Multiferroic quantum criticality

Effects of third-neighbor interactions on the frustrated quantum Ising model

We investigate thermal and quantum phase transitions of the J_{1}-J_{2}-J_{3} transverse Ising model on the square lattice. The model is studied within a cluster mean-field decoupling, which allows us to describe phase diagrams and the free-energy landscape in the neighborhood of phase transitions. Our findings indicate that the third-neighbor coupling (J_{3}) can affect the nature of phase transitions of the model. In particular, ferromagnetic third-neighbor couplings favor the onset of continuous order-disorder phase transitions, eliminating the tricritical point of the superantiferromagnetic-paramagnetic (SAFM-PM) phase boundary. On the other hand, the enhancement of frustration introduced by weak antiferromagnetic J_{3} gives rise to the staggered dimer phase favoring the onset of discontinuous classical phase transitions. Moreover, we find that quantum annealed criticality (QAC), which takes place when the classical discontinuous phase transition becomes critical by the enhancement of quantum fluctuations introduced by the transverse magnetic field, is eliminated from the SAFM-PM phase boundary by a relatively weak ferromagnetic J_{3}. Nevertheless, this change in the nature of phase transitions can still be observed in the presence of antiferromagnetic third-neighbor couplings being also found in the staggered-dimer phase boundary. Therefore, our findings support that QAC persists under the presence of frustrated antiferromagnetic third-neighbor couplings and is suppressed when these couplings are ferromagnetic, suggesting that frustration plays a central role in the onset of QAC.

When Quantum Fluctuations Meet Structural Instabilities: The Isotope- and Pressure-Induced Phase Transition in the Quantum Paraelectric NaOH

Anhydrous sodium hydroxide, a common and structurally simple compound, shows spectacular isotope effects: NaOD undergoes a first-order transition, which is absent in NaOH. By combining ab initio electronic structure calculations with Feynman path integrals, we show that NaOH is an unusual example of a quantum paraelectric: zero-point quantum fluctuations stretch the weak hydrogen bonds (HBs) into a region where they are unstable and break. By strengthening the HBs via isotope substitution or applied pressure, the system can be driven to a broken-symmetry antiferroelectric phase. In passing, we provide a simple quantitative criterion for HB breaking in layered crystals and show that nuclear quantum effects are crucial in paraelectric to ferroelectric transitions in hydrogen-bonded hydroxides.

Dielectric Relaxation by Quantum Critical Magnons

We report the experimental observation of dielectric relaxation by quantum critical magnons. Complex capacitance measurements reveal a dissipative feature with a temperature-dependent amplitude due to low-energy lattice excitations and an activation behavior of the relaxation time. The activation energy softens close to a field-tuned magnetic quantum critical point at H=H_{c} and follows single-magnon energy for H>H_{c}, showing its magnetic origin. Our study demonstrates the electrical activity of coupled low-energy spin and lattice excitations, an example of quantum multiferroic behavior.

Octahedra-Tilted Control of Displacement Disorder and Dielectric Relaxation in Mn-Doped SrTiO3 Single Crystals

Strontium titanate SrTiO₃ (STO) is a canonical example of a quantum paraelectric, and its doping with manganese ions unlocks its potential as a quantum multiferroic candidate. However, to date, the specifics of incorporation of the manganese ion into the perovskite lattice and its impact on structure-property relationships are debatable questions. Herein, using high-precision X-ray diffraction of a Mn (2 atom %)-doped STO single crystal, clear fingerprints of the displacement disorder of Mn cations in the perovskite B-sublattice are observed. Moreover, near the temperature of the antiferrodistortive transition, the off-center Mn position splits in two, providing the unequal potential barrier's distribution for possible local atomic hopping. A link with this was found via analysis of the dielectric response that reveals two Arrhenius-type relaxation processes with similar activation energies (35 and 43 meV) and attempt frequencies (1 × 10¹¹ and ∼1.6 × 10¹⁰ Hz), suggesting similar dielectric relaxation mechanisms.

