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Using density-functional theory, we demonstrate that the formal layer charges of the metallic samarium nickelate electrode influence the spontaneous ferroelectric polarization of the barium titanate in SmNiO$_3$/BaTiO$_3$ capacitors. We find that, despite the metallic screening of SmNiO$_3$, the spontaneous polarization of BaTiO$_3$ always aligns with the layer polarization of the SmNiO$_3$ formal charges. We also find zero critical thickness for the ferroelectricity in BaTiO$_3$ in this orientation. The opposite polarization direction is highly disfavored for thin BaTiO$_3$ slabs but becomes less unstable with increasing slab thickness. We construct a simple electrostatic model that allows us both to study the behavior for thicker BaTiO$_3$ and SmNiO$_3$ slabs and to extract the influence of various material parameters on the behavior. We mimic a metal-insulator transition in the SmNiO$_3$ by varying the metallic screening length, which we find greatly influences the stability of the ferroelectric polarization. Our results show that the layer charges in the metal electrodes strongly influence the properties in ferroelectric capacitors and in fact can provide new ways to control the ferroelectric properties.

We investigate the role of electric toroidal dipoles in the prototypical ferroaxial materials NiTiO$_3$ and K$_2$Zr(PO$_4$)$_2$, which undergo ferroaxial structural phase transitions of order-disorder and displacive type, respectively. Using first-principles electronic structure theory, we compute the evolution across the ferroaxial transitions of the local electric toroidal dipole moments, defined both in terms of the vortices formed by local dipoles, as well as as the cross product of orbital and spin angular momenta. Our calculations confirm that the electric toroidal dipole acts as the order parameter for these ferroaxial transitions and highlight the importance of spin-orbit coupling in generating a non-zero atomic-site electric toroidal dipole moment. We find that, while the ferroaxial phases of NiTiO$_3$ and K$_2$Zr(PO$_4$)$_2$ preserve global inversion symmetry, they contain inversion-symmetry-broken sub-units that generate vortices of local electric dipole moments. In addition to causing the net electric toroidal dipole moment, these vortices induce a hidden spin polarization in the band structure., Comment: 8 pages, 7 figures

We analyze the effects on the structural and electronic properties of vanadium dioxide (VO$_2$) of adding an empirical inter-atomic potential within the density-functional theory$+V$ (DFT$+V$) framework. We use the DFT$+V$ machinery founded on the extended Hubbard model to apply an empirical self-energy correction between nearest-neighbor vanadium atoms in both rutile and monoclinic phases, and for a set of structures interpolating between these two cases. We observe that imposing an explicit intersite interaction $V$ along the vanadium-vanadium chains enhances the characteristic bonding-antibonding splitting of the relevant bands in the monoclinic phase, thus favoring electronic dimerization and the formation of a band gap. We then explore the effect of $V$ on the structural properties and the relative energies of the two phases, finding an insulating global energy minimum for the monoclinic phase, consistent with experimental observations. With increasing $V$, this minimum becomes deeper relative to the rutile structure, and the transition from the metallic to the insulating state becomes sharper. We also analyze the effect of applying the $+V$ correction either to all or only to selected vanadium-vanadium pairs, and both in the monoclinic as well as in the metallic rutile phase. Our results suggest that DFT$+V$ can indeed serve as a computationally inexpensive unbiased way of modeling VO$_2$ which is well suited for studies that, e.g., require large system sizes.

We use first-principles density functional theory to investigate how the polar distortion is affected by doping in multiferroic hexagonal yttrium manganite, h-YMnO$_3$. While the introduction of charge carriers tends to suppress the polar distortion in conventional ferroelectrics, the behavior in improper geometric ferroelectrics, of which h-YMnO$_3$ is the prototype, has not been studied to date. Using both background charge doping and atomic substitution, we find an approximately linear dependence of the polar distortion on doping concentration, with hole doping suppressing and electron doping enhancing it. We show that this behavior is a direct consequence of the improper geometric nature of the ferroelectricity. In addition to its doping effect, atomic substitution can further suppress or enhance the polar distortion through changes in the local chemistry and geometry.

We perform first-principles density functional calculations to elucidate structural, electronic and magnetic properties at the interface of \ce{(0001)Cr2O3-(111)Pt} bilayers. This investigation is motivated by the fact that, despite the promise of \ce{Cr2O3-Pt} heterostructures in a variety of antiferromagnetic spintronic applications, many key structural, electronic, and magnetic properties at the \ce{Cr2O3-Pt} interface are poorly understood. We first analyze all inequivalent lateral interface alignments to determine the lowest energy interfacial structure. For all lateral alignments including the lowest-energy one, we observe an accumulation of electrons at the interface between \ce{Cr2O3} and Pt. We find an unexpected reversal of the magnetic moments of the interface Cr ions in the presence of Pt compared to surface Cr moments in vacuum-terminated \ce{(0001)Cr2O3}. We also find that the heterostructure exhibits a magnetic proximity effect in the first three Pt layers at the interface with \ce{Cr2O3}, providing a mechanism by which the anomalous Hall effect can occur in \ce{(0001)Cr2O3-(111)Pt} bilayers. Our results provide the basis for a more nuanced interpretation of magnetotransport experiments on \ce{(0001)Cr2O3-(111)Pt} bilayers and should inform future development of improved antiferromagnetic spintronic devices based on the \ce{Cr2O3-Pt} material system.

