ALKALI METAL METALATE COMPOUNDS WITH MAGNETIC EXCHANGE BIAS AND IONIC CONDUCTIVITY PROPERTIES

Abstract

Please cancel the abstract of this application and replace it with the following amended abstract presented in clean form according to the procedures outlines in MPEP 714(II)(B): It is provided an alkali metal metalate compound with high magnetic exchange bias and ionic conductivity properties having the general formulae (I) A.sub.2[M.sup.1.sub.3-x M.sup.2.sub.x Z.sub.4] with A being one of Li, Na, K; M.sup.1, M.sup.2 being one or more of Cr, Mn, Fe, Co, Ni, Cu, Zn; Z being S or Se; x being 0-3, preferably 0, 0.01, 0.1, 0.5, 1, 1.5, 2, 3; whereby the compounds K.sub.2[Ni.sub.3S.sub.4], K.sub.2[Zn.sub.3S.sub.4], K.sub.2[Mn.sub.3S.sub.4], Na.sub.2[Mn.sub.3Se.sub.4] and K.sub.2[Ni.sub.3Se.sub.4] are exempted.

Claims

1. An alkali metal metalate compound with magnetic exchange bias and ionic conductivity properties having the general formulae (I) $\begin{array}{cc}{A}_2\left[{M^1}_{3-x}{M^2}_x{Z}_4\right]& \left(I\right)\end{array}$ with A being one of Li, Na, K, M.sup.1, M.sup.2 being one or more of Cr, Mn, Fe, Co, Ni, Cu, Zn, Z being S or Se, x being 0-3, preferably 0, 0.01, 0.1, 0.5, 1, 1.5, 2, 3, whereby the compounds K.sub.2[Ni.sub.3S.sub.4], K.sub.2[Zn.sub.3S.sub.4], K.sub.2[Mn.sub.3S.sub.4], Na.sub.2[Mn.sub.3Se.sub.4], and K.sub.2[Ni.sub.3Se.sub.4] are exempted.

2. The compound according to claim 1, having the general formulae (II) $\begin{array}{cc}{A}_2\left[{M^1}_{3-x}{M^2}_x{Z}_4\right]& \left(\mathrm{II}\right)\end{array}$ with A being Na or K, M.sup.1 being Fe; M.sup.2 being one or more of Cr, Mn, Co, Ni, Cu, Zn, Z being S or Se, x being 0-3, preferably 0, 0.01, 0.1, 0.5, 1, 1.5, 2, 3.

3. The compound according to claim 1, having the general formulae (III) $\begin{array}{cc}{A}_2\left[{\mathrm{Fe}}_{3-x}{M^2}_x{Z}_4\right]& \left(\mathrm{III}\right)\end{array}$ with A being Na or K, M.sup.2 being one or more of Cr, Mn, Co, Ni, Cu, Zn, Z being S or Se, x being 0, 0.01, 0.1, 0.5, 1, 1.5, 2, 3.

4. The compound according to claim 1, wherein, the compound is one of the following: A.sub.2[Fe.sub.3S.sub.4]; A.sub.2[Fe.sub.2CoS.sub.4]; A.sub.2[Fe.sub.1.5Co.sub.1.5S.sub.4]; A.sub.2[FeCo.sub.2S.sub.4]; A.sub.2[Co.sub.3S.sub.4]; A.sub.2[Fe.sub.2NiS.sub.4]; A.sub.2[Fe.sub.1.5Ni.sub.1.5S.sub.4]; A.sub.2[FeNi.sub.2S.sub.4]; A.sub.2[Ni.sub.3S.sub.4]; A.sub.2[Fe.sub.2CuS.sub.4]; A.sub.2[Fe.sub.1.5Cu.sub.1.5S.sub.4]; A.sub.2[FeCu.sub.2S.sub.4]; A.sub.2[Cu.sub.3S.sub.4]; A.sub.2[Fe.sub.2ZnS.sub.4]; A.sub.2[Fe.sub.1.5Zn.sub.1.5S.sub.4]; A.sub.2[FeZn.sub.2S.sub.4]; A.sub.2[Zn.sub.3S.sub.4]; A.sub.2[Fe.sub.2MnS.sub.4]; A.sub.2[Fe.sub.1.5Mn.sub.1.5S.sub.4]; A.sub.2[FeMn.sub.2S.sub.4]; A.sub.2[Mn.sub.3S.sub.4]; A.sub.2[Fe.sub.2CrS.sub.4]; A.sub.2[Fe.sub.1.5Cr.sub.1.5S.sub.4]; A.sub.2[FeCr.sub.2S.sub.4]; A.sub.2[Cr.sub.3S.sub.4]; A.sub.2[Fe.sub.3Se.sub.4]; with A being Na or K.

5. The compound according to claim 1, wherein the compound is one of the following: K.sub.2[Fe.sub.3S.sub.4]; Na.sub.2[Fe.sub.3S.sub.4]; K.sub.2[Fe.sub.2CoS.sub.4]; K.sub.2[Fe.sub.1.5Co.sub.1.5S.sub.4]; K.sub.2[Co.sub.3S.sub.4]; K.sub.2[Cr.sub.3S.sub.4]; K.sub.2[Fe.sub.3Se.sub.4].