Competing electronic states emerging on polar surfaces

Excess charge on polar surfaces of ionic compounds is commonly described by the two-dimensional electron gas (2DEG) model, a homogeneous distribution of charge, spatially-confined in a few atomic layers. Here, by combining scanning probe microscopy with density functional theory calculations, we show that excess charge on the polar TaO2 termination of KTaO3(001) forms more complex electronic states with different degrees of spatial and electronic localization: charge density waves (CDW) coexist with strongly-localized electron polarons and bipolarons. These surface electronic reconstructions, originating from the combined action of electron-lattice interaction and electronic correlation, are energetically more favorable than the 2DEG solution. They exhibit distinct spectroscopy signals and impact on the surface properties, as manifested by a local suppression of ferroelectric distortions.

Evidence for a single-layer van der Waals multiferroic

Multiferroic materials have attracted wide interest because of their exceptional static^1-3 and dynamical^4-6 magnetoelectric properties. In particular, type-II multiferroics exhibit an inversion-symmetry-breaking magnetic order that directly induces ferroelectric polarization through various mechanisms, such as the spin-current or the inverse Dzyaloshinskii-Moriya effect^3,7. This intrinsic coupling between the magnetic and dipolar order parameters results in high-strength magnetoelectric effects^3,8. Two-dimensional materials possessing such intrinsic multiferroic properties have been long sought for to enable the harnessing of magnetoelectric coupling in nanoelectronic devices^1,9,10. Here we report the discovery of type-II multiferroic order in a single atomic layer of the transition-metal-based van der Waals material NiI₂. The multiferroic state of NiI₂ is characterized by a proper-screw spin helix with given handedness, which couples to the charge degrees of freedom to produce a chirality-controlled electrical polarization. We use circular dichroic Raman measurements to directly probe the magneto-chiral ground state and its electromagnon modes originating from dynamic magnetoelectric coupling. Combining birefringence and second-harmonic-generation measurements with theoretical modelling and simulations, we detect a highly anisotropic electronic state that simultaneously breaks three-fold rotational and inversion symmetry, and supports polar order. The evolution of the optical signatures as a function of temperature and layer number surprisingly reveals an ordered magnetic polar state that persists down to the ultrathin limit of monolayer NiI₂. These observations establish NiI₂ and transition metal dihalides as a new platform for studying emergent multiferroic phenomena, chiral magnetic textures and ferroelectricity in the two-dimensional limit.

Atomic Scale Control and Visualization of Topological Quantum Phase Transition in π-Conjugated Polymers Driven by Their Length

Quantum phase transitions (QPTs) driven by quantum fluctuations are transitions between distinct quantum phases of matter. At present, they are poorly understood and not readily controlled. Here, scanning tunneling microscopy (STM) and noncontact atomic force microscopy (nc-AFM) are used to explore atomic scale control over quantum phase transitions between two different topological quantum states of a well-defined π-conjugated polymer. The phase transition is driven by a pseudo Jahn-Teller effect that is activated above a certain polymer chain length. In addition, theoretical calculations indicate the presence of long-lasting coherent fluctuations between the polymer's two quantum phases near the phase transition, at finite temperature. This work thus presents a new way of exploring atomic-scale control over QPTs and indicates that emerging quantum criticality in the vicinity of a QPT can give rise to new states of organic matter.

Optical phonon contribution to the thermal conductivity of a quantum paraelectric

Motivated by recent experimental findings, we study the contribution of a quantum critical optical phonon branch to the thermal conductivity of a paraelectric system. We consider the proximity of the optical phonon branch to transverse acoustic phonon branch and calculate its contribution to the thermal conductivity within the Kubo formalism. We find a low temperature power law dependence of the thermal conductivity asT^α, with 1 <α< 2, (lower thanT³behavior) due to optical phonons near the quantum critical point. This result is in accord with the experimental findings and indicates the importance of quantum fluctuations in the thermal conduction in these materials.

Highly Confined Phonon Polaritons in Monolayers of Perovskite Oxides

Two-dimensional (2D) materials are able to strongly confine light hybridized with collective excitations of atoms, enabling electric-field enhancements and novel spectroscopic applications. Recently, freestanding monolayers of perovskite oxides have been synthesized, which possess highly infrared-active phonon modes and a complex interplay of competing interactions. Here, we show that this new class of 2D materials exhibits highly confined phonon polaritons by evaluating central figures of merit for phonon polaritons in the tetragonal phases of the 2D perovskites SrTiO₃, KTaO₃, and LiNbO₃, using density functional theory calculations. Specifically, we compute the 2D phonon-polariton dispersions, the propagation-quality, confinement, and deceleration factors, and we show that they are comparable to those found in the prototypical 2D dielectric hexagonal boron nitride. Our results suggest that monolayers of perovskite oxides are promising candidates for polaritonic platforms that enable new possibilities in terms of tunability and spectral ranges.

