Structural, magnetic, and dielectric properties of charge-order phases in manganite

Structural, magnetic, and dielectric properties of charge-order phases in manganite

La(Ca _0.8 Sr _0.2 ) ₂ Mn ₂ O ₇

Cite as: J. Appl. Phys.127, 104104 (2020);doi: 10.1063/1.5120608

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Submitted: 23 July 2019 · Accepted: 22 February 2020 · Published Online: 12 March 2020

J. H. Zhang,^1,a) S. H. Zheng,¹ Y. S. Tang,¹Y. Q. Li,¹ G. Z. Zhou,¹P. Z. Chen,¹L. Lin,¹Z. B. Yan,¹X. P. Jiang,² and J.-M. Liu^1,3

AFFILIATIONS

1Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

2School of Materials Science, Jingdezhen Ceramic Institute, Jingdezhen 333403, China

3Institute for Advanced Materials, South China Normal University, Guangzhou 510036, China

a)Author to whom correspondence should be addressed:[email protected]

ABSTRACT

Charge-ordered layered manganites ReA2Mn2O7(Re = rare-earth species and A = Ca, Sr, Ba, etc.) are believed to offer a number of fascinat- ing electronic and magnetic properties, including the long-time claimed but not yet confirmed ferroelectricity associated with charge-order- ing. Experimental observations of the charge-order induced transport and electrically polar behaviors have been insufficient. In this work, we synthesize the La(Ca0.8Sr0.2)2Mn2O7 (LCSMO) single crystal and investigate its structural, magnetic, and dielectric properties. It is revealed that LCSMO undergoes two consecutive charge-ordering transitions upon decreasing temperatureTbefore entering an antiferro- magnetic state in the low-Trange. The first charge-order transition occurs at temperatureT_CO1∼314 K from the high-Tparamagnetic state.

This charge-order state (CO1 state) is transferred into another charge-order state (CO2 state) by a sequence starting from∼290 K, and the resultant CO2 state is dynamic and polar-like. The dynamic behaviors of this polar-like CO2 state is confirmed by the remarkable dielectric relaxation associated with this state. The present work provides a connection between the charge-ordering and electrically polar response in LCSMO, while ferroelectricity remains yet to be an issue.

Published under license by AIP Publishing.https://doi.org/10.1063/1.5120608

I. INTRODUCTION

Perovskite-based manganites, in which rich emergent phe- nomena associated with the charge, spin, orbital, and lattice degrees of freedom are available, have been attracting much attention because of their significance in fundamental physics and promising applications.^1,2 For example, the coexistence and coupling between ferroelectricity and magnetism, i.e., multifer- roicity, were demonstrated in various manganites (e.g., TbMnO3

and TbMn₂O₅) and have become the research forefront of con- densed matter physics.^3–6 So far, those promising multiferroic materials can be roughly categorized into two types. Type-I mul- tiferroics include materials in which ferroelectricity and magne- tism are only weakly coupled. Type-II multiferroics, typically manganites, have ferroelectricity to be generated from a specific spin order and thus strong magnetoelectric coupling. Consequently,

perovskite-based manganites become highly attractive for designing and discovering multiferroics.

Along this line, in one aspect, promising mechanisms such as hybrid improper multiferroicity were proposed,⁷ raising interest in those well-known 327 manganites and titanates (Ca₃Ti₂O₇,^8,9 Ca3Mn2O7,^10,11etc.). In these materials, a combination of two non- polar lattice modes, e.g., the rotation mode X₂⁺and tilt mode X₃⁻of the oxygen octahedra, is necessary for generating weak ferromagne- tism and ferroelectricity simultaneously. In the other aspect, attention has also been paid to possible ferroelectricity caused by different charge-order (CO) forms.¹²These proposed CO states are associated with half-doped perovskite manganites and ferrites, while evidence with the electrically polar-like behaviors has not yet been sufficient although second harmonic generation (SHG) signals in Pr(Ca, Sr)2Mn2O7, one of the 327 manganites, were detected.

The CO state is rather ubiquitous in mixed-valent transition metal oxides, and the mechanism for local electric dipole genera- tion is schematically drawn inFig. 1 while a detailed description was given in the literature.^13,14 Here, one considers the one- dimensional chain where equal charge (zero) and equivalent bonds are situated on each site. If charge-ordering and dimerization occur simultaneously, the initial homogeneous ion chain will evolve into two sets: one set of ions has a larger charge and the other set has a smaller charge. The two sets of ions alternate along the chain direc- tion, generating a site-centered CO state, as shown inFig. 1(b). On the other hand, a dimerization of the two sets of ions can make the strong bonds and weak bonds to align alternatively, constituting the bond-centered CO state. Certainly, the coexisting site-centered and bond-centered charge states, if properly aligned, will lead to the spatial inversion symmetry breaking and thus to the generation of ferroelectric polarization.