6. The compound according to claim 1, having an ionic conductivity in a range between 110.sup.1 and 110.sup.3 Scm.sup.1, preferably in a range between 110.sup.2 and 110.sup.3 Scm.sup.1, more preferably between 210.sup.2 and 810.sup.2 Scm.sup.1.

7. The compound according to claim 1, having an exchange bias field in a range between 20 and 50 mT, preferably between 30 and 40 mT, more preferably between 33 and 38 mT at 3K.

8. A method for obtaining a compound according to claim 1, comprising the step of reacting A.sub.2Z with equivalents of M.sup.1Z and M.sup.2Z at a temperature between 1073 K and 1473 K, preferably between 1123 K and 1373 K, more preferably between 1173 K and 1273 K, under inert gas atmosphere for 5-30 min, preferably 10-20 min.

9. The method according to claim 8, wherein A.sub.2Z is obtained from reacting elemental A and elemental Z in liquid NH.sub.3 under inert gas atmosphere.

10. (canceled)

11. (canceled)

12. Compound according to claim 1, applicable for exchange bias applications, in particular in transistors, MOSFETs, MRAMs, or as solid-state electrolytes, in particular in solid-state electrolytes, in particular in alkali-metal batteries.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The solution is explained in the following by means of the examples with reference to the figures.

[0060] FIG. 1a shows depiction of the crystal structure of K.sub.2[Fe.sub.3S.sub.4].

[0061] FIG. 1b shows temperature dependent magnetization curves of. K.sub.2[Fe.sub.3S.sub.4].

[0062] FIG. 1c shows magnetization curves after cooling under applied field of 3 T of K.sub.2[Fe.sub.3S.sub.4].

[0063] FIG. 1d shows dielectric and complex impedance properties of K.sub.2[Fe.sub.3S.sub.4].

[0064] FIG. 2a shows depiction of the crystal structure of Na.sub.2[Fe.sub.3S.sub.4].

[0065] FIG. 2b shows dielectric and complex impedance properties of Na.sub.2[Fe.sub.3S.sub.4].

[0066] FIG. 2c shows magnetization curves of Na.sub.2[Fe.sub.3S.sub.4].

[0067] FIG. 3a shows depiction of the crystal structure of K.sub.2[Co.sub.3S.sub.4].

[0068] FIG. 3b shows magnetization curves of K.sub.2[Co.sub.3S.sub.4].

[0069] FIG. 3c shows dielectric and complex impedance properties of K.sub.2[Co.sub.3S.sub.4].

[0070] FIG. 4a shows depiction of the crystal structure of K.sub.2[Fe.sub.3Se.sub.4].

[0071] FIG. 4b shows magnetization curves of K.sub.2[Fe.sub.3Se.sub.4].

[0072] FIG. 4c shows dielectric and complex impedance properties of K.sub.2[Fe.sub.3Se.sub.4].

[0073] FIG. 5a shows depiction of the crystal structure of K.sub.2[(Fe/Co).sub.3Se.sub.4].

[0074] FIG. 5b shows magnetization curves of K.sub.2[(Fe/Co).sub.3Se.sub.4].

[0075] FIG. 5c shows complex impedance properties of K.sub.2[(Fe/Co).sub.3Se.sub.4].

[0076] FIG. 6 shows depiction of the crystal structure of K.sub.2[Cr.sub.3S.sub.4].

DETAILED DESCRIPTION

Example 1: Synthetic Details

[0077] All proposed alkali metal sulfido metalate compounds with the stoichiometry ratio of A.sub.2[M.sup.1.sub.3-xM.sup.2.sub.xS.sub.4] have been synthesized through the solid state reactions, by mixing the starting materials and subsequent heat treatment. Regarding the air- and moisture-sensitivity of the compound and most of the starting materials, all steps of the synthesis processes were performed under inert atmosphere conditions using Ar-filled glovebox and/or Schlenk lines. The purity of all products was investigated and confirmed by the results of X-ray diffraction and Energy-dispersive X-ray spectroscopy measurements. The description of the synthetic details for each compound are listed in table 2. More details about the synthesis processes are provided in following parts.

TABLE-US-00002 TABLE 2 Starting Reaction Reaction Color of Yield Compound materials temperature time product per run K.sub.2[Fe.sub.3S.sub.4] K.sub.2S + 3 FeS 1173 K 10 min Dark green 20 g Na.sub.2[Fe.sub.3S.sub.4] Na.sub.2S + 3 FeS 1123 K 6 min Dark green 18 g K.sub.2[Co.sub.3S.sub.4] K.sub.2S + 3 CoS 1173 K 10 min Dark gray 20 g K.sub.2[Ni.sub.3S.sub.4] K.sub.2S + 3 Ni + 3 S 1173 K 10 min Golden 20 g K.sub.2[Cr.sub.3S.sub.4] K.sub.2S + 3 Cr + 3 S 1273 K 15 min Gray 15 g K.sub.2[Zn.sub.3S.sub.4] K.sub.2S + 3 ZnS 1173 K 10 min Brown 20 g K.sub.2[Fe.sub.3xCo.sub.xS.sub.4] K.sub.2S + (1.5).sub.1x 1173 K 10 min Dark gray 20 g FeS + (1.5).sub.x CoS

Starting Materials

[0078] FeS, CoS, ZnS, Ni, Cr, Se and S are purchased in commercial grades and purity of all of them have been evaluated and confirmed before using.