Large Magnetic Moment in Flexoelectronic Silicon at Room Temperature

Time-dependent rotational electric polarizations have been proposed to generate temporally varying magnetic moments, for example, through a combination of ferroelectric polarization and optical phonons. This phenomenon has been called dynamical multiferroicity, but explicit experimental demonstrations have been elusive to date. Here, we report the detection of a temporal magnetic moment as high as 1.2 μ_B/atom in a charge-doped thin film of silicon under flexural strain. We demonstrate that the magnetic moment is generated by a combination of electric polarization arising from a flexoelectronic charge separation along the strain gradient and the deformation potential of phonons. The effect can be controlled by adjusting the external strain gradient, doping concentration, and dopant and can be regarded as a dynamical multiferroic effect involving flexoelectronic polarization instead of ferroelectricity. The discovery of a large magnetic moment in silicon may enable the use of nonmagnetic and nonferroelectric semiconductors in various multiferroic and spintronic applications.

Non-collinear magnetism & multiferroicity: the perovskite case

The most important types of non-collinear magnetic orders that are realized in simple perovskite oxides are outlined in relation to multiferroicity. These orders are classified and rationalized in terms of a mimimal spin Hamiltonian, based on which the notion of spin-driven ferroelectricity is illustrated. These concepts find direct application in reference materials such as BiFeO3, GdFeO3 and TbMnO3 whose multiferroic properties are briefly reviewed.

Thermal magnetic fluctuations of a ferroelectric quantum critical point

Entanglement of two different quantum orders is of an interest of the modern condensed matter physics. One of the examples is the dynamical multiferroicity, where fluctuations of electric dipoles lead to magnetization. We investigate this effect at finite temperature and demonstrate an elevated magnetic response of a ferroelectric near the ferroelectric quantum critical point (FE QCP). We calculate the magnetic susceptibility of a bulk sample on the paraelectric side of the FE QCP at finite temperature and find enhanced magnetic susceptibility near the FE QCP. We propose quantum paraelectric strontium titanate as a candidate material to search for dynamic multiferroicity. We estimate the magnitude of the magnetic susceptibility for this material and find that it is detectable experimentally.

Finite temperature effects in quantum systems with competing scalar orders

The study of the competition or coexistence of different ground states in many-body systems is an exciting and actual topic of research, both experimentally and theoretically. Quantum fluctuations of a given phase can suppress or enhance another phase depending on the nature of the coupling between the order parameters, their dynamics and the dimensionality of the system. The zero temperature phase diagrams of systems with competing scalar order parameters with quartic and bilinear coupling terms have been previously studied for the cases of a zero temperature bicritical point and of coexisting orders. In this work, we apply theMatsubara summationtechnique from finite temperature quantum field theory to introduce the effects of thermal fluctuations on the effective potential of these systems. This is essential to make contact with experiments. We consider two and three-dimensional materials characterized by a Lorentz invariant quantum critical theory, i.e., with dynamic critical exponentz= 1, such that time and space scale in the same way. We obtain that in both cases, thermal fluctuations lead to weak first-order temperature phase transitions, at which coexisting phases arising from quantum corrections become unstable. We show that above this critical temperature (Tc), the system presents scaling behavior consistent with that approaching a quantum critical point. Below the transition the specific heat has a thermally activated contribution with a gap related to the size of the domains of the ordered phases. We obtain thatTcdecreases as a function of the distance to the zero temperature classical bicritical point (ZTCBP) in the coexistence region, implying that in our approach, the system attains the highestTcabove the fine tuned value of this ZTCBP.