We present a combined density-functional theory and single-site dynamical mean-field theory (DMFT) study of vanadium dioxide (VO$_2$) using an unconventional set of bond-centered orbitals as the basis of the correlated subspace. VO$_2$ is a prototypical material undergoing a metal-insulator transition (MIT), hosting both intriguing physical phenomena and the potential for industrial applications. With our choice of correlated subspace basis, we investigate the interplay of structural dimerization and electronic correlations in VO$_2$ in a computationally cheaper way compared to other state-of-the-art methods such as cluster DMFT. Our approach allows us to treat the rutile and M1 monoclinic VO$_2$ phases on an equal footing and to vary the dimerizing distortion continuously, exploring the energetics of the transition between the two phases. The choice of basis presented in this work hence offers a complementary view on the long-standing discussion of the MIT in VO$_2$ and suggests possible future extensions to other similar materials hosting molecular-orbital-like states.

We combine the non-relativistic effective theory of dark matter (DM) - electron interactions with linear response theory to obtain a formalism that fully accounts for screening and collective excitations in DM-induced electronic transition rate calculations for general DM-electron interactions. In the same way that the response of a dielectric material to an external electric field in electrodynamics is described by the dielectric function, so in our formalism the response of a detector material to a DM perturbation is described by a set of generalised susceptibilities which can be directly related to densities and currents arising from the non-relativistic expansion of the Dirac Hamiltonian. We apply our formalism to assess the sensitivity of non-spin-polarised detectors, and find that in-medium effects significantly affect the experimental sensitivity if DM couples to the detector's electron density, while being decoupled from other densities and currents. Our formalism can be straightforwardly extended to the case of spin-polarised materials., Comment: 27 pages, 4 figures

We use a combination of first-principles density functional calculations and spin-dynamics simulations to explain the unusual diffuse inelastic neutron scattering in the hexagonal multiferroic yttrium manganite, YMnO$_3$. Using symmetry considerations, we construct a model spin Hamiltonian with parameters derived from our density functional calculations and show that it captures the measured behavior. We then show that the observed directionality in the structured diffuse scattering in momentum space is a hallmark of the triangular geometry, and that its persistence across a wide range of temperatures, both above and below the N\'eel temperature, T$_\text{N}$, is a result of the strong magnetic frustration. We predict that this diffuse scattering exists in a yet-to-be-observed modulated continuum of energies, that its associated spin excitations have distinct in-plane and out-of-plane character and that the frustration influences the magnetism below the N\'eel temperature. Finally, we show that visualizing the magnetic order in terms of composite trimer magnetoelectric monopoles and toroidal moments, rather than individual spins, provides insight into the real space fluctuations, revealing clusters of emerging order in the paramagnetic state, as well as collective short-range excitations in the ordered antiferromagnetic phase. Our understanding of this directional diffuse scattering in such a wide temperature range, both below and above T$_\text{N}$, provides new insight into the magnetic phase transitions in frustrated systems.

Clarifying the underlying mechanisms that govern ordering transitions in condensed matter systems is crucial for comprehending emergent properties and phenomena. While transitions are often classified as electronically driven or lattice-driven, we present a departure from this conventional paradigm in the case of the double perovskite Ba$_2$MgReO$_6$. Leveraging resonant and non-resonant elastic x-ray scattering techniques, we unveil the simultaneous ordering of structural distortions and charge quadrupoles at a critical temperature of $T_\mathrm{q}$$\sim$33 K. Using a variety of complementary first-principles-based computational techniques, we demonstrate that while electronic interactions drive the ordering at $T_\mathrm{q}$, it is ultimately the lattice that dictates the specific ground state that emerges. Our findings highlight the crucial interplay between electronic and lattice degrees of freedom, providing a unified framework to understand and predict unconventional emergent phenomena in quantum materials.

Antiferromagnets are normally thought of as materials with compensated magnetic sublattices. This adds to their technological advantages but complicates readout of the antiferromagnetic state. We demonstrate theoretically the existence of a Dzyaloshinskii-Moriya interaction (DMI) which is determined by the magnetic symmetry classes of Cr$_2$O$_3$ surfaces with an in-plane magnetic easy axis. The DMI explains a previously predicted out-of-plane magnetization at the nominally compensated surfaces of chromia, leading to a surface-localized canted ferrimagnetism. This is in agreement with magnetotransport measurements and with density functional theory predictions which further allow us to quantify the strength of DMI. The temperature dependence of the transversal resistance for these planes shows distinct behavior in comparison with that of the Cr$_2$O$_3$ $c$ plane, which we attribute to the influence of DMI. Our work provides a framework to analyze surface-driven phenomena in antiferromagnets, and motivates the use of nominally compensated chromia surfaces for antiferomagnetic spintronics and magnonics., Comment: 8 pages, 3 figures, 73 references

We demonstrate that two phenomena, the kinetic magneto-electric effect and the non-linear Hall effect, are universal to polar metals, as a consequence of their coexisting and contraindicated polarization and metallicity. We show that measurement of the effects provides a complete characterization of the nature of the polar metal, in that the non-zero response components indicate the direction of the polar axis, and the coefficients change sign on polarization reversal and become zero in the non-polar phase. We illustrate our findings for the case of electron-doped PbTiO$_3$ using a combination of density functional theory and model Hamiltonian-based calculations. Our model Hamiltonian analysis provides crucial insight into the microscopic origin of the effects, showing that they originate from inversion-symmetry-breaking-induced inter-orbital hoppings, which cause an asymmetric charge density quantified by odd-parity charge multipoles. Our work both heightens the relevance of the kinetic magneto-electric and non-linear Hall effects, and broadens the platform for investigating and detecting odd-parity charge multipoles in metals., Comment: 9 pages, 7 figures