[0079] Synthesis K.sub.2S (applicable method for K.sub.2Se, using selenium instead of sulfur with adjusted masses): 20 g (2 eq, 0.5115 mol) K (ACROS organics, 98%) were placed in three necks flask connected to NH.sub.3 gas flow. Using the cooling bath of ethanol and dry ice, the temperature of the flask was decreased to around 198 K to condense NH.sub.3 from the gas phase to liquid form. Since the reaction of elemental potassium and sulfur could be very exothermic, potassium chucks were initially dissolved in the liquid NH.sub.3 under inert atmosphere up to a change of the color of the stirring solution to dark blue. Afterwards, 8.2 g (1 eq, 0.2557 mol) S (abcr, 99% sublimed) was gradually added to the solution at the temperature of around 240 K. The mixture was stirred overnight to complete the reaction and slowly release NH.sub.3 by allowing the temperature to increase to room temperature. Inside the glovebox, the powder was grinded and prepared for powder X-ray diffraction analysis to verify the purity.

[0080] Synthesis Na.sub.2S: 17.68 g (2 eq, 0.7693 mol) Na (ACROS organics, 98%) were placed in three necks flask connected to NH.sub.3 gas flow. Using the cooling bath of ethanol and dry ice, the temperature of the flask was decreased to around 197 K to condense NH.sub.3 from the gas phase to liquid form. Since the reaction of elemental sodium and sulfur could be very exothermic, sodium chucks were initially dissolved in the liquid NH.sub.3 under an inert atmosphere up to a change of the color of the stirring solution to dark blue. Afterwards, 12.32 g (1 eq, 0.3842 mol) S (abcr, 99% sublimed) was gradually added to the solution at the temperature of around 240 K. The mixture was stirred overnight to complete the reaction and slowly release NH.sub.3 by allowing the temperature to increase to room temperature. Inside the glovebox, the powder was grinded and prepared for powder X-ray diffraction analysis to verify the purity.

Ternary Compounds

[0081] Synthesis of K.sub.2[Fe.sub.3S.sub.4]: 10 g (1 eq, 0.091 mol) of synthesized K.sub.2S and 23.91 g (3 eq, 0.272 mol) FeS (Sigma-Aldrich) were homogenously mixed and placed in a quartz ampoule. The ampoule was connected to a Schlenk line with pressure release option and heated to approx. 1173 K (orange glowing of the ampule) for about 10 minutes under Ar flow and allowed to cool to room temperature. After cooling down, the ampule was transferred into the glovebox, carefully broken, and compound blocks were removed. Multigram of pure product was obtained as dark green, air and moisture sensitive powder. The structure for this compound is depicted in FIG. 1a.

[0082] K.sub.2[Fe.sub.3S.sub.4] crystallizes in 14/mmm space group with two units in the unit cell with a=3.7730(2) , c=13.3526(9) , V=190.08(2) .sup.3. The iron atoms are tetrahedrally coordinated by sulfur atoms with FeS bond lengths of 2.344(8) . [Fe.sup.IIS.sub.4].sup.6 tetrahedra are edge-sharing to form anionic layers. The iron positions statistically occupied at 75%, which was also confirmed by the X-ray diffraction and energy-dispersive X-ray spectroscopy measurements. K.sub.2[Fe.sub.3S.sub.4] is the first potassium sulfidoferrate compound with pure Fe (II) and a layered anionic sublattice.

[0083] Synthesis of Na.sub.2[Fe.sub.3S.sub.4]: 10 g (1 eq, 0.128 mol) of synthesized Na.sub.2S and 33.79 g (3 eq, 0.384 mol) FeS (Sigma-Aldrich) were homogenously mixed and placed in a quartz ampoule. The ampoule was connected to a Schlenk line with pressure release option and heated to approx. 1123 K for about 6 minutes under Ar flow and allowed to cool to room temperature. After cooling down, the ampule was transferred into the glovebox, carefully broken, and compound blocks were removed. Multigram of pure product was obtained as dark green, air and moisture sensitive powder. The structure for this compound is depicted in FIG. 2a.

[0084] Na.sub.2[Fe.sub.3S.sub.4] crystallizes in P-3m1 space group with one unit in the unit cell with a=3.8495(3) , c=6.7606(5) , V=86.761(15) .sup.3. The iron atoms are tetrahedrally coordinated by sulfur atoms. [Fe.sup.IIS.sub.4].sup.6 tetrahedra are edge-sharing to form anionic layers with two perpendicular conductivity channels for Na ions in parallel and perpendicular to the ab plane. The iron positions statistically occupied at 75%, which was also confirmed by the X-ray diffraction measurements.

