Crystal structural, magnetic, and dielectric properties of Cobalt−doped breathing pyrochlore LiInCr4−xCoxO8

Here, the structural, magnetic, and dielectric features of breathing pyrochlore LiInCr4−xCoxO8 were investigated. The XRD analysis showed changes in Cr–Cr length and distorted CrO6 octahedral as Co ion doping level rises. The x-ray photoemission spectroscopy measurements showed that there are both Co2+ and Co3+ ions in the LiInCr4−xCoxO8 compounds. The difference between temperature-dependent magnetization curves during field cooling and zero-field cooling suggested that there is a spin-glass state, which was verified by the heat capacity measurement. Doping affects the bond length, which affects the magnetic properties and electronic properties. The dielectric characteristics were systematically studied, and the temperature dependence of the dielectric loss and dielectric constant was examined in the temperature range of 323−573 K at various frequencies. The dielectric behavior strongly changes with the change in temperature and/or frequency. The activation energies of grain boundary resistance of doped samples show a decreasing trend with increasing doping.


Introduction
Magnetic materials have great potential in practical applications, and the theoretical exploration thereof has always been a research hotspot in condensed matter physics and material physics.Breathing pyrochlore (AA′B 4 X 8 ) is also a typical material to study geometric frustration [1,2].AA′B 4 X 8 is composed of two sets of spinel structure (AB 2 X 4 ) compounds, which belong to the cubic system, and the space group is f-43m.A, B, and A′ are metal cations, and X is an anion, such as O, s, Se, and Te.In the crystal cell structure, the X ions with larger ion radii are densely stacked to form a face-centered cubic lattice, while the metal ions with smaller ion radii are embedded between the gaps of oxygen ions.The ions at the A-site form a diamond sublattice, while those at B-site are arranged at the top corner of the tetrahedron to form a pyrochlore sublattice.If the B-site ion is magnetic and the A-site ion is non-magnetic, the geometric frustration caused by magnetic interaction makes the system form a highly degenerate disordered ground state with strong spin fluctuations at low temperatures [3].
In LiMCr 4 O 8 , Cr ions are located in the center of the oxygen octahedron (CrO 6 ).Under the influence of the octahedral crystal field, the d-level is split into low-energy t 2g and high-energy e g orbitals.The compound is a Mott insulator with S = 3/2, and the unfilled j eff = 3/2 band of great significance for magnetoelectric properties.Existing research on breathing pyrochlore has mainly focused on LiInCr 4 O 8 , LiGaCr 4 O 8 , and their corresponding A-site replacement or doping systems [4][5][6][7][8].Although LiInCr 4 O 8 and LiGaCr 4 O 8 are Mott insulators [6], their magnetic phase transition is accompanied by the change of lattice structure, but different bond alternation indices lead to great differences in their magnetism.Bond alternation index B f is defined as J′/J (J′ < J), where J′ and J are nearest-neighbor magnetic interactions in the large and small tetrahedral, respectively.The Cr-Cr distance of large and small tetrahedral, denoted as d′ and d, and the value of d′/d is inversely related to value of B f [4]; Using magnetic data and Monte Carlo fitting, experiments and theories show that compared to LiInCr 4 O 8 , LiGaCr 4 O 8 has a larger bond alternation index (B f ≈ 0.6), a closer overall magnetic behavior to that of conventional spinel oxide ZnCr 2 O 4 [9,10], no spin energy gap [11], and with a stronger frustration index [6]; LiGaCr 4 O 8 also has a lower magnetic phase transition temperature (13.8 K) than In compounds; Curie−Weiss temperature thereof (−658.8K) shows stronger antiferromagnetism, and the effective magnetic moment is 4.024 μ B per unit chromium atom [1,5,6].
In compounds have a relatively small bond alternation index (B f ≈ 0.1), and similar magnetic properties to the singlet tetramer.The magnetic susceptibility and NMR data show that its spin energy gap is approximately 31 − 57 K; The structure transition is accompanied by the establishment of a weak magnetic order.The temperature of the long-range magnetic order is maintained at 12.9 K; 7 Li nuclear magnetic resonance (NMR) shows a first-order antiferromagnetic transition and nuclear spin-lattice relaxation in the compounds [2,5].Curie−Weiss temperature is also small at −331.9 K [4].However, the magnetic structure of this material system is sensitive to chemical doping.