We establish the sign of the linear magnetoelectric (ME) coefficient, $\alpha$, in chromia, Cr$_2$O$_3$. Cr$_2$O$_3$ is the prototypical linear ME material, in which an electric (magnetic) field induces a linearly proportional magnetization (polarization), and a single magnetic domain can be selected by annealing in combined magnetic (H) and electric (E) fields. Opposite antiferromagnetic domains have opposite ME responses, and which antiferromagnetic domain corresponds to which sign of response has previously been unclear. We use density functional theory (DFT) to calculate the magnetic response of a single antiferromagnetic domain of Cr$_2$O$_3$ to an applied in-plane electric field at 0 K. We find that the domain with nearest neighbor magnetic moments oriented away from (towards) each other has a negative (positive) in-plane ME coefficient, $\alpha_{\perp}$, at 0 K. We show that this sign is consistent with all other DFT calculations in the literature that specified the domain orientation, independent of the choice of DFT code or functional, the method used to apply the field, and whether the direct (magnetic field) or inverse (electric field) ME response was calculated. Next, we reanalyze our previously published spherical neutron polarimetry data to determine the antiferromagnetic domain produced by annealing in combined E and H fields oriented along the crystallographic symmetry axis at room temperature. We find that the antiferromagnetic domain with nearest-neighbor magnetic moments oriented away from (towards) each other is produced by annealing in (anti-)parallel E and H fields, corresponding to a positive (negative) axial ME coefficient, $\alpha_{\parallel}$, at room temperature. Since $\alpha_{\perp}$ at 0 K and $\alpha_{\parallel}$ at room temperature are known to be of opposite sign, our computational and experimental results are consistent., Comment: 11 pages, 5 figures

We use symmetry analysis and density functional theory to characterize antiferromagnetic (AFM) materials which have a finite equilibrium magnetization density on particular surface terminations. A nonzero magnetic dipole moment per unit area or "surface magnetization" can arise on particular surfaces of many AFMs due to the bulk magnetic symmetries. Such surface magnetization plays an essential role in numerous device applications, from random-access magnetoelectric (ME) memory to exchange bias. However, at this point a universal description of AFM surface magnetization is lacking. We first introduce a classification system based on whether the surface magnetization is sensitive or robust to roughness, and on whether the surface of interest is magnetically compensated or uncompensated in the bulk magnetic ground state. We show that uncompensated surface magnetization can be conveniently described in terms of ME multipoles at the local-moment, unit cell level, and demonstrate that the symmetry of the multivalued "multipolization lattice" distinguishes between roughness-robust and roughness-sensitive surface magnetization. We then demonstrate that magnetization on bulk-compensated surfaces arises due to ME multipoles (in addition to higher-order magnetic terms) at the atomic site level. These can further be understood in terms of bulk ME responses, arising from the effective electric field resulting from the surface termination. We also show with density functional calculations that nominally compensated surfaces in Cr2O3 and FeF2 develop a finite magnetization density at the surface, in agreement with our predictions based on both group theory and the linear and higher-order ME response tensors. Our analysis provides a comprehensive basis for understanding the surface magnetic properties in AFMs, and has important implications for phenomena such as exchange bias coupling., Comment: 32 pages, 18 figures

We present a method to constrain local charge multipoles within density-functional theory. Such multipoles quantify the anisotropy of the local charge distribution around atomic sites and can indicate potential hidden orders. Our method allows selective control of specific multipoles, facilitating a quantitative exploration of the energetic landscape outside of local minima. Thus, it enables a clear distinction between electronically and structurally driven instabilities. We demonstrate the effectiveness of this method by applying it to charge quadrupoles in the prototypical orbitally ordered material KCuF$_3$. We quantify intersite multipole-multipole interactions as well as the energy-lowering related to the formation of an isolated local quadrupole. We also map out the energy as a function of the size of the local quadrupole moment around its local minimum, enabling quantification of multipole fluctuations around their equilibrium value. Finally, we study charge quadrupoles in the solid solution KCu$_{1-x}$Zn$_x$F$_3$ to characterize the behavior across the tetragonal-to-cubic transition. Our method provides a powerful tool for studying symmetry breaking in materials with coupled electronic and structural instabilities and potentially hidden orders.

We use a formalism that describes electron ejections from graphene-like targets by dark matter (DM) scattering for general forms of scalar and spin 1/2 DM-electron interactions in combination with state-of-the-art density functional calculations to produce predictions and reach estimates for various possible carbon-based detector designs. Our results indicate the importance of a proper description of the target electronic structure. In addition, we find a strong dependence of the predicted observed signal for different DM candidate masses and interaction types on the detailed geometry and design of the detector. Combined with directional background vetoing, these dependencies will enable the identification of DM particle properties once a signal has been established., Comment: 22 pages, 15 figures, 2 appendices. The DFT code can be found under https://github.com/urdshals/QEdark-EFT

We develop a formalism to describe electron ejections from graphene-like targets by dark matter (DM) scattering for general forms of scalar and spin 1/2 DM-electron interactions and compare their applicability and accuracy within the density functional theory (DFT) and tight binding (TB) approaches. This formalism allows for accurate prediction of the daily modulation signal expected from DM in upcoming direct detection experiments employing graphene sheets as the target material. A key result is that the physics of the graphene sheet and that of the DM and the ejected electron factorise, allowing for the rate of ejections from all forms of DM to be obtained with a single graphene response function. We perform a comparison between the TB and DFT approaches to modeling the initial state electronic wavefunction within this framework, with DFT emerging as the more self-consistent and reliable choice due to the challenges in the embedding of an appropriate atomic contribution into the TB approach., Comment: 29 pages, 12 figures, 5 appendices. The TB and DFT codes can be found under https://github.com/temken/Darphene and https://github.com/urdshals/QEdark-EFT respectively

