Colossal-permittivity behaviors in A-site distorted double perovskite

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Colossal-permittivity behaviors in A-site distorted double perovskite LiCuNb3O9 with correlated magnetoelectric effect and variable-range-hopping Dandan Gao, Jiyang Xie, Xiao-Ming Jiang, Huan Liu, Guanghui Li, Jing Wang, Luran Zhang, Fei Xiong, and Wanbiao Hu ACS Appl. Electron. Mater., Just Accepted Manuscript • DOI: 10.1021/acsaelm.8b00013 • Publication Date (Web): 20 Dec 2018 Downloaded from http://pubs.acs.org on December 22, 2018

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ACS Applied Electronic Materials

Colossal-permittivity behaviors in A-site distorted double perovskite LiCuNb3O9 with correlated magnetoelectric effect and variable-range-hopping Dandan Gao, † Jiyang Xie, † Xiao-Ming Jiang, ‡ Huan Liu, † Guanghui Li, † Jing Wang, † Luran Zhang, † Fei Xiong, † Wanbiao Hu†,* †School

of Materials Science and Engineering, Yunnan University, Kunming 650091, P. R. China

‡State

Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou 350002, P. R. China

ACS Paragon Plus Environment

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ABSTRACT There is a general perception that the colossal permittivity in non-ferroelectric oxides is usually ascribed to barrier layer capacitor (BLC) effect but the states of the involved charges as well as corresponding physical picture for the charge transport in the materials are yet clear, which hinder the explorations and applications for new colossal permittivity materials and devices. Here, we present the polaronic conduction mechanism in terms of Mott variable-range-hopping coupled with magnetoelectric effect for apparent colossal-permittivity in double perovskite LiCuNb3O9. Valence state and defect analysis reveals that A-site Cu ions have mixed valences with determined ratio of Cu+/Cu2+ equals to 1: 9 and exist intrinsic A-site deficiency that is balanced through oxygen vacancies. Structural refinement combined bond valence sum (BVS) calculation indicate that Cu+ (BVS=1.3476) is overbonded while both Cu2+ (BVS=1.9140) and Nb5+ (BVS=4.7998) are underbonded, permitting the formation of quasi CuO4 tetrahedra, distorted NbO6 octahedra and possible polarons. The LiCuNb3O9 ceramic shows room-temperature colossal permittivity (ε’>104), but quickly decreases down to around 100 at temperature range of 80-150 K, a freezing/activation process, which originates from the electrons in Cu+/Cu2+ that exhibit paramagnetic characteristic but could distort the lattice to form polarons when hopping. These polarons transport deviates the Arrhenius law but in Mott variable-range-hopping mechanism that can be manipulated by external magnetic field through magnetoelectric coupling that could increase the hopping activation energy and hopping distance. Our results therefore provide significant experimental evidences and understanding for the magneto-dielectric correlation in terms of polaronic hopping phenomenon, which may guide to explore a wider range of magnetoelectric oxide materials.


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KEYWORDS: colossal-permittivity, local chemistry, double perovskite, Mott VRH, magnetoelectric


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1. INTRODUCTION Colossal-permittivity (CP, ε > 103) materials continue to evoke extensive interest as they have been the most sought-after candidates for high-capacity electrostatic capacitors and device miniaturization.1-2 A large amount of studies have been dedicated to improving and optimizing the performances in existing material systems while on the other hand, to exploring and casting about for new materials with superior dielectric properties.3-5 Many material systems have thus been explored and developed, e.g. earliest ferroelectric-based materials, e.g. BaTiO3,6 with characters of spontaneous polarizations and phase transitions, as well as their derivative relaxors, but the most attractive systems may be the ones based on the transition-metals, which have also brought about new intriguing, but debatable mechanisms. A prominent instance is double-perovskite-structured CaCu3Ti4O12 (CCTO)7 and Ca-site-substituted derivatives with like Cd,8-9 Na1/2Y1/2,10-11 A-site deficient Bi2/3,12-13 Na1/3Bi1/3,14 or Ln2/3 (Ln=lanthanide);15 the related mechanisms e.g. intrinsic local dipole fluctuation model,16-17 internal/surface/nanoscale barrier layer capacitors (BLC),18-20 twinning,21 structure-frustrated relaxor,22 nanoscale disorder23 etc are referred. Likewise, some burgeoning classes of new CP materials, e.g. (Li/Na, Ti/Zr) doped NiO,24-26 La2-xSrxNiO4,27 (Mg/Al/In/Ga/Ln2/3, Nb/Ta) doped rutile TiO2,1, 28-32 in which new mechanisms such as charge phase segregation or inhomogeneity and electron-pinned defect dipoles were put forward, are also subject to a similar predicament. It is serious that none of existing mechanisms/models to explain the CP behaviors is fully accepted, some of them are even contradictory. This challenges in a comprehensive understanding from fundamental physical insights, which however, is not only quite necessary and significant but also highly timely, in order to guide for the exploration of both new CP materials and mechanisms.


