Staging model of the ordered stacking of vacancy layers and phase separation in the layered NaCoO(x > 0.71) single crystals
G. J. Shu, F.-T. Huang, M.-W. Chu, J.-Y. Lin, Patrick A. Lee, F. C. Chou
aa r X i v : . [ c ond - m a t . s t r- e l ] J u l Staging model of the ordered stacking of vacancy layers and phase separation in thelayered Na x CoO ( x > ∼ G. J. Shu , F. -T. Huang , , , M. -W. Chu , J. -Y. Lin , Patrick A. Lee , and F. C. Chou , ∗ Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan Taiwan International Graduate Program, Academia Sinica,Taipei 10115,Taiwan Department of Chemistry,National Taiwan University,Taipei 10617,Taiwan Department of Physics, National Jiao-Tong University, HsinChu 30076, Taiwan Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA and National Synchrotron Radiation Research Center, HsinChu 30076, Taiwan (Dated: October 26, 2018)Phase diagram of Na x CoO (x > ∼ < ∼ x < ∼ < ∼ x < ∼ ∼
8K and is only reachable through slow cooling. In addition, x = 0.859 is found to be responsiblefor the highest A-AF transition temperature at about 29K. Staging model based on ordered stackingof multi-vacancy layers is proposed to explain the hysteretic behavior and A-AF correlation lengthfor x ∼ PACS numbers: 74.62.Bf, 74.25.Bt, 74.62.Dh, 74.78.Fk
I. INTRODUCTION
Layered material Na x CoO has a rich electronic andmagnetic phase diagram as a function of x, from A-type antiferromagnetic ordering for x > ∼ ∼ ∼ Although A-typeAF magnetic ordering transition below 22K has been re-ported in all samples of nominal x from 0.75 to 0.85, thedifference among these concentrations has usually beenignored, either due to poorly controlled Na level frommelt growth or roughly estimated Na content.
Thehigh Na vapor loss during high temperature melt growthis well known and the diffusive nature of Na ions atroom temperature makes the control of Na content evenmore difficult, which can often lead to an inhomoge-neous mixture of phases for x > ∼ The newly found evidence of super-structure formed by multi-vacancy clusters in x ∼ Recent studies of x ∼ et al. conclude that Na ordering is highly depen-dent on the cooling rate, where an additional magneticordering below 8K appears only after the sample is slowlycooled through the 300-200K range. However, the realimpact of the successive Na rearrangement processes re-mains to be clarified and the phase diagram must berevisited. Herein, using results from additionally improved elec-trochemical techniques, specific heat and high resolutionsingle crystal synchrotron X-ray Laue diffraction, we re-port detailed magnetic and structural phase diagram inthe region of 0.71 < ∼ x < ∼ √
13a is maintainedin all samples with x in the range of 0.82-0.86, the mag-netic ground state turns out to be distinctively different.In fact, there are three distinct A-AF transition tem-peratures of T N =22K, T N =8K and T N =29K foundin this range, corresponding to a proposed specific multi-vacancy layer stack ordering of well-defined stoichiometryof x = 0.820, 0.833, and 0.859 respectively, plus x=0.763that shows a spin glass like behavior below ∼
3K and witha significantly larger superlattice of √ √ ×√ × Applying a layered stagingmodel similar to that used in graphite intercalated com-pounds (GIC), for example, T N phase (x=0.820) canbe described as a stage-2 compound, i.e., where correctstoichiometry is obtained by introducing two more Na va-cancies into the original ideal √ ×√ ×
3c super unitcell, and these defects create tri-vacancy layers that aresandwiched between every two di-vacancy layers. On theother hand, T N phase (x=0.833) corresponds to stage-5,i.e., tri-vacancy layers are sandwiched between every five (cid:1029) (cid:1029) (cid:1029) DDTDDT DDDDDT DDDDDMT N1 T N2 T N3 (a) P ha s e S epa r a t i on P ha s e S epa r a t i on c (c) DTM (b)