We present ab initio calculations of hidden magnetoelectric multipolar order in Cr$_2$O$_3$ and its iron-based analogue, $\alpha$-Fe$_2$O$_3$. First, we discuss the connection between the order of such hidden multipoles and the linear magnetoelectric effect. Next, we show the presence of hidden antiferroically-ordered magnetoelectric multipoles in both the prototypical magnetoelectric material Cr$_2$O$_3$, and centrosymmetric $\alpha$-Fe$_2$O$_3$, which has the same crystal structure as Cr$_2$O$_3$, but a different magnetic dipolar ordering. In turn, we predict anti-magnetoelectric effects, in which local magnetic dipole moments are induced in opposite directions under the application of an external electric field, to create an additional antiferromagnetic ordering. We confirm the predicted induced moments using first-principles calculations. Our results demonstrate the existence of hidden magnetoelectric multipoles leading to local linear magnetoelectric responses even in centrosymmetric materials, where a net bulk linear magnetoelectric effect is forbidden by symmetry.

The concept of chirality is of great relevance in nature, from chiral molecules such as sugar to parity transformations in particle physics. In condensed matter physics, recent studies have demonstrated chiral fermions and their relevance in emergent phenomena closely related to topology. The experimental verification of chiral phonons (bosons) remains challenging, however, despite their expected strong impact on fundamental physical properties. Here we show experimental proof of chiral phonons using resonant inelastic X-ray scattering with circularly polarized X rays. Using the prototypical chiral material, quartz, we demonstrate that circularly polarized X rays, which are intrinsically chiral, couple to chiral phonons at specific positions in reciprocal space, allowing us to determine the chiral dispersion of the lattice modes. Our experimental proof of chiral phonons demonstrates a new degree of freedom in condensed matter that is both of fundamental importance and opens the door to exploration of novel emergent phenomena based on chiral bosons, Comment: 5

We propose a method for detecting single chiral phonons that will enable their use as dark-matter detectors. We suggest metal--organic frameworks (MOFs) as detector materials, as their flexibility yields low-energy chiral phonons with measurable magnetic moments, and their anisotropy leads to directional sensitivity, which mitigates background contamination. To demonstrate our proposal, we calculate the phononic structure of the MOF InF$_3$($4,4'$-bipyridine), and show that it has highly chiral acoustic phonons. Detection of such chiral phonons via their magnetic moments would dramatically lower the excitation energy threshold for dark matter detection to the energy of a single phonon. We show that single phonon detection in a MOF would extend detector reach ten or more orders of magnitude below current limits, enabling exploration of a multitude of as-yet-unprobed dark matter candidates., Comment: 12 pages, 4 figures

We address magnetic neutron scattering in the presence of local non-centrosymmetric asymmetries of the magnetization density. Such inversion-symmetry breaking, combined with the absence of time-reversal symmetry, can be described in terms of magnetoelectric multipoles which form the second term after the magnetic dipole in the multipole expansion of the magnetization density. We provide a pedagogical review of the theoretical formalism of magnetic neutron diffraction in terms of the multipole expansion of the scattering cross-section. In particular, we show how to compute the contribution of magnetoelectric multipoles to the scattering amplitude starting from ab initio calculations. We also provide general guidelines on how to experimentally detect long-ranged order of magnetoelectric multipoles using either unpolarized or polarized neutron scattering. As a case study, we search for the presence of magnetoelectric multipoles in CuO by comparing theoretical first-principle predictions with experimental spherical neutron polarimetry measurements., Comment: 17 pages, 8 figures

We show that time-reversal symmetry broken, centrosymmetric antiferromagnets with nonrelativistic spin-splitting are conveniently described in terms of the ferroic ordering of magnetic octupoles. The magnetic octupoles are the lowest-order ferroically ordered magnetic quantity in this case, and so are the natural order parameter for the transition into the magnetically ordered state. They provide a unified description of the broken time-reversal symmetry and the non-relativistic spin splitting as well as a platform for manipulating the latter, and account for other phenomena, such as piezomagnetism, characteristic of this class of antiferromagnets. Unusually for antiferromagnets, we show that the magnetic octupoles cause a non-zero magnetic Compton scattering, providing a route for their direct experimental detection. We illustrate these concepts using density-functional and model calculations for the prototypical non-relativistic spin-split antiferromagnet, rutile-structure manganese difuoride, MnF2., Comment: 13 pages, 6 figures

Motivated by the recent experimental discovery of strongly surface-plane-dependent superconductivity at surfaces of KTaO$_3$ single crystals, we calculate the electron-phonon coupling strength, $\lambda$, of doped KTaO$_3$ along the reciprocal-space high-symmetry directions. Using the Wannier-function approach implemented in the EPW package, we calculate $\lambda$ across the experimentally covered doping range and compare its mode-resolved distribution along the [001], [110] and [111] reciprocal-space directions. We find that the electron-phonon coupling is strongest in the optical modes around the $\Gamma$ point, with some distribution to higher $k$ values in the [001] direction. The electron-phonon coupling strength as a function of doping has a dome-like shape in all three directions and its integrated total is largest in the [001] direction and smallest in the [111] direction, in contrast to the experimentally measured trends in critical temperatures. This disagreement points to a non-BCS character of the superconductivity. Instead, the strong localization of $\lambda$ in the soft optical modes around $\Gamma$ suggests an importance of ferroelectric soft-mode fluctuations, which is supported by our findings that the mode-resolved $\lambda$ values are strongly enhanced in polar structures. The inclusion of spin-orbit coupling has negligible influence on our calculated mode-resolved $\lambda$ values.

