SOLID STATE TUNABLE IONIC OSCILLATOR DIELECTRIC MATERIALS AND RESONANT DEVICES

Abstract

An article comprising a ferroelectric material in its ferroelectric phase, wherein the article is configured to enable low-loss propagation of signals with ultra-low dielectric loss at one or more select frequencies.

Claims

1. (canceled)

2. An article comprising a ferroelectric material including a high density of one or more fluctuating ferroelectric domain walls, wherein the article contains domain walls that enable efficient propagation of signals with ultra-low dielectric loss (10.sup.3<Q<10.sup.7, or 10.sup.−3>tan δ>10.sup.−7) at one or more select frequencies, wherein the density of domain walls of ranges from 1-100 per 50,000 nm2.

3. The article of claim 2, wherein the article is configured to enable low-loss propagation of signals with ultra-low dielectric loss (10.sup.3<Q<10.sup.7, or 10.sup.−3>tan δ>10.sup.−7) at or within 20% of T.sub.C of the ferroelectric material.

4. An article comprising a ferroelectric material in thin film form in its ferroelectric phase, wherein the composition and strain of the material are selected to stabilize the material, for a given temperature, in or about two or more energetically equivalent thermodynamically predicted domain wall variant types as specified by a domain wall variant boundary or vertex of intersecting boundaries, thereby enabling efficient propagation of signals with ultra-low loss (10.sup.3<Q<10.sup.7, or 10.sup.−3>tan δ>10.sup.−7) at select frequencies.

5. The article of claim 4, wherein a range and/or values of fluctuation frequency and/or frequencies are controlled based on changes in domain wall oscillation frequency in response to electric field applied to the ferroelectric material.

6. The article of claim 4, wherein the one or more select frequencies are between 0.01 GHz and 300 GHz.

7. The article of claim 4, wherein a range and/or values of fluctuation frequency or frequencies of the article are controlled based on the density of domain walls.

8. The article of claim 4, wherein the magnitude of the quality factor Q is controlled by the density of domain walls and increases with domain wall density.

9. The article of claim 4, wherein the range and/or values of fluctuation frequency or frequencies are controlled based on the type and/or types of ferroelectric domain wall variants.

10. The article of claim 4, wherein the range and/or values of fluctuation frequency or frequencies are controlled based on the degree of strain.

11. The article of claim 4, wherein ferroelectric material is in a phase comprising one of: normal ferroelectric, improper ferroelectric, hybrid improper ferroelectric, or multi-ferroic ferromagnetic or antiferromagnetic ferroelectric.

12. The article of claim 4, wherein the range and/or values of fluctuation frequency and/or frequencies are controlled based on changes in domain wall oscillation in response to magnetic field applied across the multiferroic ferromagnetic (or antiferromagnetic) ferroelectric material due to multiferroic coupling of magnetic field to ferroelectric polarization.

13. The article of claim 4, wherein the ferroelectric material has 1-100 per 40,000 nm2 of engineered planar two-dimensional topological defects that, under selected electric DC bias or zero electric DC bias, oscillate at the one or more select frequencies and within 100 degrees C. of the T.sub.C of the ferroelectric material.

14. The article of claim 13, wherein the select frequencies are between 0.1 GHz and 300 GHz.

15. The article of claim 13, wherein the planar two-dimensional topological defects comprise domain walls, and wherein the domain walls, under the application of a DC or AC electric field or under zero DC or AC electric field, oscillate or fluctuate in their position with respect to time.

16. The article of claim 15, wherein the timescale or rate of the fluctuations vary depending upon the electrostatic potential landscape and domain width or domain wall density, applied field, temperature, strain (coherent or relaxed) and/or stress.

17. The article of claim 4, wherein ferroelectric material comprises perovskites, Ba.sub.xSr.sub.1−xTiO.sub.3 (BST.sub.x), PbTiO.sub.3, Pb(Zr, Ti)O.sub.3, (Pb, Sr)TiO.sub.3, BiFeO.sub.3, Bi(Fe,Mn)O.sub.3 or Ruddelson-Popper phases A.sub.n+1B.sub.nX.sub.3n+1, or Ruddelson-Popper phases A.sub.n+1A′.sub.2B.sub.nX.sub.3n+1 where A and A′ represent alkali and/or alkaline earth metals, and B denotes a rare earth metal, and X═O or other ferroelectrics, or a combination thereof.

18. A method of making the article of claim 4.

19. A resonator comprising the article of claim 4.

20. An oscillator or system/collection of coupled oscillators in a ferroelectric material that exhibits resonances at odd integer multiple frequencies of the fundamental domain wall switching resonance frequency due to the noise-induced fluctuation of the system between two sides of the double well.

21. The article of claim 2, wherein the one or more select frequencies are between 0.01 GHz and 300 GHz.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The file of this patent or application contains at least one drawing/photograph executed in color. Copies of this patent or patent application publication with color drawing(s)/photograph(s) will be provided by the Office upon request and payment of the necessary fee.

[0028] FIG. 1: design of domain wall variant-rich material and its microwave dielectric tunability. a, Thermodynamic landscape of in-plane polarization favoring domain wall variants showing calculated average value of in-plane polarization |P.sub.1| as a function of temperature and in-plane strain, for Ba.sub.0.8Sr.sub.0.2TiO.sub.3. Arabic numerals denote various thermodynamically predicted domain wall variant structures.

[0029] FIG. 2: Phase field simulations of domain structure for equivalent strains and corresponding non-degenerate (vertical dashed lines I and III) and degenerate (II) domain variant phase states in BaTiO.sub.3 at ≈10 K<T.sub.C under zero field (b,df) reveal high out-of-plane (b) and in-plane (d, f) domain wall densities that persist even under a moderate in-plane field of 0.1 MV/cm applied along [100] (c,e,g). Plotted in b and c are plane-normal polarization P.sub.3, with colormap range of ±30 μC/cm.sup.2. In (d-g) plotted is the angle of in-plane polarization θ=±90°, where θ is the angle between [100] and the sum of the two in-plane components P.sub.1+P.sub.2.

[0030] FIG. 3. The effect of proximity to this domain phase variant degeneracy point is seen, showing theoretically-predicted in-plane quasi-static field tunability of relative dielectric permittivity ε.sub.11/ε.sub.0 in Ba.sub.0.8Sr.sub.0.2TiO.sub.3 films on SrTiO.sub.3, on SmScO.sub.3, and on BaTiO.sub.3, corresponding to strain states I, II and III, respectively, calculated using the GLD model.

[0031] FIG. 4 Illustration of the experimental two-port, interdigitated electrode capacitor geometry.