FIG. 1: (color online) (a) A revised phase diagram ofNa x CoO in the range of 0.71-0.86 and the proposedstaging models for x=0.820(T N =22K), 0.833(T N =8K)and 0.859(T N =29K). Magnetic ordering temperatures aremarked by red cross. (b) Na layers with tri-vacancy (T), di-vacancy (D) and mono-vacancy (M), where Na2 ions (blue)move from the original Na2 site (empty circle) to the Na1site (red). (c) Crystal structure for γ -Na x CoO of P6 /mmcsymmetry with vacant Na1 sites shown in empty circles. di-vacancy layers. Most interestingly, the staging modelsuggests that the trivacancy layers serve as nucleationcenters for the interlayer AF ordering. This picture nat-urally explains why x=0.820 has a higher T N than thatof x=0.833 because of its shortest inter-trivacancy layerdistance. The observed phase separation phenomenon isa natural consequence of the competing multi-vacancycluster size, superlattice size, and interlayer magneticcorrelation. II. EXPERIMENTAL
High quality single crystals of well controlled Na con-tent were prepared using electrochemical de-intercalationtechnique starting from high Na content crystal of x ∼ The exact Nacontent has been cross checked with c-axis vs. x lin-ear relationship constructed from combined high angle (degree) I n t en s i t y ( a r b . un i t ) x=0.838x=0.846x=0.871 x=0.783x=0.792x=0.801x=0.814 (a)(b) FIG. 2: (color online) (a) X-ray diffraction results of (008)peak for samples with x in the ranges of (a) 0.83-0.87 and(b) 0.76-0.82 at room temperature. The linear x-dependenceof relative change of (008) diffraction integrated intensitiessuggests the phase separation phenomenon. The broadeneddiffraction peak for x > x CoO crystal samplessample N (K)* 3** 22 22 8 8/29*slow cooling **spin glass like behavior X-ray diffraction (008) peak position, Inductively Cou-pled Plasma (ICP) and Electron Probe Microanalysis(EPMA) techniques.
In particular, current study usesc(x) linear function that is further calibrated by the phaseseparated boundaries and EPMA is averaged out fromfreshly cleaved crystal surface for more than 100 points.A complete list of samples studied is summarized in Ta-ble I. Due to the active diffusive nature of Na ions atroom temperature and the minute differences of Na con-tent, all measurements were done on freshly preparedcrystals within days. Otherwise crystal samples must bestored within L-N2 dewar below 200K in order to sup-press Na loss from the surface. Synchrotron Laue diffrac-tion for Na superstructure investigation was performedwith synchrotron source in Taiwan NSRRC, and mag-netic property characterization was done using QuantumDesign SQUID MPMS-XL.
III. RESULTS AND DISCUSSIONS
While zooming in the region of x > (100) o (010) o (cid:1029) (cid:1029) (cid:1029) m FIG. 3: (color online) Synchrotron X-ray Laue pattern forx=0.801(5) at room temperature, where three twin sets ofhexagonal units are shown in the reciprocal space (upper in-set), which correspond to hexagonal √
13a (blue), √
12a (red)and √
19a (green) superlattices in the real space (lower inset). is demonstrated by the x-dependent evolution of (008)diffraction peak integrated intensities, where the growthof one end phase is at the expense of the other at the mis-cibility gap boundaries without continuous intermediatephase in between. As shown in Fig. 1 and Fig. 2, phaseseparation phenomenon is found to occur in two regionsof x ∼ > ∼ Purex ∼ Enforcing more Na into the matrix electrochem-ically destroys its ordering as indicated by the broadeneddiffraction peaks that correspond to x > ∼ √ √
13a and √
12a in the real space,the latter two can be compared with the published sin-gle phase Laue patterns of x = 0.71 ( √ √ The newly found √
19a superlattice must be
Temperature (K) -0.0030.0000.0030.0060.0090.012 M / H ( c m / m o l e ) x=0.842x=0.819 H=0.01T, //ab0 10 20 30 40 50 Temperature (K) M / H ( c m / m o l e ) Na x CoO , H=1T, //c x=0.801x=0.832x=0.842 x=0.820 FIG. 4: (color online) Magnetic susceptibility measurementresults for x > χ c and the onsets of low field hysteresisshown in the inset. due to Na ordering for x ∼ √