[0085] Synthesis of K.sub.2[Co.sub.3S.sub.4]: 10 g (1 eq, 0.091 mol) of synthesized K.sub.2S and 24.75 g (3 eq, 0.272 mol) CoS (Sigma-Aldrich) were homogenously mixed and placed in a quartz ampoule. The ampoule was connected to a Schlenk line with pressure release option and heated to approx. 1173 K (orange glowing of the ampule) for about 10 minutes under Ar flow and allowed to cool to room temperature. After cooling down, the ampule was transferred into the glovebox, carefully broken, and compound blocks were removed. Multigram of pure compound was obtained as dark gray, air and moisture sensitive powder. The structure for this compound is like the structure of K.sub.2[Fe.sub.3S.sub.4] as an isotypic structure.

[0086] The crystal structure of K.sub.2[Co.sub.3S.sub.4] is depicted in FIG. 3a: (a) Depicted along a including edge-sharing [CoS.sub.4].sup.6-tetrahedra. (b) 2D anionic substructure of [Co.sub.3S.sub.4].sup.2 as layers in the ab plane (c) Edge-sharing tetrahedra connections to create anionic layers (d) Light microscopy photograph of single crystals of K.sub.2[Co.sub.3S.sub.4] at 60 magnification. Selected bond lengths and angles: CoS: 2.3054(31) , KS: 3.3163(33) , SCoS: 109.066(31)-109.674(12). Partial occupations of cobalt atoms are omitted for clarity.

[0087] Synthesis of K.sub.2[Fe.sub.3Se.sub.4]: K.sub.2Se, Fe, and Se were mixed together in stoichiometric ratios. The preparation was performed under inert conditions. The precursor K.sub.2Se was synthesized by using K (14.82 g, 379.04 mmol, 2 eq.) dissolved in an NH.sub.3 solution. After that, Se (15.07 g, 189.97 mmol, 1 eq.) was added to the stirred solution. After passing through, the color change from dark blue to gray and then turns beige after stirring overnight. The solid was dried under a vacuum. The PXRD confirmed K.sub.2Se without impurities. After that, K.sub.2Se (2.80 g, 17.82 mmol, 1 eq.), Fe (2.98 g, 53.45 mmol, 3 eq.), and Se (4.22 g, 53.45 mmol, 3 eq.) were transferred to a fused silica ampule. With a methane-oxygen torch around 1250 K for 10 minutes, all starting materials were reacted under argon. The cooled ampule was transferred to an Ar-filled glovebox. K.sub.2[Fe.sub.3Se.sub.4] was obtained as a black metallic powder.

[0088] K.sub.2[Fe.sub.3Se.sub.4] crystallizes in the tetragonal space group 14/mmm (no. 139) with two independent units per unit cell. Each iron atom is tetrahedrally surrounded by four selenium atoms; potassium atoms serve as counter ions. FIG. 4a indicates the crystal structure, showing a statistical occupation on the iron atom position of 75%. The figure shows the crystal structure along the ac-plane, information about distances and atom positions are listed in the electronic supporting information.

[0089] Synthesis of K.sub.2[Cr.sub.3S.sub.4]: 10.54 g (1 eq.) of synthesized K.sub.2S and 8.72 g (3 eq.) S were homogenously mixed and placed in a quartz ampoule. 14.14 g (3 eq.) elemental chromium were placed in a Schlenk flask and connected to the quartz ampoule. The ampoule was connected to a Schlenk line with pressure release option and heated to approx. 773 K to melt the mixture of K.sub.2S and sulfur and then gradually added the elemental chromium to the molten phase and heated it to approx. 1273 K (yellow glowing of the ampule) for about 15 minutes under Ar flow and allowed to cool to room temperature. After cooling down, the ampule was transferred into the glovebox, carefully broken, and compound blocks were removed. Multigram of pure compound was obtained as gray, air and moisture sensitive powder. The obtain structure crystallizes in C2/m space group with two units in the unit cell with a=13.503 (2) , b=3.6078 (4) , c=7.7210 (13) , =90, =105.701 (6), =90, V=362.10 (9) .sup.3. The chromium atoms are tetrahedrally coordinated by sulfur atoms. The structure for this compound is depicted in FIG. 6

[0090] Synthesis of K.sub.2[Ni.sub.3S.sub.4]: 10 g (1 eq.) of synthesized K.sub.2S and 8.72 g (3 eq.) S were homogenously mixed and placed in a quartz ampoule. 16 g (3 eq.) elemental nickel were placed in a Schlenk flask and connected to the quartz ampoule. The ampoule was connected to a Schlenk line with pressure release option and heated to approx. 773 K to melt the mixture of K.sub.2S and sulfur and then gradually added the elemental chromium to the molten phase and heated it to approx. 1173 K (yellow glowing of the ampule) for about 10 minutes under Ar flow and allowed to cool to room temperature. After cooling down, the ampule was transferred into the glovebox, carefully broken, and compound blocks were removed. Multigram of pure compound was obtained as golden, air and moisture sensitive powder.

[0091] Synthesis of K.sub.2[Zn.sub.3S.sub.4]: 10 g (1 eq, 0.091 mol) of synthesized K.sub.2S and 26.51 g (3 eq, 0.272 mol) ZnS were homogenously mixed and placed in a quartz ampoule. The ampoule was connected to a Schlenk line with pressure release option and heated to approx. 1173 K (orange glowing of the ampule) for about 10 minutes under Ar flow and allowed to cool to room temperature. After cooling down, the ampule was transferred into the glovebox, carefully broken, and compound blocks were removed. Multigram of pure compound was obtained as dark gray, air and moisture sensitive powder. The obtain structure for this compound is like the structure of K.sub.2[Fe.sub.3S.sub.4] as an isotypic structure.

