Structure, charge ordering and physical properties of LuFe2O4

Y. Zhang, H. X. Yang, Y. Q. Guo, C. Ma, H. F. Tian, J. L. Luo, and J. Q. Li*Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences,

Beijing 100080, People’s Republic of China�Received 28 June 2007; revised manuscript received 26 September 2007; published 8 November 2007�

Microstructural properties, phase transitions, and charge ordering of LuFe2O4 have been extensively inves-tigated by means of transmission electron microscopy �TEM� in a large temperature range from 20 to 550 K.The experimental results demonstrate that the LuFe2O4 crystal is commonly modulated by charge ordering�CO�, which is often recognizable by superstructure reflections. The �001� twinning domains as a commondefect often appear in the LuFe2O4 crystals along the c-axis direction, with the crystals across each �001�boundary rotated by 180° with respect to one another. The in situ cooling TEM observations from 300 K downto 20 K reveal remarkable alternations of the superstructures, suggesting a complex CO process in the presentsystem. Careful analysis shows that the CO in the frustrated ground state is characterized by a modulation witha wave vector of q1= �1/3 1/3 2�. In situ heating TEM observations from 300 to 550 K clearly reveal that theCO modulation in LuFe2O4 becomes invisible above a critical temperature of about TC=530 K. These factssuggest that the CO should be the essential driving force for the structural transitions and ferroelectricityobserved in this kind of layered material. Experimental measurements on the ferroelectricity show that theLuFe2O4 material, in general, has a large dielectric constant of about 10 000 at room temperature. In order tounderstand the properties of low-temperature phase transitions, the magnetization and specific heat from300 to 4 K have been briefly discussed.

DOI: 10.1103/PhysRevB.76.184105 PACS number�s�: 77.84.�s, 71.27.�a, 61.14.�x, 71.23.An

I. INTRODUCTION

In recent years, extensive investigations of the charge-frustrated RFe2O4 system �R=Y, Er, Yb, Tm, and Lu� re-vealed a rich variety of interesting physical properties, suchas ferroelectricity, magnetodielectric effects, and spin and/orcharge ordering.1–5 These remarkable properties could yieldimmense potential in these kind of materials for technicalapplications.3,6–8 Actually, the ferroelectricity in the RFe2O4systems has been studied for decades due to their large di-electric constants and notable frequency dependence.4,5 Re-cently, the giant room-temperature magnetodielectric re-sponse was observed in a LuFe2O4 single crystallinematerial;3 this distinctive phenomenon is considered a sig-nificant feature for developing a new generation of multi-functional devices for microelectronics.6–8 It is also notedthat the LuFe2O4 material undergoes sequential phase transi-tions under low temperature conditions as revealed by meansof x-ray, neutron, and electron diffractions.9–11 Moreover, theanomalies in dielectric behaviors often become visible incorrelation with these phase transitions.12 It is believed thatthe presence of CO and the charge and/or spin frustrationhave evident effects on the remarkable physical properties inthese materials.13,14 From a structural point of view, RFe2O4materials belong to the rhombohedral system �R-3m� andconsist of two typical layers stacked alternately along thec-axis direction, the hexagonal double layers of Fe ions withan average valence of +2.5 are sandwiched by thick R2O3layers.15–17 Theoretical interpretation for the electronic ferro-electricity and the magnetoelectric effect in these materialshas been discussed based on several plausible microscopicmodels considering the nonlinear coupling among charge,spin, orbital, and lattice degree of freedom.18,19 The funda-mental ferroelectric polarization in LuFe2O4 is directly deter-

mined by the specific configuration of charges. The magne-tocapacitance effect at room temperature was interpreted interms of charge fluctuation arising from the interconversionbetween the two different types of charge orders.25 Thoughresearch on the microstructure and phase transitions havebeen published,20,21 the microstructure features, detailedstructural changes in connection with the CO modulation,and common structural defects are not well understood atthis time. In this paper, we will first report on the fundamen-tal structural properties as obtained from well-characterizedLuFe2O4 material by means of transmission electron micros-copy �TEM�, and then we report the in situ TEM observationin a wide temperature range of 20–550 K. Structural phasetransitions, especially the CO process, have also been exten-sively analyzed in detail. Measurements of fundamentalphysical properties, such as magnetic susceptibility, specificheat, and dielectric properties, as a function of temperature,have also been analyzed to help in understanding the essen-tial properties of LuFe2O4 at low temperatures.