[0032] FIG. 5. Measured in-plane field tuning of in-plane normalized capacitance C.sub.norm(E) at selected frequencies for a 400 nm-thick manifold domain-wall-variant material (or meta-material) film sample (Ba.sub.0.8Sr.sub.0.2TiO.sub.3/SmScO3(110)), compared with that for epitaxial paraelectric (Ba,Sr)TiO.sub.3 (BST)[C. J. G. Meyers, C. R. Freeze, S. Stemmer, and R. A. York, (Ba, Sr)TiO.sub.3 tunable capacitors with RF commutation quality factors exceeding 6000, Appl. Phys. Lett. 109, 112902 (2016)] and Sr.sub.7Ti.sub.6O.sub.19 [C.-H. Lee, N. D. Orloff, T. Birol, Y. Zhu, V. Goian, E. Rocas, R. Haislmaier, E. Vlahos, J. A. Mundy, L. F. Kourkoutis, et al., Exploiting dimensionality and defect mitigation to create tunable microwave dielectrics, Nature 502, 532-536 (2013)].

[0033] FIG. 6. A and B: microwave spectroscopy revealing field-dependent resonant domain wall spectral signatures of ultra-low loss, and tunable resonant performance. Experimentally determined Q plotted as a function of frequency and DC in-plane bias field for a 100 nm-thick film with a, ten and b, six IDC electrode pairs, distinguished by the period 2W defined by the electrode finger width w and inter-electrode spacing d as shown in the optical micrographs that appear as an inset within each (scale bar: 10 μm). C and D: extracted values of frequency and field for which Q peaks are obtained for devices in A and B showing that the spectra of voltage-dependent frequencies for which the resonant Q peaks occur are essentially the same, and that the resonant frequency can be bias tuned by ≈400%, from ≈2 GHz at ≈0.1 MV/cm, to ≈10 GHz at ≈0.67 MV/cm, with 10.sup.3 approximately less than or equal to Q approximately less than or equal to 10.sup.6. Representative traces of DC field-dependent Q, for selected frequencies shown in the legend, corresponding to devices shown in FIG. 6a and b.

[0034] FIG. 7. Peak Q collected at 100 frequencies in four different devices showing an increase of more than one order of magnitude over approximately one decade of frequency, deviating strongly from the usual 1/f scaling law. Shown for comparison are highest values for bulk single crystal quartz, sapphire, and AlN film piezoelectric resonators, none of which are intrinsically tunable (each point represents an individual device), and those reported for intrinsically tunable BST films, including for a film bulk acoustic wave solidly-mounted resonator (BAW-SMR).

[0035] FIG. 8. MD simulation of Q. a, An illustration of the MD supercell and domain fluctuations at E.sub.x=0.6 MV/cm with the P.sub.y>0 domain shown in black and P.sub.y<0 domain shown in gray.

[0036] FIG. 9. Q obtained experimentally (left panel) and Q.sub.y of MD simulations (right panel) for the aa.sub.1/aa.sub.2 domain structure. Experimental data shown for E=0.09, E=0.25 MV/cm, and E=0.5 MV/cm). MD data are shown for E=0, E=0.3 MV/cm (green), and E=0.6 MV/cm.

[0037] FIG. 10. Q(f) for the bulk-like layers 100-113 and DW layers 73-84 from MD simulations at E=0.6 MV/cm.

[0038] FIG. 11. Hopping rates for individual layers of the 120×10×10 supercell.

[0039] FIG. 12. Total P time autocorrelation functions obtained from MD simulations for E=0, E=0.3 MV/cm, and E=0.6 MV/cm.

[0040] FIG. 13. Phase field simulations of Case II with a cell containing 64×64×64 grid points using three different initial conditions.

[0041] FIG. 14. Phase field simulations of Case II with a cell containing 128×128×128 grid points using different values for G.sub.11, BTO as indicated below each figure panel.

[0042] FIG. 15. X-ray diffraction collected on 100 nm and 400 nm thick BST epitaxial films deposited on SmScO.sub.3(110). The small peaks in addition to the film and substrate are attributed to Umweg peaks.

[0043] FIG. 16. Reciprocal space maps (RSMs) showing, left-to-right (103) film and (332) SSO substrate reflections in 100 nm and 400 nm thick x=0.8 film samples, confirming that the films are epitaxial and strain coherent.

[0044] FIG. 17. Rutherford backscattering spectroscopy analysis results, obtained on a BST film, confirming no A-site deficiency, within the known 1% error.

[0045] FIG. 18. Dual-amplitude resonance tracking (DART™) lateral-force piezoresponse force microscopy (PFM) images (amplitude on the left, and phase on the right) collected on a ≈100-120-nm thick Ba.sub.0.8Sr.sub.0.2TiO.sub.3 film on SSO, with crystallographic orientation denoted. The diagonal pattern confirms that the films possess dense aa.sub.1/aa.sub.2/aa.sub.1/aa.sub.2 type superdomain structure as described in the main text. The scale bar corresponds to 1 μm.

[0046] FIG. 19. Optical micrograph of a representative two-port ten interdigitated-finger electrode capacitor (IDC) devices; the devices shown above were fabricated on a 100 nm-thick film, and have inter-electrode gap spacing of 3 μm.

[0047] FIG. 20. Representative measured S parameter data collected from a 400 nm-thick film device.

[0048] FIG. 21. Frequency dependence of tunability n(f) for in-plane |E|=0.67 MV/cm for 100 and 400 nm-thick film devices.

[0049] FIG. 22. Measured quality factor Q at 0.5 MV/cm.

[0050] FIG. 23. Measured zero-bias temperature-dependent capacitance and loss at 1 MHz.

[0051] FIG. 24. Illustration of voltage-time measurement sequence employed in voltage sweeps.

[0052] FIG. 25. Measured field dependence of Q corresponding to the sample presented in FIG. 1h of the main text, at the same frequencies.

[0053] FIG. 26. The commutation quality factor CQF(f)=(n(f)−1)2Q(0,f) Q(E,f)/n(f) [I. B. Vendik, O. G. Vendik, and E. L. Kollberg, Commutation quality factor of two-state switchable devices, IEEE Transactions on Microwave Theory and Techniques 48, 802-808 (2000).], a key metric that incorporates n(E) and Q(E) shows values that, in this range, are greater than those of the best films reported [C. J. G. Meyers, C. R. Freeze, S. Stemmer, and R. A. York, (Ba, Sr)TiO.sub.3 tunable capacitors with RF commutation quality factors exceeding 6000, Appl. Phys. Lett. 109, 112902 (2016)] to date.

[0054] FIG. 27. data plotted as quality factor-frequency product as a function of frequency, for four widely tunable MDVM film devices, and values for other BST and not intrinsically tunable devices. Cited references correspond to those in the main text.

[0055] FIG. 28. Bond valence molecular dynamics (BVMD)-calculated single domain Q for bulk BaTiO.sub.3 supercells at selected temperatures above and below T.sub.C , permitting identification of the frequency- and temperature-dependent intrinsic limit of dielectric loss.

[0056] FIG. 29. BVMD calculated Q for a single domain with and without clamping by the substrate and with and without applied E field.