Quaternary Compounds

[0092] Synthesis of K.sub.2[Fe.sub.3-xCo.sub.xS.sub.4] (x=0, 1, 2): For synthesizing these compounds, the stoichiometric rations of synthesized K.sub.2S, FeS, and CoS were homogenously mixed and placed in a quartz ampoule. The ampoule was connected to a Schlenk line with pressure release option and heated to approx. 1173 K (orange glowing of the ampule) for about 10 minutes under Ar flow and allowed to cool to room temperature. After cooling down, the ampule was transferred into the glovebox, carefully broken, and compound blocks were removed. Multigram of pure product was obtained as dark green, air and moisture sensitive powder. The obtain structures for these compounds are like the structure of K.sub.2[Fe.sub.3S.sub.4] and K.sub.2[Co.sub.3S.sub.4] as the potential isotypic structures.

Example 2: Analytics of K.SUB.2.[Fe.SUB.3.S.SUB.4.]

Exchange Bias Effects

[0093] Magnetic properties of K.sub.2[Fe.sub.3S.sub.4] were evaluated based on the curves of magnetization as a function of the applied magnetic field at different temperatures and fields. To determine the magnetic structure of K.sub.2[Fe.sub.3S.sub.4], the magnetization-field curves can be employed while their shape and trend identify the type of magnetic ordering. Field dependent magnetization plots of K.sub.2[Fe.sub.3S.sub.4] at constant temperatures (not shown) indicate non-linear narrow hysteresis loops. The observed hysteresis loop at low fields is a sign of ferromagnetic (FM) ordering while the unsaturated linear part at high fields is a known characteristic of antiferromagnetic (AFM) structures. This combination indicates a complex magnetic structure in K.sub.2[Fe.sub.3S.sub.4] consisting of a coexistence of both ordering types.

[0094] The temperature-dependent magnetization curves at constant fields and after cooling under zero applied field, which are denoted field cooled (FC) and zero field cooled (ZFC) curves respectively, provide more information about the magnetic ordering. FIG. 4a depicts the FC/ZFC curves of K.sub.2[Fe.sub.3S.sub.4] in the temperature range of 1 to 380 K. The first obvious point in the figure is the separation of the FC and the ZFC curves over the whole temperature range and particularly at low temperatures. The separation of the curves indicates the existence of a spin-glass structure. Starting at low temperatures the difference of the magnetization values between the FC and the ZFC curves is increased up to around 20 K. At higher temperatures the difference dramatically decreased as a function of temperature. To clearly identify the characteristics of both AFM and spin-glass orderings the tendency of the variation can be followed by the first derivative of the magnetization difference, d[M.sub.FCM.sub.ZFC]/dT. Accordingly, the minimum value of the d[M.sub.FCMZ.sub.FC]/dT curve (FIG. 4a) shows the magnetic freezing temperature at around 20 K, that corresponds to the changing point of the slope in the ZFC curve.

[0095] At temperatures around 314 K there are small cusps in both, the FC and the ZFC curves which correspond to the Nel temperature of the AFM phase. Above the Nel temperature, the dominant magnetic structure is transformed from an AFM to a paramagnetic ordering. In addition, the ZFC invers susceptibility (X) curve indicates a significant deviation from the fitting line of the Curie-Weiss law at around 314 K (not shown), validating the Nel temperature determination of the AFM phase. The negligible change in the slope of FC curve at temperatures slightly below the freezing temperature can be considered as another confirmation of the spin-glass effects. To confirm the AFM ordering and Nel transition temperature, the magnetization variation of FC curve can be investigated as the derivation equation of dM.sub.FC/dT. The maximum value of dM.sub.FC/dT curve (FIG. 4b) demonstrates the same obtained Nel temperature of 314 K.

[0096] FIG. 4b indicates another characteristic temperature of the complex ordering, bifurcation temperature, which is defined as a starting point of FC/ZFC curves separation. The bifurcation temperature in K.sub.2[Fe.sub.3S.sub.4], according to the difference variations of the FC/ZFC values, indicates the reversibility character of the magnetic behavior. The curve of M=M.sub.FCM.sub.ZFC as a function of the temperature determines that the irreversibility (bifurcation) temperature of the structure is higher than 380 K, which is the maximum available measurement range.

[0097] A detailed analysis of the field-magnetization curve at 3 K (not shown) indicates the asymmetric hysteresis loops including shifts in both the remanence, and the coercivity. Under applied fields the shifts are observed in opposite directions. The observed asymmetries are a well-known sign of exchange bias effects that horizontally and vertically shift the hysteresis loop. To investigate the induced (exchange bias) EB field more precisely, the FC hysteresis loops were measured at different temperatures after cooling under an applied field of 3 T (FIG. 5a). The field-dependent magnetization curves at 3 and 20 K demonstrate asymmetric half hysteresis loops in opposite directions of applied magnetic field, with the significant shifting for both remanence and coercivity values. FIG. 5b shows the variations of the EB field, which is equivalent to shifts in the coercivity, and the remanence as a function of increased temperature. By increasing the temperature beyond 100 K, both the EB field and the remanence are dramatically decreased to negligible values and approach a plateau at temperatures higher than 200 K. Such behavior is in good agreement with the calculated freezing temperature of spin glass phase based on the FC/ZFC curves.