In spite of this theoretical prediction, experimental realization of such CO-induced ferroelectricity has not yet been evidenced. In some cases, whether the consequent lattice structure is polar or not remains yet unclear, not to mention the ferroelectricity. The first observation was made on LuFe2O4rather than manganites,¹⁵while subsequent verifications gave somewhat negative results.¹⁶In spite of these problems, the CO physics of ferroelectricity in manganites remains attractive enough simply because the charge-ordering occurs at high temperature, and the CO state can also be easily destroyed by external stimuli, two advantages absent but crucial for most of the type-II multiferroics. Therefore, substantial effort is being made.

In fact, layered manganites are under continuous focus far beyond ferroelectricity alone, since the work of Tokunagaet al.on Pr(Ca_0.9Sr_0.1)₂Mn₂O₇ (PCSMO).¹⁷ The resistivity, magnetization, optical SHG, and synchrotron x-ray oscillation measurements con- firmed two distinct CO states (CO1 and CO2 states) appearing at tem- peratureT=TCO1∼370 K and T=TCO2∼300 K. The two states are different by the 90° orbital stripe rotation from thea-axis to theb-axis below T_CO2. The CO2 state should be electronically polar-like and thus attractive for the CO-induced ferroelectricity. Experimentally, optical SHG microscopy carried out by Itohet al., observed the polar domains and domain walls in Pr(Ca_0.85Sr_0.15)₂Mn₂O₇.¹⁸

In contrast, the high-resolution structural observation by Maet al.¹⁹ confirmed that the A-site Pr and Ca/Sr occupations are majorly ordered, where Pr ions prefer to take the sites in the oxygen octahe- dra layers while Ca/Sr ions prefer to take the layers in between the octahedra layers. This A-site ordered occupation results in a high degree of orbital-ordering and associated collaborative lattice distor- tion. Therefore, ferroelectric polarization, if any, should be from the contribution of Mn ion off-central shifting due to the lattice distor- tion. In the other words, charge-ordering as a source of polar state in such 327 manganites is still in question.

While a number of band structure and microstructure issues with PCSMO remain to be checked, one may think of other candi- dates for such an electronic polar state. In addition, besides static characterizations on the polar domains, less investigation on the dynamic aspect of the polar state has been performed. Surely, due to the high density of mobile carriers and narrow bandgap, static evidence with ferroelectricity may not be easy to access, or these 327 manganites may not accommodate long-range ferroelectric order even if the polar CO state exists. Instead, a dynamic polar state should be easily developed, hinting that the CO2 state is most likely inhomogeneous and thus dynamic. Certainly, such a polar- like CO state can be detectable using the dielectric relaxation mea- surement, which, however, can act as an alternative to explore the polar state in such 327 manganites if any.

In proceeding, one considers the A-site size of these 327 man- ganites. On one hand, it is found that the MnO6octahedra network would be less distorted when the A-site size is larger. A large A-site may drive the shifting of the oxygen O1 ion connecting the neigh- boring two oxygen octahedra. While no clear correlation between the polar distortion and octahedra tilting has been claimed, the O1 ion shifting would be benefiting to the polar distortion. On the other hand, it is still a question whether a 327 manganite with large A-site size promotes the CO stability or not. Along this line, we consider another 327 manganite La(Ca0.8Sr0.2)2Mn2O7(LCSMO). It has a larger A-site size than Pr-based 327 manganites. An investiga- tion of the charge-ordering, magnetism, and dielectric responses of this 327 manganite would be appreciated to check the polar-like state if any, which is a topic of this work. We report the synthesis of LCSMO single crystals and investigations of the structure, transport, magnetic, and dielectric properties. Indeed, LCSMO does undergo two consequent CO events, respectively, with decreasing T. More importantly, dielectric relaxation features associated with the polar- like behavior in the CO2 state is identified, suggesting that this CO2 state is dynamic without a clear indication of the long-range ferro- electric order.

