Ferromagnetic Metallic State Research Articles

Ground state of a three-band Hubbard model with Hund’s coupling: Janus-faced behavior in presence of magnetic order

We study the ground state of the three-band degenerate Hubbard model on a square lattice at integer fillings using the variational slave-spin mean field method. At half-filling, the method reproduces the well known result that the ground state is antiferromagnetic (AF) insulating at smaller values of Hubbard onsite repulsion U, while it becomes Mott insulating with Néel AF order at higher U. Away from half-filling, for two particles per site, we show that the model supports a ferromagnetic (FM) metallic state with fully polarized spins at sufficiently large U. The FM state occurs irrespective of the value of Hund’s coupling J. The ferromagnetism at J = 0 can be explained by the Stoner mechanism while that for J > 0 is shown to arise from the superexchange process. At this band filling, the Hund’s coupling J is known to have the Janus-faced effect on electronic correlations where it enhances correlations at smaller U while reducing it at higher U. We show that these two effects are separated by the paramagnetic (PM) to FM transition point. The former effect is obtained at the PM state while the latter occurs in the FM state. The FM phase also occurs for one particle per site but here Hund’s coupling J reduces the effect of electronic correlations at all U.

Kinetic pathway facilitated by a phase competition to achieve a metastable electronic phase

We show that ground state phase competition significantly decreases the critical cooling rate required for the kinetic avoidance of a first-order phase transition and thus facilitates the creation of metastable electronic states. This principle is revealed for the phase transition between antiferromagnetic charge-orbital-ordered insulating and ferromagnetic metallic states in the so-called colossal magnetoresistive manganite ${\mathrm{Nd}}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_{3}$. In a phase competition situation, we achieve reversible and nonvolatile control of bulk magnetization by $1{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ and resistivity by $\ensuremath{\sim}1000%$ by applying electric pulses to exploit electric heating and subsequent rapid cooling.

Visualization of the contrasting domain configurations during the melting and reappear-then-melting processes in a manganite film

We report cryogenic magnetic force microscopy studies of anisotropic-strained (La0.8Pr0.2)2/3Ca1/3MnO3/NdGaO3(001) thin films. Real-space magnetic imaging reveals a robust charge-ordered insulating (COI) magnetic phase with a strong relaxation feature. Remarkably, in the first melting and reappear-then-melting processes, the ferromagnetic metallic (FMM) domain configurations differ dramatically, showing a droplet-like and a stripe-like pattern, respectively. These observations illustrate that the FMM nuclei are randomly self-organized distributed in the virgin highly COI-dominant phase separation state recorded after zero field cooling. Regardless of how to reach the saturated FMM state, the anisotropic nature of the long-range strain involves in and dominates to form well-ordered FMM stripes eventually. Our results facilitate the control and manipulation of phase separation morphology at the micrometer scale.

Ferroelectricity and ferromagnetism in a VOI2 monolayer: Role of the Dzyaloshinskii-Moriya interaction

Multiferroics with intrinsic ferromagnetism and ferroelectricity are highly desired but rather rare, while most ferroelectric magnets are antiferromagnetic. A recent theoretical work [Phys. Rev. B {\bf 99}, 195434 (2019)] predicted that oxyhalides VO$X_2$ ($X$: halogen) monolayers are two-dimensional multiferroics by violating the empirical $d^0$ rule. Most interestingly, the member VOI$_2$ are predicted to exhibit spontaneous ferromagnetism and ferroelectricity. In this work, we extend the previous study on the structure and magnetism of VOI$_2$ monolayer by using density functional theory and Monte Carlo simulation. The presence of the heavy element iodine with a strong spin-orbit coupling leads an effective Dzyaloshinskii-Moriya interaction in the polar structure, which favors a short-period spiral a magnetic structure.. Another interesting result is that the on-site Coulomb interaction can strongly suppress the polar distortion thus leading to a ferromagnetic metallic state. Therefore, the VOI2 monolayer is either a ferroelectric insulator with spiral magnetism or a ferromagnetic metal, instead of a ferromagnetic ferroelectric system. Our study highlights the key physical role of the Dzyaloshinskii-Moriya interaction.