Experiment
The sample LiInCr 4−x Co x O 8 (x = 0, 0.05, 0.15, 0.3) series was synthesized using the standard solid-state reaction method.The stoichiometric mixture of Li 2 CO 3 (99.99%),In 2 O 3 (99.99%),and Cr 2 O 3 /Co 3 O 4 (99.99%) was presintered at 200 °C for 10 h and subsequently weighed according to reasonable molar ratio.The sample qualities were characterized by x-ray diffraction (XRD) (Cu Kɑ radiation, λ = 1.54 Å) with a scanning step size of 0.01°in the angle range 20 − 80°.Raman spectra in wavenumber range of 200 − 800 cm −1 had been measured using a triple spectrometer (Jobin−Yvon,T64000).The back scattered light was a Kr + − Ar + mixed gas laser (λ = 514.5 nm).The actual composition of the samples was determined using energy dispersive x-ray spectrometry (EDX) using a field emission scanning electron microscope (Hitachi-SU8010) and x-ray Spectroscopy (XPS) measurement was carried out.The magnetic properties were measured using a Quantum design magnetic property measurement system (MPMS) with magnetic field of H = 100 Oe between 2 and 300 K.The specific heat characteristics are determined using Quantum Design.The dielectric measurement was performed using a dielectric impedance analyzer (DMS10004PBG3030, BALAB).