[0057] FIG. 30. Normalized capacitance from MD simulations. Normalized capacitance (static dielectric constant c obtained from the fluctuations of the total polarization in MD simulations of the 120×10×10 aa.sub.1/aa.sub.2 domain supercell. Peak capacitance is obtained at ≈170K, 30K lower than the T.sub.C of 200K obtained from single domain calculations.

[0058] FIG. 31. Polarization Trajectories of MD simulations. Overall supercell polarization in the y-direction as a function of time for the two simulations used to calculated Q(f). The raw P.sub.y trajectories of the two simulations are shown in black and green. Smoothed trajectories using a Gaussian window function with the full width-half maximum (FWHM) of 16 ps are shown in orange and blue. For (a) E=0 MV/cm, (b) E=0.3 MV/cm, (c) E=0.6 MV/cm. Large P.sub.y fluctuations are observed corresponding to the movement of the domain walls. Domain wall hopping is faster for E=0.3 MV/cm and E=0.6 MV/cm, leading to more rapid large oscillations of P.sub.y.

[0059] FIG. 32. Polarization auto-correlation functions MD simulations. Total polarization time auto-correlation functions (ACFs) for the P.sub.y component for individual simulations at E=0 MV/cm (black), E=0.3 MV/cm (green) and E=0.6 MV/cm (red). Large oscillations can be seen in all cases and it is clear that the ACF oscillations become more frequent with higher field. Sampling quality of the ACF decreases with greater time, with ACFs of E=0 MV/cm trajectories showing divergence earlier ≈8 ns) then the ACFs of E=0.3 MV/cm and E=0.6 MV/cm trajectories ≈12 ns).

[0060] FIG. 33. Loss tangent from MD simulations. Low-frequency tan δ(f) obtain from the Fourier transform of the first 9 ns of the ACFs of the individual MD simulations (black and red) and the averaged tan δ(f) (blue) for (a) E=0 MV/cm, (b) E=0.3 MV/cm, (c) E=0.6 MV/cm. The tan δ(f) of the two simulations are similar to each other, indicating that the 14 ns trajectories are sufficiently long for generating reproducible results for the positions of the tan δ(f) peaks and troughs. However, the values of the peaks and troughs show some variation, indicating the uncertainty in the obtained tan δ(f) and Q values. This is particularly significant for Q because a small difference in tan δ(f) can lead to a very large difference in Q. The values of tan δ(f) are more converged for E=0.3 MV/cm, and E=0.6 MV/cm. Nevertheless, negative tan δ(f) values and rapid tan δ(f) oscillations can be seen even for E=0.3 MV/cm and E=0.6 MV/cm data, indicating the presence of noise and the need for further smoothing of the data.

[0061] FIG. 34. Smoothed Loss tangent from MD simulations. Low-frequency tan δ(f) obtained from the average of the tan δ(f) of the individual MD simulations (black) and red) and smoothed tan δ(f) obtained using a Gaussian window function with the FWHM of 0.2 (green) and 0.3 GHz (magenta) for (a) E=0 MV/cm, (b) E=0.3 MV/cm, (c) E=0.6 MV/cm. The use of the smoothing function eliminates the unphysical negative tan δ(f) values and rapid and large oscillations of tan δ(f). In some cases smoothing with the FWHM of 0.05 is sufficient but in other cases smoothing using larger FWHM is necessary

[0062] FIG. 35. Q(f) from MD simulations. Q(f) obtained from the inverse of the average tan δ(f) of the individual MD simulations using Fourier transform of different lengths of the ACF. tan δ(f) from 3, 4, 5, 6 and 7 ns of ACFs are shown in black, red, green, blue and yellow, respectively for (a) E=0 MV/cm, (b) E=0.3 MV/cm, (c) E=0.6 MV/cm. The Q(f) curves are obtained from tan δ(f) smoothed using Gaussian window functions with the FWHM of 0.05 and 0.1 GHz. Q(f) from 3, 7, 8, 9, 10, 11 and 12 ns of ACFs are shown in black, yellow, brown, orange, violet, cyan, and magenta, respectively for (d) E=0 MV/cm, (e) E=0.3 MV/cm, (f) E=0.6 MV/cm. It can be see that for E=0 MV/cm, Q(f) curves obtained using ACFs of greater than 7 ns show wide variation in the position of loss peaks (dips in Q), whereas for E of 0.3 MV/cm and 0.6 MV/cm, the loss peak positions and the peak Q positions are largely preserved. The absolute values of Q vary with the length of the ACFs, reaching ≈10.sup.4 in some cases. Nevertheless, despite the uncertainties in the absolute values of Q, it is clear that resonance peaks above the baseline are present in the MD system and can even be larger than the extrapolation of the 1/f high-frequency rise of Q with decreasing f.

[0063] FIG. 36. Comparison of Q(f) from MD simulations for different electric fields. Q(f) obtained the inverse of the average tan δ(f) of the individual MD simulations using Fourier transform for E=0 MV/cm (black), E=0.3 MV/cm (green) and E=0.6 MV/cm (red). The Q(f) are shown for Fourier transforms performed on (a) 7 ns of ACFs (b) 9 ns of ACFs and (c) 11 ns of ACFs). A shift to higher frequencies and greater rise of the resonance peaks from the baseline and higher maximum Q are observed upon the application of the field.

[0064] FIG. 37. Autocorrelation functions for different layers in MD simulation. Polarization time autocorrelation function for different layers in the domain wall region (layers 74-86) and in the bulk region (layers 100-113) obtained from MD simulations trajectory for E=0.6 MV/cm. The ACF DW layers show large oscillations with a long period while the bulk layer ACFs show small oscillations with a small period and appear as a cyan line around zero in the plot.

[0065] FIG. 38. Movement of DW position as a function of time. An illustration of the MD supercell and domain fluctuations at E.sub.x=0 MV/cm (a) and E.sub.x=0.3 MV/cm (b) with the P.sub.y>0 domain shown in black and P.sub.y<0 domain shown in red.

[0066] FIG. 39 shows a comparison of Q(f) obtained from stochastic model simulations. Comparison of the Q(f) obtained from stochastic model simulations using two different parameter sets, with Q(f) for parameter set A shown in black and Q(f) for parameter set B shown in red. Similar to the MD-obtained Q(f) shown in FIG. 3, a slight shift to higher frequencies and higher Q peaks can be obtained by a change in the stochastic model potential.

[0067] FIG. 40. Schematic illustrations of (a) the LFE-type device, namely out-of-plane piezoelectric resonance oscillations of wavevector k.sub.3 in a film resulting from in-plane bias and polarization achieved using IDC electrodes, and (b) the resonance and anti-resonance frequencies calculated for a t=100 nm Ba.sub.0.8Sr.sub.0.2TiO.sub.3 thin film for 0% and 0.05% in-plane strain us from the substrate.

[0068] FIG. 41. Schematic illustrations of (a) in-plane piezoelectric resonance oscillations of wavevector k.sub.1 in a film resulting from in-plane bias and polarization achieved using (b) an IDC electrode containing n fingers with finger gap d, width w and length l, where the periodicity 2W=2(w+d), and (c) calculated results of resonance and anti-resonance frequencies for 2W=20.6 μm and 34.4 μm.

