Monoclinic Ground State Research Articles

First-principles predictions of HfO2-based ferroelectric superlattices

The metastable nature of the ferroelectric phase of HfO2 is a significant impediment to its industrial application as a functional ferroelectric material. In fact, no polar phases exist in the bulk phase diagram of HfO2, which shows a dominant non-polar monoclinic ground state. As a consequence, ferroelectric orthorhombic HfO2 is stabilized either kinetically or via epitaxial strain. Here, we propose an alternative approach, demonstrating the feasibility of thermodynamically stabilizing polar HfO2 in superlattices with other simple oxides. Using the composition and stacking direction of the superlattice as design parameters, we obtain heterostructures that can be fully polar, fully antipolar or mixed, with improved thermodynamic stability compared to the orthorhombic polar HfO2 in bulk form. Our results suggest that combining HfO2 with an oxide that does not have a monoclinic ground state generally drives the superlattice away from this non-polar phase, favoring the stability of the ferroelectric structures that minimize the elastic and electrostatic penalties. As such, these diverse and tunable superlattices hold promise for various applications in thin-film ferroelectric devices

New monoclinic ground state of FeSi

By means of ab initio techniques with the hybrid functional we show the existence of a new phase of FeSi with the monoclinic symmetry (space group P21) originated from the B20 cubic structure (space group P213) due to slight orthorhombic distortion, which is turned out to be the ground state. The monoclinic FeSi not only displays the minimum in the total energy, but it is also characterized by a phonon spectrum without imaginary frequencies and by conducting properties (contrary to semiconducting properties of cubic FeSi) with antiferromagnetic ordering and the magnetic moment of 2.3 μB for each Fe atom. These findings are supported by data of X-ray diffraction and high-resolution transmission electron microscopy of ultrathin FeSi films (∼3nm in thickness) grown on Si(111) by solid-phase epitaxy indicating the monoclinic symmetry to fit better the film structure as compared to the cubic symmetry, as well as by resistivity versus temperature measurements within a wide temperature range (2–300 K) pointing out bad metal properties. The analysis of field and temperature dependences of the magnetic moment of ultrathin FeSi films shows the presence of a ferromagnetic-antiferromagnetic two-phase state. We also discuss how our findings of the new phase of FeSi can interpret its known experimental data on electronic, transport and optical properties without involving the metal–insulator transition and Kondo-like effects.

Theoretical approach to ferroelectricity in hafnia and related materials

Hafnia ferroelectrics combine technological promise and remarkable behaviors. Their peculiarity stems from the many active extrinsic mechanisms that contribute to their properties and from a continuously growing number of novel intrinsic features. Partly because of their unconventional nature, basic questions about these materials remain open and one may wonder about the pertinence of some frequent theoretical assumptions. Here, aided by first-principles simulations, we show that, by adopting an original high-symmetry reference phase as the starting point of the analysis, we can develop a mathematically simple and physically transparent treatment of the ferroelectric state of hafnia. The proposed approach describes hafnia as a uniaxial ferroic, as suggested by recent studies of (woken-up) samples with well-developed polarization. Also, it is compatible with the occurrence of polar soft modes and proper ferroelectric order. Further, our theory provides a straightforward and unified description of all low-energy polymorphs, shedding light on old questions such as the prevalence of the monoclinic ground state, pointing at exciting possibilities like an antiferroelastic behavior, and facilitating the future development of perturbative theories, from Landau to second-principles potentials. Our work thus yields a deeper understanding of hafnia ferroelectrics, improving our ability to optimize their properties and induce new ones.

Elucidating the photovoltaic effect of monoclinic K2SnBr6 by mixed-cation mixed-halide substitution from first-principles calculations

Vacancy-ordered double perovskites (A2BX6) have recently received impressive attention for photovoltaic applications, and the compound K2SnBr6 has desirable features for use in solar cells in such a way that it exhibits direct bandgap behaviour with dispersed band edges. However, the large bandgap value limits its use in higher-efficiency solar cells. Therefore, we have carried out exploratory research by analysing the photovoltaic effect of K2SnBr6 by tuning its bandgap with cation and anion substitutions. We studied the properties of K(2−y)RbySnBr(6−x)I x and K2Sn(1−z)Ti z Br(6−x)I x compounds to explore the photovoltaic effect by gradual substitution of Rb+, Ti4+ and I−1 for K+, Sn4+ and Br−1, respectively. Our density functional calculations in the monoclinic ground state crystal structure with the space group P121 /n revealed that the K(2−y)Rb y SnBr(6−x)I x compounds considered in this study exhibit direct bandgap behaviour with well-dispersed band edges. Moreover, the bandgap value decreases as a function of the Rb and I concentrations. In addition to the low charge carrier effective mass, low excitonic binding energy values and low recombination rate, these compounds exhibit comparatively greater absorption coefficients in the visible range. The charge carrier transport properties, such as carrier mobility, carrier relaxation time, carrier diffusion coefficient and carrier diffusion length, are also seen in higher ranges for these Rb- and I-substituted compounds when compared to the parent compound. In addition, we have calculated the open-circuit voltage, fill factor, short-circuit current and power conversion efficiency for each compound. From the calculations and analysis, we observed that Rb and I substitution in K2SnBr6 increases the photovoltaic effect, and thus K(2−y)Rb y SnBr(6−x)I x compounds may be employed as absorbing layers in higher-efficiency solar cells.