DFT – GGA calculations of magnetic, elastic, thermodynamic and thermoelectric properties of Co2YAl (Y = Ti, V) full Heusler alloy systems

This study used first principles calculations within the generalized gradient approximation (GGA) via plane-wave pseudo-potential scheme to extensively study the magnetic, elastic, thermodynamic and thermoelectric properties of Co2TiAl and Co2VAl Heusler alloys at their optimized lattice constants. Elastic properties of these alloys were obtained by fitting the stress-strain relationship via Voigt-Reuss-Hill approximations. Thermodynamic properties were calculated within the implementation of thermo_pw package while thermoelectric properties were estimated from non-spin polarized calculations via Boltzmann semi-classical approach as implemented in BoltzTraP package at temperatures between 0 and 800 K. Calculations reaffirmed the stable electronic and magnetic states for the alloys to be half metallic ferromagnetic (HMF) states. The estimated band gaps in the minority spin channels were 0.431 and 0.399 eV for Co2TiAl and Co2VAl alloys respectively and these were justified by their corresponding density of states. The calculated magnetic moments for the respective alloys were 0.949 and 1.978 μB, which agreed with experimental, theoretical and Slater-Pauling rule determined magnetic moments. Elastic constants (C11, C12 and C44) obtained for these cubic systems fulfilled Born-Huang mechanical stability criteria, from which other elastic related quantities were extracted. Elastic calculations predicted these alloys to be metallic bonded, extremely incompressible, highly anisotropic and ductile in nature. Thermodynamic calculations showed that Debye vibrational energies, entropies and constant volume heat capacities of the alloys increased remarkably as temperature increased whereas vibrational free energies decreased steadily with increased temperature. Thermoelectric properties were also determined, with Co2TiAl having higher figure of merit (ZT) than Co2VAl within the investigative temperatures.

Structural, magnetic and magneto-transport properties of Bi0.7-xLaxSr0.3MnO3 manganites

In the present study, the structural, magnetic, and magneto-transport properties of Bi0.7-xLaxSr0.3MnO3 manganites have been investigated. Systematic replacement of Bi3+ with La3+, reduces the distortion in the crystal structure and the system transforms from antiferromagnetic insulating (AFMI) state to ferromagnetic metallic (FMM) state. For partial doping of La3+, the system shows a low temperature drop in ZFC which could be attributed to the spin-glass transition in addition to the antiferromagnetic ordering. dc electrical resistivity describes the insulating behavior of the system which is consistent with antiferromagnetic (AFM) ground state for partial La3+ doping. The activation energy estimated from the small polaron hopping model, shows a systematic decrease as a function of La3+ concentration. The observed results could be explained by considering the dilution of 6s lone pair character of Bi3+ with La3+ doping.

Manipulation of electronic and magnetic properties of Cr2CX2 (X=F,O,OH) monolayer by applying mechanical strains

Adjusting the electronic and magnetic properties of materials by strain engineering is an effective strategy to improve the performance of electronic and spin electronic devices. In this paper, we study the electronic and magnetic properties of Cr2C and Cr2CX2 (X = F, O,OH) under mechanical strain based on density functional theory. In the strain-free state, Cr2C and Cr2CO2 are in the ferromagnetic (FM) metallic ground states, while Cr2CF2 and Cr2C(OH)2 are in the antiferromagnetic (AFM) semiconducting states. Applying tensile strain can enhance the magnetic moments of the Cr atoms of all the Cr2C and Cr2CX2 (X = F, O, OH) systems. The electronic structure can also be affected with the increase of strain, e.g., resulting in narrowing of the band gap of the AFM semiconducting systems (Cr2CF2 and Cr2C(OH)2) and enhancing the spin-splitting of the FM metallic systems (Cr2C and Cr2CO2). The results indicate a possible broadened applicability of strained Cr2C-based MXenes in future spintronics.

