phonon coupling and related local anisotropic lattice distortion at the polaron site. We show that these polaronic states are stable at 0 GPa with a binding energy of ∼ 0.35 eV. Upon increasing the pressure, the polaron binding energy is reduced with the electron–phonon coupling strength of Γ and M modes, enabling the electrical phase transition to occur at ∼ 3.8 GPa. Further compression increases the total electron–phonon coupling strength up to a maximum at 10 GPa, which is a strong evidence of dome-shaped superconductivity transition with Tc = 1.67 K.

First-principles study of the crystal and magnetic structures of multiferroic Cu2OCl2

Recently, the discovery of multiferroicity in pyrochlore-like compound Cu2OCl2 has generated significant interest, and several studies have been performed in this area. This transition metal oxychloride is unique because the divalent copper atoms create an correlated insulator and the pyrochlore lattice tends to frustrate spins. From neutron powder diffraction measurements, an incommensurate magnetic order of the ordering vector emerges below the Néel temperature of 70 K. At this temperature or slightly above, ferroelectricity (FE) or antiferroelectricity, accompanying a lattice distortion, has been observed. Experimentally, some discrepancies remain. In this paper, we report our first-principles simulation results by evaluating the possible lattice and spin spiral states. We found that the Fddd structure is not more stable than , which is supported by our reexamination of the x-ray diffraction data. In addition, we find that after we include magnetism in the calculation, it predicts that the lattice with a helical (proper screw) spin structure is energetically more stable than other spin configurations. Our results indicate charge-order-driven FE that subsequently induces magnetism.

Interplay between structural, magnetic, and electronic states in the pyrochlore iridate Eu2Ir2O7

We address the concomitant metal-insulator transition (MIT) and antiferromagnetic ordering in the novel pyrochlore iridate Eu2Ir2O7 by combining x-ray absorption spectroscopy, x-ray and neutron diffractions and density functional theory (DFT) based calculations. The temperature dependent powder x-ray diffraction clearly rules out any change in the lattice symmetry below the MIT, nevertheless a clear anomaly in the Ir-O-Ir bond angle and Ir-O bond length is evident at the onset of MIT. From the x-ray absorption near edge structure (XANES) spectroscopic study of Ir-L3 and L2 edges, the effective spin-orbit coupling is found to be intermediate, at least quite far from the strong atomic spin-orbit coupling limit. Powder neutron diffraction measurement is in line with an all-in-all-out magnetic structure of the Ir-tetrahedra in this compound, which is quite common among rare-earth pyrochlore iridates. The sharp change in the Ir-O-Ir bond angle around the MIT possibly arises from the exchange striction mechanism, which favors an enhanced electron correlation via weakening of Ir-Ir orbital overlap and an insulating phase below TMI . The theoretical calculations indicate an insulating state for shorter bond angle validating the experimental observation. Our DFT calculations show a possibility of intriguing topological phase below a critical value of the Ir-O distance, which is shorter than the experimentally observed bond length. Therefore, a topological state may be realized in bulk Eu2Ir2O7 sample if the Ir-O bond length can be reduced by the application of sufficient external pressure.

Weak ferromagnetism linked to the high-temperature spiral phase of YBaCuFeO5

The layered perovskite ${\mathrm{YBaCuFeO}}_{5}$ is a rare example of a cycloidal spiral magnet whose ordering temperature ${T}_{\text{spiral}}$ can be tuned far beyond room temperature by adjusting the degree of ${\mathrm{Cu}}^{2+}/{\mathrm{Fe}}^{3+}$ chemical disorder in the structure. This unusual property qualifies this material as one of the most promising spin-driven multiferroic candidates. However, very little is known about the response of the spiral to magnetic fields, crucial for magnetoelectric cross-control applications. Using bulk magnetization and neutron powder diffraction measurements under magnetic fields up to 9 T, we report here a temperature-magnetic field phase diagram of this material. Besides revealing a strong stability of the spiral state, our data uncover the presence of weak ferromagnetism coexisting with the spiral modulation. Since ferromagnets can be easily manipulated with magnetic fields, this observation opens new perspectives for the control of the spiral orientation, directly linked to the polarization direction, as well as for a possible future use of this material in technological applications.

On the Crystal Chemistry of Photochromic Yttrium Oxyhydride

Yttrium oxyhydride exhibits photochromic properties at ambient temperature and pressures. Although oxygen plays an important role in determining the optoelectronic properties of the material, the question remains open regarding the site that it occupies in the crystal structure. In this paper, we address the issue by synchrotron radiation and neutron powder diffraction measurements. We report that the oxide anions occupy tetrahedral sites together with hydride anions in the face-centered cubic structure.