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Perovskite-structured transition-metal oxides could be the attractive candidates in CP regard with the potential to display a wide variety of electronic and magnetic properties defined by their sensitivity to structures, local perturbations, defect states, chemical modifications and charge transport etc, which directly determine the CP property in such sorts of materials.17, 33-35 A-site Na1/2Bi1/2 substitution in CCTO could thus alter the lattice polar soft modes (f0~ 34 cm-1) to achieve an incipient ferroelectricity (T0~ -155 K) but retain cubic symmetry (space group Im3),36 while Bsite doped Mn makes CCTO completely lose the CP, only giving a permittivity of 80.37 Moreover, the basic polarizations and involved charges in these CP materials always interact with the electrons, phonons and locally chemical bonding etc as these usually refer to the d/f-electron transport. This is why concurrent EXAFS modeling reveals that Cu-Ca and Ca-Cu coordination numbers, NCu-Ca~2.8 and NCa-Cu~2.4 respectively in CCTO, significantly deviate from theoretical values.23 Similarly, charge-frustrated CP material LuFe2O4 with feature of charge ordering in Fe2+/Fe3+ could generate the electronic ferroelectricity.38 The charge hopping in this material follows the typical nearest-neighbor-hopping, i.e. a fully thermally activated Debye relaxation in Arrhenius law that also exhibits colossal-permittivity BLC effect. But in Sc-doped and nanocrystalline systems, the CP characteristic is losing.39-40 As a matter of fact, in these d/f-electron correlated systems, the existence of special local states, spin-lattice interaction, Jahn-Teller lattice distortion phenomena etc would greatly influence the local/microscopical charge transfer or transport,41-44 thus making the apparent CP more complicated that not simply the BLC could be properly interpreted. This is perhaps why currently the debate, controversy and even ambiguity to some extent always happen in understanding and existing mechanisms when referring to such sorts of CP material systems. Therefore, a clear and distinct dielectric CP mechanism and physical picture from local structure, electron/spin transport


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aspects, to solve currently poor understanding at a fundamental level, is not yet but to be established. Bear these in mind, in this work, we choose a typical double-perovskite-structured colossalpermittivity material, i.e. LiCuNb3O9, as a prototype compound to address the aforementioned issues. LiCuNb3O9 crystallizes basically in the same structure CuTa2O6,45 also possessing a CP characteristic.46 B-site Nb atom coordinates in six-fold by oxygen atoms to form a slightly distorted octahedral arrangement. A-site atoms Cu/Li, in addition to 1/9 intrinsic vacancies, have square coordinations with 50% occupancy for each other but without any long-range compositional ordering.47 This is quite similar to a distorted double-perovskite material CaCu3Mn4O12,48 with a same structure and similar composition as CCTO. Therefore, the common issues in those wellknown CP materials aforementioned are also aroused in LiCuNb3O9. Up to date, only one work reported the CP property. A comprehensive investigation on the origin of the charges, states of the charge transport etc. as well as the correlated understanding is still lacking.46 The goal of this study is to positively answer all the open questions aforementioned by performing exhaustive investigations from fundamentally locally chemical bonding, valence states, and defects e.g. oxygen vacancies to charge transport and associated colossal permittivity. The square-planar coordination for A-site Cu in LiCuNb3O9 is related to the Jahn-Teller distortion, which would be exacerbated to expose great influences on the charge transport and finally to the observed CP given the involved structural and transport properties are fluctuated. We thus initiated the valence state determination, bond valence sum (BVS) calculation,49 electronic states and transport, and magnetic-dielectric effect, with aiming to uncover the Mott polaronic hopping50 and magnetoelectric correlation behaviors in LiCuNb3O9 CP material. 2. EXPERIMENTAL DETAILS


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2.1. Sample preparation: Polycrystalline LiCuNb3O9 ceramics were synthesized through conventional solid state reaction from stoichiometric mixture of raw materials Li2CO3 (99.99%), CuO (99.99%) and Nb2O5 (99.99%). The ceramic preparation follows the standard two-step ball milling and sintering procedures. Firstly, raw materials were carefully weighted and transferred into Teflon cans with using ethanol and zirconia media for milling for 12 h. Afterwards, the mixture was dried and calcined at 850 oC for 4 h. Secondly, the pre-calcined powders were ballmilled again for 12 h for green-pellet preparation. The green pellets with diameter/thickness of 12/1.5 mm were made by axial pressure at 400 MPa with adding PVA binder. The high-density LiCuNb3O9 ceramics were finally obtained by sintering the green pellets at 950 oC for 2 h in the air. 2.2. Sample characterizations and property measurements: The crystalline structure and purity of the samples were examined by using powder X-ray diffraction (XRD, Rigaku Smartlab). The valence and defect states were determined by X-ray photoelectronic spectroscopy (XPS, Thermofisher Escalab 250Xi) and electron paramagnetic resonance (EPR, Bruker ELEXSYS E500) techniques. For the dielectric measurement, sliver paste and sputtering Au electrodes were coated on the two surfaces of the ceramic samples to ensure the good electric contact with firing at 550 oC. Electric and dielectric property measurement was performed on the probe station (Lakeshore CRX-VF) coupled with impedance analyzer (Keysight 4990A) and electrometer (Keithley 6517B). The measurement temperature range was varied by 10 K - 360 K, with applying a vertical magnetic field of 1 T. Magnetic properties were measured on physical property measurement system (PPMS, Dynacool) with temperature range of 5 K - 300 K. 3. RESULTS AND DISCUSSION 3.1. Valence and defect state characterization