II. EXPERIMENTAL DETAILS

Species La³⁺ has its ionic radius of 136 pm, larger than 129 pm, the ionic radius of Pr³⁺. The average A-site size for LCSMO is∼136 pm and that for Pr(Ca_0.8Sr_0.2)₂Mn₂O₇(PCSMO) is ∼133 pm, given that the (Ca_0.8Sr_0.2)²⁺ average ionic size is 136 pm. Therefore, LSCMO would exhibit less octahedra tilting than PCSMO. Following earlier reports on the synthesis of LaCa₂Mn₂O₇,²⁰LCSMO polycrystalline powder was prepared by the solid state reaction method. High-purity powder of La₂O₃ (99.95%), SrCO3(99.99%), CaCO3(99.9%), and Mn2O3 (99.9%) FIG. 1.A schematic drawing of electric dipole formation associated with the

site-center and bond-center charge-ordering. The ordered alignment of these dipoles contributes to ferroelectric polarization. Here, the green, red, and orange spheres represent the neutral, cation, and anion species, respectively. (a) A neutral one-dimensional chain formed by ions with equal charges. (b) Coexisting site-center and bond-center charge-order in one-dimensional chain leads to the red arrow denoted net electric polarization.

were mixed, ground, pelletized, and sintered at 1350 °C for totally 90 h with several intermediate grindings to ensure a complete reac- tion. The as-prepared powder was submitted to the standard process- ing of polycrystalline bars for subsequent single crystal growth using the floating-zone method based on a light furnace equipped with double-elliptical mirrors (Cyberstar, MF-2400, France). The growth was run in the atmosphere of 8.0 atm O₂ambient with the seeding and feeding speed of 4 mm/h and 4.5 mm/h, respectively.

It should be mentioned that some of the as-prepared single crys- tals contain local twin-like regions. In order to exclude the possible influence from these twin-like structures, the samples for the subse- quent measurements were carefully chosen and only those crystals without twin-like contrast in the optical microscopy were took for measurement. The crystallinity of the as-grown crystals was character- ized by x-ray diffraction (XRD) in two different ways: single crystal and polycrystalline powder crushed from the single crystals, using the Bruker D8 Advance x-ray diffractometer with CuK_αradiation (wave- lengthλ= 0.154 06 nm). For the single crystal, the bar was cut into typical size of 2.5 × 2× 0.5mm³. For the polycrystalline powder, the XRD data were fitted with the Rietveld structural refinement using the GSAS program.²¹ It was shown that the powder exhibits the single-phase crystallinity, fitting well to the orthorhombic symmetry.

The chemical composition distributions of the as-grown single crys- tals were detected using scanning electron microscopy with the energy dispersive x-ray spectroscopy (EDX) unit.

The electric resistivity along the c-axis (ρc) and along the a/

b-axis (ρaandρb) as functions of temperatureTin the cooling and heating sequences, respectively, were measured using the Quantum Design physical property measurement system (PPMS) under the zero magnetic field condition. Thedcmagnetic moments along the c-axis andb-axis as functions ofT, respectively, were measured using the Quantum Design superconducting quantum interference device magnetometer (SQUID). The resistivity data were obtained using the conventional four-probe method. The heat capacity (Cp) was mea- sured by PPMS in a standard procedure over the temperature range from 16 K to 200 K. Despite no reliable data were obtained from the second harmonic generation (SHG) experiment, it is still necessary to describe the SHG experimental procedure. It was performed in a home-made measuring system where an amplified mode-locked Ti:

Sapphire laser (spectra Physics Hurricane, 1.41 eV) with a pulse width of 100 fs and a repetition rate of 1 kHz was used for excitation.

The energy per pulse was 15μJ focused on a spot of 0.5 mm diame- ter on the selected surface of the single crystals under measurement.

The second harmonic signals were detected in the reflection geome- try with a∼5° incident angle of the laser beam, while the second harmonic signals at an energy of 2.82 eV was selected by color filters and detected using a photomultiplier.

The dielectric constant along theb- andc-axis as functions of Tand ac signal frequencyf was measured in the in-plane inter- digital electrode mode and plane-parallel capacitor mode on a sample of 2.5 × 2.0 × 0.5 mm³, using the HP4294A impedance ana- lyzer in the frequency range of 1.0 kHz–1 MHz at a measuring voltageVac= 0.1 V. This measurement was based on the assump- tion that electric polarization, if any, would be aligned along the b-axis. Furthermore, due to the large leakage of the samples due to the relatively small bandgap, the measured dielectric signals may contain some contribution from the carrier motion, and thus we

also measured the dielectric response along thec-axis for a compar- ison. The inter-digital electrodes were sputtered using the simple evaporation method, and careful calibration was made so that the probed signals are intrinsic.