We address the degeneracy of the ground state multiplet on the 5$d^1$ Re$^{6+}$ ion in double perovskite Ba$_{2}$MgReO$_{6}$ using a combination of specific heat measurements and density functional calculations. For Ba$_{2}$MgReO$_{6}$, two different ground state multiplets have previously been proposed - a quartet (with degeneracy $N$=4) [1] and a doublet ($N$=2) [2]. Here we employ two independent methods for the estimation of phonon contribution in heat capacity data to obtain the magnetic entropy $S_{mag}$, which reflects the degeneracy of the ground state multiplet $N$ through $S_{mag}=R$ln$N$. In both cases, we obtain a better fit to $S_{mag}=R$ln2 indicating evidence of $N$=2 degeneracy in the range from 2 to 120~K. The detailed nature of the ground state multiplet in Ba$_{2}$MgReO$_{6}$ remains an open question., Comment: 5 pages, 4 figures

The search for sub-GeV dark matter (DM) particles via electronic transitions in underground detectors attracted much theoretical and experimental interest in the past few years. A still open question in this field is whether experimental results can in general be interpreted in a framework where the response of detector materials to an external DM probe is described by a single ionisation or crystal form factor, as expected for the so-called dark photon model. Here, ionisation and crystal form factors are examples of material response functions: interaction-specific integrals of the initial and final state electron wave functions. In this work, we address this question through a systematic classification of the material response functions induced by a wide range of models for spin-0, spin-1/2 and spin-1 DM. We find several examples for which an accurate description of the electronic transition rate at DM direct detection experiments requires material response functions that go beyond those expected for the dark photon model. This concretely illustrates the limitations of a framework that is entirely based on the standard ionisation and crystal form factors, and points towards the need for the general response-function-based formalism we pushed forward recently [1,2]. For the models that require non-standard atomic and crystal response functions, we use the response functions of [1,2] to calculate the DM-induced electronic transition rate in atomic and crystal detectors, and to present 90% confidence level exclusion limits on the strength of the DM-electron interaction from the null results reported by XENON10, XENON1T, EDELWEISS and SENSEI., Comment: 35 pages, 6 figures

We review the class of materials known as polar metals, in which polarity and metallicity coexist in the same phase. While the notion of polar metals was first invoked more than 50 years ago, their practical realization has proved challenging, since the itinerant carriers required for metallicity tend to screen any polarization. Huge progress has been made in the last decade, with many mechanisms for combining polarity and metallicity proposed, and the first examples, LiOsO3 and WTe2, identified experimentally. The availability of polar metallic samples has opened a new paradigm in polar metal research, with implications in the fields of topology, ferroelectricity, magnetoelectricity, spintronics, and superconductivity. Here, we review the principles and techniques that have been developed to design and engineer polar metals and describe some of their interesting properties, with a focus on the most promising directions for future work.

Dynamical perturbations modify the states of classical systems in surprising ways and give rise to important applications in science and technology. For example, Floquet engineering exploits the possibility of band formation in the frequency domain when a strong, periodic variation is imposed on parameters such as spring constants. We describe here Kapitza engineering, where a drive field oscillating at a frequency much higher than the characteristic frequencies for the linear response of a system changes the potential energy surface so much that maxima found at equilibrium become local minima, in precise analogy to the celebrated Kapitza pendulum where the unstable inverted configuration, with the mass above rather than below the fulcrum, actually becomes stable. Our starting point is a quantum field theory of the Ginzburg-Devonshire type, suitable for many condensed matter systems, including particularly ferroelectrics and quantum paralectrics. We show that an off-resonance oscillatory electric field generated by a laser-driven THz source can induce ferroelectric order in the quantum-critical limit. Heating effects are estimated to be manageable using pulsed radiation; ``hidden" radiation-induced order can persist to low temperatures without further pumping due to stabilization by strain. We estimate the Ginzburg-Devonshire free-energy coefficients in SrTiO${}_{3}$ using density-functional theory (DFT) and the stochastic self-consistent harmonic approximation accelerated by a machine-learned force field. Although we find that SrTiO${}_{3}$ is not an optimal choice for Kapitza stabilization, we show that scanning for further candidate materials can be performed at the computationally convenient density-functional theory level. We suggest second-harmonic-generation, soft-mode-spectroscopy, and X-ray-diffraction experiments to characterize the induced order., Comment: 9+4 pages, 5+2 figures, submitted to Physical Review X

We use a combination of density functional theory and Monte Carlo calculations to calculate the surface magnetization in magnetoelectric $\mathrm{Cr_2O_3}$ at finite temperatures. Such antiferromagnets, lacking both inversion and time-reversal symmetries, are required by symmetry to posses an uncompensated magnetization density on particular surface terminations. Here, we first show that the uppermost layer of magnetic moments on the $(001)$ surface remain paramagnetic at the bulk N\'{e}el temperature, bringing the theoretical estimate of surface magnetization density in line with experiment. We demonstrate that the lower surface ordering temperature compared to bulk is a generic feature of surface magnetization when the termination reduces the effective Heisenberg coupling. We then propose two methods by which the surface magnetization in $\mathrm{Cr_2O_3}$ could be stabilised at higher temperatures. Specifically, we show that the effective coupling of surface magnetic ions can be drastically increased either by a different choice of surface Miller plane, or by $\mathrm{Fe}$ doping. Our findings provide an improved understanding of surface magnetization properties in AFMs., Comment: Supplementary material included as appendix

We examine the role of charge, structural, and spin degrees of freedom in the previously poorly understood phase transition in the 5$d^1$ transition-metal double perovskite Cs$_2$TaCl$_6$, using a combination of computational and experimental techniques. Our heat capacity measurements of single-crystalline Cs$_2$TaCl$_6$, reveal a clear anomaly at the transition temperature, $T_\mathrm{Q}$, which was not previously observed in polycrystalline samples. Density functional calculations indicate the emergence of local charge quadrupoles in the cubic phase, mediated by the paramagnetic spins or local structural distortions which then develop into long-range ordered charge quadrupoles in the tetragonal phase. Our resonant elastic x-ray scattering on Cs$_2$TaCl$_6$, single crystals lend support to our calculations. Our work provides new insight into the phase transition in Cs$_2$TaCl$_6$, at $T_\mathrm{Q}$, and demonstrates the utility of this combination of techniques in understanding the complex physics of hidden orders in paramagnetic spin-orbit-entangled compounds.