Electronic, magnetic and optical properties of transition-metal and hydroxides doped monolayer g-C3N4: a first principles investigation

The graphitic carbon nitride (g-C3N4) is a promising layered two-dimension material with an opened bandgap. It is of interest to explore the tunability of the bandgap together with the magnetism by doping transition metal atoms. In this work, we investigated the transition metals (Mn, Fe, Co, Ni) and their hydroxides doped g-C3N4 monolayers. The electron correlations between the 3d electrons of the doped transition metal atoms are self-consistently calculated and analyzed based on the density functional theory. The magnetism, electronic band structures and optical properties are systematically investigated. It reveals that the transition metal doped g-C3N4 is ferromagnetic (FM) state at small doping concentration, where the two spins show different bandgaps. When the doping is high enough, it turns to metallic antiferromagnetic (AFM) state except that Mn doped g-C3N4 is metallic FM state. On another hand, the system shows variable absorption spectra at different doping level. When the vacancy sites are fully occupied, a large absorption peak appears around 1.5 eV suitable for visible light. Moreover, within the transition metal hydroxides doped g-C3N4, the global ground state shows as AFM, and the absorption spectra within low energy range is distinct due to the presence of hydroxyl group. Therefore, doping with transition metal atoms and hydroxides can effectively tune the bandgap, magnetism and optical properties of g-C3N4 so as to promote its applications.

Impact of uniaxial strain on the electronic and magnetic properties of Sr2CrReO6

Among the double perovskite oxides, Sr2CrReO6 has been attractive a lot of attention due its half-metallic ferrimagnetic nature and the highest magnetic transition temperature of 635 K. Here, we systematically investigated the influence of uniaxial strain along [100]-direction on the electronic and magnetic properties of double perovskite oxide Sr2CrReO6 using first-principle calculations. Our results show that a critical tensile strain of +2% leads the system to the ferromagnetic metallic state from half-metallic ferrimagnetic with a spin-polarization of 64%. Because, tensile strain decreases the anti-ferromagnetic coupling between Cr and Re ions, which results in ferromagnetic ordering. The admixture of Cr/Re dx2−y2, dxz, and dyz orbitals are mainly responsible for metallicity. Along with this, the total magnetic moment gets enhanced and almost close to an integral value of 5 μB for higher tensile strains. On the other hand, compressive strains exhibit no substantial impact on the physical properties of Sr2CrReO6. Moreover, it is also found that spin-polarization optimized with a further increase of tensile strains. Close to half-metallic ferromagnetic state due to tensile strain, this material shows a wide range of scientific and technological applications in spintronics.

Properties of La0.7Ca0.3MnO3 under extreme tensile strain

The complex phase diagram of manganites with simultaneously active spin, charge, orbital, and lattice degrees of freedom continues providing surprises. In a recent groundbreaking experiment, membranes of the perovskite manganite La$_{0.7}$Ca$_{0.3}$MnO$_3$ (LCMO) deposited on a flexible polymer layer were strained up to 8\% [S.~S. Hong {\it et al.}, Science {\bf 368}, 71 (2020)], much more than achieved by regular strain induced by a rigid substrate. By increasing this strain a metal-insulator transition was reported. Here we reproduce the results of the experiments using Monte Carlo simulations of the two-orbital double-exchange model including Jahn-Teller distortions, at hole density $x=1/3$. The full phase diagram with varying temperature and Jahn-Teller coupling $\lambda$ is presented. When the bandwidth $W$ of mobile electrons is reduced, thus when the effective Jahn-Teller coupling $\lambda/W$ is increased, a metal-insulator transition is found in our simulations, between a ferromagnetic metallic state with uniform charge distribution and an insulator with diagonal charge stripes that retains its ferromagnetic character. In between the hole-rich diagonals, staggered orbital order occurs. We also report resistivity and magnetization measurements alongside with spin correlations and charge structure factors. Our overall conclusions are in agreement with the recent experimental and density functional theory results by Hong {\it et al.}, and we confirm much earlier ground state predictions of striped ferromagnetic order using energy optimization techniques by T. Hotta {\it et al.}, Phys. Rev. Lett. {\bf 86}, 4922 (2001). The experimental observation of one of the states predicted by theory suggests that diagonal stripes could be achieved at other hole densities as well, such as $x=1/4$, if LCMO membranes with that hole doping were subject to similar strains.