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Charge states appear to be closely related to the local chemistry, polarization and transport behaviors for the materials studied. Thus, the first goal of our experiments is to investigate the chemical valences as well as the involved defect states in LiCuNb3O9. To these, electron paramagnetic resonance (EPR) and X-ray photoelectric spectroscopy (XPS) were carried out (Figure 1). A strong, symmetrical EPR signal was detected at 77 K with a g-value of 2.15, which is ascribed to be the Cu2+ in 3d9 configuration (Figure 1a).51 This can be attributed to strong copperhole (3d9 electronic wave function) delocalization on the four next-neighboring oxygen ions.52 There are no any traces for the existence of low-valence Nb ions (e.g. Nb4+) within the broad magnetic span, indicating that Nb in LiCuNb3O9 forms in a normal oxidation state i.e. Nb5+ as EPR is highly sensitive even for very tiny amounts.53 As is known that monovalent Cu+ with 3d10 configuration is EPR silent,54 XPS was performed to qualitatively detect the possibility for Cu+ and further, if indeed existing, to quantitatively analyze the Cu+/Cu2+ ratio. Because XPS is a highly surface-sensitive technique, particular care is necessary in sample preparation to avoid involving, otherwise, the artifacts. Likewise, the Cu2p XPS spectrum collected directly from ceramic surface contains low-valence Cu+ that was nondetectable from EPR, with its ratio in mole to Cu2+ is 20: 80 (Figure 1b). While quite differently, after peeling off the ceramic’s surface by Ar+ ion bombardment, the Cu+ becomes dominated in Cu2p XPS spectrum with ratio of Cu+/ Cu2+ =60: 40 (Figure 1c), which should be attributed to the Cu2+ reduction because of Ar+ ion bombardment. Similar phenomenon was observed in transition-metal oxides e.g. Fe2O3 could be reduced to Fe3O4 under Ar+ ion bombardment for XPS analysis.55 How to determine the accurate ratio of Cu+/ Cu2+ seems still a question, which however is directly associated to the charge transport. To this end, we cut the ceramic sample under the N2 atmosphere and collected the XPS signals from the fresh section of


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ceramic to keep the nature of valence states (Figure 1d). Cu 2p3/2 level contains a main peak at 934.25 eV corresponding to the Cu2+, with a low-energy minor shoulder at 932.39 eV that can be ascribed to the Cu+.56 The accurate ratio of Cu+/ Cu2+ in mole was thus calculated to be 10: 90. The existence of the Cu+ indicates that oxygen vacancies must be created to maintain the charge neutral. Very strong shaking lines from Cu2+ were also observed, like many other Cu(II)-based oxides.4, 57-58 It is noted that no low-valence Nb (e.g. Nb4+) but only normal Nb5+ was detected from Nb 3d level (not presented), consistent with the EPR result. (a)

(b)

+

measured XPS

Intensity (a.u.)

2+

EPR Intensity (a.u.) 3.2

g=2.15

2.8

2.4

2.0

1.6

1.2

satellites

measured XPS 2+

Cu background

950

2+

Cu

+

satellites

950

Cu

940

930

Binding Energy (eV)

+ Ar bombardment Cu 2p3/2 + Cu sum + Cu 2+

Cu 2p1/2

960

Cu 2p3/2

Cu sum

Cu 2p1/2

960

Cu

940

930

(d)

N2 atmosphere

measured XPS 2+

Intensity (a.u.)

(c)

without Ar bombardment +

Cu background

g factor

Intensity (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Cu 2p3/2

+

Cu backgroud

Cu sum

2+

satellites

Cu 2p1/2

Cu satellites

+

Cu

960

Binding Energy (eV)

950

940

930

Binding Energy (eV)

Figure 1. Valence and charge state characterizations of LiCuNb3O9 ceramic. (a) EPR spectrum recorded at the temperature 77 K; (b) XPS spectrum of Cu2p collected directly from the ceramic’s surface; (c) XPS spectrum of Cu2p collected after Ar+ ion bombardment; (d) XPS spectrum of Cu2p collected from the fresh section of ceramic that was cut under the N2 atmosphere in order to protect the possible Cu+ oxidation.


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3.2. Structure and local chemistry analysis Structural chemical analysis, quite necessary to identify the ways for charge transport, was studied through XRD structural refinement and subsequent bond valence sum (BVS) calculation. Structural refinement was performed with using initial cell parameters and atomic positions reported in the literature. As indicated in Figure 2a, the as-synthesized LiCuNb3O9 ceramic/powder samples are in high-purity without any other undesirable phases. The refined pattern matches well the experimental XRD, yielding the structural parameters shown in Table 1. Sato and Hama reported that there exists NbO6 octahedron tilting in LiCuNb3O9 that is associated with locally chemical bonding.47 Thus, bond valence sum (BVS) calculation was performed with using refined structural parameters as well as taking into account the Cu+ occupancy and oxygen vacancies. Results are shown in Table 1. Cu+ is obviously overbonded with a BVS of 1.3476 that makes Cu+ metastable in LiCuNb3O9, thus apt to donating excess electrons under external fluctuations, e.g. alternative-current (AC) electric field or magnetic field, to interact with e.g. the lattice and/or spin or electrons in terms of forming hopping polarons. The BVS of Cu2+ and Nb5+ are calculated to be 1.9140 and 4.7998, respectively, which are slight underbonded to permit both Cu2+ and Nb5+ to take part in the transportation of hopping electrons. This thus suggests a physical scene for the crystal structure and chemical coordination as schematically shown in Figure 2b. The NbO6 octahedra connect with sharing vertex oxygen in three-dimensional space. A-site Cu/Li plannerly (or e.g. CuO4) connects four NbO6 octahedra by bridging vertex oxygen. It is specially noted that no any sharing oxygen atoms happen between any two CuO4. This means the charge hopping/transport in Cu+/Cu2+ cations must involve the medium NbO6 octahedra for even the nearest-neighbor case. The charge fluctuation on Cu cations leads to the distortion in the original CuO4 planes, with the oxygen