II. EXPERIMENT

Polycrystalline samples of LuFe2O4 material were synthe-sized from stoichiometric mixtures of Lu2O3 �99.99%� andFe2O3 �99.99%�, and LuFe2−xMgxO4 sample was made bysubstituting MgO for some Fe2O3. After mixing and milling,the raw materials were sintered by conventional solid-statereaction under a controlled oxygen partial pressure atmo-sphere using a CO2-H2 mixture at 1200 °C for 48 h. Struc-tural and phase purity characterizations were carried out bypowder x-ray diffraction �XRD� using a RIGAKU diffracto-meter with Cu K� radiation. Microstructure and chemicalcomposition were analyzed on a Philips XL30 scanning elec-tron microscope �SEM�. TEM investigations were performed

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on a Tecnai F20 �200 kV� electron microscope equippedwith both low-temperature �down to 20 K� and high-temperature �up to 1200 K� holders. TEM samples were pre-pared by mechanical polishing, dimpling, and ion milling.The magnetization measurements between 5 and 300 K werecarried out on a commercial superconductor quantum inter-ference device magnetometer. The zero-field-cooling �ZFC�and field-cooling �FC� curves were obtained at applied fieldsof 100 Oe. Their complex dielectric permittivity was mea-sured with a parallel-plate capacitor coupled to a HewlettPackard 4192A, capable of measuring frequencies rangingfrom 5 to 13 MHz. The capacitor temperature can be con-trolled from 200 to 500 K. The samples in the form of pel-lets with an average diameter of 1 cm were shaped to fit inthe capacitor, while silver was painted on their surfaces toensure good electrical contact with the plates of the capaci-tor.

III. RESULTS AND DISCUSSION

A. Crystal structure and common defects

Figure 1�a� shows the XRD pattern taken from a LuFe2O4sample at room temperature. All diffraction peaks can bewell indexed as a hexagonal cell with R-3m space group andlattice parameters of a=0.3444 nm and c=2.5259 nm; nopeaks from impurity phase are observed. Figure 1�b� shows aschematic structural model of the LuFe2O4 crystal, clearlyillustrating the alternating sequence of Lu-O layers and theFe-O double layers stacked along the c-axis direction. Thislayered structural feature could primarily affect the growth ofLuFe2O4 crystal. Figure 1�c� shows a SEM image of a typi-cal sample showing the notable layered structural features.Our careful structural examinations of the samples preparedunder slightly different conditions suggest that the LuFe2O4crystal, in general, grows by following a layer-by-layer modeas evidently recognizable in the SEM image.

In order to fully understand the microstructure features ofthe LuFe2O4 material, we have performed a series of inves-tigations by means of selected-area electron diffraction andhigh-resolution transmission electron microscopy �HRTEM�.Figure 2�a� shows the �001� zone-axis convergent beam elec-tron diffraction �CBED� pattern of LuFe2O4. This patternexhibits 3m symmetry with a threefold axis along the c axis,and three mirror planes are respectively indicated in the pat-tern with a partition angle of 120°. It is known that the radiiof high-order Laue-zone rings in this CBED pattern are re-lated to the periodicity along the zone-axis direction, andtherefore, the c-axis parameter corresponding to the first ringin Fig. 2�a� is estimated to be 2.5 nm for LuFe2O4 consistentwith the results of x-ray diffraction. Figures 2�b�–2�f� show aseries of the selected-area electron diffraction patterns taken

along relevant �001�, �11̄1̄�, �331̄�, �100� and �11̄0� zone-axisdirections at room temperature, respectively. The appear-ances of main diffraction spots with strong intensity followsrightly with the reflection condition of −H+K+L=3n for theR-3m space group. The most interesting structural phenom-enon is the appearance of superlattice modulation caused bycharge ordering as analyzed in previous literature.22 Careful

examination reveals that these satellite spots are usually in-visible in the �001� zone-axis diffraction pattern, and becomeprogressively observable at around 1/3�110� positions when

we tilt the specimen to a �11̄1̄� zone axis as shown in Fig.