We present a density-functional theory (DFT) study of the structural, electronic, and chemical bonding behaviour in germanium (Ge)-doped vanadium dioxide (VO$_2$). Our motivation is to explain the reported increase of the metal-insulator transition temperature under Ge doping and to understand how much of the fundamental physics and chemistry behind it can be captured at the conventional DFT level. We model doping using a supercell approach, with various concentrations and different spatial distributions of Ge atoms in VO$_2$. Our results suggest that the addition of Ge atoms strongly perturbs the high-symmetry metallic rutile phase and induces structural distortions that partially resemble the dimerization of the experimental insulating structure. Our work, therefore, hints at a possible explanation of the observed increase in transition temperature under Ge doping, motivating further studies into understanding the interplay of structural and electronic transitions in VO$_2$.

The relaxor ferroelectric transition in Cd$_2$Nb$_2$O$_7$ is thought to be described by the unusual condensation of two $\Gamma$-centered phonon modes, $\Gamma_4^-$ and $\Gamma_5^-$. However, their respective roles have proven to be ambiguous, with disagreement between $\textit{ab initio}$ studies, which favor $\Gamma_4^-$ as the primary mode, and global crystal refinements, which point to $\Gamma_5^-$ instead. Here, we resolve this issue by demonstrating from x-ray pair distribution function measurements that locally, $\Gamma_4^-$ dominates, but globally, $\Gamma_5^-$ dominates. This behavior is consistent with the near degeneracy of the energy surfaces associated with these two distortion modes found in our own $\textit{ab initio}$ simulations. Our first-principles calculations also show that these energy surfaces are almost isotropic, providing an explanation for the numerous structural transitions found in Cd$_2$Nb$_2$O$_7$, as well as its relaxor behavior. Our results point to several candidate descriptions of the local structure, some of which demonstrate two-in/two-out behavior for Nb displacements within a given Nb tetrahedron. Although this suggests the possibility of a charge analog of spin ice in Cd$_2$Nb$_2$O$_7$, our results are more consistent with a Heisenberg-like description for dipolar fluctuations rather than an Ising one. We hope this encourages future experimental investigations of the Nb and Cd dipolar fluctuations, along with their associated mode dynamics., Comment: 9 pages, 6 figures, published in Physical Review Research

We develop a method combining machine learning (ML) and density functional theory (DFT) to predict low-energy polymorphs by introducing physics-guided descriptors based on structural distortion modes. We systematically generate crystal structures utilizing the distortion modes and compute their energies with single-point DFT calculations. We then train a ML model to identify low-energy configurations on the material's high-dimensional potential energy surface. Here, we use BiFeO3 as a case study and explore its phase space by tuning the amplitudes of linear combinations of a finite set of distinct distortion modes. Our procedure is validated by rediscovering several known metastable phases of BiFeO3 with complex crystal structures, and its efficiency is proved by identifying 21 new low-energy polymorphs. This approach proposes a new avenue toward accelerating the prediction of low-energy polymorphs in solid-state materials.

We discuss the second-order magnetoelectric effect, in which a quadratic or bilinear electric field induces a linear magnetization, in terms of the ferroic ordering of magnetic octupoles. We present the decomposition of a general rank-3 tensor into its irreducible spherical tensors, then reduce the decomposition to the specific case of the magnetic octupole tensor, $\mathcal{M}_{ijk} = \int \mu_i (\mathbf{r}) r_j r_k d^3 \mathbf{r}$. We use first-principles density functional theory to compute the size of the local magnetic multipoles on the chromium ions in the prototypical magnetoelectric Cr$_2$O$_3$, and show that, in addition to the well established local magnetic dipoles and magnetoelectric multipoles, the magnetic octupoles are non-zero. The magnetic octupoles in Cr$_2$O$_3$ have an anti-ferroic arrangement, so their net second-order magnetoelectric response is zero. Therefore they form a kind of hidden order, which could be revealed as a linear magnetic (antiferromagnetic) response to a non-zone-center (uniform) quadratic electric field.

We use a combination of symmetry analysis, phenomenological modelling and first-principles density functional theory to explore the interplay between the magnetic ground state and the detailed atomic structure in the hexagonal rare-earth manganites. We find that the magnetic ordering is sensitive to a breathing mode distortion of the Mn and O ions in the $ab$ plane, which is described by the K\textsubscript{1} mode of the high-symmetry structure. Our density functional calculations of the magnetic interactions indicate that this mode particularly affects the single-ion anisotropy and the inter-planar symmetric exchanges. By extracting the parameters of a magnetic model Hamiltonian from our first-principles results, we develop a phase diagram to describe the magnetic structure as a function of the anisotropy and exchange interactions. This in turn allows us to explain the dependence of the magnetic ground state on the identity of the rare-earth ion and on the K\textsubscript{1} mode.