Results and discussion
Figure 1 shows the room temperature XRD spectrum of the doped LiInCr 4 O 8 powder.Compared with the standard JCPDS card, these peaks exhibit a typical F-43m space group of a cubic structure.In 2 O 3 impurity peaks, which are marked with asterisks, appear at approximately 30.6°.The concentration of impurities is estimated to be 0.1% in the following refinement.Figure 2 shows the SEM micrographs and the average size of samples through Nano Measurer analysis.To study the structural changes of LiInCr 4 O 8 after doping, the XRD data were refined using the Fullproof software.Table 1 shows the refined lattice constant a, cell volume V 0 and Cr-Cr bond length of each sample.All three parameters have changed.All substituting concentrations and chemical compositions of the studied polycrystals are determined by the EDX measurement and scanning electron microscope.All samples exhibit small grains and polygon morphology.
The sample exhibits five Raman active modes: (A 1g +E g +3F 2g ) at approximately 313 cm −1 , 447 cm −1 , 494 cm −1 , 594 cm −1 , and 722 cm −1 .The one at 313 cm −1 (F 1 2g ) is related to the moving of tetrahedral Li(In)O 4 unit in the lattice.The peak at 447 cm −1 (E g ) originates from the stretching vibration of the Cr-O and Li/In-O bonds.The peak at 494 cm −1 (F 2 2g ) is related to the bending vibration of the Cr-O bonds.The modes at 594 cm −1 (F 3 2g ) and 722 cm −1 (A 1g ) are ascribed to the Cr-O stretching vibration of CrO 6 .The Raman modes exhibit a redshift that gradually weakens with the doping increase.The red shift is due to the doping of heavier Co atom for Cr and smaller lattice parameters in the lattice.The shoulders around 494 cm −1 , 594 cm −1 , and 722 cm −1 may be ascribed to a small amount of In 2 O 3 (exhibited by the x-ray diffraction measurement), vacancies, or cation disorder.
A chemical state analysis of elements is one of the most important applications of XPS [12][13][14][15].Figure 4 shows the change in magnetic susceptibility with temperature from 2 to 300 K in both zero field cooling (ZFC) and field cooling (FC) conditions in an applied field H = 100 Oe.For LiInCr 4 O 8 , below ≈ 64 K, there is a spin-gap opening as shown by quickly magnetic susceptibility curve decreasing with decreasing temperature [4].However, the spin gap behavior is quickly depressed for the x = 0.05 and x = 0.15 samples.The ionic radius of cobalt is different from that of chromium.The CrO 6 octahedra in the doped sample begin to tilt owing to cobalt doping.It is well known that the sample has the periodic expansion and contraction of pyrochlore sublattice formed by B-site ions.The lattice distortion and special structure of the doped sample cause the huge difference in exchange couplings and spin gaps between the parent sample and the doped sample.This phenomenon is similar to that of MAl 2 O 4 of cubic spinels and layered vanadates CaV 4 O 9 [16,17] The effective magnetic moment μ eff is calculated for all samples.μ eff increases when the Co concentration increases (table 2).Here, we assume that the spin-only contribution for Cr 3+ has a magnetic moment of 3.9 μ B /Cr.In addition, Co 2+ (HS) and Co 3+ (HS) have magnetic moments of 3.87 μ B /Co and 4.9 μ B /Co respectively.From the XPS result, the Co 3+ /Co 2+ ratio in the samples is 3/2.Then, the theoretical effective magnetic moment μ eff per f.u.can be calculated as Cr .The estimated μ eff is 7.68, 7.698, 7.735, and 7.790 for the doped samples with x = 0, 0.05, 0.15, and 0.3, respectively.LiInCr 4 O 8 is known to be antiferromagnetic.Certainly, the ferromagnetic interaction at low temperatures may also originate from the Co-Co exchange interaction [18].From previous research, the Cr-Cr interaction is AFM [19].We speculate that the Cr-Cr interaction should weaken with the increase in Co doping; then, the antiferromagnetism of the sample decrease.However, the samples continue to show stronger antiferromagnetism, so the Cr-Co interaction must be an AFM interaction.There is competition among Cr-Cr (AFM), Cr-Co(AFM), and the Co-Co(FM) interactions.The ferromagnetic and antiferromagnetic phases coexist in the system and magnetic frustration may arise.The M(H) curve does not show a saturated state in the field up to 80 kOe, which indicates the basic antiferromagnetic property and a paramagnetic state [18,19].Here, the residual entropy confirms the existence of a glass-type phase [18,24].
Then, we characterized the dielectric constant (ε r ) and dielectric loss (tanδ) of LiInCr 4−x Co x O 8 compounds in the temperature range of 323 − 573 K at eight different frequencies.Figure 7 shows the relative dielectric constant versus temperature at different frequencies.There are many theoretical explanations for the high dielectric properties of ceramics, including the internal barrier capacitance, internal stress, charge transfer, thermal activation, and defect structure [25][26][27].For LiInCr 4 O 8 , at 420 K, ε r exhibits an obvious humplike anomaly, which may be due to some electric order.In the doping samples, the humplike anomaly is more obvious, which suggests that the electric order strengthens.In addition, the humplike anomaly tends to move towards low temperatures.Generally, a peak in dielectric constant versus temperature plot indicates the ferroelectric Curie temperature.In figure 7, when the doping amounts are x = 0.05, x = 0.15, and x = 0.3, the corresponding Curie temperatures are 550 K, 425 K, and 375 K, respectively.The tolerance factor changed owing to the increased Co content.This changed tolerance factor increased the Curie temperature.In future research, we will further investigate the ferroelectric properties of the samples in detail.
The inhomogeneous dielectric structure in the sample is assumed to consist of two layers.As we know, the grain boundary layer with poor conductivity is very active at low frequencies, while the grain layer with good conductivity is active at high frequencies.In figure 7, large ε r is observed at low frequency, and small ε r is observed at high frequency.
Figure 8 shows the temperature dependence of tanδ at different frequencies (20 Hz−10 MHz) for all Co 3 O 4 -doped samples.At low frequencies (< 1 kHz) and high temperature (> 475 K), the dielectric losses rapidly increase with the increase in temperature.The space-charge polarization is controlled by space-charge carriers.The increasing trend of ε r and tanδ values can be explained by the strengthened formation of spacecharge polarization because there are more carriers with higher temperatures.Then, ε r and tanδ values increase with higher temperatures.At high frequencies ( 1 kHz), ε r and tanδ hardly change in the entire measuring temperature range.Therefore, this material may have potential applications in microelectronic devices.
Figure 9(a) shows the impedance spectrum at room temperature.The larger the doping amount, the smaller the diameter of the semicircle, and the smaller the grain boundary resistance.As the doping amount increases, the grain size increases and the number of grain boundaries decreases, resulting in a significant decrease in grain boundary resistance.Then, we measured the variable temperature impedance spectrum at 423 K, 473 K, 523 K, and 573 K [x = 0.05, see inset in figure 9(b)].With the increase of temperature, the resistance of grains and grain      of grain boundary resistance of doped samples (x = 0.05, 0.15, 0.3) obtained by fitting are 0.6910 eV, 0.5239 eV, and 0.3247 eV, respectively.The activation energy shows a decreasing trend with increasing doping.
Figure 10(a) shows the variation of real part of impedance with frequency taken on a log scale at 423 K, 473 K, 523 K, and 573 K, respectively.Z′ shows almost a sharp decrease with the increase in frequency in lower frequency range.Z′ is also found to decrease with the increase in temperature.At higher frequencies, Z′ becomes almost independent of frequency as well as temperature and achieves nearly a very low constant value.It is mainly due to low frequency dispersion at lower frequencies and release of space charge at higher frequencies.Figure 10(b) shows the variation of imaginary part of impedance Z" of the samples with frequency taken on a log scale at 423 K, 473 K, 523 K, and 573 K, respectively.Z" decrease with increase in temperature as well as frequency and achieves a very low constant value at higher frequencies where it becomes independent of both frequency and temperatures.