2�c�. The �331̄� zone-axis diffraction pattern of Fig. 2�d�shows clear and sharp satellite spots in good agreement withour low-temperature data.22 Clearer views of charge modu-lation in the LuFe2O4 material can be carried out along the

�11̄0� zone-axis direction. Figure 2�f� shows a typical patternobtained at room temperature, illustrating diffuse streaks at1 /3�h h l� running along the c* direction. These structuralfeatures have been extensively illustrated in previous worksfor interpreting the electronic ferroelectricity in the presentsystem.9,21 On the other hand, the intensity of superstructuresdepends evidently on temperature in a large temperaturerange and also frequently changes from one sample to an-other. Diffraction observations between 200 and 300 K al-ways reveal the superstructure reflections as diffuse streakson �h /3 ,h /3 , l� lines along the c* direction. Moreover, thesuperstructure reflections always contain notable contribu-tions from the CO twinning, which often results in zigzag

FIG. 1. �a� X-ray diffraction pattern from a LuFe2O4 sample. �b�A structural model schematically illustrating the Lu-O layer andFe-O double layer stacking alternatively along the c axis; O atomsare omitted for clarity. �c� A SEM image of LuFe2O4, clearly illus-trating layered structural features in this material.

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type superstructure streaks as noted in previouspublications.1,21,22

Figure 3�a� shows a HRTEM image taken along the �100�zone-axis direction, clearly displaying the atomic structuralfeatures of the LuFe2O4 crystal. This image was obtainedfrom a thin region of crystal under the defocus value ataround the Scherzer defocus ��−36 nm�. The metal atompositions are, therefore, recognizable as dark dots. Image cal-culations based on the proposed structure model of Fig. 1�b�were carried out by varying the crystal thickness from2 to 5 nm and the defocus value from −30 to +60 nm. Acalculated image with a defocus value of −36 nm and athickness of 3 nm, superimposed on the image, appears to bein good agreement with the experimental one.

In order to reveal the microstructure features of the chargeordered state in LuFe2O4, we have performed a number ofhigh-resolution TEM examinations in the temperature rangefrom 300 K down to 100 K. It is commonly noted that the

average thickness of the CO lamellae at room temperature isestimated to be smaller than 5 nm along the c-axis direction.Figure 3�b� shows a high-resolution TEM image obtained byusing the superstructure streaks, illustrating the short-rangeordered states in the marked layers or areas. It should bementioned that the coherence length of the CO states, as wellas the ferroelectric structure, has notable anisotropic featuresin this layered system, e.g., the coherence length at roomtemperature as estimated from TEM images is about20–30 nm within the a-b plane and about 1–3 nm along thec-axis direction, which is in good agreement with the dataobtained from diffraction.

The common defect in LuFe2O4 as observed in our TEMinvestigations is the structural twinning along the c-axis di-rection. Figure 4�a� shows a bright-field TEM image illus-trating the twinning domains in a LuFe2O4 crystal. Con-trasted anomalies at the twin boundaries directly suggest thepresence of crystal defects and local strains in associationwith these planar defects. These twinning planes, in general,are parallel to the basic a-b plane. Figures 4�b�–4�d� showthe corresponding electron diffraction patterns taken fromthree representative areas indicated in Fig. 4�a�, illustrating

FIG. 2. Electron diffraction patterns of LuFe2O4. �a� Convergentbeam pattern along �001�, and selected-area diffraction patterns

along �b� �001�, �c� �11̄1̄�, �d� �331̄�, �e� �100�, and �f� �11̄0� zone-axis directions at room temperature, respectively. All main diffrac-tion spots can be well indexed by an R-3m structure with latticeparameters of a=0.344 nm, and c=2.5259 nm. The weak super-structure modulation spots and streaks at the systematic positions of�1/3 1/3 L� correspond to charge ordering.

FIG. 3. �a� �100� zone-axis HRTEM image clearly displayingthe atomic structure of LuFe2O4. Inset shows large magnification

image with the theoretical simulation. �b� �11̄0� zone-axis HRTEMimage using the satellite spots, showing the short-range ordering forthe CO states.

FIG. 4. �a� Bright-field TEM image showing the twinning lamel-lae along the c-axis direction. �b�, �c�, and �d� show the �100� zone-axis selected-area diffraction pattern from areas I, II, and III, re-spectively, clearly demonstrating a twinning relationship across theboundary.