III. RESULTS AND DISCUSSION A. Microstructural characterizations

First of all, a schematic of the lattice structure is plotted in Fig. 2(a) only for a guide of eyes. The XRDθ–2θdata for single crystal plates are plotted inFig. 2(b) where the optical image of one plate-like crystal is inserted. The well-defined (00L) reflections from L= 4 toL= 16 are detected with the full-width at half-height (FWHH) of∼0.3° for the (0010) peak, evidencing the good quality of the single crystals. Given the relatively remarkable difference between these lattice constants (a,b,c), the absence of any peak splitting in the XRD spectrum seems to be a hint that the out-of-plane (c-axis) twinning structure if any should be little although there likely exists an in-plane twining structure. Furthermore, we check the composi- tion homogeneity of the as-grown single crystals, and the EDX in-plane images of the spatial distributions of La, Ca, Sr, Mn, and O are presented in Figs. 3(a)–3(e), while the EDX determined atomic ratios are La(Ca0.82Sr0.18)2.02Mn2.01O6.5, agreeing roughly with the nominal composition.

It is believed that LCSMO belongs to the Ruddlesden–Popper (RP) series, whose crystal structure can be viewed as the alternative

FIG. 2. (a) Lattice structure of double-layered perovskite La(Ca1−xSrx)2Mn2O7

where the dark green, purple, and red spheres denote the La/Ca/Sr, Mn, and O atoms, respectively. (b) The room temperature XRD θ–2θspectrum for a La (Ca0.8Sr0.2)2Mn2O7single crystal plate with the (001) oriented surface (inserted with the SEM image of the plate). (c) The room temperature XRDθ–2θspec- trum for the La(Ca0.8Sr0.2)2Mn2O7powder ground from the single crystals. The Rietveld refined data are shown also for comparison.

stacking of double-layered pseudo-cubic (La,Ca,Sr)MnO₃ and rock salt sheets like (La,Ca,Sr)O along thec-axis. To the best of our knowl- edge, no report on the crystal structure of La(Ca1−xSrx)2Mn2O7is available until now, but it is believed that La(Ca_1−xSrx)2Mn2O7shares the same lattice symmetry as LaCa₂Mn₂O₇ with the Cmcm space group. For further checking of the crystallinity, the single crystals were ground into powder and theθ–2θdata are plotted inFig. 2(c) with the structure fitting. In our data fitting, theAmamspace group has been used as the initial model for our Rietveld refinement of the room temperature XRD data, according to an earlier literature study.²⁰Indeed, theAmamstructure can be well fitted with LCSMO.

Here, it should be mentioned that both the Cmcm symmetry andAmamone belong to the same group number (No. 63) although they have the different setting coordinates. In theCmcmsetting, as used in the Rietveld refinement of LaCa2Mn2O7in the literature, the axis with the largest lattice constant is defined as the a-axis with a>b>c, where (a,b,c) are the lattice constants. However, as used in the present work and others,¹⁷for theAmamsetting, the axis with the largest lattice constant is the c-axis with c>b>a. In order to avoid this inconsistency, in our Rietveld refinement of the XRD data, we performed the coordinate transform from theCmcmsetting to theAmamsetting by rotating the lattice by 90° clockwise around the b-axis. Therefore, the results and conclusion are the same.

While the fitting data are highly reliable, evidenced with the squared fit goodnessχ²= 2.529, agreement factor R_p= 4.54%, and weighted agreement factor R_wp= 6.72%, it is confirmed that the lattice structure does belong to the Amam point group. The as-obtained lattice constants and ionic coordinates are listed in Table I. For the site occupation, it is found that the A-sites prefer the highly ordered occupation. In detail, the A-site at coordinates (−0.75,y, 0.50) is occupied by the La³⁺, Ca²⁺, and Sr²⁺ions at a prob- ability of 0.612, 0.264, and 0.124, respectively, suggesting that La³⁺

ions prefer to take the perovskite layers while most Ca²⁺/Sr²⁺ions take the rock salt sheets, similar to the cases of Pr(Ca_0.9Sr_0.1)₂Mn₂O₇¹⁹ and LaCa2Mn2O7.²⁰In our samples, the Mn−O bond lengths of the

perovskite units are different, and the average in-plane Mn−O bond length is 1.9316 Å while the length along thec-axis is 1.954 Å, sug- gesting a length ratio of 1.0116. This ratio is larger than 0.996, the value for LaCa2Mn2O7,²⁰indicating that the Sr substitution of Ca makes the lattice to expand along thec-axis.

For a better illustration of the lattice distortion, we plot in Fig. 4(a)thea-axis projection of the lattice. The shifting of oxygen ions along the b-axis is clearly illustrated. The two oxygen ions O1 and O2 in identical octahedral shift in the same b-axis direction, while either O1 or O2 in the neighboring octahedra shift along the opposite directions. The shifting of O1 ion along the b-axis in LCSMO is remarkably larger than that in LaCa2Mn2O7, suggesting more serious distortion along theb-axis, noting that this shifting ben- efits to the polar state formation. The project plot along thec-axis is shown in Fig. 4(b) where the in-plane Mn−O−Mn bond angle is

∼176°. All these data suggest that the in-plane lattice distortion is rel- atively weak while the out-of-plane distortion (c-axis lattice expansion and large shifting of O1 and O2 along theb-axis) becomes strong.