Orbital Hybridization and Magnetic Coupling at Cuprate–Manganite Interfaces Driven by Manganite Doping

AbstractFundamental understanding of interface mechanisms that generate unexpected physical properties in the cuprate/manganite heterostructures is essential for possible applications as spintronic devices. Here, CaCuO2/La1−xSrxMnO3 (CCO/LSMO) superlattices are investigated, where the infinite‐layer cuprate CCO does not have apical oxygen for Cu in the Ca‐plane so that the Mn–O–Cu superexchange coupling can be only present at the MnO2–(La,Sr)O–CuO2 interface. Two different doping states for the manganites are studied, namely x = 0.1 and x = 0.3, corresponding to the ferromagnetic insulating and ferromagnetic metallic states, respectively, in the manganite phase diagram. Linear and circular dichroism in X‐ray absorption by synchrotron radiation at Cu and Mn L‐edges clearly demonstrate that in the absence of apical oxygen in the cuprate block, the magnetic coupling between the LSMO and CCO is weakly ferromagnetic when LSMO is metallic, while it is antiferromagnetic when LSMO is insulating, along with an increased Cu 3d(3z2–r2) and Mn 3d(3z2–r2) orbital occupation. It is proposed that the Mn 3d valence band upward shift driven by the enhancement of Mn3+ content in the underdoped sample enhances the orbital hybridization. The stronger hybridization at the interface MnO2–(La,Sr)O–CuO2 gives rise to the antiferromagnetic coupling between cuprate and underdoped manganite.

Electronic properties in itinerant ferromagnet SrRu1−xTixO3

Here, we study the electrical transport and specific heat in 4d based ferromagnetic material SrRuO3 and its Ti substituted SrRu1−xTixO3 series (x ⩽ 0.7). The SrRuO3 is a metal and shows itinerant ferromagnetism with transition temperature Tc ∼ 160 K. The nonmagnetic Ti4+ (3d0) substitution would not only weaken the active Ru–O–Ru channel but is also expected to tune the electronic density and electron correlation effect. A metal to insulator transition has been observed around x ∼ 0.4. The nature of charge transport in paramagnetic-metallic state (x ⩽ 0.4) and in insulating state (x > 0.4) follows modified Mott’s variable range hopping model. In ferromagnetic-metallic state, resistivity shows a T2 dependence below Tc which though modifies to T3/2 dependence at low temperature. In Ti substituted samples, temperature range for T3/2 dependence extends to higher temperature. Interestingly, this T3/2 dependence dominates in whole ferromagnetic regime in presence of magnetic field. This evolution of electronic transport behavior can be explained within the framework of Fermi liquid theory and electron–magnon scattering mechanism. The negative magnetoresistance exhibits a hysteresis and a crossover between negative and positive value with magnetic field which is connected with magnetic behavior in series. The decreasing electronic coefficient of specific heat with x supports the increasing insulating behavior in present series. We calculate a high Kadowaki–Woods ratio (x ⩽ 0.3) for SrRuO3 which increases with substitution concentration. This signifies an increasing electronic correlation effect with substitution concentration.

Effect of hybridization on half metallic properties of some diluted chalcopyrites for spintronic applications

Based on the ab initio electronic structure calculations performed by Korring–Kohn–Rostoker method combined with the coherent potential approximation, the effect of transition metals impurities on the electronic states and magnetic properties of ZnXAs2 (X = Sn, Ge) chalcopyrites has been investigated. Electronic density of states, Curie temperature TC, ferromagnetic (FM), antiferromagnetic (AF) and spinglass-like (DLM) energies and their variation as well as crystal field splitting energy ΔCF and exchange interactions Δe and are all discussed in detail. The analysis of the densities of states of Zn(Sn, TM)As2 and Zn(Ge, TM)As2 shows that these compounds exhibit half-metallic character and high-spin ferromagnetic state. The importance of different exchange mechanisms like double exchange, ferromagnetic and antiferromagnetic super-exchange in Zn(Sn, TM)As2 and Zn(Ge, TM)As2 chalcopyrites is also discussed. The result as derived in this report shows that and doped ZnSnAs2 and ZnGeAs2 chalcopyrites exhibit a stable ferromagnetic half metallic state, whereas doping manifests antiferromagnetic and spinglass-like states. These results make Zn(Sn, TM)As2 and Zn(Ge, TM)As2 chalcopyrites useful for spintronic applications.

Uniaxial Strain-Controlled Ground States in Manganite Films.