Magnetic structure of an antiferromagnet NdRh2Zn20 investigated by powder neutron diffraction

Powder neutron diffraction measurements were carried out to investigate the magnetic structure of the antiferromagnet NdRh2Zn20. The magnetic reflections observed for T ≤ 1.0 K are indexed by the propagation vector of k = (1/2, 1/2, 1/2). From the analysis of the intensity of magnetic reflections, a magnetic structure described by the Γ6 representation is proposed. The magnetic moments are parallel to the or direction and stacked with a sequence of up-up-down-down along the [111] direction.

Contrasting magnetic structures in SrLaCuSbO6 and SrLaCuNbO6 : Spin- 12 quasi-square-lattice J1−J2 Heisenberg antiferromagnets

We report the magnetic properties of the double perovskites SrLaCuSbO$_6$ (SLCSO) and SrLaCuNbO$_6$ (SLCNO). The temperature dependence of the magnetic susceptibilities of both compounds shows a broad maximum characteristic of an $S\,=\,1/2$ square lattice Heisenberg antiferromagnet. Magnetic ordering occurs at $T_{\rm N}\,{=}\,13.6$ and 15.7 K for SLCSO and SLCNO, respectively. Neutron powder diffraction measurements reveal contrasting spin structures in both compounds. The spin structures of SLCSO and SLCNO below $T_{\rm N}$ are N\'{e}el antiferromagnetic and collinear antiferromagnetic, respectively. This result demonstrates that the nearest-neighbor interaction is dominant in SLCSO, whereas the next-nearest-neighbor interaction is dominant in SLCNO. The magnitude of the ordered moment was evaluated at 3.5 K to be $m\,{=}\,0.39(3)\,\mu_{\rm B}$ for SLCSO and $0.37(1)\,\mu_{\rm B}$ for SLCNO, which are significantly smaller than those calculated using linear spin wave theory. We infer that the small ordered moment is caused by the effect of exchange bond randomness arising from the site disorder of Sr and La ions.

Doping-induced structural transformation in the spin-1/2 triangular-lattice antiferromagnet Na2Ba1-xSrxCo(PO4)2

The effects of Sr doping on the structural properties of Na2BaCo(PO4)2, a spin-1/2 triangular-lattice antiferromagnet as a quantum spin liquid candidate, are investigated by complementary x-ray and neutron powder diffraction measurements. It is found that in Na2Ba1−xSrxCo(PO4)2 (NBSCPO), the trigonal phase (space group P3̅m1) with a perfect triangular lattice of Co2+ ions is structurally stable when the doping level of Sr is below 30% (x≤ 0.3), while a pure monoclinic phase (space group P21/a) with slight rotations of CoO6 octahedra and displacements of Ba2+/Sr2+ ions will be established when the Sr doping level is above 60% (x≥ 0.6). Such a doping-induced structural transformation in NBSCPO is supported by first-principles calculations and Raman spectroscopy. Na2SrCo(PO4)2, a novel spin-1/2 antiferromagnet with glaserite-type structure, although monoclinically distorted, exhibits no long-range magnetic order down to 2 K and a similar negative Curie-Weiss temperature as Na2BaCo(PO4)2 with a perfect triangular lattice, suggesting the robustness of magnetic exchange interaction against the Ba/Sr substitutions.

Evolution from helical to collinear ferromagnetic order of theEu2+spins inRbEu(Fe1−xNix)4As4

The ground-state magnetic structures of the ${\mathrm{Eu}}^{2+}$ spins in recently discovered $\mathrm{RbEu}{({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x})}_{4}{\mathrm{As}}_{4}$ superconductors have been investigated by neutron powder diffraction measurements. It is found that as the superconductivity gets suppressed with the increase in Ni doping, the magnetic propagation vector of the Eu sublattice diminishes, corresponding to the decrease in the rotation angle between the moments in neighboring Eu layers. The ferromagnetic Eu layers are helically modulated along the $\mathit{c}$ axis with an incommensurate magnetic propagation vector in both the ferromagnetic superconductor $\mathrm{RbEu}{({\mathrm{Fe}}_{0.95}{\mathrm{Ni}}_{0.05})}_{4}{\mathrm{As}}_{4}$ and the superconducting ferromagnet $\mathrm{RbEu}{({\mathrm{Fe}}_{0.93}{\mathrm{Ni}}_{0.07})}_{4}{\mathrm{As}}_{4}$. Such a helical structure transforms into a purely collinear ferromagnetic structure for nonsuperconducting $\mathrm{RbEu}{({\mathrm{Fe}}_{0.91}{\mathrm{Ni}}_{0.09})}_{4}{\mathrm{As}}_{4}$, with all the ${\mathrm{Eu}}^{2+}$ spins lying along the tetragonal (1 1 0) direction. The evolution from helical to collinear ferromagnetic order of the ${\mathrm{Eu}}^{2+}$ spins with increasing Ni doping is supported by first-principles calculations. The variation of the rotation angle between adjacent ${\mathrm{Eu}}^{2+}$ layers can be well explained by considering the change of magnetic exchange couplings mediated by the indirect Ruderman-Kittel-Kasuya-Yosida interaction.