All we have discussed above are the room temperature data. It is known that the high-T high symmetry Pr(Ca0.8Sr0.2)2Mn2O7

belongs to theAmamspace group, and a sequence of two consecu- tive charge-order transitions lowers the symmetry from the high-T Pbnm group to the low-T Am2m group.¹⁷ It is expected that LCSMO would undergo symmetry transition with decreasing T since similar charge-ordering and orbital-ordering transitions occur here too. The conventional XRD technique is insufficient to detect such transitions while high-resolution diffraction, for example, high revolution synchrotron radiation (SR) x-ray diffraction, may be needed for such a clarification.

B. Magnetism, specific heat, and transport

Now, we look at the magnetic and thermodynamic behaviors along the in-planea- andb-axes (IP) andc-axis (OP), respectively.

The dc magnetic susceptibility (χ=M/H) at H= 1.0 kOe as a FIG. 3.Planar EDX mapping images of species distribu- tions in the La(Ca1−xSrx)2Mn2O7 single crystals. The as-calculated chemical composition is listed in (f ).

function of T in the three major axes are plotted in Figs. 5(a) and5(b)with the zero-field-cooling (ZFC) and field-cooling (FC) modes respectively. While the three sets ofχ(T) curves are different in quantitative sense, they are qualitatively similar and on the same

order of magnitude, suggesting the absence of serious orientation anisotropy of magnetism in terms of the anomalies in the χ(T) curves. Basically, for LCSMO, similar to other 327 manganites, the magnetic transition sequence upon decreasing T is complicated.

TABLE I.Structural parameters of the as-prepared LSCMO single crystals as determined from the Rietveld refinement of room temperature XRD data;x,y, andzare the frac- tional coordinates of each atom; and Occ is the occupancy of each atom.

Space group

Crystal system Amam

Lattice parameters Orthorhombic

Atom

a= 5.45272 Å b= 5.46058 Å c= 19.54296 Å

Occ

α= 90° β= 90° γ= 90°

x/a y/b z/c

La1 −0.750 000 0.2448(13) 0.500 000 0.612(3)

La2 −0.750 000 0.2622(10) 0.685 45(9) 0.127(2)

Ca1 −0.750 000 0.2448(13) 0.500 000 0.264(1)

Ca2 −0.750 000 0.2622(10) 0.685 45(9) 0.745(2)

Sr1 −0.750 000 0.2448(13) 0.500 000 0.124(3)

Sr2 −0.750 000 0.2622(10) 0.685 45(9) 0.128(2)

Mn −0.750 000 0.7536(15) 0.599 53(12) 1.063(3)

O1 −0.750 000 0.8251(19) 0.500 00 0.773(15)

O2 −0.750 000 0.7024(29) 0.6949(4) 1.08(20)

O3 0.000 000 0.000 000 0.4025(8) 0.905(15)

O4 0.000 000 0.500 000 0.5942(9) 0.825(15)

Bond lengths (Å) Bond angles (°)

Mn−O1 1.9838(35) Mn−O1−Mn 157.3(8)

Mn−O2 1.924(8) Mn−O3−Mn 177.6(10)

Mn−O3 × 2 1.916(6) Mn−O4−Mn 173.9(11)

Mn-O4 × 2 1.946(6) O1−Mn−O3 80.9(5)

Mn−Ca1 3.3523(13) O1−Mn−O4 95.0(4)

Mn−Ca2 3.162(8) O2−Mn−O3 97.2(6)

Mn−La1 3.310(9) O2−Mn−O4 87.0(7)

Mn−La2 3.242(8) O3−Mn−O4 86.848(26)

FIG. 4. Thebc-plane andab-plane projected lattice struc- ture, obtained from the Rietveld refinement. The O1/O2 shifting along theb-axis is clearly illustrated.

Just referring to the data plotted inFig. 5, one does see this com- plexity. We take the curves along thec-axis shown inFig. 5(b)as an example. Upon decreasingTfrom 400 K down to the lowestT in this experiment, two consecutive peaks and then a broad valley can be identified at temperatures T1 (TCO1), T2, and T3

(TAF), respectively, where definitions in the parenthesis will be discussed subsequently.