Metaelectric multiphase transitions in a highly polarizable molecular crystal

Metaelectric transition, i.e. an abrupt increase in polarization with an electric field is just a phase change phenomenon in dielectrics and attracts increasing interest for practical applications such as electrical energy storage and highly deformable transducers. Here we demonstrate that both field-induced metaelectric transitions and temperature-induced phase transitions occur successively on a crystal of highly polarizable bis-(1H-benzimidazol-2-yl)-methane (BI2C) molecules. In each molecule, two switchable polar subunits are covalently linked with each other. By changing the NH hydrogen location, the low- and high-dipole states of each molecule can be interconverted, turning on and off the polarization of hydrogen-bonded molecular ribbons. In the low-temperature phase III, the tetragonal crystal lattice comprises orthogonally crossed arrays of polar ribbons made up of a ladder-like hydrogen-bond network of fully polarized molecules. The single-step metaelectric transition from this phase III corresponds to the forced alignment of antiparallel dipoles typical of antiferroelectrics. By the transition to the intermediate-temperature phase II, the polarity is turned off for half of the ribbons so that the nonpolar and polar ribbons are orthogonal to each other. Considering also the ferroelastic-like crystal twinning, the doubled steps of metaelectric transitions observed in the phase II can be explained by the additional switching at different critical fields, by which the nonpolar ribbons undergo "metadielectric" molecular transformation restoring the strong polarization. This mechanism inevitably brings about exotic phase change phenomena transforming the multi-domain state of a homogeneous phase into an inhomogeneous (phase mixture) state.

Multiband Quantum Criticality of Polar Metals

Motivated by recent experimental realizations of polar metals with broken inversion symmetry, we explore the emergence of strong correlations driven by criticality when the polar transition temperature is tuned to zero. Overcoming previously discussed challenges, we demonstrate a robust mechanism for coupling between the critical mode and electrons in multiband metals. We identify and characterize several novel interacting phases, including non-Fermi liquids, when band crossings are close to the Fermi level and present their experimental signatures for three generic types of band crossings.

Tuning ferroelectricity and ferromagnetism in BiFeO3/BiMnO3 superlattices

Multiferroic materials with multifunctional characteristics play a critical role in the field of microelectronics. In a perovskite oxide, ferroelectric polarization and ferromagnetism usually cannot coexist in a single-phase material at the same time. In this work, we design a superlattice structure composed of alternating BiFeO₃ and BiMnO₃ layers and illustrate how tuning the supercell size of epitaxial BiFeO₃/BiMnO₃ superlattices facilitates ferroelectric polarization while maintaining relatively strong ferromagnetism. A comprehensive investigation reveals that the enhanced ferroelectric polarization of BiMnO₃ layers originates from the induction effect induced by a strong polarization field generated by the adjacent ferroelectric BiFeO₃ layers. For the magnetic behavior, we consider the existence of interfacial antiferromagnetic superexchange interaction of Fe-O-Mn between BiFeO₃ and BiMnO₃ layers in our superlattices. This modulation effect of artificial superlattices provides a platform to accurately control the multiple order parameters in a multiferroic oxide system.

Effect of strain and doping on the polar metal phase in LiOsO3

We systematically investigate the effect of strain and doping on the polar metal phase in lithium osmate, LiOsO₃, using first-principles calculations. We demonstrate that the polar metal phase in LiOsO₃ can be controlled by biaxial strain. Based on density functional calculations, we show that a compressive biaxial strain enhances the stability of the polar R3c phase. On the other hand, a tensile biaxial strain favors the centrosymmetric [Formula: see text] structure. Thus, strain emerges as a promising control parameter over polar metallicity in this material. We uncover a strain-driven quantum phase transition under tensile strain, and highlight intriguing properties that could emerge in the vicinity of this polar to non-polar metal transition. We examine the effect of charge doping on the polar metal phase. By means of electrostatic doping as well as supercell calculations, we find that screening from additional charge carriers, expected to suppress the polar distortions, have only a small effect on them. Rather remarkably, and in contrast to conventional ferroelectrics, the polar metal phase in LiOsO₃ remains robust against charge doping up to large doping values.

Multiferroics beyond electric-field control of magnetism

Multiferroic materials, with their combined and coupled magnetism and ferroelectricity, provide a playground for studying new physics and chemistry as well as a platform for the development of novel devices and technologies. Based on my July 2017 Royal Society Inaugural Lecture, I review recent progress and propose future directions in the fundamentals and applications of multiferroics, with a focus on initially unanticipated developments outside of the core activity of electric-field control of magnetism.