[0069] FIG. 42. Optical micrograph images collected at different magnifications, of representative devices possessing different electrode finger/gap periodicity (F10 and F06), as described above.

DETAILED DESCRIPTION

[0070] The present disclosure relates to a framework for a microwave dielectric oscillating medium based on atomic-scale domain wall fluctuations that enables new devices. These novel meta-dielectric thin film materials enable low losses that overcome the material-specific intrinsic limit. These polar media are distinguished by their possessing a high density of specially engineered planar defects that, under selected DC bias, oscillate at several selected frequencies. The axis of vibration of the internal oscillators is not random, but instead oriented along one or more preferred direction(s), indicating that DC field-driven collective oscillations can support traveling EM waves. Additionally, experimental observations and model calculations results indicate that the oscillation frequencies can be controlled and tuned. The availability of a solid state microwave medium where resonant frequencies are dependent a priori not on the geometric dimensions and acoustic modes, but on tunable nanoscale oscillators that arise within the medium, opens a wide array of possibilities for frequency selectivity, spectrum management and reduced power requirements, through material non-linear response characteristics.

[0071] A material that possesses a ferroelectric instability, and within or near its ferroelectric phase, possessing high density of ferroelectric domain walls such that: [0072] a. The domain walls, under the application of a DC or AC field of sufficient magnitude and selected frequency, or under zero field, oscillate or fluctuate in their position with time (e.g., yielding a spectrum with resonance frequencies associated with the ferroelectric domain wall motions). [0073] b. The timescale or rate of these fluctuations vary depending upon the electrostatic potential landscape and domain width or domain wall density, applied field, temperature, strain (coherent or relaxed) and/or stress. [0074] c. The corresponding frequency spectrum associated with these fluctuations exhibits one or more minima in material dielectric loss (or peaks in reciprocal loss, Q) along an axis parallel to the axis of the domain wall and perpendicular to its fluctuations [0075] d. The width of the domain separating the domain walls fluctuates [0076] e. The material may be a ferroelectric in its ferroelectric phase (normal ferroelectric, improper ferroelectric, hybrid improper ferroelectric, relaxor ferroelectric), any which exhibits domain walls of density of 1-100 per 50,000 nm.sup.2. [0077] f. Examples of ferroelectric materials are BaTiO.sub.3, (Ba,Sr)TiO.sub.3 (including combination of Ba and/or Sr), PbTiO.sub.3, PZT, (Pb,Sr)TiO.sub.3, BiFeO.sub.3, Bi(Fe,Mn)O.sub.3 and numerous other compounds, in a combination of composition and strain state permitting the aforementioned high domain wall density, whereby domain structure with polarization components lying completely or partially in the plane of a film even in the presence of weak or strong (e.g., 1 MV/cm) ordering electric field. As a non-limiting example, the ferroelectric materials may comprise perovskites BaxSrl-xTiO3 (BSTx), PbTiO3, Pb(Zr,Ti)O3, (Pb,Sr)TiO3, BiFeO3, Bi(Fe,Mn)O3 and related solid solutions; Ruddelson-Popper phases An+1BnX3n+1, or more generally An+1A′2BnX3n+1 where A and A′ represent alkali and/or alkaline earth metals, and B denotes a rare earth metal, such as A=Sr or Ba, B=Ti, and X═O, or other ferroelectrics, such as SrBi2Ta2O9 and related solid solutions BaTiO3, (Ba,Sr)TiO3, PbTiO3, PZT, (Pb,Sr)TiO3, BiFeO3, Bi(Fe,Mn)O3. [0078] g. Temperatures within 100 degrees C. of the ferroelectric phase transition temperature Tc [0079] h. Domain walls may be of any type. Examples include c+/c−/c+/c−, a.sub.1/a.sub.2/a.sub.1/a.sub.2, aa.sub.1/aa.sub.2, r.sub.1/r.sub.2/r.sub.1/r.sub.2, a/c/a/c, ca.sub.1/ca.sub.2/ca.sub.1/ca.sub.2, ca*/aa*/ca*/aa*, c/a/c/a, or other structure identified in the appendices, or any mixture thereof [0080] i. Domain wall densities of 1-100 per 50,000 nm.sup.2; other domain wall densities may be used such as 1-100 per 40,000 nm.sup.2 or 1-100 per 60,000 nm.sup.2 or

[0081] Domain wall oscillations produce one or more frequencies or frequency bands at which the dielectric material loss can be very low, and material Q can exceed the intrinsic limit, and contain the following features: [0082] a. These frequencies corresponding to high Q can remain fixed with applied field, or shift to higher or lower frequencies, with applied field. [0083] b. Frequencies can range from 0.01 GHz to 300 GHz, depending on the material, domain structure, domain wall density, strain, temperature and applied field.

[0084] Material containing domain wall (DW) oscillations whereby the low dielectric loss/high Q is anisotropic (it does not necessarily occur in all directions under application of a field), thereby allowing microwave and RF-band electromagnetic energy to propagate with considerably less loss in one or more preferred directions.

[0085] A microwave cavity supporting propagation of transverse electromagnetic (TEM) waves with little or no dissipation, carried and/or modulated by domain wall oscillations.

[0086] The present disclosure relates to (a) the origin of the unusually large experimentally observed Q spikes using the comparison of experimental data and data obtained from bond-valence potential molecular dynamics (MD) simulations of a model BaTiO.sub.3 (BTO) system (Methods), (b) the voltage (or electric field) tunability of the observed Q spikes that is also exceptionally large, and (c) occurrence of both (frequency-tunable) Q spikes and exceptionally high voltage tunability of dielectric permittivity in the RF and microwave bands in the same material.

[0087] Thermodynamic Ginzburg-Landau-Devonshire (GLD) model calculations support the hypothesis that large in-plane permittivity values can be obtained via in-plane domains. Application of the phenomenological GLD model permits calculation of in-plane strain us-temperature (T)-polarization (P) phase diagrams (FIG. 1) with a number of additional, domain variants (“superdomain”[ S. Matzen, O. Nesterov, G. Rispens, J. A. Heuver, M. Biegalski, H. M. Christen, and B. Noheda, Super switching and control of in-plane ferroelectric nanodomains in strained thin films, Nature Commun. 5, 4415 (2014)]) predicted for BST films (FIG. 1). Focusing, for example, on x=0.8, which produces a vertex in the phase diagram where a number of domain wall variant phases are predicted to intersect near room temperature (FIG. 1). Noting the close proximity and high accessibility among the different variants, where this region of the phase diagram may be referred to as a manifold domain wall-variant material (MDVM).