First, we look at the peak atT₁∼314 K, which is obviously the character for the first charge-ordering sequence (CO1) and thus we

assign T1=TCO1. Above TCO1, the χ(T) curves in the IP and OP geometries can be well fitted by the Curie–Weiss lawχ(T) =C/(T+Θ), where the Curie constant C=N_A⋅μeff2/3k_BandΘis the Weiss tem- perature,N_Ais the Avogadro constant,k_Bis the Boltzmann constant, andμeffis the effective magnetic moment. By fitting the data above TCO1, theb-axis effective moment of 4.18μBand thec-axis moment of 4.31μB are obtained. The two evaluated moments both fall in between the calculated moment for Mn³⁺, 4.9μB, and the moment for Mn⁴⁺, 4.0μB. The corresponding Weiss temperaturesθb=−123.47 K andθc=−113.59 K. It is thus indicated that the system exhibits strong antiferromagnetic interactions along all major axes.

Second, we discuss the valley atT₃which is∼90 K forχ(T) along the c-axis and∼30 K forχ(T) along thea-axis andb-axis.

To clarify the nature of this valley, we plot the measured specific heatC_P(T) data inFig. 5(c). Clearly, a relatively big bump peaked atT₃∼90 K can be observed, and no more anomalies below this temperature were detected. Certainly, this peak marks another antiferromagnetic re-ordering along the c-axis since the peak location is consistent with the valley point of the χ(T) curve along thec-axis (T₃=T_AF). The upturn ofχ(T) belowT_AFmay be related to weak spin canting while details of this canting deserve further investigation.

Third, we come back to the event occurring aroundT₂. The peak at T₂∼200 K is not easily assigned. In analogy again to the 327 manganites, this peak should be related to the second charge-ordering (CO2) event. For Pr-based 327 manganites, this CO2 event is actually a consequence of a thermally driven 90° rota- tion of the orbital stripes from the alignment along thea-axis (CO1 state) to that along the b-axis (CO2 state). Two features for this CO1–CO2 transition are expected. First, this transition is thermally driven and thus a clear thermal hysteresis would be expected.

Second, the CO2 state was predicted to be ferroelectric but the CO1 state is not, and thus it will be highly concerned. To check the two features, we present inFig. 6the measured magnetization (M) data along theb-axis andc-axis, each as a function ofTin the cooling– heating cycle, where the black arrows indicate the measuring path.

At the same time, the measureddcresistivities along the three main axes (ρa,ρb, andρc) in the same cycle are also plotted.

On one hand, clearM(T) hysteresis loops along theb-axis and c-axis exist in betweenT_CO1andT₂, suggesting the CO1–CO2 tran- sition, the first feature mentioned above. However, theM(T) hyster- esis along the b-axis expands the gap fromTCO1toT2, while the hysteresis along thec-axis is slightly narrower than that along the b-axis. On the other hand, the threeρ(T) loops all start at T_CO1 from the high-T side. The loop along the c-axis ends at ∼230 K from the low-Tside, but the loops along thea-axis andb-axis do not close untilT<T₂from the low-Tside. These behaviors suggest that the CO1–CO2 transition seems to expand over a broad T range, e.g., from a temperature right below TCO1(∼290 K) down- ward some temperature above T2 (∼230 K). In other words, one may argue that, different from Pr(Ca, Sr)₂Mn₂O₇,^17,22here LCSMO does not have a clear CO1–CO2 transition point T_CO2, and this transition most likely covers a broad Trange. It is thus suggested that no long-range CO2 state can be developed in LCSMO, and thus no long-range ferroelectric order can be generated if this CO2 phase is ferroelectric. For convenience, one may assignT_CO2as aT range instead of a clear temperature, as marked inFigs. 5and6.

FIG. 5. The measureddc magnetic susceptibilityχ along (a) the [010] and [100] (in-plane) directions and (b) the [001] (out-of-plane) direction under the ZFC and FC modes, respectively. The cooling and measuring fields are both 0.1 T. The temperature dependent heat capacity measured at zero magnetic field is shown in (c).

Based on the assignment of the CO1 state, CO2 state, and low-T AFM transition at TAF, we can now discuss the possible physics related to the magnetism and transport. It is understood that forT>T_CO1, Mn³⁺and Mn⁴⁺ions are randomly distributed in theab-plane, allowing the itineration ofe_gelectrons in the lattice.

This itineration becomes localized with decreasing T down to TCO1∼314 K, where Mn³⁺and Mn⁴⁺ions are ordered and form the checkerboard-type CO state. At the same time, ordered orbital stripes are developed in the MnO₂plane. Upon further cooling from TCO1, similar to Pr(Ca0.9Sr0.1)2Mn2O7,¹⁷ another charge-ordering occurs inside theTCO2range, accompanied with the 90° rotation of ordered orbital stripes. This CO2 state may not be homogeneous but droplet-like, embedded in the matrix of the CO1 phase. Therefore, the CO2 phase is most likely dynamic in nature without the long- range order and accommodates both the site-central and bond- central configurations. One says it is polar-like. Here, it should be mentioned that no identifiable difference in theχ(T) curve between the ZFC and FC modes is observed, suggesting the absence of glass- like feature often observed in perovskite manganites.