[0098] At 3 K, the large EB field and the EB remanence are 35 mT and 0.27 Am.sup.2 kg.sup.1, respectively (FIG. 5c). The disordered spin-glass moments can interact with antiferromagnetically ordered moments and pin them to induce the EB behavior. Indeed, the iron vacancies could play a mechanistic role to provide spontaneous EB effects by pinning the ordered magnetic areas. These findings could confirm the Fe vacancy effects on the recently introduced EB field in the AFM/spin-glass combined orderings.

Ionic Conductivity

[0099] The dielectric properties of pellets of K.sub.2[Fe.sub.3S.sub.4] sintered at 1103 K were measured at room temperature as a function of the alternating current, AC, with electrical field frequencies in the range of 100 Hz to 100 kHz. The real part () of the electrical permittivity can provide the dielectric constant k. The electrical permittivity was calculated according to the measured capacitance (C), surface of electrode plates (A), distance between electrode plates (d), and permittivity of vacuum (.sub.0: 8.8510.sup.12 m.sup.3 kg.sup.1 s.sup.4A.sup.2) through equation 2.

[00004]$\begin{array}{cc}=Cd{}_0^{-1}{A}^{-1}& \left(2\right)\end{array}$

[0100] FIG. 6a (main frame) depicts the variations of the dielectric constant of K.sub.2[Fe.sub.3S.sub.4] as a function of the frequency. Starting from low frequencies, the dielectric constant is rapidly reduced with an increase in the frequency due to the pining of charge domains and vanishing of the space charge polarization mechanism. Grain boundaries, disordering and displacements in the grains, vacancies, and other defects could significantly act as a pinning agent. At frequencies lower than 400 Hz, the measurement results were not reliable and thus omitted. In addition, there is an unexpected slight increase at frequencies between 400 to 800 Hz that might be caused by fringe effects. The average measured k at 1 kHz is 1119, that is comparable with barium titanate as a well-known commercial capacitor material, and higher than many other dielectric materials, such as strontium titanate, barium strontium titanate, and zirconate titanate.

[0101] The dielectric constant gradually reduces with an increase in the frequency; however, the rate of decrease is relatively low. Indeed, although the space charge polarization mechanism becomes ineffectual at high frequencies, the vacancies could still work as charge carriers and defects dipoles which are polarizable up to the MHz frequency range. FIG. 6b depicts the scanning electron microscopy micrograph in the backscattered electron mode from the cross-section surface of sintered pellets of K.sub.2[Fe.sub.3S.sub.4], indicating the sintered grains and grain boundaries.

[0102] In addition, the complex impedance measurements were employed to investigate the electrical conductivity of K.sub.2[Fe.sub.3S.sub.4]. Since the disordered areas including grain boundaries, and other structural defects could act as the efficient polarization areas, the Nyquist plot could be utilized to recognize these effects according to the equivalent circuit model including two parallel resistor-constant phase element series for ordered and disordered areas (FIG. 6c). The plot indicates two semicircular arcs with a small overlap, which can be assigned to ordered and disordered areas, respectively. This combination is in agreement with the model of graingrain boundaries for solid-state electrolytes in Li/Na-ion batteries. Besides the semicircular arcs, there is a linear spike at low frequency range, which is related to the polarization of the electrode. This indicates an ionic contribution to the electrical conductivity.

[0103] K.sub.2[Fe.sub.3S.sub.4] demonstrates very high ionic conductivity while the low ionic conductivity is the main drawback of the solid-state electrolytes in all solid-state batteries. The ionic conductivity and activation energy calculated by means of the Nyquist and Arrhenius equations yields 24.37 mScm.sup.1 and 0.089 eV, respectively. The calculated ionic conductivity for K.sub.2[Fe.sub.3S.sub.4] is much higher than usual solid state electrodes and could be comparable with the common liquid electrolytes.

Example 3: Analytics of Na.SUB.2.[Fe.SUB.3.S.SUB.4.]

[0104] FIG. 2b (a) indicates the dielectric constants of the samples as a function of electrical field frequency in the range of 0.1 to 100 kHz. In all samples, the dielectric constant rapidly decreases with increasing frequency up to around 10 kHz, and then continuously decrease at a reduced rate. At frequencies lower than a critical range (approx. 1 to 10 kHz, depending on the materials and measurement conditions), the dominant polarization contribution is assumed to result from the space-charge mechanism which, in Na.sub.2[Fe.sub.3S.sub.4], sharply vanishes at frequencies around 1 kHz. The dielectric constant of Na.sub.2[Fe.sub.3S.sub.4]-923 (sintered at 923 K) is around 1850 at a frequency of 1 kHz, significantly higher than some benchmark dielectric materials such as barium and strontium titanates. Lower sintering temperatures result in lower dielectric constants.