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the structural evolution across a boundary. Diffraction pat-terns from area I and area III have a well-defined twinningrelationship as clearly demonstrated in Fig. 4�c�. Hence,these structural lamellae can be well interpreted as 180°twins, and the LuFe2O4 crystals that cross each boundary arerotated by 180° with respect to one another. Figure 5�a� is a�100� zone-axis HRTEM image at higher magnification,clearly showing the atomic structural feature at a twinboundary. Careful examinations on the crystal structure invicinal regions of a boundary suggest that stacking faultsoften appear at this kind of boundary. For instance, Fig. 5�b�shows a HRTEM image for a twin boundary. Careful analy-sis and theoretical simulation for this boundary reveal a lay-ered sequence of “LuO-FeO-FeO-FeO-FeO-LuO” in contrastwith the atomic sequence of “LuO-FeO-FeO-LuO-FeO-FeO-LuO” in the LuFe2O4 crystal along the c-axis direction.

B. Charge ordering and phase transitions

It is commonly accepted that the complex superlattice re-flections in the present system arise essentially from certaintypical arrangements of the mixed valence Fe ions. In addi-tion, the noteworthy temperature dependence of the super-structure spots suggests an evident dynamic feature for theCO process in this layered system. Recently, we have carriedout a series of in situ TEM investigations on the structuralchanges of LuFe2O4 and focused on the charge ordering andlow-temperature phase transitions as partially reported byZhang et al.22 The in situ cooling TEM observations demon-strated that the CO in the ground state of LuFe2O4 could bewell characterized by two structural modulations at low tem-peratures.

Figures 6�a�–6�d� show the selected-area electron diffrac-

tion patterns taken respectively along the relevant �11̄1̄�,�331̄�, �100�, and �11̄0� zone-axis directions at about 100 K.In comparison with room-temperature data as shown in Fig.2, the superstructure spots become visibly stronger andsharper. The most striking feature revealed at about 100 K isthe appearance of pairs of sharp superstructure satellite spotsat the systematic position of �0 0 3L /2� as shown in Figs.6�c� and 6�d�. This type of satellite spots often has visiblechanges in either intensity or position from one sample to

another. In previous literature, this superstructure modulationis interpreted as a type of antiphase structure in low-temperature conditions.21

Figure 7�a� shows the �11̄0� zone-axis diffraction patterntaken at about 20 K, demonstrating the presence of clearsuperstructure spots following the main diffraction spots.These superstructure spots can be assigned respectively totwo structural modulations �q1 and q2� as clearly illustratedin the schematic pattern of Fig. 7�b�. Our careful analysissuggests that the q1 modulation, with a wave vector of q1

FIG. 5. �a� HRTEM image showing the atomic structure near aboundary. The insets show the structure model for this twinningstructure. �b� A HRTEM image with a large magnification clearlydisplaying a stacking fault on the boundary.

FIG. 6. Electron diffraction patterns of LuFe2O4 taken along �a��11̄1̄�, �b� �331̄�, �c� �100�, and �d� �11̄0� zone-axis directions atliquid nitrogen temperature, respectively. The intensity of themodulation reflections at �1/3 1/3 L� becomes visibly stronger, andnew pairs of satellites show up at �0 0 3L /2� at low temperature.

FIG. 7. �Color online� �a� �11̄0� zone diffraction pattern at about20 K, demonstrating the presence of clear superstructure spots fol-lowing the main diffraction spots �after Ref. 22, Fig. 1.a�. �b� Aschematic illustration for the q1 and q2 modulations at low tempera-ture �after Ref. 22, Fig. 1.c�. �c� Structural model schematicallyillustrating the Fe2.5−�-Fe2.5-Fe2.5+� order in the ground state.