[0088] Zero- and finite-field phase-field model calculations for three selected strain states (denoted in FIG. 1 by yellow dashed lines I, II, and III) confirm the expected c.sup.+/c.sup.− structure for a compressively strained film (I), and in-plane domain structure for a film under moderate tensile strain (III) (FIG. 2). Application of a moderately large field (0.1 MV/cm along [100]) leaves the domain structure in I and III essentially unchanged (FIG. 2). For case II, which corresponds to the MDVM material, the aa.sub.1/aa.sub.2 domain wall variant structure at zero field is predicted, suggestive of multiple domain wall variant coexistence consistent with its location in the phase diagram. Despite the softer three-dimensional potential energy landscape for II as compared with I and III, domain structure is not eliminated at moderate field (FIG. 1), consistent with reports on epitaxial films in which domain structures cannot be eliminated [Griggio, F. et al. Composition dependence of local piezoelectric nonlinearity in (0.3)Pb(Ni.sub.0.33Nb.sub.0.67)O.sub.3- (0.7)Pb(Zr.sub.xTu.sub.1−x)O.sub.3 films. J. Appl. Phys. 110, 044109 (2011]) under applied electric field.

[0089] Dielectric permittivity values for the MDVM-engineered films exceed the composition-specific state-of-the-art for dielectric thin films: theoretically predicted values for zero-field relative dielectric permittivity ε.sub.11/ε.sub.0 easily exceed 10,000, reaching 10.sup.5 for selected combinations. Higher permittivity promotes enhanced dielectric and capacitance tunability n(E)=ε.sub.r,max/ε.sub.r,min(=C.sub.max/C.sub.min), where ε.sub.r is the real part of the dielectric permittivity, C.sub.max and C.sub.min are the capacitances at zero and applied electric field E, aided by proximity to the phase boundary.

[0090] Theoretically calculated quasi-static in-plane tunability in MDVM films can be remarkably large. For example, an x=0.8 film coherently strained on SmScO.sub.3(110) (u.sub.s≈0.05%, case II) is predicted to have tunability n(E.sub.1)>20 at E.sub.1=0.3 MV/cm, whereas n for films on SrTiO.sub.3 (I) and BaTiO.sub.3 (III) is considerably weaker (FIG. 3).

[0091] Experimental results support the GLD theory predictions. Epitaxial x=0.8 films, 100 and 400 nm thick, were deposited on SmScO.sub.3(110) by pulsed-laser deposition and were characterized using a variety of techniques.

[0092] Compared with the bulk, the smaller out-of-plane lattice parameters in our films favor in-plane domain formation, and plane-normal and lateral dual-amplitude resonance tracking (DART™) piezoresponse force microscopy (PFM) confirms the presence of in-plane oriented domains, with domain walls aligned along the [100] or [010], consistent with the aa.sub.1/aa.sub.2/aa.sub.1/aa.sub.2 domain structure (SI).

[0093] Voltage-dependent capacitance data in the co-planar geometry (FIG. 4) at selected frequencies across the measurement range demonstrate high capacitance tunability at modest fields (FIG. 5), in agreement with our calculations, and persisting to beyond 20 GHz. This capacitance tunability, even at equivalent fields, is considerably greater than the current state of the art in molecular beam epitaxy-grown films, including Ruddelson-Popper (R-P) Sr.sub.7Ti.sub.6O.sub.19 [C.-H. Lee, N. D. Orloff, T. Birol, Y. Zhu, V. Goian, E. Rocas, R. Haislmaier, E. Vlahos, J. A. Mundy, L. F. Kourkoutis, et al., Exploiting dimensionality and defect mitigation to create tunable microwave dielectrics, Nature 502, 532-536 (2013)], and (Ba,Sr)TiO.sub.3 [C. J. G. Meyers, C. R. Freeze, S. Stemmer, and R. A. York, (Ba, Sr)TiO.sub.3 tunable capacitors with RF commutation quality factors exceeding 6000, Appl. Phys. Lett. 109, 112902 (2016)] (FIG. 5).

[0094] Remarkably, n(f) remains greater than 13 (at 0.67 MV/cm) throughout nearly the entire frequency range studied, peaking at n≈18.5 at 15.2 GHz (FIG. 21). The deposited films also exhibit low losses (high Q values). This is in contrast to the usual observation of high losses accompanying high tunabilities. MDVM films exhibit low Q at zero field, but large Q (<Q(f)>≈1200, frequency-averaged from 0.1-20 GHz) at maximum field. Q at the highest applied field ranges generally between 10.sup.2-10.sup.3 over 2-10 GHz (FIG. 22).

[0095] A closer examination revealed extraordinary features in thinner films: combinations of field and frequency for which Q oscillates with frequency easily exceed the frequency-dependent bulk intrinsic limit for BaTiO.sub.3 near T.sub.C (less than or approximately equal to 10.sup.3, FIG. 28), reaching and even exceeding 10.sup.5 (FIG. 6). To put such Q values in context, these are much greater than the best reported to date in intrinsically tunable film materials [Meyers, C. J. G. et al., (Ba,Sr)TiO.sub.3 tunable capacitors with RF commutation quality factors exceeding 6000] Appl. Phys. Lett. 109, 112902 (2016); Vorobiev, A. et al. Correlations between microstructure and Q-factor of tunable thin film bulk acoustic wave resonators. J. Appl. Phys. 110, 054102 (2011)], including ferroelectrics considered for high Q dielectrics [Budimir, M. Damjanovic, D. and Setter, N. Extension of the dielectric tunability range in ferroelectric materials by electric bias field antiparallel to polarization. Appl. Phys. Lett. 88, 082903 (2006); Rojac, T. et al. Piezoelectric nonlinearity and frequency dispersion of the direct piezoresponse of BiFeO.sub.3 ceramics. J. Appl. Phys. 112, 064114 (2012); Vorobiev, A. et al., J. Appl. Phys. 110, 054102 (2011)], greater than in AlN films [Rinaldi, M. et al. Super-high two-port AlN contour-mode resonators for RF applications. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 38-45 (2010); Rinaldi, M. et al. 5-10 GHz AlN contour-mode nanoelectromechanical resonators. In 2009 IEEE 22nd International Conference on Micro Electro Mechanical Systems 916-919(IEEE, 2009)], which are the leading non-ferroelectric (i.e., not intrinsically tunable) piezoelectrics. The experimentally determined Q values are comparable, in fact, to measured values for bulk single-crystal quartz [Krupka, J,. et al. Extremely high-Q factor dielectric resonators for millimeter-wave applications. IEEE Trans. Microw. Theory Tech. 53, 702-712 (2005); Harnett, J. G. et al., Room temperature measurement of the anisotropic loss tangent of sapphire using the whispering gallery mode technique. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53 34-38 (2006)], and ZnO [Magnusson, E. B. et al. Surface acoustic wave devices on bulk ZnO crystals at low temperature. Appl. Phys. Lett. 106, 063509 (2015)]. The field dependence of the resonant frequency f.sub.r(E) shows exceptional variation across one decade, spanning L (1-2 GHz), S (2-4 GHz) and C (4-8 GHz) bands, and extending into the X band (8-12 GHz), all in a single device. The commutation quality factor CQF(f)=(n(f)−1).sup.2Q(0,f) Q(E,f)/n(f) [Vendik, I. B. et al., Commutation quality factor of two-state switchable devices. IEEE Trans. Microw. Theory Tech. 48, 802-808 (2000)], a key metric that incorporates n(E) and Q(E), shows values that are greater than those of the best reported BST films [Meyers, C. J. G. et al., Appl. Phys. Lett. 109, 112902 (2016).