Spin Seebeck effect at low temperatures in the nominally paramagnetic insulating state of vanadium dioxide

The low temperature monoclinic, insulating phase of vanadium dioxide is ordinarily considered nonmagnetic, with dimerized vanadium atoms forming spin singlets, though paramagnetic response is seen at low temperatures. We find a nonlocal spin Seebeck signal in VO2 films that appears below 30 K and that increases with a decrease in temperature. The spin Seebeck response has a nonhysteretic dependence on the in-plane external magnetic field. This paramagnetic spin Seebeck response is discussed in terms of prior findings on paramagnetic spin Seebeck effects and expected magnetic excitations of the monoclinic ground state.

Effect of Dopant Ordering on the Stability of Ferroelectric Hafnia

Films of the all‐important compound hafnia (HfO2) can be prepared in an orthorhombic ferroelectric (FE) state that is ideal for applications, e.g., in memories or negative‐capacitance field‐effect transistors. The origin of this FE state remains a mystery, though, as none of the proposed mechanisms for its stabilization—from surface and size effects to formation kinetics—is fully convincing. Interestingly, it is known that doping HfO2 with various cations favors the occurrence of the FE polymorph; however, existing first‐principles works suggest that doping by itself is not sufficient to stabilize the polar phase over the usual nonpolar monoclinic ground state. Herein, first‐principles methods are used to re‐examine this question. Two representative isovalent substitutional dopants, Si and Zr, are considered, and their preferred arrangement within the HfO2 lattice is studied. The results reveal that small atoms like Si can adopt very stable configurations (forming layers within specific crystallographic planes) in the FE orthorhombic phase of HfO2 but comparatively less so in the nonpolar monoclinic one. Further, it is found that, at low concentrations, such a dopant ordering yields a FE ground state, the usual paraelectric phase becoming a higher‐energy metastable polymorph. The implications of the findings are discussed.

Low-Energy Phases of Bi Monolayer Predicted by Structure Search in Two Dimensions.

We employ an ab-initio structure search algorithm to explore the configurational space of bismuth in quasi-two dimensions. A confinement potential is introduced to restrict the movement of atoms within a predefined thickness to find the stable and metastable forms of monolayer Bi. In addition to the two known low-energy structures (puckered monoclinic and buckled hexagonal), our calculations predict three new phases: α, β, and γ. Each phase exhibits peculiar electronic properties, ranging from metallic (α and γ) to semiconducting (puckered monoclinic, buckled hexagonal, and β)monolayers. Topologically nontrivial features are predicted for buckled hexagonal and γ phases. We also remark on the role of 5d electrons on the electronic properties of Bi monolayer. We conclude that Bi provides a rich playground to study distortion-mediated metal-insulator phase transitions in quasi-2D.

Two types of magnetic shape-memory effects from twinned microstructure and magneto-structural coupling in Fe1+yTe

A detailed experimental investigation of Fe1+y Te (y = 0.11, 0.12) using pulsed magnetic fields up to 60 T confirms remarkable magnetic shape-memory (MSM) effects. These effects result from magnetoelastic transformation processes in the low-temperature antiferromagnetic state of these materials. The observation of modulated and finely twinned microstructure at the nanoscale through scanning tunneling microscopy establishes a behavior similar to that of thermoelastic martensite. We identified the observed, elegant hierarchical twinning pattern of monoclinic crystallographic domains as an ideal realization of crossing twin bands. The antiferromagnetism of the monoclinic ground state allows for a magnetic-field-induced reorientation of these twin variants by the motion of one type of twin boundaries. At sufficiently high magnetic fields, we observed a second isothermal transformation process with large hysteresis for different directions of applied field. This gives rise to a second MSM effect caused by a phase transition back to the field-polarized tetragonal lattice state.