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= �1/3 ,1 /3 ,2�, can be interpreted by a three-dimensional or-der of Fe2.5−�, Fe2.5, and Fe2.5+�, where � is the value ofcharge disproportionation �0���0.5�. For convenience, theionic model of Fe2+, Fe2.5+, and Fe3+ is commonly used inrecent studies with �=0.5. The q2 modulation, in general, ismuch weaker than the q1 modulation, and its average wavevector at 20 K can be roughly written as q2= �0,0 ,3 /2�+q1 /10. Further experimental measurements indicate thatthe q2 modulation also depends evidently on local defectivestructures. Therefore, characterization of the fundamentalstructural features of the q1 modulation is considered as thekey issue for understanding the electronic ferroelectricity inthis charge-frustrated system. Of course, the charge distribu-tion cannot be detected directly by electron diffraction; in-stead, we measure the modulation of atomic positions asso-ciated with the charge modulation. Hence, based on asystematical TEM observation, it is possible for us to con-clude certain typical features about the charge ordered statein LuFe2O4. Figure 7�c� shows a schematic charge orderedpattern in accordance with our experimental observations. Itis remarkable that positive charges �Fe2.5+� sites� and nega-tive charges �Fe2.5−� sites� are actually crystallized in parallelcharge stripes going along the viewing direction. This chargestripe phase shows up as a clear monoclinic feature with anevident electric polarity.22

In order to facilitate the analysis on the electric polariza-tion, we can also characterize the charge concentration in thisstripe phase as a charge-density wave �CDW� in associationwith the q1 modulation. This CDW running along the �116�direction is not accomplished in a simple sinusoidal fashion,but is strongly affected by charge frustration as illustrated inFig. 8�a�. It is easily seen that the average centers of Fe2.5−�

�negative� and Fe2.5+� �positive� planes have a clear relativeshift and directly result in a local electric polarization alongthe q1 direction. It is worth pointing out that the charge frus-tration could evidently affect the degeneracy of the groundstate in this system as similarly discussed for the spin frus-tration in a triangular lattice.23 As a typical result, the pres-ence of charge frustration of a ground state of LuFe2O4 couldyield a degenerate Fe site with an average valence of +2.5.On the other hand, if we analyze this system based on Fe2.5−�

and/or Fe2.5+� ordering without considering the frustrated de-generacy �Fe2.5+ state�, a charge-density wave would behavein a simple sinusoidal fashion. This kind of CO state cannotresult in visible ferroelectricity due to coincidence of thecenters of positive and negative charges in a supercell �i.e., aperiodic CDW� as illustrated in Fig. 8�b�. We therefore con-clude that structural models based simply on Fe2.5−� andFe2.5+� �or the ionic Fe2+ and Fe3+� ordering contain essentialdifficulties when interpreting the ferroelectricity in LuFe2O4,and also have an apparent contradiction with our low-temperature experimental results.

From a ferroelectric point of view, the frustrated type ofcharge configuration has a notable similarity with the coher-ent arrangement of electric dipoles discussed commonly inthe conventional ferroelectric materials. Therefore, theLuFe2O4 crystal has a ferroelectric CO ground state in whichthe coherent arrangements of electric dipoles are realized bycharge stripe ordering. It is noted that the parent phase ofLuFe2O4 has a rhombohedral symmetry with the R-3m space

group, and therefore, the CO modulation, together with thelocal electric polarization, could appear evenly in three crys-tallographically equivalent �116� directions around the rhom-bohedral axis, and the resultant spontaneous electric polar-ization would go along the c-axis direction.22 In LuFe2O4,this conclusion is in good agreement with the major experi-mental data reported in previous literature.4,24 In comparisonwith the theoretical results as reported in recent literature, thecharge configuration within an Fe-O double layer as pre-dicted by the Monte Carlo simulation25 is qualitatively con-sistent with our experimental data. Moreover, our carefulanalysis suggests that certain structural features as revealedin experimental observations have not been discussed in the-oretical studies, especially the configuration of the orderedstates in correlation with interlayer coupling along the c-axisdirection. Hence, our systematical experimental resultsshould play a key role for the understanding of the coopera-tive ordering in LuFe2O4 and also provide the essential ele-ments needed for the development of the microscopicmechanism.

In the LuFe2O4 material, two important phase transitionsare proposed in the high-temperature range, i.e., the ferro-electric phase transition at about 350 K and a charge order todisorder transition at about 530 K. We, thus, carried out an insitu heating TEM observation to reveal the temperature de-pendency of the superstructure reflections in the present sys-tem. Figures 9�a�–9�d� show a series of diffraction patternstaken in the temperature range from 300 to 530 K, illustrat-ing the changes of superstructure streaks. The experimental

FIG. 8. �a� The CDW in nonsinusoidal fashion corresponding tothe q1 modulation. The resultant polarization is indicated �after Ref.22, Fig. 2.c�. �b� A CDW in a sinusoidal fashion; no polarization isexpected due to the coincidence of the positive and negative chargecenters for the supercell.