[0096] Bulk dielectric and film resonators rely on electromechanical coupling of microwave power through piezoelectric oscillations which appear as resonant and anti-resonant features that can be voltage tuned by <4.5% in the best tunable materials [Berge, J. and Gevorgian, S. Tunable bulk acoustic wave resonators based on Ba.sub.0.25Sr.sub.0.75TiO.sub.3 thin films and a HfO.sub.2/SiO.sub.2 Bragg reflector. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2768-2771 (2011)]. Considering the change in piezoelectric coupling coefficient, the calculated bias field dependence of resonance and anti-resonance frequencies of in-plane piezoelectric oscillations for Ba.sub.0.8Sr.sub.0.2TiO.sub.3 in our experimental geometry amounts to not more than ≈3% for 0-0.6 MV/cm (FIG. 42), hundreds of times less than that observed in our devices.

[0097] Furthermore, the design of piezoelectric resonators utilizing in-plane piezoelectric oscillations operating at fundamental (or higher mode) frequency relies on interdigitated capacitor (IDC) electrode periodicity, [Gevorgian, S. S., Tagantsev, A. K. and Vorobiev, A. K. Tunable Film Bulk Acoustic Wave Resonators (Springer, New York, 2013)]. Comparison of the spectrum obtained in devices that differ in electrode finger width instead reveals spectra that are essentially the same (FIG. 6), further demonstrating that it is highly unlikely that piezoelectric oscillations cause the observed spectrum.

[0098] The origin of the unusual experimentally observed Q spikes may be observed using the data obtained from molecular dynamics (MD) simulations of a model BaTiO.sub.3 (BTO) system (Methods). Analytical theory of intrinsic dielectric response [Tagantsev, 2003] predicts a 1/f dependence of Q(f) as is also found in our single-domain MD simulations (FIG. 28), indicating that the unusual f-dependence of Q is due to extrinsic effects. Examination of static dielectric response shows that the peak dielectric constant value is observed in the FE phase; such a DW-driven shift of the dielectric response peak to the FE phase was previously experimentally observed in BaTiO.sub.3 in the FE phase close to T.sub.c [Hoshia, T. et al. Domain size effect on dielectric properties of barium titanate ceramics., Jpn. J. Appl. Phys. 47, 7607-7611 (2008); Wang, Y. L. et al. Giant domain wall contribution to the dielectric susceptibility in BaTiO.sub.3. Appl. Phys. Lett. 91, 062905 (2007)] and reversible domain wall oscillations are also found to lead to the peak dielectric constant in the FE phase for the model aa.sub.1/aa.sub.2 DW supercell in our MD simulations (FIG. 2 and FIG. 8). The main reason for this domain-wall contribution to dielectric permittivity is the existence of very low-energy modes localized on the 2D domain walls. The strong impact of domain wall oscillations on the dielectric response and the presence of a high density of domain walls in our sample superdomain state suggest that these oscillations may also be the cause of Q(f) oscillations.

[0099] To understand the relationships between the reversible domain wall dynamics and Q(f), long (14 ns) simulations may be performed using a model system containing two aa.sub.1/aa.sub.2 domain walls in a 120×10×10 supercell (FIG. 8) at 50K below the FE-PE transition temperature and then obtain Q(f) from the fluctuations of the total polarization of the supercell. This size may be selected because at this domain length (24 nm), a clear distinction is observed between the domain wall and the bulk-like regions in the sample as can be seen in FIG. 8. Additionally, GLD theory predicts that the domain size should be on the order of 30 nm.

[0100] Comparison of the experimental and MD-obtained Q(f) shows several similar features (FIG. 9). First, at zero DC bias, the linear or almost linear rise in Q value with decreasing f is succeeded by flattening out of Q with gentle oscillations owing to the onset of relaxation at about 18 GHz (marked by black arrow). This observation is in agreement with the expectation that the presence of domain walls leads to higher loss and lower Q as can be seen from the much lower Q for f in the low f region (<2 GHz for experiment and <18 GHz for MD) than that expected from the intrinsic 1/f Q dependence. Second, at higher bias, Q peaks above the baseline appear at certain frequencies (marked by blue arrows) with the Q curve shifting to higher frequencies with higher DC bias. Finally, a greater number of narrow Q peaks is observed at higher bias. The Q.sub.y(f) data from the E=0 MV/cm and E=0.6 MV/cm Q.sub.y(f) for the MD simulations are qualitatively similar to the E=0.09 and E=0.25 MV/cm Q(f) data obtained experimentally, albeit at higher frequencies due to the difference between the experimental BST and the computational BTO systems (FIG. 9). The uniform shift to higher Q with higher DC bias is not observed for MD simulation and this difference is likely due to the difference between the simple model used in MD simulations and the much more complex E-field profile in experimental samples.

[0101] Analysis of Q(f) of individual layers shows that the bulk-like layers (i.e., layers in the middle of the domain that do not show switching) exhibit bulk-like 1/f dependence of Q on f, whereas the DW layers exhibit Q(f) spikes and a flattening out of the Q(f) at low f, similar to the experimentally observed data and the Q(f) obtained computationally for the total system (FIG. 10). Comparison of the autocorrelation function (ACF) for the bulk-like and DW layers (SI) shows that the bulk-like layer ACF shows the normal behavior of rapid decay followed by small fluctuations around 0, whereas the DW layers show slow ACF decays and large amplitude and period of oscillation due to the much larger magnitude of the fluctuations of DW layer P between the two sides of the double-well potential compared to the oscillations of P inside a well. Therefore, DW fluctuations dominate the dielectric response at low f.

[0102] Analysis of the polarization switching (from −P.sub.y to +P.sub.y and vice versa) rates for individual layers in the supercell shows that hopping rates increase with increasing DC bias (FIG. 11) which can also be seen from the oscillations of the overall polarization time autocorrelation functions (FIG. 12). Thus, the application of the DC bias accelerates the rate of DW oscillations and leads to the shift of the Q(f) curves to higher f With no DW oscillations, a bulk-like 1/f Q spectrum is obtained, whereas for slow DW hopping a relaxation-driven flattening out is observed with gentle oscillations in Q and sharp Q peaks are obtained for faster hopping. This strongly suggests that the experimental Q spectrum with gentle oscillations at zero bias is due to the slow oscillations of the high density of DW and the experimentally observed appearance of sharp Q peaks is due to the acceleration of the DW hopping by the application of DC bias.