Conclusion
In this study, the polycrystalline sample of LiInCr 4−x Co x O 8 with the breathing pyrochlore structure was synthesized by conventional solid-state reaction.The summary of the findings is as follows: (1) With the increase in Co doping concentration, the lattice constants decrease, and the CrO 6 octahedral distortion strengthens.The XPS measurement shows that there are Co 2+ and Co 3+ in the LiInCr 4−x Co x O 8 compounds.
(2) Compared with the spin gap in the parent compound LiInCr 4 O 8 , the spin gap behavior here is quickly depressed in the doped samples (x = 0.05 and x = 0.15), and the spin gap nearly disappears for the x = 0.3 sample.The difference between the temperature-dependent magnetization curves during field-cooling and zero-field cooling suggests a spin-glass state.A clear magnetization hysteresis loop appears for x = 0.3 sample.The magnetism should be ascribed to the competition among the Cr-Cr AFM interaction, Cr-Co AFM, and Co-Co FM interactions.This issue is also confirmed by specific heat measurements.The doping affects the bond length, which affects the magnetic and dielectric properties.
(3) Furthermore, ε r and tanδ measurably changes with the change in Co content.ε r decreases with increasing frequency.At higher frequencies (1 kHz), both ε r and tanδ hardly change over the measuring temperature range.For x = 0.3 sample, ε r exhibits more obvious humplike anomaly compared with (x = 0.05 and x = 0.15 samples).The ferroelectric Curie temperature moves towards lower temperature owing to changed tolerance factor.Tanδ shows an increasing trend with increasing doping.The activation energies of grain boundary resistance of doped samples obtained by fitting shows a decreasing trend with increasing doping.
(4) Due to the temperature range limitation of the dielectric testing instrument, we did not measure the dielectric properties of the sample at low temperatures, thus unable to obtain the direct relationship between magnetism and dielectric properties at low temperatures.In future research, we will further investigate whether there is a magnetodielectric effect in the samples at low temperatures.
Figure1shows the room temperature XRD spectrum of the doped LiInCr 4 O 8 powder.Compared with the standard JCPDS card, these peaks exhibit a typical F-43m space group of a cubic structure.In 2 O 3 impurity peaks, which are marked with asterisks, appear at approximately 30.6°.The concentration of impurities is estimated to be 0.1% in the following refinement.Figure2shows the SEM micrographs and the average size of samples through Nano Measurer analysis.To study the structural changes of LiInCr 4 O 8 after doping, the XRD data were refined using the Fullproof software.Table1shows the refined lattice constant a, cell volume V 0 and Cr-Cr bond length of each sample.All three parameters have changed.All substituting concentrations and chemical compositions of the studied polycrystals are determined by the EDX measurement and scanning electron microscope.All samples exhibit small grains and polygon morphology.The sample exhibits five Raman active modes: (A 1g +E g +3F 2g ) at approximately 313 cm −1 , 447 cm −1 , 494 cm −1 , 594 cm −1 , and 722 cm −1 .The one at 313 cm −1 (F 1 2g ) is related to the moving of tetrahedral Li(In)O 4 unit in the lattice.The peak at 447 cm −1 (E g ) originates from the stretching vibration of the Cr-O and Li/In-O bonds.The peak at 494 cm −1 (F 2 2g ) is related to the bending vibration of the Cr-O bonds.The modes at 594 cm −1 (F 3 2g ) and 722 cm −1 (A 1g ) are ascribed to the Cr-O stretching vibration of CrO 6 .The Raman modes exhibit a redshift that gradually weakens with the doping increase.The red shift is due to the doping of heavier Co atom for Cr and smaller lattice parameters in the lattice.The shoulders around 494 cm −1 , 594 cm −1 , and 722 cm −1 may be ascribed to a small amount of In 2 O 3 (exhibited by the x-ray diffraction measurement), vacancies, or cation disorder.A chemical state analysis of elements is one of the most important applications of XPS[12][13][14][15]. Figure 3(a) shows the change in the Co 2p XPS spectra with various Co doping concentrations.For the lowest doping . The spin gap nearly disappears for the x = 0.3 sample in figure 4(d).Compared with x = 0.05 and x = 0.15 samples, the value of d′'/d in x = 0.3 sample decreased, resulting in an increase of B f .The degree of expansion and contraction of Cr 4 tetrahedra in x = 0.3 sample weakens, which leads to a more uniform lattice.Then the spin gap nearly disappears.The arrows in the insets of figures 4(c) and (b) show the irreversibility temperature T = 4.0 K and T = 6.5 K, respectively, where weak irreversibility occurs in doped samples.Below T = 4.0 K (x = 0.15) and T = 6.5 K (x = 0.3), some divergences occur between ZFC and FC curves, which suggests that a spin-glass state may appear.The inset in figure 4(b) shows the inverse of χ (magnetic susceptibility) for LiInCr 4−x Co x O 8 .Above 100 K, the χ −1 ∼ T curve is approximately linear, and follows Curie-Weiss law χ = C/(T-θ CW ), where θ CW and C are the Weiss temperature and Curie constant, respectively.The fitting shows different values of C and θ CW in table 2. The frustration index f = |θ CW /T| (T denote Néel temperature or ZFC-FC bifurcation temperature) is used to express the degree of frustration in magnetic samples.