[0105] Samples of Na.sub.2[Fe.sub.3S.sub.4]-823 (sintered at 823 K) and Na.sub.2[Fe.sub.3S.sub.4]-723 (sintered at 723 K) indicate dielectric constants of 1002 and 998 at 1 kHz, respectively. The dependency of dielectric constants to the sintering temperature can be explained by the considerable impacts of the sintering temperature on the bulk density of materials as a well-known phenomenon in electronic materials. At higher temperatures, a higher number of sintering mechanisms is activated, leading to potentially higher bulk density of materials. Lower sintering temperatures result in lower dielectric constants.

[0106] In a similar trend the dielectric losses of all samples are decreased for an increase of the measurement frequency, while the sample sintered at higher temperature shows lower loss values (FIG. 2b (a), inset frame). The dielectric losses of Na.sub.2[Fe.sub.3S.sub.4]-923, Na.sub.2[Fe.sub.3S.sub.4]-823, and Na.sub.2[Fe.sub.3S.sub.4]-723 are around 0.045, 0.057, and 0.059, respectively, at 1 kHz.

[0107] Complex impedance measurements at ambient temperature were carried out to investigate the transport properties of the samples, by plotting the Nyquist curves of real and imaginary parts of the impedance. FIG. 2a (b) displays the Nyquist plots of samples sintered at different temperatures in the frequency range of 100 mHz to 1 MHz. Plots for all samples indicate a semicircular trend. The simulated curves were plotted by designing an equivalent circuit of two subsequent sections of parallel capacitor and resistor elements, with the sections representing the grain-grain boundary model on the complex impedance. The intersections of the curves with the Z axis were considered as the total bulk resistivity of the samples to calculate their ionic conductivity. The value of bulk resistivity is decreased by increasing the sintering temperature, from approx. 1955 for the sample of Na.sub.2[Fe.sub.3S.sub.4]-723, to 932 for Na.sub.2[Fe.sub.3S.sub.4]-823, and to 647) for Na.sub.2[Fe.sub.3S.sub.4]-923. As the sintering at higher temperature principally results in a higher density of the bulk material, the potential porosities within the samples sintered at lower temperatures can act as non-conductive barriers for the ion transfer through the microstructure. The calculated ionic conductivity of the sample of Na.sub.2[Fe.sub.3S.sub.4]-923 is 3.37 ms.Math.cm.sup.1 which is in the range of highest reported values for sodium ionic conductivity.

Example 4: Analytics of K.SUB.2.[Co.SUB.3.S.SUB.4.]

[0108] The conducted magnetometry measurements of K.sub.2[Co.sub.3S.sub.4] at different temperatures, including field-dependent magnetization curves and temperature-scan curves, are presented in FIG. 3b. The magnetization curves as a function of external applied field up to 4.00 T (FIG. 3b (a)) indicate the hysteresis curves at low temperatures of 3, 20, and 100 K, while the by increasing the temperature the curves change to the narrower loops, decreasing the coercivity and remanent magnetization values. At these temperatures, the plots show a linear trend upon the applied field of higher than 0.35 T, which could consider as a minor sign of AFM structure. At the temperature of 300 K, the curve shows a fully linear trend of magnetization plot, as evidence of the paramagnetic structure. To reveal the main magnetic ordering of the structure, the susceptibility measurements were carried out. The inverse of magnetic susceptibility curve versus temperature, is displayed in FIG. 3b(b), indicating a deviation from the fitting line of the Curie-Weiss law. The negative value of Curie-Weiss constant of around 780 K is evidence of the AFM structure of K.sub.2[Co.sub.3S.sub.4]. The high absolute value of Curie-Weiss constant proves the strong AFM interaction in the structure. The calculated effective moment is around 20 B. The utilized equation and calculation details of effective moment are presented in the SI. The deviation point shows a Nel temperature of around 200 K, as a transition temperature to the paramagnetic behavior of K.sub.2[Co.sub.3S.sub.4], which agrees with the linear paramagnetic curve at 300 K, in the field-dependent measurements (FIG. 3b(a)). The temperature-dependent magnetization curves consisting of the FC and ZFC measurements' results are illustrated in FIG. 3b (c). ZFC and FC curves indicate four transition points including the Nel temperature at 200 K, the irreversible bifurcation temperature (T.sub.Irr) at around 65 K, and two anomalies at around 35 and 105 K, which are abbreviated as T.sub.1 and T.sub.2, respectively. At the temperatures lower than T.sub.Irr, the magnetization is increased because of the occurred spin canting in the AFM structure. In addition, at low temperatures, the hysteresis loops (FIG. 3b(a)) display the shifting deviation from the zero point which is considered as a sign of exchange bias (EB) effect. EB effect is a magnetic interfacial phenomenon, theoretically raised from the combination of two different magnetic orders, most commonly ferromagnetic and antiferromagnetic structures.