We report the development of a combined machine-learning and high-throughput density functional theory (DFT) framework to accelerate the search for new ferroelectric materials. The framework can predict potential ferroelectric compounds using only elemental composition as input. A series of machine-learning algorithms initially predict the possible stable and insulating stoichiometries with a polar crystal structure, necessary for ferroelectricity, within a given chemical composition space. A classification model then predicts the point groups of these stoichiometries. A subsequent series of high-throughput DFT calculations finds the lowest energy crystal structure within the point group. As a final step, non-polar parent structures are identified using group theory considerations, and the values of the spontaneous polarization are calculated using DFT. By predicting the crystal structures and the polarization values, this method provides a powerful tool to explore new ferroelectric materials beyond those in existing databases.

We develop a general theory to classify magnetic skyrmions and related spin textures in terms of their magnetoelectric multipoles. Since magnetic skyrmions are now established in insulating materials, where the magnetoelectric multipoles govern the linear magnetoelectric response, our classification provides a recipe for manipulating the magnetic properties of skyrmions using applied electric fields. We apply our formalism to skyrmions and anti-skyrmions of different helicities, as well as to magnetic bimerons, which are topologically, but not geometrically, equivalent to skyrmions. We show that the non-zero components of the magnetoelectric multipole and magnetoelectric response tensors are uniquely determined by the topology, helicity and geometry of the spin texture. Therefore, we propose straightforward linear magnetoelectric response measurements as an alternative to Lorentz microscopy for characterizing insulating skyrmionic textures., Comment: 6 pages, 4 figures

In condensed-matter systems, competition between ground states at phase boundaries can lead to significant changes in material properties under external stimuli, particularly when these ground states have different crystal symmetries. A key scientific and technological challenge is to stabilize and control coexistence of symmetry-distinct phases with external stimuli. Using BiFeO3 (BFO) layers confined between layers of the dielectric TbScO3 as a model system, we stabilize the mixed-phase coexistence of centrosymmetric and non-centrosymmetric BFO phases with antipolar, insulating and polar, semiconducting behavior, respectively at room temperature. Application of in-plane electric (polar) fields can both remove and introduce centrosymmetry from the system resulting in reversible, nonvolatile interconversion between the two phases. This interconversion between the centrosymmetric insulating and non-centrosymmetric semiconducting phases coincides with simultaneous changes in the non-linear optical response of over three orders of magnitude, a change in resistivity of over five orders of magnitude, and a change in the polar order. Our work establishes a materials platform allowing for novel cross-functional devices which take advantage of changes in optical, electrical, and ferroic responses., Comment: L Caretta and Y-T Shao contributed equally. 64 pages, 4 figures, 25 supplemental figures, 1 supplemental table

We present an inexpensive first-principles approach for describing quantum paraelectricity that combines density functional theory (DFT) treatment of the electronic subsystem with quantum mechanical treatment of the ions through solution of the single-particle Schr\"odinger equation with the DFT-calculated potential. Using BaTiO$_3$, SrTiO$_3$ and KTaO$_3$ as model systems, we show that the approach can straightforwardly distinguish between ferroelectric, paraelectric and quantum paraelectric materials, based on simple quantities extracted from standard density functional and density functional perturbation theories. We calculate the influence of isotope substitution and strain on the quantum paraelectric behavior, and find that, while complete replacement of oxygen-16 by oxygen-18 has a surprisingly small effect, experimentally accessible strains can induce large changes. Finally, we collect the various choices for the phonon mass that have been introduced in the literature. We identify those that are most physically meaningful by comparing with our results that avoid such a choice through the use of mass-weighted coordinates.

Magnetic fields have been regarded as an additional stimulus for electro- and photocatalytic reactions, but not as a direct trigger for catalytic processes. Multiferroic/magnetoelectric materials, whose electrical polarization and surface charges can be magnetically altered, are especially suitable for triggering and control of catalytic reactions solely with magnetic fields. Here, we demonstrate that magnetic fields can be employed as an independent input energy source for hydrogen harvesting by means of the magnetoelectric effect. Composite multiferroic CoFe2O4-BiFeO3 core-shell nanoparticles act as catalysts for the hydrogen evolution reaction (HER) that is triggered when an alternating magnetic field is applied to an aqueous dispersion of the magnetoelectric nanocatalysts. Based on density functional calculations, we propose that the hydrogen evolution is driven by changes in the ferroelectric polarization direction of BiFeO3 caused by the magnetoelectric coupling. We believe our findings will open new avenues towards magnetically induced renewable energy harvesting., Comment: 26pages including supplementary information, 4 figures

Magnetic Compton scattering is an established tool for probing magnetism in ferromagnetic or ferrimagnetic materials with a net spin polarization. Here we show that, counterintuitively, {\it non-magnetic} systems can also have a non-zero magnetic Compton profile, provided that space-inversion symmetry is broken. The magnetic Compton profile is antisymmetric in momentum and, if the inversion symmetry is broken by an electric-field switchable ferroelectric distortion, can be reversed using an electric field. We show that the underlying physics of the magnetic Compton profile and its electrical control are conveniently described in terms of $k$-space magnetoelectric multipoles, which are reciprocal to the real-space charge dipoles associated with the broken inversion symmetry. Using the prototypical ferroelectric lead titanate, PbTiO$_3$, as an example, we show that the ferroelectric polarization introduces a spin asymmetry in momentum space that corresponds to a pure $k$-space magnetoelectric toroidal moment. This in turn manifests in an antisymmetric magnetic Compton profile which can be reversed using an electric field. Our work suggests an experimental route to directly measuring and tuning hidden $k$-space magnetoelectric multipoles via their magnetic Compton profile., Comment: 6 pages, 4 figures

"Underlying the whole treatment is the assumption that the physical properties of a solid are closely related to its structure, and that the first step to understanding the physical properties is to understand the structure." Helen D. Megaw, Preface to Ferroelectricity in Crystals, Methuen & Co Ltd, London, 1957.