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shifting off the center (Figure 2c) to form quasi tetrahedra (Figure 2d). Figures 2c-2f demonstrate the slightly distorted CuO4 tetrahedra viewing from different a, b, and c of crystal axis. These CuO4 tetrahedra alternatively arrange in 3D space, with planner-perpendicular format in adjacent two tetrahedra, but again without any oxygen sharing. The charge carrier, i.e. Cu+, bonds with four O oxygen and further the adjacent Cu2+ (could be also the Cu+) through bridging the medium NbO6 octahedra. The distances for six Nb-O bonds in one NbO6 octahedron are not all same (Table 1), proving the NbO6 octahedra are apparently tilted and distorted, which with polarized for itself could favor to accelerate the charge transport in Cu-O chains. (a)

Measured Refined Bragg Position

Intensity (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(c)

(d)

Difference

10

20

30

40

50

60

70

80

[100]

2 (degree) (b)

Tilted [100]

(f)

(e)

[010]

Tilted [001]

CuO4

[001] NbO6

Figure 2. Rietveld powder XRD refinement and resulting crystal structure of LiCuNb3O9. (a) Powder XRD pattern and refined results. Experimental, refined and their difference curves are also shown. The refined parameters are also given in Table 1. (b) The resulting crystal structure viewed from slightly tilted c direction. (c)-(f) A-site configurations of Cu/Li-O4 planer (or quasi-


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tetrahedral) coordination viewed from different directions. The arrows in (c) denote the oxygen (red) off-plane shift directions with leading to the distorted CuO4 demonstrated in (d). Table 1. Crystal structural parameters and chemical coordinations from Rietveld powder XRD refinement and bond valence sum (BVS) calculation for as-synthesized LiCuNb3O9. Note that “×number” e.g. “×3” and “×4” represents the number of chemical bonds with same length in one polyhedron.

a=b=c= 7.5290 Å

α=β=γ= 90°

Space group: I23

Atom

Site

x

y

z

Li/Cu

6a

0.00000

0.50000

0.50000

Nb

8c

0.26210

0.26210

0.26210

O

24f

0.00715

0.30211

0.17476

Chemical bond

Bond length/Å

BVS of ions/v. u.

Nb-O (1)

2.0513 ×3

Nb-O (2)

1.9656 ×3

Cu-O (1)

2.8669 ×4

Cu-O (2)

1.9885 ×4

Cu-O

1.9885 ×4

Cu: 1.3476

Li-O

1.9885 ×4

Li: 1.0601

Nb: 4.7998

Cu: 1.9140

3.3. Dielectric property and relaxation behavior Frequency-dependent dielectric properties (permittivity ε’ and loss tan δ) of LiCuNb3O9 ceramic (ε’) were measured at different temperatures firstly, shown in Figure 3. Colossal permittivity (CP) > 104 in a broad frequency range (102~105 Hz) was achieved at room temperature (300 K), which gradually decreases with increasing the measurement frequencies, finally stabilizing to approx. 100 at the frequency over MHz degree. Around the frequency region where the permittivity


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quickly falls, a Debye-like dielectric relaxation occurs on the tan δ curve (Figure 3b).12, 59 This is quite similar to the commonly reported interfacial polarizations in many transition-metal systems as also ascribed to be the internal barrier layer capacitor effect (IBLC) previously for LiCuNb3O9 ceramic.60-61 On the other hand, the CP ε’ decreases overall with decreasing the measurement temperatures at all frequencies and exhibits only approx. 100 below 50 K, naturally undergoing a significantly sudden change. To gain detailed characteristics for the dielectric relaxations, external magnetic field was performed. It was found that the ε’ and tan δ change unconspicuously at 300 K when 1T magnetic field was applied to the ceramic, but which becomes predominant at lower temperatures on both values and temperature/frequency-relaxation positions. Therefore, the reported IBLC mechanism may be not correct or at least not completely accurate because additionally surface BLC effect was observed when comparing with the dielectric results collected using Ag-coated and Au-sputtered electrodes (not presented). As a result, more experimental evidences as well as comprehensive understanding, in order to reach a clearer physical picture, are necessary for present colossalpermittivity LiCuNb3O9 ceramic.


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(b)

H=0

8 6

5

10

'

10

4

3

10

1

10

(c)

H=1T

7

10

(d)

H=1T

T (K)

tan 

(a)

H=0

7

10

360 310

2

260

0 10

210 160

8

'

4

3

10

tan 

110

6

5

10

60 10

2

1

10

2

10

3

10

4

10

5

10

6

10

f (Hz)

2

10

3

4

10

10

5

10

6

10

0

f (Hz)

Figure 3. Frequency dependences of dielectric spectra (ε’ and tan δ) of LiCuNb3O9 ceramic measured at different temperatures. (a) and (b) were tested under the magnetic field of H = 0. (c) and (d) were tested under H = 1 T. The scatter (open-circle) curves denote the room-temperature (300 K) dielectric properties.