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results demonstrate that the intensities of the superstructurereflections decrease progressively with increasing tempera-ture, and typically disappear above 530 K. The disappear-ance of the diffuse lines directly suggests that the electroncharges in this material become disordered above this criticaltemperature. Figure 9�e� shows the microphotometric densitycurves measured along the a*+b* direction, clearly illustrat-ing the decrease of the intensities of the superstructure peaksat high temperatures. TEM investigations also reveal that thistransition is reversible, and the superstructure reflections be-come visible again as the temperature is lowered below500 K. Careful measurements on the superstructure couldreveal certain hysteretic behaviors, and this fact suggests acomplex nature for this phase transition in the LuFe2O4 ma-terial.

C. Specific heat, magnetization, and dielectric properties

In order to characterize the essential properties of low-temperature phase transitions, the specific heat of a LuFe2O4sample has been measured from 300 to 4 K, as shown inFig. 10. It is remarkable that a clear anomaly appears at thetemperature of 235 K, similar to what is observed inYbFe2O4.10 This anomaly corresponds to a magnetic transi-tion as discussed in previous literature,10 where the low-temperature magnetic ordering does not develop into a longrange one and the correlation length in doubled Fe layersextends to about 5 nm. Our further studies reveal that thistransition tends to evidently broaden in an applied field of10 T as shown in Fig. 10�a�. This fact could be essential inconnection with the giant magnetodielectric effect observedin this material.3 At low temperatures, the specific heat isdominated by phonon contribution in this CO insulatingstate, and can be well described by the Debye formula C=9R�T /�D�3�0

�D/T��4e� / �e�−1�2�d� below 15 K in Fig.10�b�. After fitting the curve, �D is determined to be about281 K for LuFe2O4.

It is commonly noted that the LuFe2O4 material often hasa large dielectric constant ranging from 6000 to 10 000 atroom temperature,4,12 thus this material could possibly play

an important role in the development of novel electric andelectronic devices.26 Figure 11�a� shows a typical set of ex-perimental data obtained from well-characterized LuFe2O4and Mg doped LuFe1.85Mg0.15O4 samples, illustrating the di-electric constants crossing the ferroelectric phase transitiontemperature ��330 K� for two different frequencies. Actu-ally, our results demonstrated that the dielectric constant de-creases gradually with increasing frequency. The most re-markable feature revealed in Fig. 11�a� is that the highdielectric constant of about 10 000 can be maintained in alarge temperature range, and almost give rise to a “plateau”in the range 280–380 K. This behavior is noticeably differ-ent from the tendency stated by the Curie-Weiss law, sug-gesting a different mechanism for ferroelectricity in thepresent system. On the other hand, the continuous decreaseof the dielectric constant from 280 to 200 K can be well un-derstood by the gradual appearance of ferroelectric domainsbelow the critical temperature. Careful analysis demonstratesthat the temperature dispersion in this temperature range canbe qualitatively interpreted as a Debye-type relaxation. Con-sidering the giant magnetodielectric response in the presentsystem, we have also performed an extensive investigationon the materials with nominal compositions of LuFe2−xMxO4�M =Mg and Zn�, in which the magnetic correlation withinthe doubled Fe layers is expected to be altered. The experi-mental results showed that certain materials with visiblechanges of magnetic properties have remarkable ferroelectricfeatures comparable with that observed in the LuFe2O4 ma-terial. Figure 11�a� shows the dielectric constant ofLuFe1.85Mg0.15O4 as a function of temperature in comparisonwith the data of LuFe2O4. The substitution of Mg2+ for Femakes the transition temperature move toward a lower tem-perature as also demonstrated by the measurements of mag-netic properties. Figure 11�b� shows the ZFC and FC mag-netizations of LuFe2O4 and LuFe1.85Mg0.15O4 as a functionof temperature at an applied field of 100 Oe. Results ob-tained from both samples show clear cusplike peaks in theZFC curves; similar field-cooling effects are also observed. Itis also visible that the magnetic ordering transition decreasesremarkably from �235 K to a lower temperature of about182 K in LuFe1.85Mg0.15O4. Actually, the strong exchangefrustration in double Fe layers could be partially releasedwhen a triangular antiferromagnet is diluted with nonmag-netic ions such as Mg2+. LuFeMgO4 has been reported to bethe simplest model diluted antiferromagnet with strong geo-

FIG. 10. �a� The specific heat data as a function of temperaturefor LuFe2O4 with and without magnetic field. �b� The fitting for thespecific heat of LuFe2O4 by the Debye formula at low temperaturesin zero field.