Impact of lattice dynamics on the phase stability of metamagnetic FeRh: Bulk and thin films

We present phonon dispersions, element-resolved vibrational density of states (VDOS) and corresponding thermodynamic properties obtained by a combination of density functional theory (DFT) and nuclear resonant inelastic X-ray scattering (NRIXS) across the metamagnetic transition of B2 FeRh in the bulk material and thin epitaxial films. We see distinct differences in the VDOS of the antiferromagnetic (AF) and ferromagnetic (FM) phase which provide a microscopic proof of strong spin-phonon coupling in FeRh. The FM VDOS exhibits a particular sensitivity to the slight tetragonal distortions present in epitaxial films, which is not encountered in the AF phase. This results in a notable change in lattice entropy, which is important for the comparison between thin film and bulk results. Our calculations confirm the recently reported lattice instability in the AF phase. The imaginary frequencies at the $X$-point depend critically on the Fe magnetic moment and atomic volume. Analyzing these non vibrational modes leads to the discovery of a stable monoclinic ground state structure which is robustly predicted from DFT but not verified in our thin film experiments. Specific heat, entropy and free energy calculated within the quasiharmonic approximation suggest that the new phase is possibly suppressed because of its relatively smaller lattice entropy. In the bulk phase, lattice degrees of freedom contribute with the same sign and in similar magnitude to the isostructural AF-FM phase transition as the electronic and magnetic subsystems and therefore needs to be included in thermodynamic modeling.

Tetrahedral tilting and ferroelectricity in Bi2AO5 (A=Si, Ge) from first principles calculations

The properties of a tetrahedron containing Bi2AO5 (A=Si, Ge) are examined using Ab initio calculations and symmetry mode analysis. Stabilization of the polar phase is observed in both compounds with a monoclinic Cc phase. In the monoclinic ground state, the tilting angle (ϕ1) of tetrahedron is 7.21° and 21.94° for the Si and Ge compound, respectively. The relationship between a primary order parameter and the tetrahedral tilting is identified and an analytical formula between them is proposed by analyzing the structure. The detailed layer-by-layer polarization calculations shows that the main polarization component originates from the tetrahedron tilting of the AO4 unit, and the analytical relationship between the primary order parameter and spontaneous polarization is also calculated. This B3LYP hybrid functional calculation provides a band gap of 4.44eV and 4.18eV for Bi2SiO5 and Bi2GeO5, respectively. The main difference between the two compounds is also analyzed based on the electronic structure and electron localization function analysis.

Magnetic structure determination from the magnetic pair distribution function (mPDF): ground state of MnO.

An experimental determination of the magnetic pair distribution function (mPDF) defined in an earlier paper [Frandsen et al. (2014). Acta Cryst. A70, 3-11] is presented for the first time. The mPDF was determined from neutron powder diffraction data from a reactor and a neutron time-of-flight total scattering source on a powder sample of the antiferromagnetic oxide MnO. A description of the data treatment that allowed the measured mPDF to be extracted and then modelled is provided and utilized to investigate the low-temperature structure of MnO. Atomic and magnetic co-refinements support the scenario of a locally monoclinic ground-state atomic structure, despite the average structure being rhombohedral, with the mPDF analysis successfully recovering the known antiferromagnetic spin configuration. The total scattering data suggest a preference for the spin axis to lie along the pseudocubic [10{\overline 1}] direction. Finally, r-dependent PDF refinements indicate that the local monoclinic structure tends toward the average rhombohedral R{\overline 3}m symmetry over a length scale of approximately 100 Å.

Ab initiostudy of the structural phase transitions of the double perovskitesSr2MWO6(M=Zn, Ca, Mg)

We study the interplay of structural distortions in double perovskites ${\text{Sr}}_{2}M{\text{WO}}_{6}$ ($M=$ Zn, Ca, Mg) by means of first-principles calculations and group theoretical analysis. Structure relaxations of the cubic, tetragonal, and monoclinic phases show that the ground states of the three compounds are monoclinic, although the energy difference between the monoclinic and tetragonal structures is very small in the case of ${\text{Sr}}_{2}\text{Mg}{\text{WO}}_{6}$. The symmetry analysis of the distortions involved in the experimental and calculated low-temperature structures shows that the amplitude of two primary distortions associated to rigid rotations of the $MX$${}_{6}$ and WO${}_{6}$ octahedra are dominant, although the amplitude of a third mode related to deformations of the $MX$${}_{6}$ groups can not be neglected. The energy maps of the space spanned by the three relevant modes are calculated, and the couplings among the modes are evaluated, showing that the role of a hard secondary mode (in the Landau sense) coupled trilinearly to the two primary instabilities is crucial to stabilize the monoclinic ground state. Results suggest that the key role of the trilinear coupling among three modes could be rather common. A phenomenological theory including the effects of the chemical pressure is also developed. We find that the evolution of the stiffness constants in terms of the atomic substitution follows an accurate linear dependence and that the influence of quantum saturation of the order parameters could stabilize the tetragonal phase of ${\text{Sr}}_{2}\text{Mg}{\text{WO}}_{6}$.