(b)

H=0

H=0

122 K @100 Hz

5

2

3

10

1

10

7

10

(c)

H=1T

H=1T

(d) 176 K @100 Hz

5

10

f (Hz)

106

1

105

0 5

104

4 103

3 2

3

10

102

1

1

10

4 3

'

10

5

tan 

10

(a)

tan 

7

'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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50 100 150 200 250 300 350

Temperature (K)

0 50 100 150 200 250 300 350

Temperature (K)


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Figure 4. Temperature-dependent dielectric spectra (ε’ and tan δ) of LiCuNb3O9 ceramic measured at given frequencies from 100 Hz to 1M Hz with applying external magnetic field. (a) and (b) were tested under 0T. (c) and (d) were tested under 1T magnetic field. The dashed rectangles in (a and c) denote the temperature span change for the dielectric plateau/abnormity at 100 Hz after magnetic field application. The arrows (b and d) direct to the dielectric peaks with temperature changes at 100 Hz. Temperature dependences of dielectric properties were thus measured with applying magnetic field (0T or 1T) in order to fully understand and uncover the polarization origin of CP materials of this type, shown in Figure 4. The colossal dielectric permittivity decreases gradually with the temperatures decrease from high temperature (e.g. 360 K) down to relatively low temperatures (e.g. 100 K), appearing a plateau above around 150 K for the dielectric spectrum of 100 Hz with exhibiting high dielectric permittivity over 104. Below this temperature, the permittivity ε’ quickly falls for 2-order magnitude down to around 100 and unchanged within lower temperatures (10 K), still quite higher than many non-ferroelectric-based materials.62-63 More than this strikingly, the low-temperature dielectric relaxations, i.e. the dielectric plateau/abnormity, experience an obvious shift towards higher temperatures under 1T magnetic field (dashed rectangles highlighted in Figure 4), e.g. the relaxation temperature for the dielectric relaxation at 100 Hz changes from 122 K to higher 176 K. Such a large variation should be related to the hopping resistance of the polarized spins under the magnetic field as addressed later. We noted that the low-temperature dielectric permittivity of around 100, namely termed the “ground-state dielectric permittivity” ε∞, is due to the phonon modes and lattice vibrations like the Cu2Ta4O12 with tilted NbO6 octahedron configurations.45 However, with regard to the colossal permittivity of over 104 at higher temperatures (> approx. 150 K), it is well-known that phonon


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vibrations cannot contribute such a high permittivity for non-ferroelectric LiCuNb3O9 which is centrosymmetric with space group I23. Instead, similar to those transition-metal oxide systems, the dielectric abnormity at around 100 K, i.e. with permittivity changing for 2-order magnitudes, should be related to the behaviors of electrons, that is, a relaxation process that electrons are frozen and/or activated. It is thus quite clear that the 3d10 from Cu+ should be the sole origin responsible for electrons. Now the questions arise: (1) In which states the electrons exist in the material? (2) In which ways the electrons move in the material? As stated that with increasing the frequencies, the dielectric relaxation peaks in tan δ spectra (Figure 4b) around 150 K shift to higher temperatures (Tm), like a thermal activation behavior. Therefore, the temperature-dependent relaxation frequency (fp ) can generally be described as f p (in logarithm scale) ~ T - S , with S = 1 for Arrhenius type nearest neighbor hopping (NNH)

while 1/4 for Mott variable-range-hopping (Mott-VRH).64 Figure 5 shows the relation of f p ~ T - S as well as the fitting results. It can be clearly seen that the plot of f p vs.

1

Tm

deviates the linear

Arrhenius law, not a purely thermal activation behavior. Regardless of the inaccuracy for Arrhenius law in this case, the resulting fitting could still give the estimated values of eigen frequency f0 and activation energy (ΔE) are 1.5×107 Hz and 0.13 eV, respectively. These values are in analogous level but slightly lower than those in CaCu3Ti4O12 (CCTO).65 For CCTO, both NNH and VRH were reported,41, 65 making the mechanism still in controversial. Alternatively, fitting using two Arrhenius process could also better describe the low-temperature relaxations with giving the quite close ΔE of 0.11 eV and 0.17 eV, respectively. However, it is worth noting that there should only involve one hopping mechanism in present LiCuNb3O9, because: (1) the trend in the intensity of dielectric loss peak monotonously increases with the temperature below 260 K; (2) low-temperature only refers to the behavior of electrons. Although oxygen vacancies (VO) exist


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in LiCuNb3O9, the activation energy should be very high (normally above 0.6 eV) as those VOrelated defect dipoles in TiO2 with ΔE of 0.76 eV,1 and 1.04 eV in SrTiO3 that only happen at high temperatures of over 600 K.66

1000/Tm (K-1) 10

3

4

5

6

7

H=0 E=0.17 eV E=0.13 eV

104

E=0.11 eV

103

102 0.24

105

104

fp (Hz)

5

fp (Hz)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


103

0.26

102 0.30

0.28

Tm-1/4 (K-1/4) Figure 5. Plots of dielectric relaxation frequency fp versus relaxation temperature Tm of LiCuNb3O9 ceramic. Mott VRH (red: bottom scale) model was used for fitting. Meanwhile, the curves (top scale) were also fitted for comparison purpose by using the one Arrhenius (green) or two Arrhenius typed models (orange), yielding corresponding activation energy (ΔE). The double arrows direct to the coordinate axes with corresponding models used. By contrast, the Mott VRH model can well fit the relaxation frequency curve (Figure 5) that is associated with the polaronic conduction as described below,

f  f 0 exp[(T0 / Tm )1/ 4 ]