Disorder-Induced Structural Complexity in the Barlowite Family of S = 1/2 Kagomé Magnets

We present a comprehensive structural and magnetic characterization of the barlowite family of S = 1/2 kagomé magnets, Cu4(OH)6FX, where X = Cl, Br, or I. Through high-resolution synchrotron X-ray and neutron powder diffraction measurements, we reveal two sources of structural complexity within this family of materials, namely, compositional disorder of the halide species that occupy sites in between the kagomé layers and the positional disorder of the interlayer Cu2+ ions that persists well into the Pnma structural ground state. We demonstrate that understanding these inherent structural disorders is key as they correlate with the degree of partial order in the magnetic ground states of these quantum frustrated magnets.

Revised crystal structure and electronic properties of high dielectric Ba(Fe1/2Nb1/2)O3 ceramics

Ba ( Fe 1 / 2 Nb 1 / 2 ) O 3 ceramics are considered to be promising for technological applications owing to their high dielectric constant over a wide range of temperatures. However, there exists considerable discrepancy over the structural details. We address this discrepancy through a combined x-ray diffraction at room temperature and neutron powder diffraction measurements in the range from 5 K up to room temperature, supplemented by a comparative analysis of the earlier reported structures. Our study reveals a cubic structure with space group Pm3¯m at all measured temperatures. Further, the x-ray near edge structure and extended x-ray absorption fine structure studies on the local environment of the Fe ions is consistent with the cubic symmetry. An appropriate value of U for DFT+U calculations is obtained by comparison with x-ray absorption spectroscopy, which agrees well with the earlier reported electronic properties.

Defect engineering on V2O3 cathode for long-cycling aqueous zinc metal batteries

Defect engineering is a strategy that is attracting widespread attention for the possibility of modifying battery active materials in order to improve the cycling stability of the electrodes. However, accurate investigation and quantification of the effect of the defects on the electrochemical energy storage performance of the cell are not trivial tasks. Herein, we report the quantification of vanadium-defective clusters (i.e., up to 5.7%) in the V2O3 lattice via neutron and X-ray powder diffraction measurements, positron annihilation lifetime spectroscopy, and synchrotron-based X-ray analysis. When the vanadium-defective V2O3 is employed as cathode active material in an aqueous Zn coin cell configuration, capacity retention of about 81% after 30,000 cycles at 5 A g−1 is achieved. Density functional theory calculations indicate that the vanadium-defective clusters can provide favorable sites for reversible Zn-ion storage. Moreover, the vanadium-defective clusters allow the storage of Zn ions in V2O3, which reduces the electrostatic interaction between the host material and the multivalent ions.

Disentangling the phase sequence and correlated critical properties in Bi0.7La0.3FeO3 by structural studies

This work addresses the study of the high-temperature phase sequence of ${\mathrm{Bi}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{FeO}}_{3}$ by undertaking temperature-dependent high-resolution neutron powder diffraction (NPD) and Raman spectroscopy measurements. A determination of lattice parameters, phase fractions, and modulation wave vector was performed by Pawley refinement of the NPD data. The analysis revealed that ${\mathrm{Bi}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{FeO}}_{3}$ exhibits an incommensurate modulated orthorhombic $Pn{2}_{1}a(00\ensuremath{\gamma})000$ structure at room temperature, with a weak ferromagnetic behavior, likely arising from a canted antiferromagnetic ordering. Above ${T}_{1}=543\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, the low-temperature modulated $Pn{2}_{1}a(00\ensuremath{\gamma})000$ evolves monotonically into a fractionally growing Pnma structure up to ${T}_{\mathrm{N}}=663\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. At 663 K, the low-temperature canted antiferromagnetic phase is suppressed concurrently with the switching of the former into a nonmodulated $Pn{2}_{1}a$ structure that continues to coexist with the Pnma one, until the latter is expected to reach the 100% fraction of the sample volume at high temperatures above 733 K. The $Pn{2}_{1}a$ space group is obtained from the Pnma one through the ${\mathrm{\ensuremath{\Gamma}}}_{4}^{\ensuremath{-}}$ polar distortion. Neutron diffraction and Raman spectroscopy results provide evidence for the emergence of noteworthy linear spin-phonon coupling. In this regard, magnetostructural coupling is observed below ${T}_{\mathrm{N}}$, revealed by the relation between the weak ferromagnetism of the canted iron spins and the ${\mathrm{FeO}}_{6}$ octahedra symmetric stretching mode. The correlation between magnetization and structural results from NPD provides definite evidence for the magnetic origin of the structural modulation. The analysis of the temperature-dependent magnetization and the magnetic peak intensity as well yields a critical exponent (\ensuremath{\beta}) value of 0.38. The lower limit of the phase coexistence temperature ${T}_{1}=543\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, marking the emergence of the Pnma phase, is also associated with the temperature whereupon the modulation magnitude starts to decrease.