Figure 1 .
Figure 1.(a) XRD patterns; (b) Plot of the lattice parameters with Co content; (c) Rietveld refinement figure of the x = 0 sample; (d) Raman spectra of the parent sample; Raman shift versus x value (inset).

Figure 2 .
Figure 2. SEM image of samples.Insets of (a)−(c) show the Nano Measurer analysis.

Figure 5 (
Figure 5(d) clearly shows the magnetization hysteresis loops of LiInCr 4−x Co x O 8 for x = 0.3.From the corresponding M(H) curve, the Co substitution of LiInCr 4 O 8 includes the weak ferromagnetic moment.LiInCr 4 O 8 is known to be antiferromagnetic.Certainly, the ferromagnetic interaction at low temperatures may also originate from the Co-Co exchange interaction[18].From previous research, the Cr-Cr interaction is AFM[19].We speculate that the Cr-Cr interaction should weaken with the increase in Co doping; then, the antiferromagnetism of the sample decrease.However, the samples continue to show stronger antiferromagnetism, so the Cr-Co interaction must be an AFM interaction.There is competition among Cr-Cr (AFM), Cr-Co(AFM), and the Co-Co(FM) interactions.The ferromagnetic and antiferromagnetic phases coexist in the system and magnetic frustration may arise.The M(H) curve does not show a saturated state in the field up to 80 kOe, which indicates the basic antiferromagnetic property and a paramagnetic state[18,19].Figure 6(a) shows C p versus T of LiInCr 4−x Co x O 8 (x = 0.3) due to further study of the magnetism of the sample.For LiInCr 4 O 8 , a sharp peak at T N = 15.9K shows long-range order [4].In the inset of figure 6(a), the derivative of C p with respect to the temperature (x = 0.3 doping compound) shows only a small peak at 7.3 K, which corresponds to the result of the inverse of χ (T) curve for LiInCr 3.7 Co 0.3 O 8 (an upturn at T = 6.5 K).Then, the long-range order is suppressed when Co is added to the sample.In figure 6(b), C p /T quickly increases with increasing temperature blow 10 K.At 10-16 K, C p /T slowly increases with increasing temperature, possibly due to the stronger frustration from Co doping.At low temperatures, the change in specific heat with temperature for the LiInCr 3.7 Co 0.3 O 8 sample is described by the following formula, C p /T = C 0 +C 1 T+C 2 T 2 +C 3 T 3 +C 4 T 4 , where the first two terms are related to the electronic contribution and the latter three terms are associated with the lattice contribution [18, 20-23].Figure 6(b) shows the fitting result.The calculated C 0 = −24.70088mJ/mol K 2 and C 1 = 137.8981mJ/mol K 3 constitute approximately 0.9433% of the total specific heat.Compared with the lattice contribution, the calculated values of C 0 and C 1 are small, which suggests an insulating property for the doped sample.In the inset of figure 6(b), the total entropy S of the sample is determined by integrating C P (T)/T from 1.8 K to 16 K.The sample has a much lower S value than an ideal Ising sample with Cr 3+ (S mag = 4Rln4 = 46.07).Here, the residual entropy confirms the existence of a glass-type phase[18,24].Then, we characterized the dielectric constant (ε r ) and dielectric loss (tanδ) of LiInCr 4−x Co x O 8 compounds in the temperature range of 323 − 573 K at eight different frequencies.Figure7shows the relative dielectric