[0103] To show that the DW fluctuation mechanism alone can give rise to the observed sharp Q(f) peaks, stochastic simulations were performed using a simple model of coupled bistable oscillators with a domain wall (SI). We find that DW position oscillations and Q(f) profiles qualitatively similar to those obtained in MD can be obtained by adjusting the double-well parameters of the oscillators (SI), demonstrating that DW oscillations can give rise to the observed sharp variation in Q(f).

[0104] The hypothesis that the domain wall position fluctuations give rise to the anomalous Q observed at high static bias in experiments explains why such Q characteristics have not been observed previously. To obtain Q oscillations, a large domain wall density corresponding to domain size of <100 nm is necessary because otherwise the high Q arising from the domain walls will be averaged out by the normal behavior of the bulk of the domain. Secondly, this effect is likely to appear only close to T.sub.C where the thickness of the DW is larger and the barrier to switching is very low, enabling the hopping of the DW layer between the two alternate P.sub.y orientations at GHz frequencies. At lower T, the energy barrier for switching P.sub.y of the layer is too high so that the time necessary to cross the barrier between the two alternative P.sub.y states is too long and high Q would only be observed at f in the MHz range or below where such effect may not be apparent due to the high Q of the bulk dielectric response at such low f Finally, very high quality films are necessary to observe these effects because variation in the frequencies of the very low dielectric loss resonance due to defects, grain boundaries and compositional variations would lead to averaging out of the low loss and the disappearance of the high Q peaks.

[0105] The product of Q and frequency f is one of the most often cited metrics for all dielectric microwave resonators, where acoustic attenuation parameterized by α∝f.sup.2 in the Akhiezer limit for phonon-phonon scattering leads to Qf equaling a material-specific constant. We note that the Qf product in the material deviates from the usual monotonic Q(f) dependence for 1<f.sub.r<10 GHz in our experimental films, showing a strong increase of Qf in this range. This suggests that the effective scattering rate due to thermal phonons is much lower than f.sub.r, providing additional experimental evidence that our domain wall resonant films overcome intrinsic losses in this range. Meanwhile, simulations of BTO indicate that the expected frequency band of voltage-tuned domain wall resonances is material-specific and can be higher than that experimentally observed for BST.

[0106] Thus, these experimental and computational simulation results show that engineered domain structure can in fact be exploited for ultra-low loss and exceptional frequency selectivity without piezoelectric resonance, and very large voltage tunability of capacitance, and without hysteresis. The materials are defined not merely by chemical composition, but rather by the proximity of and accessibility among thermodynamically predicted strain-induced, ferroelectric domain wall variants [Pertsev, N. A. et al. Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films. Phys. Rev. Lett. 80 1988-1991 (1998)] to achieve gigahertz microwave tunability and dielectric loss that surpass those for the current best film devices by 1-2 orders of magnitudes, attaining values comparable to bulk single crystals, but in an intrinsically tunable material. The nearly isotropic free energy-polarization landscape of these materials (and correspondingly lower barrier to polarization rotation) is expected to lead to a rich phase diagram and a large response to an applied electric field. Magnitudes of the measured quality factor Q exceed the theoretically predicted zero-field intrinsic limit owing to domain-wall fluctuations rather than the usual piezoelectric oscillations. Resonant frequency tuning across the entire L, S and C microwave bands is achieved in an individual device, about 100 times larger than the current best intrinsically tuned material. Extrinsically-driven MDVM tunable dielectric materials exhibit Q near T.sub.C that exceeds the intrinsic limit without piezoelectric oscillations, and are promising for achieving similar values of Q at a wider range of frequencies. These results point to a rich phase space of possible nanodomain structures that can be used to surmount current limitations and demonstrate a fundamentally new and promising strategy for ultrahigh frequency agility and low-loss microwave devices.

[0107] The present disclosure comprises at least the following aspects: [0108] 1. An article (e.g., which may be comprise in a resonator, oscillator, device, etc.) comprising a ferroelectric material in its ferroelectric phase, wherein the article is configured to enable low-loss propagation of signals with ultra-low dielectric loss (10.sup.3<Q<10.sup.7, or 10.sup.3>tan δ>10.sup.−7) at select frequencies. [0109] 2. An article comprising a ferroelectric material possessing a high density of one or more (thermally) oscillating ferroelectric domain walls, wherein the article contains domain walls that enable efficient propagation of signals with ultra low dielectric loss (10.sup.3 <Q<10.sup.7, or 10.sup.−3>tan δ>10.sup.−7) at select frequencies, wherein the density of domain walls of ranges from 1-100 per 50,000 nm.sup.2. [0110] 3. An article comprising a ferroelectric material in its ferroelectric phase, wherein the article is configured to enable low-loss propagation of signals with ultra low dielectric loss (10.sup.3<Q<10.sup.7, or 10.sup.−3>tan δ>10.sup.−7) at select frequencies and at or within 20% of Tc of the ferroelectric material. [0111] 4. An article comprising a ferroelectric material in thin film form in its ferroelectric phase, wherein the composition and strain of the material are selected to stabilize the material, for a given temperature, in two or more energetically equivalent, or nearly energetically equivalent thermodynamically predicted domain wall variant types as specified by a domain wall variant boundary or vertex, thereby enabling efficient propagation of signals with ultra-low loss (10.sup.3<Q<10.sup.7, or 10.sup.−3>tan δ>10.sup.−7) at select frequencies [0112] 5. A dielectric, field-tunable article comprising a ferroelectric material, wherein a range and/or values of article frequency and/or frequencies are controlled based on changes in domain wall oscillation frequency in response to electric field applied to the ferroelectric material. [0113] 6. The article of any one of aspects 1-5, wherein the select frequencies are between 0.01 GHz and 300 GHz. [0114] 7. The article of any one of aspects 1-5, wherein a range and/or values of article frequency or frequencies of the article are controlled based on the density of domain walls. [0115] 8. The article of any one of aspects 1-5, wherein the magnitude of the quality factor Q is controlled by the density of domain walls and increases with domain wall density. [0116] 9. The article of any one of aspects 1-5, wherein the range and/or values of article frequency or frequencies are controlled based on the type and/or types of ferroelectric domain wall variants. [0117] 10. The article of any one of aspects 1-5, wherein the range and/or values of article frequency or frequencies are controlled based on the degree of strain.

[0118] 11. The article of any one aspects 1-10 wherein ferroelectric material is in a phase comprising one of: normal ferroelectric, improper ferroelectric, hybrid improper ferroelectric, relaxor ferroelectric, incipient ferroelectric phase, or multi-ferroic ferromagnetic or antiferromagnetic ferroelectric. [0119] 12. An article of aspects 1-11, wherein the range and/or values of article frequency and/or frequencies are controlled based on changes in domain wall oscillation in response to magnetic field applied across the multiferroic ferromagnetic (or antiferromagnetic) ferroelectric material due to multiferroic coupling of magnetic field to ferroelectric polarization. [0120] 13. The article of any one of aspects 1-12, wherein the chemical composition of the ferroelectric material comprises BaTiO.sub.3, (Ba,Sr)TiO.sub.3, PbTiO.sub.3, PZT, (Pb,Sr)TiO.sub.3, BiFeO.sub.3, and related solid solutions.