Strongly correlated perovskite oxides exhibit a plethera of intriguing phenomena and stimulate a great potential for multifunctional device applications. Utilizing tunable uniaxial strain, rather than biaxial or anisotropic strain, delivered from the crystallography of a single crystal substrate to modify the ground state of strongly correlated perovskite oxides has rarely been addressed for phase-space control. Here, we show that the physical properties of La2/3Ca1/3MnO3 (LCMO) films are remarkably different depending on the crystallographic orientations of the orthorhombic NdGaO3 (NGO) substrates. More importantly, the antiferromagnetic charge-ordered insulating (COI) phase induced in the (100) or (001)-oriented LCMO films can be dramatically promoted (or suppressed) by a uniaxial tensile (or compressive) bending stress along the in-plane [010] direction. By contrast, the COI phase is nearly unaffected along the other transverse in-plane directions. Results from scanning transmission electron microscopy reveal that the (100)- or (001)-oriented LCMO films are uniaxially tensile strained along the [010] direction, while the LCMO/NGO(010) and LCMO/NGO(110) films remaining as a bulklike ferromagnetic metallic state exhibit a different strain state. Density functional theory calculations further reveal that the cooperatively increased Jahn-Teller distortion and charge ordering may be indispensible for the inducing and promoting of the COI phase. These findings provide a path to understand the correlation between local and extended structural distortions imparted by coherent epitaxy and the electronic states for quantum phase engineering.

Multi-messenger nanoprobes of hidden magnetism in a strained manganite.

The ground-state properties of correlated electron systems can be extraordinarily sensitive to external stimuli, offering abundant platforms for functional materials. Using the multi-messenger combination of atomic force microscopy, cryogenic scanning near-field optical microscopy, magnetic force microscopy and ultrafast laser excitation, we demonstrate both 'writing' and 'erasing' of a metastable ferromagnetic metal phase in strained films of La2/3Ca1/3MnO3 (LCMO) with nanometre-resolved finesse. By tracking both optical conductivity and magnetism at the nanoscale, we reveal how strain-coupling underlies the dynamic growth, spontaneous nanotexture and first-order melting transition of this hidden photoinduced metal. Our first-principles calculations reveal that epitaxially engineered Jahn-Teller distortion can stabilize nearly degenerate antiferromagnetic insulator and ferromagnetic metal phases. We propose a Ginzburg-Landau description to rationalize the co-active interplay of strain, lattice distortions and magnetism nano-resolved here in strained LCMO, thus guiding future functional engineering of epitaxial oxides into the regime of phase-programmable materials.

Magnetic-Competition-Induced Colossal Magnetoresistance in n -Type HgCr2Se4 under High Pressure

The n-type HgCr_{2}Se_{4} exhibits a sharp semiconductor-to-metal transition (SMT) in resistivity accompanying the ferromagnetic order at T_{C}=106 K. Here, we investigate the effects of pressure and magnetic field on the concomitant SMT and ferromagnetic order by measuring resistivity, dc and ac magnetic susceptibility, as well as single-crystal neutron diffraction under various pressures up to 8GPa and magnetic fields up to 8T. Our results demonstrate that the ferromagnetic metallic ground state of n-type HgCr_{2}Se_{4} is destabilized and gradually replaced by an antiferromagnetic, most likely a spiral magnetic, and insulating ground state upon the application of high pressure. On the other hand, the application of external magnetic fields can restore the ferromagnetic metallic state again at high pressures, resulting in a colossal magnetoresistance (CMR) as high as ∼ 3×10^{11}% under 5T and 2K at 4GPa. The present study demonstrates that n-type HgCr_{2}Se_{4} is located at a peculiar critical point where the balance of competition between ferromagnetic and antiferromagnetic interactions can be easily tipped by external stimuli, providing a new platform for achieving CMR in a single-valent system.

Percolation like transitions in phase separated manganites La0.5Ca0.5Mn1-Al O3-

We show that the replacement of Mn with Al strongly affects the magnetization and electrical transport behaviors in La 0.5 Ca 0.5 Mn 1- x Al x O 3- δ ( x = 0, 0.05, 0.07 and 0.09). Nonmagnetic Al 3+ ions substitution at Mn sites dilutes Mn 3+ -O 2- -Mn 4+ network, thus suppresses the ferromagnetic metallic state in La 0.5 Ca 0.5 MnO 3- δ and causes a phase separation phenomenon, in which ferromagnetic phase coexists with antiferromagnetic charge ordered phase at low temperatures. With applying sufficiently high magnetic field, step-like metamagnetic transitions were observed in x = 0.05–0.09 systems below helium temperature, in which the antiferromagnetic charge ordered phase collapsed into ferromagnetic phase. Corresponding to the sharp step-like metamagnetic transitions, the resistivity decreases dramatically with increasing magnetic field, exhibiting a percolative insulator-metal transition. The variation of temperature and magnetic field changes the relative fractions of ferromagnetic and charge ordering phases, and percolative insulator-metal transition occurs due to the development of percolation paths between the growing FM domains.