High-pressure phases and transitions of the layered alkaline earth nitridosilicatesSrSiN2 andBaSiN2

We investigate the high-pressure phase diagram ofSrSiN2 andBaSiN2 with density-functional calculation. Searching a manifold of possiblecandidate structures, we propose new structural modifications ofSrSiN2 andBaSiN2 attainable in high-pressure experiments. The monoclinic ground state ofSrSiN2 transforms at 3 GPainto an orthorhombic BaSiN2 type. At 14 GPa a CaSiN2-type structure becomes the most stable configuration ofSrSiN2. A hithertounknown Pbcm modification is adopted at 85 GPa and, finally, at 131 GPa aLiFeO2-type structure. Thehigher homologue BaSiN2 transforms to a CaSiN2 type at41 GPa and further to a Pbcm modification at 105 GPa. Both systems follow the pressure-coordination rule: thecoordination environment of Si increases from tetrahedral through trigonal bipyramidal tooctahedral. Some high-pressure phases are related in structure through simplegroup–subgroup mechanisms, indicating displacive phase transformations with lowactivation barriers.

Incorporating anisotropic electronic structure in crystallographic determination of complex metals: iron and plutonium

Anisotropic electronic structure is incorporated in crystallographic determination of the structure of ferromagnetic Fe, δ-Pu and a Pu–3.7 at% Ga alloy. This is achieved by using anisotropic aspects of the inter-atomic bonds as a motif in combination with the high-symmetry cubic lattice. In the case of Fe, it is shown that ferromagnetic ordering reduces the symmetry of the structure from body centred cubic to body centred tetragonal with an associated effect on elasticity. Thus, the ferromagnetic α- and paramagnetic β-phase are separate and unique phases that should both be addressed on the Fe phase diagrams. In the case of Pu, first-principles density-functional theory calculations are used to show that the bond strengths between the 12 nearest neighbours in δ-plutonium vary greatly. Employing the calculated bond strengths as a motif in crystallographic determination yields a structure with the monoclinic space group Cm for δ-Pu rather than face-centred cubic . The reduced space group for δ-Pu illuminates why it is the only metal with a monoclinic ground state, why lattice distortions of the metal are viable and has implications for the behaviour of the material as it ages due to self-irradiation. Results for a Pu–3.7 at% Ga alloy show that the nearest neighbour bond strengths around a Ga atom are more uniform – a result that explains why Ga stabilizes face-centred cubic δ-Pu. This paper illustrates how an expansion of classical crystallography, which accounts for anisotropic electronic and magnetic structure, can explain complex materials in a novel way.

Phase Diagram ofPb(Zr,Ti)O3Solid Solutions from First Principles

A first-principles-derived scheme that incorporates ferroelectric and antiferrodistortive degrees of freedom is developed to study finite-temperature properties of Pb(Zr1-xTix)O3 solid solution near its morphotropic phase boundary. The use of this numerical technique (i) resolves controversies about the monoclinic ground state for some Ti compositions, (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions.

Advances in First-Principles Studies of Transducer Materials

We have used first-principles linear response calculations and molecular dynamics to study the relaxor ferroelectric Pb(Mg 1/3 Nb 2/3 )O 3 -xPbTiO 3 (PMN-x PT). First-principles calculations for ordered PMN show a low-symmetry monoclinic ground state. A new set of phase transitions to lower symmetry rhombohedral and monoclinic structures is predicted for PT at high pressures, showing predicted piezoelectric response as high as is seen in the giant coupling relaxor ferroelectrics. We have developed a transferable shell-model potential for PMN-x PT by fitting to first-principles data. The potential qualitatively reproduces the compositional phase diagram for PMN-x PT. A new exchange-correlation potential, which gives excellent predictions for ferroelectric materials, is discussed.