[0109] FIG. 3c(a) displays the results of dielectric measurements, at room temperature, of the samples sintered at three different temperatures of 903, 1003, and 1103 K which are abbreviated as samples K.sub.2[Co.sub.3S.sub.4]-903, K.sub.2[Co.sub.3S.sub.4]-1103, and K.sub.2[Co.sub.3S.sub.4]-1103, respectively. At 1 kHz, as an accepted standard frequency for the applications, the dielectric constants (K) of K.sub.2[Co.sub.3S.sub.4]-903, K.sub.2[Co.sub.3S.sub.4]-1003, and K.sub.2[Co.sub.3S.sub.4]-1103 are around 550, 1220, and 2650, respectively. The values, particularly the latest one, are significantly higher than benchmark dielectric materials for the applications as the circuit capacitors such as barium and strontium titanates (=1000 to 2000) as well as high-K dielectric gate standard material (SiO.sub.2, =3.9) for the MOSFET applications. The enhanced values of dielectric constants as a function of sintering temperature can be explained by higher density as well as larger domain to domain boundary ratio which potentially create larger space charge polarization areas. For all samples, by increasing the frequency the dielectric constant values decreased, sharply in the initial step from 0.1 to 2 kHz, and then gradually in the range of 4 to 100 kHz. As a well-stablished phenomenon, the sharp decreasing is attributed to the vanishing of space charge polarization mechanisms at high frequencies, while it is dominant mechanism at frequencies lower than 10 kHz. In parallel, the dielectric loss values of all samples are decreased by increasing the frequency. At frequency of 1 kHz, for all samples these values are lower than 0.1, as a well-defined criterion of dielectric loss for the capacitor and MOSFET applications, indicating the reliability of the measurements. In addition, the increase in sintering temperature leads to slightly decrease the loss values due to the higher density of samples sintered at higher temperatures.

[0110] The Nyquist plots of conducted impedance measurements, at room temperature, of the samples sintered at different temperatures as well as the simulated complex impedance plots are shown in FIG. 3c(b). All samples present the semi-circular arcs with the intercept points with the real impedance (Z) axis of around 161 for K.sub.2[Co.sub.3S.sub.4]-903, 153 for K.sub.2[Co.sub.3S.sub.4]-1003, and 81 for K.sub.2[Co.sub.3S.sub.4]-1103. The corresponding ionic conductivity values calculated based on the Nyquist equation.sup.21 are 9.4, 11.1, and 21.3 ms.Math.cm.sup.1 for the samples of K.sub.2[Co.sub.3S.sub.4]-903, K.sub.2[Co.sub.3S.sub.4]-1003, and K.sub.2[Co.sub.3S.sub.4]-1103, respectively.

Example 5: Analytics of K.SUB.2.[Fe.SUB.3.Se.SUB.4.]

[0111] The field dependent magnetization (M-H) curves at different temperatures are shown in FIG. 4b. According to these results, the general ordering of K.sub.2[Fe.sub.3Se.sub.4] is antiferromagnetic, while the tiny hysteresis loops at the curves, especially at the low temperatures could be considered as a magnetic disordering such as ferro-/ferri-magnetic phase or spin glass phase.

[0112] The applied field was up to 5.00 T. After field cooling, the applied field was up to 3.00 T. At all temperatures, the trend of hysteresis behavior is visible. The magnetization values seem temperature dependent, with increasing temperature values the magnetization decreases.

[0113] The curves of low temperatures of 2 and 20 K (not shown) show a strong sign of exchange bias effects, indicating large exchange bias fields of around 0.22 T at 2 K and 0.13 T at 20 K. The results of magnetic measurements and the observed exchange bias effects are in agreement with the obtained results for the isotypic structures and sulfido ferrate and cobaltate. The origin of these effects could be explained by the combination of antiferromagnetic ordering of the compound and potential spin glass areas.

[0114] A decrease of dielectric constant with increasing frequency is determined. At 1 kHz at 293 K, a k-value of 2029 is determined (FIG. 4c (a)). Nyquist plot of complex impedance measurements of K.sub.2[Fe.sub.3Se.sub.4] is presented in FIG. 4c(b). The complex impedance curve is semicircular with the intercept of 75.56 with the real impedance axis, which is considered as a bulk resistance of the sample. The calculated value of ionic conductivity based on the Nyquist equation indicate a very high value of 31.04 ms.Math.cm.sup.1 at room temperature. This finding is in agreement with the obtained ionic conductivity values for the isotypic structures of sulfido ferrate and cobaltate.

Example 6: Analytics of K.SUB.2.[(Fe/Co).SUB.3.Se.SUB.4.]

[0115] Central metal deficiency in quantum materials has remarkable impacts on magnetic and electrical properties, introducing novel candidates for related applications such as energy storage devices and spintronic systems. In this work, we introduced a novel quaternary compound of potassium sulfido ferro-cobaltate of K.sub.2[Fe.sub.1.5Co.sub.1.5S.sub.4]. The central metal positions in anionic moiety are shared by iron and cobalt ions, equally, while they statistically occupied 75% of these positions, indicating 25% of central metal vacancies in the layered anionic sublattice. The impedance and dielectric investigations indicate remarkable ionic conductivity of 23.1 ms.Math.cm.sup.1, which is between the reported values for ternary potassium sulfido-cobaltate and ferrate. The obtained value is in the range of highest ever reported values for potassium-containing bulk materials. Magnetometry results illustrate the antiferromagnetic structure with an intrinsic exchange bias field of 28 mT at 2 K. The observed exchange bias field could be potentially attributed to the interfacial effects of interaction between antiferromagnetic order and distributed disordering areas in the magnetic structure of the compound.