(1)

here f0 is the attempt frequency, T0 is eigen relaxation time with their values were calculated to be 1.689×1018 Hz and 2.87×108 K, respectively. Such an eigenfrequency f0 is higher than that of


17


Page 18 of 33

CaCu3Ti4O12 with f0 = 5.02×1014 Hz, while lower than that of Fe-Ti-based oxides e.g. 5.13×1021 Hz in FeTiTaO6, 1.82×1023 Hz in FeTiNbO6 and 1.82×1033 Hz in FeTiSbO6.67 These suggest LiCuNb3O9 has slightly different hopping behaviors, which instead, more similar to those multiferroic materials e.g. Ca3CoRhO6 which possesses a variable range hopping conductivity and the opening of a Coulomb gap in the d bands, giving rise to strong magneto-dielectric effect.68 Therefore, in LiCuNb3O9, the inter-site coulomb energy should be sufficient to resist the thermal fluctuations around relaxation temperatures. The localized charge carriers from Cu 3d can hop a larger distance to an energetically favorable site. 3.4. Electric and magnetic behaviors It is quite clear that there are big discrepancies on both dielectric permittivity (ε’) and loss (tan δ) for LiCuNb3O9 ceramic with and without applying magnetic fields. When 1T vertical magnetic field was applied, the dielectric relaxation under same frequency move to higher temperatures. For instance, the relaxation peak of 1k Hz curve locates at 160 K for 0 T while 210 K under 1 T magnetic field. Accompanying with the change in low-temperature dielectric spectra, the conductance of LiCuNb3O9 ceramic also exhibits a large variation under H = 1 T as shown in Figure 6a. It is clear that the resistivity (ρ) has one or two-fold changes in magnitude under the external magnetic field of 1 T, e.g. ρ increases from 3×108 Ω·cm at H = 0 to 1010 Ω·cm at H=1 T at 100 K. Such a large change is indicative of the existence of magnetic-induced resistance, a significant hint of magnetoelectric coupling. At around the temperature range with dielectric relaxations, there also presents an obvious electric abnormality in measured ρ curves (highlighted in Figure 6a): a small plateau and two inflexion points were observed, leading to an inconsistent variation tendency, with temperature span of 70 K - 200 K for H = 0 while 120 K - 250 K for H = 1 T. This precisely coincides with electron activation/freezing temperature process where magnetic


18

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field propones the dielectric relaxations by shifting to higher temperatures. It is consequently, again, that the electron activation/freezing process in present LiCuNb3O9 is not simply a thermalactivated nearest-neighbor-hopping, but also couples with the magnetic field with spin interaction involved. To fully understand the charge states for this kind of CP material, we tested the magnetic properties of LiCuNb3O9 (Figures 6b, c). The results revealed the perfectly paramagnetic characteristic of LiCuNb3O9 as the linear

 1 ~ T plot was presented from 5 K to 300 K. No

differences on M-T (or see χ-T) measurements between the zero-filed cooling (ZFC) and filed cooling (FC) processes. No any traces of ferromagnetic and/or antiferromagnetic ordering/transition appear even at low temperature (5 K). Consistently, both low temperature and room temperature (300 K) M-H curves also present perfectly linear relationship without any possible hysteresis. These imply that the spins of the unpaired Cu2+ 3d9 electrons could easily response for the magnetic field. Under the externally magnetic field, the spin reorientation of the Cu2+ 3d9 electrons would exclude the electron with same spin orientation to fill into the orbital, which naturally elevates the electron-electron interaction energy. As a result, the process that electron hopping from one Cu+ 3d10 to Cu2+ 3d9 site with itself changing into Cu2+ 3d9 would be postponed under the external magnetic field, which would happen if experiencing enough thermal fluctuation to overcome the energy competition, that is, at higher temperatures. When electron hopping occurs, regardless of the external magnetic field is applied or not, the hopping electrons would distort the A-site polyhedron and further the lattice, to form a sort of spin polarons. This is also indicated by the polaronic hopping following.


19


(a) 1013 H=0 H=1T

11

 (cm

10

9

10

7

10

5

10

3

10

0

100

200

300

400

Temperature (K) 1/[emu] molOe)

0.04

-1

-1

(emu[molOe] )

(b) 0.05

0.03 0.02 0.01 0.00

250 200 150 100 50 0

0

100

200

300

Temperature (K) ZFC FC B=1000 Oe

0

100

200

300

Temperature (K) 3 15 K 300 K

2

-1

M (10 emumol )

(c)

1 0

3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 33

-1 -2 -3

-8

-4

0

4

8

H (T)


20

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Figure 6. Temperature dependences of electric and magnetic properties of LiCuNb3O9 ceramic. (a) Resistivity measured by four-probe at temperature range of 10 K - 360 K with and without magnetic fields. There exists obvious electric abnormality at around the temperatures with dielectric relaxation, which are highlighted by blue (70 K - 200 K for H=0) and green (120 K 250 K for H =1 T) colors, respectively. (b) Magnetic susceptibility (χ) vs. temperature (T) plot i.e.