FIG. 9. The temperature dependence of the superstructure re-flections from 300 to 530 K. The intensities of superlattice reflec-tions become weaker and more diffuse with increasing temperatureand disappear above 530 K.

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metrical frustration,27 where its magnetic transition tempera-ture is about 33 K. Our recent investigations demonstratethat the Mg2+ content in LuFe2−xMgxO4 could have greateffects on charge and/or spin ordering and ferroelectricity.These results will be reported in a forthcoming paper.

IV. CONCLUSIONS

In summary, the layered LuFe2O4 material generally con-tains remarkable CO modulations that are recognizable assuperstructure streaks at room temperature and develop intosharp superstructure spots at low temperatures. The commonstructural defect in LuFe2O4 is found to be �001� twinningdomains; the LuFe2O4 crystals that cross each twin boundaryare rotated by 180° with respect to one another. The in situcooling TEM observations reveal remarkable temperaturedependence of the superstructure modulations. Two struc-tural modulations �q1 and q2� become clearly visible at atemperature of 20 K. The q2 modulation, in general, is muchweaker than q1. The q1= �1/3 1/3 2� modulation can be wellinterpreted by the Fe2.5−�, Fe2.5, and Fe2.5+� order in a stripe-like configuration in the ground state. Moreover, it is notedthat the ferroelectric phase transition and charge order-disorder transition occur in a high-temperature range in theLuFe2O4 material; we, thus, carried out an in situ heatingTEM observation to reveal the temperature dependence ofthe superstructure reflections. As a result, the intensities ofsuperstructure reflections decrease gradually with an increase

of temperature, and become invisible at around 530 K.Based on our systematic experimental results, we can con-clude that the CO state in LuFe2O4 depends markedly ontemperatures between 530 and 20 K, which plays a criticalrole for understanding the rich structural transitions and theelectronic ferroelectricity observed in these kinds of materi-als. Experimental measurements on the ferroelectricity dem-onstrate that the LuFe2O4 material often has a large dielectricconstant of about 10 000 at room temperature. The specificheat measurements with and without applied magnetic fieldreveal clear anomalies in association with magnetic transi-tions at low temperatures. Mg substitution on Fe sites canprogressively change the magnetic properties and ferroelec-tricity. In recent literature, the giant magnetocapacitance ef-fect at room temperature is accounted in terms of chargefluctuation arising from the interconversion between the twotypes of charge order.25 It is also noted that another type ofsuperstructure is also observed in LuFe2O4 prepared by aslightly different method.28 These facts suggest that the co-existence and competition among the multitype orderedstates in the present system are essential for understandingthe properties of these materials.

ACKNOWLEDGMENTS

We thank C. J. Lu and R. I. Walton for their helpful dis-cussions. This work was supported by the National NaturalScience Foundation of China and by the Ministry of Scienceand Technology of China.

*Author to whom correspondence should be addressed;ljq@aphy.iphy.ac.cn

1 N. Ikeda, K. Kohn, H. Kito, J. Akimitsu, and K. Siratori, J. Phys.Soc. Jpn. 64, 1371 �1995�.

2 K. Yoshiia, N. Ikeda, and A. Nakamura, Physica B 378-380, 585�2006�.

3 M. A. Subramanian, T. He, J. Z. Chen, N. S. Rogado, T. G.Calvarese, and A. W. Sleight, Adv. Mater. �Weinheim, Ger.� 18,

1737 �2006�.4 N. Ikeda, K. Kohn, N. Myouga, E. Takahashi, H. Kitoh, and S.

Takekawa, J. Phys. Soc. Jpn. 69, 1526 �2000�.5 N. Ikeda, K. Kohn, H. Kito, J. Akimitsu, and K. Siratori, J. Phys.