Figure 6 (
Figure 5(d) clearly shows the magnetization hysteresis loops of LiInCr 4−x Co x O 8 for x = 0.3.From the corresponding M(H) curve, the Co substitution of LiInCr 4 O 8 includes the weak ferromagnetic moment.LiInCr 4 O 8 is known to be antiferromagnetic.Certainly, the ferromagnetic interaction at low temperatures may also originate from the Co-Co exchange interaction[18].From previous research, the Cr-Cr interaction is AFM[19].We speculate that the Cr-Cr interaction should weaken with the increase in Co doping; then, the antiferromagnetism of the sample decrease.However, the samples continue to show stronger antiferromagnetism, so the Cr-Co interaction must be an AFM interaction.There is competition among Cr-Cr (AFM), Cr-Co(AFM), and the Co-Co(FM) interactions.The ferromagnetic and antiferromagnetic phases coexist in the system and magnetic frustration may arise.The M(H) curve does not show a saturated state in the field up to 80 kOe, which indicates the basic antiferromagnetic property and a paramagnetic state[18,19].Figure 6(a) shows C p versus T of LiInCr 4−x Co x O 8 (x = 0.3) due to further study of the magnetism of the sample.For LiInCr 4 O 8 , a sharp peak at T N = 15.9K shows long-range order [4].In the inset of figure 6(a), the derivative of C p with respect to the temperature (x = 0.3 doping compound) shows only a small peak at 7.3 K, which corresponds to the result of the inverse of χ (T) curve for LiInCr 3.7 Co 0.3 O 8 (an upturn at T = 6.5 K).Then, the long-range order is suppressed when Co is added to the sample.In figure 6(b), C p /T quickly increases with increasing temperature blow 10 K.At 10-16 K, C p /T slowly increases with increasing temperature, possibly due to the stronger frustration from Co doping.At low temperatures, the change in specific heat with temperature for the LiInCr 3.7 Co 0.3 O 8 sample is described by the following formula, C p /T = C 0 +C 1 T+C 2 T 2 +C 3 T 3 +C 4 T 4 , where the first two terms are related to the electronic contribution and the latter three terms are associated with the lattice contribution [18, 20-23].Figure 6(b) shows the fitting result.The calculated C 0 = −24.70088mJ/mol K 2 and C 1 = 137.8981mJ/mol K 3 constitute approximately 0.9433% of the total specific heat.Compared with the lattice contribution, the calculated values of C 0 and C 1 are small, which suggests an insulating property for the doped sample.In the inset of figure 6(b), the total entropy S of the sample is determined by integrating C P (T)/T from 1.8 K to 16 K.The sample has a much lower S value than an ideal Ising sample with Cr 3+ (S mag = 4Rln4 = 46.07).Here, the residual entropy confirms the existence of a glass-type phase[18,24].Then, we characterized the dielectric constant (ε r ) and dielectric loss (tanδ) of LiInCr 4−x Co x O 8 compounds in the temperature range of 323 − 573 K at eight different frequencies.Figure7shows the relative dielectric