With the above knowledge, one comes to look at the magnetic and transport behaviors plotted in Fig. 6. Several major features deserve highlighting regarding the ρ(T) and M(T) dependences.

First, the resistivity along the b-axis is smaller than the out-of-plane resistivity over the wholeTrange. This is understand- able for such 327 manganites due to the layered lattice structure. In correspondence, the in-plane magnetic moment (b-axis moment) is slightly smaller than the out-of-plane moment due to the strong in-plane antiferromagnetic interaction and alignment. In spite of these delicate differences, one sees that the in-plane and out-of-plane resistivities and moments show quite similarT-dependences, a clear

indication of the dominant three-dimensional character over the two-dimensional one associated with the layered structure. Second, the gradual increasingρwith decreasingTin the paramagnetic state atT>T_CO1is observed and followed by a further and steep enhance- ment with further decreasing TfromTCO1throughTCO2untilTAF. This steep variation is the consequence of charge-ordering, accompa- nied with well-knownρ(T) hysteresis in the cooling–warming cycle.

In correspondence, magnetization M decreases with decreasing T fromTCO1due to the antiferromagnetic nature of the CO state. The slight upturn of theM(T) curves aroundTCO2with clearM(T) hys- teresis in the cooling–warming cycle indicates the well-believed 90°

rotation of the orbital stripes from thea-axis to theb-axis.¹⁷It was claimed that the two CO states below TCO1 andTCO2are both the electronic polar states. Third, the antiferromagnetic order is suffi- ciently established below T_AFafter the two charge-ordering transi- tions atT_CO1andT_CO2, evidenced by the further steep increasing of ρ(T) and decreasing ofM(T) with decreasingT.

These magnetotransport behaviors are qualitatively similar to those observed for Pr(Ca, Sr)₂Mn₂O₇ and other 327 manganites, suggesting the similar lattice and magnetic structures of the present LCSMO. With this similarity, one has reason to look into the elec- trically polar properties. In fact, the existence of ρ(T) and M(T) hysteresis loops betweenT_CO1andT_AFreflects the dynamic charac- ter of the CO phases, an advantage for checking the dielectric behaviors associated with polar state of LCSMO if any.

C. Dielectric response

As mentioned, the predicted electric polarization, if any, should be aligned along the b-axis. Referring to the resistivity data shown in Fig. 6, one sees that the samples are highly con- ductive at T> 360 K and the measured high frequency dielectric constant becomes negativeT> 400 K due to the high conductivity.

Therefore, we only discuss the dielectric data below 360 K, as shown in Figs. 7(a) and 7(b) where dielectric constants ϵb(T) and ϵc(T) over the frequency range from 1.0 kHz to 1.0 MHz are plotted. It is seen that in the b-axis all the ϵb(T) curves show a broad peak around TCO1, and this peak does not shift much with varying fre- quency although the peak height does fall down gradually with increasing frequency. On the contrary, in the non-polarc-axis, these broad peaks shift with varying frequency, especially in high fre- quency range. Therefore, we can conclude that the broad peaks in ϵb(T) curves should be a consequence of the polar charge-ordered state developed below T_CO1 along the b-axis and the frequency- dependent broad peaks in ϵc(T) curves is a consequence of ther- mally trapped charges.

It was claimed that spontaneous polarization in Pr(Ca, Sr)₂Mn₂O₇, as probed by SHG, emerges atT_CO2 instead ofT_CO1. The polar state actually emerges at TCO1 below which the local polarization is generated. Upon the transition atTCO2, correspond- ing to the 90° rotation of the orbital stripes, the local polarizations may be well ordered, and then a net polarization may emerge at TCO2. This scenario would be expected to apply to the LCSMO crys- tals here, and the appearance of a dielectric peak atTCO1is under- standable. Nevertheless, we cannot observe any reliable SHG signals over the whole T range. Instead, in the low-frequency range (1.0 kHz–30 kHz), we observe a weak kink ofϵb(T) aroundTCO2, as FIG. 6.The measured electrical resistivity ρand magnetizationMalong the

a-axis,b-axis, andc-axis in the measuring cycle as indicated by arrows. The measuring magnetic field is 0.5 T.

indicated by the coarse arrow inFig. 7(a). This kink shifts slightly toward the high-Tside with increasing frequency. A plot of the kink coordinates (T, f) inFig. 7(c) suggests that the dynamic response can be well described by the Arrhenius equationf=f₀⋅exp(−E_a/k_BT), wheref0is the characteristic frequency prefactor,Eais the activation energy, and kB is the Boltzmann constant. A fitting produces E_a= 0.9845 eV. This value fits typically the oxygen vacancy migration mechanism, suggesting that this kink is more or less related to the defect migrations associated with polar dynamics.