Ab-initio Based Diffusive Studies of Plutonium with Relevance to Nuclear Waste Management

AbstractAn approach to study the diffusion of plutonium (Pu) waste into the material of the storage containers is presented. The delta phase of Pu has been examined, in this article, using a spin and orbitally polarized ab-initio (full potential LMTO) approach [1, 2]. These computations are relatively inexpensive, and it is the intention to see if the results obtained would be satisfactory (compared to the accurate SIC-LDA computations [1-2]) for diffusive studies of Pu into the material of storage containers (for example, into FCC iron as a surrogate for steel [2]). The combination of LDA and spin and orbitally polarized LMTO calculations that we use successfully predict a delocalized 5f, (i.e. bonding) monoclinic ground state and a localized FCC excited state with a density about 8% greater than experiment (compared to the 30% error from pure LDA calculations by various groups [3-6]). The density of states is computed and compared to experimental photoemission studies; there is qualitative agreement. The spin, orbital and total magnetic moment for the FCC phase is computed; the results are qualitatively in agreement with those of other studies. An analytical method for studying the time-dependent diffusion of Pu across an interface with another atomic species is presented.

Cationic-competition-induced monoclinic phase in high piezoelectric(PbSc1/2Nb1/2O3)1−x−(PbTiO3)xcompounds

A global picture for the structural evolution in the relaxor-ferroelectric solid solution $({\mathrm{PbSc}}_{1/2}{\mathrm{Nb}}_{1/2}{\mathrm{O}}_{3}{)}_{1\ensuremath{-}x}\ensuremath{-}({\mathrm{PbTiO}}_{3}{)}_{x}$ is proposed. Thanks to x-ray profile analysis and Rietveld neutron powder refinement, a monoclinic phase has been evidenced in the morphotropic region (i.e., $x\ensuremath{\approx}0.43).$ This lower-symmetry phase ``bridges'' the rhombohedral Ti-poor phase $(x<~0.26)$ with the tetragonal Ti-rich phase $(x>~0.55),$ in a similar way as in ${\mathrm{PbMg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_{3}\ensuremath{-}{\mathrm{PbTiO}}_{3}$ or $\mathrm{Pb}({\mathrm{Zn}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}\ensuremath{-}{\mathrm{PbTiO}}_{3}.$ For weak titanium concentration, we observe a macroscopic rhombohedral state with local monoclinic symmetry resulting from the combination between Pb and Sc/Nb/Ti shifts along [001] and [111] directions, respectively. Cationic competition with Ti doping increases the coherence length of this short-range monoclinic phase, which becomes long range in the morphotropic region. This intermediate monoclinic phase is in complete agreement with our first-principles calculations which predict Pm or Cm space groups. It has been shown that these ones are very close to each other in the free-energy space, and a minor change of atomic distribution and/or a slight modification in composition or in stoichiometry is enough to alter the space group of the monoclinic ground state. Finally, in the Ti-rich region, the monoclinic ground state is destroyed in favor of a tetragonal phase.

Fundamental Studies of Plutonium Aging

Plutonium metallurgy lies at the heart of science-based stockpile stewardship. One aspect is concerned with developing predictive capabilities to describe the properties of stockpile materials, including an assessment of microstructural changes with age. Yet, the complex behavior of plutonium, which results from the competition of its 5f electrons between a localized (atomic-like or bound) state and an itinerant (delocalized bonding) state, has been challenging materials scientists and physicists for the better part of five decades. Although far from quantitatively absolute, electronic-structure theory provides a description of plutonium that helps explain the unusual properties of plutonium, as recently reviewed by Hecker. (See also the article by Hecker in this issue.) The electronic structure of plutonium includes five 5f electrons with a very narrow energy width of the 5f conduction band, which results in a delicate balance between itinerant electrons (in the conduction band) or localized electrons and multiple lowenergy electronic configurations with nearly equivalent energies. These complex electronic characteristics give rise to unique macroscopic properties of plutonium that include six allotropes (at ambient pressure) with very close free energies but large (∼25%) density differences, a lowsymmetry monoclinic ground state rather than a high-symmetry close-packed cubic phase, compression upon melting (like water), low melting temperature, anomalous temperature-dependence of electrical resistance, and radioactive decay. Additionally, plutonium readily oxidizes and is toxic; therefore, the handling and fundamental research of this element is very challenging due to environmental, safety, and health concerns.

First-principles calculations to describe zirconia pseudopolymorphs

The structural and electronic properties of four different polytypes of zirconia $({\mathrm{ZrO}}_{2})$ are studied using ab initio total-energy calculations. The calculations are performed in the framework of density-functional theory (DFT) and pseudopotential theory. We compare results obtained within the LDA (local-density approximation) and including generalized gradient corrections (GGC's) in the Perdew-Wang and Perdew-Becke formalisms. Within this approach, we are able to predict the correct monoclinic ground state at low pressure and temperature. We show that GGC's are necessary to correctly describe the high-pressure orthorhombic structure of zirconia. The tetragonal-to-cubic phase transition was studied assuming a martensitic-displacive mechanism following the approach of Jansen [Phys. Rev. B 43, 7267 (1991)].