Figure 6 (
Figure 5(d) clearly shows the magnetization hysteresis loops of LiInCr 4−x Co x O 8 for x = 0.3.From the corresponding M(H) curve, the Co substitution of LiInCr 4 O 8 includes the weak ferromagnetic moment.LiInCr 4 O 8 is known to be antiferromagnetic.Certainly, the ferromagnetic interaction at low temperatures may also originate from the Co-Co exchange interaction[18].From previous research, the Cr-Cr interaction is AFM[19].We speculate that the Cr-Cr interaction should weaken with the increase in Co doping; then, the antiferromagnetism of the sample decrease.However, the samples continue to show stronger antiferromagnetism, so the Cr-Co interaction must be an AFM interaction.There is competition among Cr-Cr (AFM), Cr-Co(AFM), and the Co-Co(FM) interactions.The ferromagnetic and antiferromagnetic phases coexist in the system and magnetic frustration may arise.The M(H) curve does not show a saturated state in the field up to 80 kOe, which indicates the basic antiferromagnetic property and a paramagnetic state[18,19].Figure 6(a) shows C p versus T of LiInCr 4−x Co x O 8 (x = 0.3) due to further study of the magnetism of the sample.For LiInCr 4 O 8 , a sharp peak at T N = 15.9K shows long-range order [4].In the inset of figure 6(a), the derivative of C p with respect to the temperature (x = 0.3 doping compound) shows only a small peak at 7.3 K, which corresponds to the result of the inverse of χ (T) curve for LiInCr 3.7 Co 0.3 O 8 (an upturn at T = 6.5 K).Then, the long-range order is suppressed when Co is added to the sample.In figure 6(b), C p /T quickly increases with increasing temperature blow 10 K.At 10-16 K, C p /T slowly increases with increasing temperature, possibly due to the stronger frustration from Co doping.At low temperatures, the change in specific heat with temperature for the LiInCr 3.7 Co 0.3 O 8 sample is described by the following formula, C p /T = C 0 +C 1 T+C 2 T 2 +C 3 T 3 +C 4 T 4 , where the first two terms are related to the electronic contribution and the latter three terms are associated with the lattice contribution [18, 20-23].Figure 6(b) shows the fitting result.The calculated C 0 = −24.70088mJ/mol K 2 and C 1 = 137.8981mJ/mol K 3 constitute approximately 0.9433% of the total specific heat.Compared with the lattice contribution, the calculated values of C 0 and C 1 are small, which suggests an insulating property for the doped sample.In the inset of figure 6(b), the total entropy S of the sample is determined by integrating C P (T)/T from 1.8 K to 16 K.The sample has a much lower S value than an ideal Ising sample with Cr 3+ (S mag = 4Rln4 = 46.07).Here, the residual entropy confirms the existence of a glass-type phase[18,24].Then, we characterized the dielectric constant (ε r ) and dielectric loss (tanδ) of LiInCr 4−x Co x O 8 compounds in the temperature range of 323 − 573 K at eight different frequencies.Figure7shows the relative dielectric

Figure 6 .
Figure 6.(a) C P and the derivative of C p /T with temperature for the X = 0.3 compound.;(b) C P /T with temperature and fitting curve.S versus temperature for X = 0.3(inset).

Figure 9 (
b) shows the Arrhenius plot of the gain boundary resistance.The grain boundary resistance satisfies the thermal activation relationship with temperature: R gb = R 0 exp(E a /κ B T).In the formula, R 0 represents the fitting coefficient.E a represents activation energy.κ B represents the Boltzmann constant.The activation energies

Figure 9 .
Figure 9. (a) Room temperature impedance spectra for doping samples (b) Arrhenius plots of the gain boundary resistance and variable temperature impedance spectrum in the inset.

Figure 10 .
Figure 10.(a) The real part of impedance Z′ versus frequency figure 10(b) The imaginary part of impedance Z" versus frequency. 4+ ).The electronic configuration of Co ions has different spin states.For example, the electronic configuration of Co 3+ has three different spin states (t g = 0, LS), intermediate spin state (S = 1, IS), and high spin state (S = 2, HS).Though the energy differences among the spin states are quite small, Cobalt oxide as a magnetic dopant has caused many novel magnetic and electrical phenomena in various compounds.Then, in this work, the structure and influence of Co doping on magnetism are analyzed.In addition, the dielectric properties for LiInCr 4−x Co x O 8 samples with various contents of Co 3 O 4 (1.25%−7.5%)are studied.

Table 1 .
Structural parameters of the compositions.(lattice parameter a, Cell volume V 0 , Cr-Cr length d′, Cr-Cr length d).