D. Absence of ferroelectricity and discussion

In fact, so far, our measurements on ferroelectricity of our crystals using theP–Eloop probes in the positive-up–negative-down (PUND) mode,²³ the pyroelectric current method, and the SHG technique all suggest the absence of spontaneous electric polariza- tion. This absence is an indication of ferroelectric ordering, which is of long-range, but it may not exclude the possible existence of a local polar state due to the charge-ordering. The absence of ferro- electricity would have several possible sources. First, no intrinsic fer- roelectricity exists, or the ferroelectric order cannot be established via the proposed mechanism of charge-ordering. This is most unlikely because so far there have been quite a few reports support- ing the existence of a polar state or ferroelectricity in similar 327 manganites. Second, the ferroelectric state cannot be maintained due to the seriously large leakage. This is however most likely the reason why one cannot obtain high-quality P–Ehysteresis and the conventional technique does not work for such leaky samples.

Third, no long-range charge-ordering is established due to the high degree of disorder in the samples even if they are single crystals. In this case, the intrinsic inhomogeneity for manganites makes the charge-order state between TCO1 and TAF likely dynamic, as con- firmed by the remarkable hysteresis in ρ(T) and M(T). Fourth, as mentioned above, in the present system, the electronic polar state can be established by the superposition of bond alternation inher- ent to the underlying chemical lattice (e.g., the alternate tilting of MnO₆octahedra along the b-axis) and the site alternation (com- mensurate charge-order) in the ab-plane. If the charge sector in the ab-plane deviates from the commensurate order, the phase mismatch between bond and site alternations can be introduced and the electric polar state will be suppressed. Therefore, a check- ing of the commensurate charge-order by means of, for example, TEM is highly needed for this possibility.

Further evidence can be seen regarding the dielectric response.

The dielectric peak at∼T_CO1is very broad, distinctly different from the sharp peak for normal ferroelectric or antiferroelectric transi- tion. This broad peak should be associated with the inhomoge- neous charge-order regions between TCO1andTAF. These regions are not strongly correlated but each such region is polar-like, con- tributing to the as-measured dielectric responses shown inFig. 7.

IV. CONCLUSION

In summary, we have successfully grown high-quality La(Ca_0.8Sr_0.2)₂Mn₂O₇ single crystals using the optical float zone method and performed a series of structural, magnetic, transport, and dielectric properties along the in-planeb-axis and out-of-plane c-axis directions. It is revealed that La(Ca0.8Sr0.2)2Mn2O7 exhibits the highly ordered A-site occupation and Amamlattice symmetry.

The O1 ion shifting along the b-axis is found to be larger in La(Ca0.8Sr0.2)2Mn2O7 than Pr(Ca0.8Sr0.2)2Mn2O7, suggesting the higher stability of the polar-like state in La(Ca_0.8Sr_0.2)₂Mn₂O₇. The magnetic and electrical measurements indicate the consecutive charge-ordering sequence at TCO1∼314 K and then the CO1 to CO2 transition. This late transition may cover a T range starting from a temperature belowT_CO1and terminating atT∼230 K, evi- denced with the magnetization and electric resistivity hysteresis loops. A broad dielectric peak at the charging ordering pointTCO1

FIG. 7. The measured dielectric constantϵas a function ofTin the cooling cycle along theb-axis for (a) and along thec-axis for (b), the dashed arrow in (b) is guide to the eyes to visualize the peak shifts varying with frequency to higher temperature. The ac signal frequencyfcovers 1.0 kHz–1.0 MHz with the signal amplitude of 0.1 V. (c) The frequency and temperature relationship for the kink as indicated by the red arrow, and the kink motion as a function of fre- quency is a feature for the dielectric relaxation, which may be related to the relaxation of electric dipoles or oxygen vacancies.

event, which is frequency-independent, is observed, indicating the emergence of a polar-like state associated with the charge-ordering.

Our measurements do not show any evidence with the long-range ferroelectricity. The ferroelectricity associated with the charge-ordered systems remains to be an issue for future investigation.

ACKNOWLEDGMENTS

The authors would like to acknowledge the financial support from the National Key Projects for Basic Researches of China (Nos. 2016YFA0300101 and 2015CB654602) and also the National Natural Science Foundation of China (NNSFC) (Nos. 51431006, 11834002, and 51721001).

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