[0121] 14. An article comprising a ferroelectric material having 1-100 per 50,000 nm.sup.2 of engineered planar two-dimensional topological defects that, under selected DC bias or zero DC bias, oscillate at select frequencies and within 100 degrees C. of the T.sub.C of the ferroelectric material. [0122] 15. The article of aspect 14, wherein the select frequencies are between 0.1 GHz and 300 GHz. [0123] 16. The article of any one of aspects 14-15, wherein an axis of vibration of the ferroelectric domain walls is oriented along one or more directions and is indicative that collective oscillations can support traveling EM waves in the presence or absence of DC bias field. [0124] 17. The article of any one of aspects 14-16, wherein the planar two-dimensional topological defects comprise domain walls, and wherein the domain walls, under the application of a DC or AC field or under zero DC or AC field, oscillate or fluctuate in their position with respect to time. [0125] 18. The article of aspect 17, wherein the timescale or rate of the fluctuations vary depending upon the electrostatic potential landscape and domain width or domain wall density, applied field, temperature, strain (coherent or relaxed) and/or stress. [0126] 19. The article of aspect 18, wherein the corresponding frequency spectrum associated with the fluctuations exhibits one or more minima in material dielectric loss (or peaks in reciprocal loss, Q) along an axis parallel (or perpendicular) to the axis of the domain wall and perpendicular to its fluctuations. [0127] 20. The article of aspect 19, where the width of the domain separating the domain walls fluctuates. [0128] 21. The article of any one of aspects 14-20, wherein ferroelectric material is in its ferroelectric or paraelectric phase (normal ferroelectric, improper ferroelectric, hybrid improper ferroelectric, relaxor ferroelectric, incipient ferroelectric, multi-ferroic ferromagnetic or antiferromagnetic ferroelectric). [0129] 22. The article of any one of aspects 14-22, wherein ferroelectric material comprise BaTiO.sub.3, (Ba,Sr)TiO.sub.3, PbTiO.sub.3, PZT, (Pb,Sr)TiO.sub.3, BiFeO.sub.3, Bi(Fe,Mn)O.sub.3. [0130] 23. A device having a microwave or mm-wave cavity supporting propagation of transverse electromagnetic (TEM) waves with less dissipation than that for the intrinsic limit of the material forming the cavity, wherein the TEM waves are carried and/or modulated by oscillations of one or more domain walls and at or near Tc of a material forming the microwave cavity, wherein the density of domain walls of ranges from 1-100 per 50,000 nm.sup.2 [0131] 24. The device of aspect 23, wherein the microwave cavity comprises a ferroelectric material comprising the one or more domain walls that, under zero bias or selected finite DC bias, oscillate at select frequencies. [0132] 25. The device of aspect 24, wherein an axis of vibration of the one or more domain walls is oriented along one or more directions and is indicative that zero-field or finite DC field-driven collective oscillations can support traveling EM waves. [0133] 26. The device of any one of aspects 23-25, wherein the ferroelectric material is in its ferroelectric or paraelectric phase (normal ferroelectric, improper ferroelectric, hybrid improper ferroelectric, relaxor ferroelectric, incipient ferroelectric, multi-ferroic ferromagnetic or antiferromagnetic ferroelectric). [0134] 27. The device of any one of aspects 23-26, wherein the ferroelectric material comprise BaTiO.sub.3, (Ba,Sr)TiO.sub.3, PbTiO.sub.3, PZT, (Pb,Sr)TiO.sub.3, BiFeO.sub.3, Bi(Fe,Mn)O.sub.3. [0135] 28. The device of any one of aspects 23-27, wherein Q may increase with increasing temperature, depending on the proximity to Tc. [0136] 29. The device of any one of aspects 23-28, wherein the magnitude of Q may depend on the amplitude of ambient stochastic noise (given by temperature) in relation to the amplitude of driving signal probing the transmission and/or reflection of RF, microwave or mm-wave energy through the article. [0137] 30. A method of making the article of any one of aspects 1-22. [0138] 31. A method of making the device of any one of aspects 23-29.

Example Applications

[0139] Transducers. The domain wall oscillating (DWO) material may be a basis for highly efficient transduction of electromechanical energy at one or more resonant frequencies, for sensing and/or actuation, via coupling to mechanical and/or electromagnetic waves. Changes in the resonant frequency associated with the binding of analytes to its surface and its influence on the thermodynamic landscape and DW oscillation conditions, changing the surface boundary condition, is distinct from conventional bulk and/or surface acoustic wave or other similar devices where eigen-frequencies are influenced by the geometry.

[0140] Communications. The availability of an ultra-high Q at room temperature, as well as other temperatures, enabled in the DWO-based devices, permits encoding, detection, sensing of information with considerably higher fidelity than current solid state oscillator materials. This includes utilization as a highly frequency-selective voltage-tuned filter, antenna, or oscillator.

[0141] Position, navigation and timing. The availability of an ultra-high Q at room temperature, as well as other temperatures, enabled in the DWO-based devices, permits more precise relationships (higher fidelity) between variables defining position, navigation and timing and Q, where frequency selectivity is the means of establishing values of these values; and lower power is necessary to transmit or receive signals relating to position, navigation and timing.

[0142] Programmability, by application of local or non-local DC or AC field, strain and/or temperature, of domain structure for reconfiguring DW orientation, oscillation vector, and wave propagation.

[0143] Although the meta-materials and articles have been described herein with reference to preferred embodiments and/or preferred methods, it should be understood that the words which have been used herein are words of description and illustration, rather than words of limitation, and that the scope of the instant disclosure is not intended to be limited to those particulars, but rather is meant to extend to all structures, methods, and/or uses of the herein described meta-materials. Those skilled in the relevant art, having the benefit of the teachings of this specification, may effect numerous modifications to the meta-materials as described herein, and changes may be made without departing from the scope and spirit of the instant disclosure, for instance as recited in the appended claims. As an example, the conventional notion of a ferroelectric having polarization-field hysteresis is not supported because it is suppressed on a macroscopic scale due to the high domain density of the present disclosure.

[0144] An oscillator or system/collection of coupled oscillators in a ferroelectric material may be configured in accordance with the present disclosure to exhibit resonances at odd integer multiple frequencies of the fundamental domain wall switching resonance frequency due to the noise-induced fluctuation of the system between two sides of the double well.

[0145] A resonator may comprise an article for which one or more of the dimension(s) and mechanical and electrical boundary conditions of the volume or cavity containing the medium or bounding the apparatus is selected in accordance with one or more of the domain wall resonance frequencies in order to promote efficient flow of mechanical and/or electromagnetic energy, thereby permitting constructive interference at wave energies in accordance with the altered modulus and/or susceptibility of the domain wall-renormalized (or -dominant) material.