Photoinduced Topological Spin Texture in a Metallic Ferromagnet

Photoinduced nonequilibrium spin structure is examined in the double-exchange model, in which itinerant electrons couple with localized spins through the ferromagnetic Hund coupling. In particular, we focus on the transient spin structure from the initial ferromagnetic metallic state to the steady antiferromagnetic ordered state reported in [Phys. Rev. Lett. 119, 207202 (2017)]. By solving the Schr\"odinger equation combined with the Landau-Lifshitz-Gilbert equation, we find finite winding number and chirality, which implies emergence of topological chiral spin textures. These observations are reproduced by a calculation where spin dynamics after sudden quench of the chemical potential are examined in larger clusters. A possible mechanism of the topological spin texture in the transient dynamics is discussed.

Correlated excited states in the narrow band gap semiconductor FeSi and antiferromagnetic screening of local spin moments

The physical properties of the semiconductor FeSi with very narrow band gap, anomalous behavior of the magnetic susceptibility and metal-insulator transition at elevated temperatures attract gross interest due to the still controversial theoretical understanding of their origin. On one side the purely band like mechanism of the gap formation in FeSi at low temperature is well established, on other side a number of experiments and their theoretical interpretation suggest a rich physics of strong correlations at finite temperature. In this work we use an ab-initio scheme based on the Random Phase Approximation and Local Spin Density Approximation (RPA@LSDA) to reveal the role of the electron correlation effects in FeSi extending it by applying a fixed spin moment constraint. In the parameter free framework we show that correlation effects essentially alter the one-electron LSDA results leading to the formation of an additional state with finite magnetic moment on Fe, whose energy is almost degenerate with the non-magnetic ground state. This explains the results of high field experiments, which found a first-order meta-magnetic phase transition into a metallic ferromagnetic state. Our results suggest a strongly correlated nature of the low-energy excitations in FeSi. From our super-cells calculations we reveal that these excitations are local and exhibit a Kondo-like behavior since a strong antiferromagnetic screening is present.

Role of oxygen vacancy in the spin-state change and magnetic ordering in SrCoO3−δ

We present the first-principles investigation of the structural, electronic, and magnetic properties of SrCoO$_{3-\delta}$ ($\delta=0, 0.25, 0.5$) to understand the multivalent nature of Co ions in SrCoO$_{3-\delta}$ along the line of topotactic transition between perovskite SrCoO$_{3}$ and brownmillerite SrCoO$_{2.5}$. From the on-site Coulomb interaction $U$-dependent ground state of stoichiometric SrCoO$_{3}$, we show the proximity of its metallic ferromagnetic ground state to other antiferromagnetic states. The structural and magnetic properties of SrCoO$_{3-\delta}$ depending on their oxygen-content provide an interesting insight into the relationship between the Co-Co distances and the magnetic couplings so that the spin-state transition of Co spins can understood by the change of $pd$-hybridization depending on the Co-Co distances. The \emph{strong} suppression of the $dp\sigma$-hybridization between Co $d$ and O $p$ orbitals in brownmillerite SrCoO$_{2.5}$ brings on the high-spin state of Co$^{3+}$ $d^{6}$ and is responsible for the antiferromagnetically ordered insulating ground state. The increase of effective Co-Co distances driven by the presence of oxygen vacancies in SrCoO$_{3-\delta}$ is consistent with the reduction of the effective $pd$-hybridization between Co $d$ and O $p$ orbitals. We conclude that the configuration of neighboring Co spins is shown to be crucial to their local electronic structure near the metal-to-insulator transition along the line of the topotactic transition in SrCoO$_{3-\delta}$. Incidentally, we also find that the \textit{I2mb} symmetry of SrCoO$_{2.5}$ is energetically stable and exhibits ferroelectricity via the ordering of CoO$_{4}$ tetrahedra, where this polar lattice can be stabilized by the presence of a large activation barrier.