 ~ T under ZFC and FC with applying magnetic field B =1000 Oe. Inset is the corresponding

 1 ~ T

curves, yielding a linear paramagnetic character. (c) M-H curves recorded at 15 K and

300 K without showing any magnetic hysteresis. 3.5. Correlation of polaronic conduction and relaxation behavior Conductance behaviors of oxides are closely linked to the dielectric property, especially for the dielectric systems with local charge/electrons hopping characteristic. To get more insight about the conduction contributing to relaxation, the electrical conductivities (σ’) at selected temperatures were calculated by using the following equation,

 '  2 f  0 "

(2)

where f is the test frequency, ε0 the free-space permittivity and ε” the imaginary part of dielectric permittivity. Results are shown in Figure 7a. The low-frequency conductivity is frequency dependent as it is with the contribution from the grain boundaries while at high frequency (f >104 Hz), a slowly varying region is observed, which is from the bulk contribution. The bulk dc conductivity was extracted by fitting the universal dielectric response (UDR) model69 at selected temperatures,

   dc   0UDR f s

(3)


21


Page 22 of 33

where σdc is the bulk dc conductivity, σ0UDR a constant, f the frequency, and S an exponent smaller than 1. Thus, the dc conductivity for LiCuNb3O9 in the temperature range of 80 - 200 K could be obtained according to eq 3, shown in Figure 7a. Similar to the case of f p vs. Tm , the function of

 dc vs. T does not obey the 1/T linear fitting for Arrhenius model, only Mott VRH model with T1/4

can fit the function well (Figure 7a). In VRH category, the hopping electronic carriers at low

temperature do not longer follow a simple tunneling transition at a certain and constant energy, but prefer interacting with lattice (phonon) to form polarons, finally accomplishing a phononassisted transition to a nearer vacant site at a different energy in terms of polaron hopping. Following is the equation describing VRH model conduction mechanism,

 dc   0 exp[(T1 / T )1/ 4 ] (4) where σ0 and T1 are constants denoting conductivity and temperature. T1 is proportional to α3/ N(EF), with α the inverse of the localization length, which is given by

T1  24 /[ k B N ( EF ) 3 ] (5) where N(EF) is the density of localized states at the Fermi level, and ξ is the decay length of the localized wave function. The decay length ξ is directly associated with the length of the chemical bonds, corresponding to the average distance between the adjacent cations under consideration that normally link with bridging oxygen in oxide materials. The average Cu-O distance for present LiCuNb3O9 is 2.4277 Å as listed in the Table 1. Thus the value of the decay length ξ should be doubled with using Cu-O length, i.e. ξ is 4.8554 Å.67 Fitting the σdc curve (Figure 7b) using VRH model eq 4 yields the values of the σ0 and T1 that are 6.969×106 S/cm and 1.46×108 K, respectively, which are comparable with the values reported for cupper-containing oxides. Taking this T1 value into eq 5 gives the N(EF) to be 5.30×1018 eV/cm3. Furthermore, the hopping activation energy (W) at a given temperature (T) can be calculated using the following relation,


22

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W  0.25k BT11/ 4T 3/ 4 (6) the values of W could be, for instance, obtained to be 0.063 eV, 0.096 eV, 0.126 eV at 80 K, 140 K and 200 K, respectively. Meanwhile, the hopping range of polarons (R) at a given temperature can be estimated by the following relation,

R   1/ 4 /[8 k B N ( EF )T ]1/ 4 (7) taking into the values of decay length ξ and N(EF) afore-obtained, the hopping ranges for Cu d electrons are estimated to be 47.94 Å, 41.68 Å and 38.13 Å at 80 K, 140 K and 200 K, respectively, around several unit cells in length. This is a quite long distance that is sufficient to form large polarons in the lattice when the one of Cu+ 3d10 electrons hops to next but not necessary/always the adjacent Cu2+ site to distort the CuO4 tetrahedron. Relative long polaronic hopping always leads to relative high bulk conductance with the scenery that the polaronic chargers can easily hop to the grain boundaries and be blocked to cause macroscopically interfacial polarizations, but different to small polarons or space charges, e.g. those surface dangling bonds or ionic defects. This is naturally responsible for the observed colossal permittivity as well as high dielectric loss in LiCuNb3O9. It is worthy that the calculated values of R and W, in turn well satisfy the conditions of both R≥ξ and W > kBT which are essential preconditions for the Mott VRH model,70 again supporting the low temperature relaxations in LiCuNb3O9 is in polaronic nature. We also noted that the conductance behavior of the LiCuNb3O9 ceramic under the externally applied magnetic field (H= 1 T) is quite similar to that of without magnetic field as comparing -S with the  ' vs. f and  dc vs. T curves (Figures 7c,d). The difference is that some basic

parameters are changed under the magnetic field e.g. the increased σ0 and T1, and decreased density of states at Fermi level N(EF). As a result, both the hopping activation energy and hopping distance are increased as listed in Table 2. It is thus clear that the polaronic hopping obeys the Mott variable-


23


Page 24 of 33

range-hopping theory and there is an electron-electron interaction (Coulomb interaction) between the transport charge carrier Cu+ 3d10 excess electrons and the Cu2+ 3d9 electrons. The Cu+ 3d10 electron can hop to next but not necessary/always the adjacent Cu2+ site to distort the CuO4 tetrahedron which will form the large polarons in the lattice and the value of hopping range (R) is around several unit cells in length, that is the Mott VRH effect with the hopping distance R as large as up to 40 Å (Table 2). It is noted from crystal structure (Figure 2b) that the nearest-neighbor hopping would involve one NbO6 octahedra. Given the hopping progresses in a chain of Cu + - [O - Nb]n - O - Cu 2+ the n could be as large as n =10-12 for the variable-range hopping, about

,

5-6 unit cells. Under external fluctuations, e.g. alternative-current (AC) electric field or magnetic field, the LiCuNb3O9 ceramic appears macroscopically colossal permittivity character and special relaxation process. The hopping polarons in such type, due to have relative long-distance hopping, usually give rise to relatively high dielectric loss and could be blocked at the interfaces or surfaces of the grains/ceramics to exhibit barrier layer capacitor (BLC) effect. However, obviously contrasting to the reported previously, this is not simply an internal barrier layer capacitor (IBLC) effect but involving complex transport and interaction between local structures, electrons, spins and/or lattices.