Soc. Jpn. 63, 4556 �1994�.6 S.-W. Cheong and M. Mostovoy, Nat. Mater. 6, 13 �2007�.7 M. Fiebig, T. Lottermoser, D. Frohlich, A. V. Goltsev, and R. V.

Pisarev, Nature �London� 419, 818 �2002�.

FIG. 11. �a� The dielectric constant of LuFe2O4 and LuFe1.85Mg0.15O4 as a function of temperature, done at frequencies of 50 and200 kHz. �b� ZFC and FC magnetizations of LuFe2O4 and LuFe1.85Mg0.15O4 as a function of temperature at an applied field of 100 Oe.Changes of magnetic properties are demonstrated.

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8 B. B. V. Aken, T. T. M. Palstra, A. Filippetti, and N. A. Spaldin,Nat. Mater. 3, 164 �2004�.

9 Y. Yamada, K. Kitsuda, S. Nohdo, and N. Ikeda, Phys. Rev. B 62,12167 �2000�.

10 J. Iide, M. Tanaka, Y. Nakagawa, S. Funahashi, N. Kimizuka, andS. Takekawa, J. Phys. Soc. Jpn. 62, 1723 �1993�.

11 N. Ikeda, Y. Yamada, S. Nohdo, T. Inami, and S. Katano, PhysicaB 241-243, 820 �1998�.

12 Y. Yamada and N. Ikeda, J. Korean Phys. Soc. 32, S1 �1998�.13 R. J. Cava, A. P. Ramirez, Q. Huang, and J. J. Krajewski, J. Solid

State Chem. 140, 337 �1998�.14 Y. Todatey, C. Kikutay, E. Himotoy, M. Tanakay, and J. Suzukiz,

J. Phys.: Condens. Matter 10, 4057 �1998�.15 K. Siratori, N. Mori, H. Takahashi, G. Oomi, J. Iida, M. Tanaka,

M. Kishi, Y. Nakagawa, and N. Kimizuka, J. Phys. Soc. Jpn. 59,631 �1990�.

16 H. Kito, S. Isida, M. Suzuki, J. Akimitsu, S. Takekawa, and K.Siratori, J. Phys. Soc. Jpn. 64, 2147 �1995�.

17 M. Isobe, N. Kimizuka, J. Iida, and S. Takekawa, Acta Crystal-logr., Sect. C: Cryst. Struct. Commun. 46, 1917 �1990�.

18 Manfred Fiebig, J. Phys. D 38, R123 �2005�.

19 Aya Nagano and Sumio Ishihara, J. Phys.: Condens. Matter 19,145263 �2007�.

20 Y. Horibe, K. Kishimoto, S. Mori, and N. Ikeda, J. Korean Phys.Soc. 46, 192 �2005�.

21 Y. Yamada, S. Nohdo, and N. Ikeda, J. Phys. Soc. Jpn. 66, 3733�1997�.

22 Y. Zhang, H. X. Yang, C. Ma, H. F. Tian, and J. Q. Li, Phys. Rev.Lett. 98, 247602 �2007�.

23 M. Mekata and K. Adachi, J. Phys. Soc. Jpn. 44, 806 �1978�.24 N. Ikeda, H. Ohsumi, K. Ohwada, K. Ishii, T. Inami, K. Kakurai,

Y. Murakami, K. Yoshii, S. Mori, Y. Horibe, and H. Kito, Nature�London� 436, 1136 �2005�.

25 H. J. Xiang and M.-H. Whangbo, Phys. Rev. Lett. 98, 246403�2007�.

26 A. Castro-Couceiro, S. Yáñez-Vilar, B. Rivas-Murias, A.Fondado, J. Mira, J. Rivas, and M. A. Señarís-Rodríguez, J.Phys.: Condens. Matter 18, 3803 �2006�.

27 Y. Todate, E. Himoto, C. Kikuta, M. Tanaka, and J. Suzuki, Phys.Rev. B 57, 485 �1998�.

28 Y. Matsuo, Y. Horibe, S. Mori, K. Yoshii, and N. Ikeda, J. Magn.Magn. Mater. 310, 349�E� �2007�.

ZHANG et al. PHYSICAL REVIEW B 76, 184105 �2007�

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