The surface charge associated with the spontaneous polarization in ferroelectrics is well known to cause a depolarizing field that can be particularly detrimental in the thin-film geometry desirable for microelectronic devices. Incomplete screening of the surface charge, for example by metallic electrodes or surface adsorbates, can lead to the formation of domains, suppression or reorientation of the polarization, or even stabilization of a higher energy non-polar phase . A huge amount of research and development effort has been invested in understanding the depolarizing behavior and minimizing its unfavorable effects. Here we demonstrate the opposite behavior: A strong polarizing field that drives thin films of materials that are centrosymmetric and paraelectric in their bulk form into a non-centrosymmetric, polar state. We illustrate the behavior using density functional computations for perovskite-structure potassium tantalate, KTaO$_3$, which is of considerable interest for its high dielectric constant, proximity to a quantum critical point and superconductivity. We then provide a simple recipe to identify whether a particular material and film orientation will exhibit the effect, and develop an electrostatic model to estimate the critical thickness of the induced polarization in terms of well-known material parameters. Our results provide practical guidelines for exploiting the electrostatic properties of thin-film ionic insulators to engineer novel functionalities for nanoscale devices., Comment: Version 2 is updated to include 3 appendices A) with DOSs for larger slabs, B) with more details of the derivations, and C) with the Matlab code for the model calculation. (Also fixed a couple of typos.)

Higgs and Goldstone modes, well known in high energy physics, have been realized in a number of condensed matter physics contexts, including superconductivity and magnetism. The Goldstone-Higgs concept is also applicable to and gives rise to new insights on structural phase transitions. Here, we show that the Leggett mode, a collective mode observed in multi-band superconductors, also has an analog in crystallographic phase transitions. Such structural Leggett modes can occur in the phase channel as in the original work of Leggett, \href{https://doi.org/10.1143/PTP.36.901}{Prog.\ Theor.\ Phys.\ \textbf{36}, 901 (1966)}. That is, they are antiphase Goldstone modes (anti-phasons). In addition, a new collective mode can also occur in the amplitude channel, an out-of phase (antiphase) Higgs mode, that should be observable in multi-band superconductors as well. We illustrate the existence and properties of these structural Leggett modes using the example of the pyrochlore relaxor ferroelectric, Cd$_2$Nb$_2$O$_7$., Comment: 7 pages, 2 figures

We present a density functional theory study of the low-temperature structural, magnetic, and proposed charge-quadrupolar ordering in the double perovskite, Ba$_2$MgReO$_6$. Ba$_2$MgReO$_6$ is a spin-orbit-driven Mott insulator with a symmetry-lowering structural phase transition at 33\,K and a canted antiferromagnetic ordering of $5d^1$ Re magnetic moments at 18\,K. Our calculations confirm the existence of the proposed charge quadrupolar order and discover an additional, previously hidden, ordered charge quadrupolar component. By separately isolating the structural distortions and the orientations of the magnetic dipoles, we determine the relationship between the charge quadrupolar, structural and magnetic orders, finding that either a local structural distortion or a specific magnetic dipole orientation is required to lower the symmetry and enable the existence of charge quadrupoles. Our work establishes the crystal structure -- magnetic dipole -- charge multipole relationship in Ba$_2$MgReO$_6$ and related 5$d^1$ double perovskites, and illustrates a method for separating and analyzing the contributions and interactions of structural, magnetic, and charge orders beyond the usual dipole level.

We present a combined theoretical and experimental investigation of the anti-symmetric Compton profile in LiNiPO$_4$ as a possible probe for magneto-electric toroidal moments. Understanding as well as detecting such magneto-electric multipoles is an active area of research in condensed matter physics. Our calculations, based on density functional theory, indicate an anti-symmetric Compton profile in the direction of the $t_y$ toroidal moment in momentum space, with the computed anti-symmetric profile around four orders of magnitude smaller than the total profile. The difference signal that we measure is consistent with the computed profile, but of the same order of magnitude as the statistical errors and systematic uncertainties of the experiment. Our results motivate further theoretical work to understand the factors that influence the size of the anti-symmetric Compton profile, and to identify materials exhibiting larger effects.

In condensed matter systems, the atoms, electrons or spins can sometimes arrange themselves in ways that result in unexpected properties but that cannot be detected by conventional experimental probes. Several historical and contemporary examples of such hidden orders are known and more are awaiting discovery, perhaps in the form of more complex composite, entangled or dynamical hidden orders., Comment: Author Accepted Manuscript

We develop a formalism to describe the scattering of dark matter (DM) particles by electrons bound in crystals for a general form of the underlying DM-electron interaction. Such a description is relevant for direct-detection experiments of DM particles lighter than a nucleon, which might be observed in operating DM experiments via electron excitations in semiconductor crystal detectors. Our formalism is based on an effective theory approach to general non-relativistic DM-electron interactions, including the anapole, and magnetic and electric dipole couplings, combined with crystal response functions defined in terms of electron wave function overlap integrals. Our main finding is that, for the usual simplification of the velocity integral, the rate of DM-induced electronic transitions in a semiconductor material depends on at most five independent crystal response functions, four of which were not known previously. We identify these crystal responses, and evaluate them using density functional theory for crystalline silicon and germanium, which are used in operating DM direct detection experiments. Our calculations allow us to set 90% confidence level limits on the strength of DM-electron interactions from data reported by the SENSEI and EDELWEISS experiments. The novel crystal response functions discovered in this work encode properties of crystalline solids that do not interact with conventional experimental probes, suggesting the use of the DM wind as a probe to reveal new kinds of hidden order in materials., Comment: 25 pages, 12 figures, typos corrected, clarifying comment added