24

Page 25 of 33

-1

1000/T (K ) (a) 10-4

H=0

2

(b)

4

6

8

10

-5

10

12

H=0

-5

10

-6

10

' (S/cm)

-6

-7

10

200K 180K 160K 140K 120K 100K 80K

-8

10

-9

10

2

10

3

10

4

10

5

10

dc (S/cm)

10

-7

10

dc

-8

10

-1/4

Linear fit of dc (T )

-9

dc

10

Linear fit of dc (1000/T)

-10

10

6

10

0.24

0.28

(c) 10-5

0.32 -1/4

f (Hz)

H=1T

2

(d)

4

0.36

-1/4

T (K ) -1 1000/T (K ) 6

8

10

10

-7

10

12

H=1T

-7

-6

10

-8

10

200K 180K 160K 140K 120K 100K 80K

-8

10

-9

10

-10

10

2

10

3

10

4

10

5

10

6

10

dc (S/cm)

' (S/cm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-9

10

dc

-10

10

-1/4

Linear fit of dc (T ) dc

-11

10

Linear fit of dc (1000/T)

0.26

f (Hz)

0.28

0.30 -1/4

T

0.32

0.34

-1/4

(K )

Figure 7. Frequency/Temperature dependences of conductivities (σ’ and σdc) for LiCuNb3O9 at given temperatures. (a) and (c) show the frequency dependences of conductivities (σ’) for H = 0 and H = 1 T, respectively. The symbols are experimental data, and solid lines are the fitting with using UDR model. (b) and (d) demonstrate the temperature dependences of dc conductivities (σdc) extracted from UDR model. The symbols are experimental data, and solid lines are the fitting with using Arrhenius model (green line) and Mott VRH model (red line), respectively.


25


Page 26 of 33

Table 2. Fitting parameters for the polaronic hopping of the LiCuNb3O9 ceramic under externally applied magnetic field.

Magnetic field H (T)

σ0 ( S/cm)

T1 (K)

N(EF) (eV/cm3)

0

6.969×106

1.46×108

5.30×1018

1

2.777×107

2.59×108

2.99×1018

Temperature (K)

W (eV)

R (Å)

0T

1T

0T

1T

80

0.063

0.073

47.94

55.32

140

0.096

0.111

41.68

48.09

200

0.126

0.145

38.13

43.99

4. CONCLUSION Colossal-permittivity LiCuNb3O9 was found to exhibit intrinsic A-site deficiency and oxygen vacancies with altered proportion of valence states in Cu cations, which was determined to be 1: 9 of Cu+/Cu2+ by combined XPS and EPR techniques. Bond Valence Sum calculation on the structural chemistry indicates that Cu+ is slight overbonded and meanwhile underbonded for Cu2+, and NbO6 octahedron is distorted. The colossal permittivity (ε’>104) experiences a relaxation at low temperature, i.e. it sharply falls down to 100 level within 80-150 K, showing a freezing/activation process of electrons with their origin from Cu+/Cu2+, and further they interact with lattice to form polarons with polarized spins under external magnetic field. Detailed dielectric and conductance analysis reveals that the polaronic hopping follows the Mott variable-rangehopping mechanism, and external magnetic field could greatly enhance the hopping activation energy and hopping distance, exhibiting typical magnetoelectric effect that can well explain the apparent colossal permittivity and related barrier layer capacitor effect in double perovskite


26

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LiCuNb3O9. Our results on LiCuNb3O9 therefore provide significant experimental evidences and understanding for the magnetoelectric capacitance that correlated with the polaronic hopping, which may guide to explore a wider range of magnetoelectric materials, especially oxide perovskites.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Author Contributions W. H conceived the idea. W. H, D. G. and J. X. analyzed the data. X. J., D. G., H. L., G. L. and J. W. conducted the experiments under the supervision from W. H., J. X., L. Z. and F. X. All authors have given approval final version of the manuscript. Notes The authors declare no competing interest. ACKNOWLEDGMENTS This work was supported by the National Key R&D Program of China (Grant No. 2017YFB0406300), Key R&D program of Yunnan Province (Grant No. 2018BA068). W. H. thanks the “One Thousand Youth Talents” Program of China. REFERENCES (1) Hu, W.; Liu, Y.; Withers, R. L.; Frankcombe, T. J.; Noren, L.; Snashall, A.; Kitchin, M.; Smith, P.; Gong, B.; Chen, H.; Schiemer, J.; Brink, F.; Wong-Leung, J. Electron-Pinned Defect-Dipoles for High-Performance Colossal Permittivity Materials. Nat. Mater. 2013, 12, 821-6.


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Colossal-permittivity behaviors in A-site distorted double perovskite

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