19a toaccount for stoichiometry of x ∼ . = 0.763 that is composed of quadri- and penta-vacancyclusters in adjacent layers for γ -Na x CoO . A detailedanalysis for x ∼ , the triple coexist-ing superlattices at constant temperature and pressuredoes not violate the phase rule, in fact it has reached theallowed maximum number of three. Considering dom-inant domains are from x ∼ √
13a with di-vacancyclusters) and x ∼ √
19a with quadri/penta-vacancyclusters), it’s reasonable to have a buffered zone at thedomain boundary which is built with tri/quadri-vacancyclusters of √
12a superlattice.Most of the magnetic susceptibility measurements forNa x CoO with x > ∼ χ c under high field. Althoughcrude magnetic phase mappings in this range before sug-gest that T N varies between 22-27K, Schulze et al. recently found an additional 8K phase for x ∼ With carefully tuned single crystals in the nar-row range of 0.82-0.86, we are able to re-visit the mag-netic phase diagram and untangle the mystery of T N variation. Magnetic susceptibility measurement results C ( ! J / K ) CoO Temperature (K) C / T ( m J / m o l e ! K ) Na x CoO cooling rate: 0.5K/min x=0.832 x=0.820 FIG. 5: (color online) Specific heat measurement results for x= 0.820(3) and 0.832(2) obtained from slowest cooling rate of0.5 K/min. The inset shows x=0.832(2) has a strong coolingrate dependence, where 8K phase grows at the expense of 16Kphase as cooling rate reduces from 15 to 0.5 K/min. are shown in Fig. 4, all measurements were done after aslow cooling rate of 2 K/min. We find that T N does notchange with x monotonously and continuously, instead,the four phases at the two miscibility gap boundariesshown in Figs. 1 and 4 are responsible for the differentcharacteristic T N ’s, where x ∼ χ c under highfiled, which occur at T N =22K, T N =8K and T N =29Kfor x = 0.820, 0.833 and 0.859 respectively, while 0.801(5)and 0.842(5) data reflect their mixed phase nature, i.e.,superposition of contributions from the end membersof 0.76-0.82 and 0.83-0.86 miscibility gaps respectively.There is ZFC/FC irreversibility found below T N for both χ c and χ ab at low field, although stronger FM satura-tion moments are seen along the ab-direction. Such A-AF ordering has been verified by the neutron scatter-ing for Na . CoO , where strong field dependence ofmagnetization below T N ∼
22K has been confirmed tobe metamagnetic. Current low field measurement is inagreement with that reported for x ∼ althoughour data indicate that the 8K phase is coming from thephase of x closer to 0.833, while a more stable phase of22K is from x closer to 0.820.We find that the different onsets of A-AF transitionbetween x = 0.820(3) and 0.832(2) are clearly demon-strated by the cooling rate dependence of T N as revealedby the specific heat data shown in Fig. 5, where 22K tran-sition for x=0.820(3) is independent of cooling rate, whilefast cooling rate moves T N discretely from 8K to 16K forx=0.832(2). 16K phase occurs in x=0.832(2) when a fastcooling is applied, while it decreases at the expense of 8K phase generation under decreasing cooling rate, al-though the existence of minor 22K is difficult to avoidcompletely for samples near the phase separated bound-ary. The ratio of the minor 22 K phase to the major 8 Kphase in the present x=0.833 sample can be estimated tobe 3.6% from the entropy change of the small anomaly at22 K for Na . CoO . Sodium ion diffusion is active atroom temperature for high x samples, but it freezes be-low ∼ for Na due to Na motion. Sample of x=0.832(2) must becooled through the temperature range of 300-200K with arate slower than 10 K/min in order to reach the magneticground state that corresponds to 8K magnetic ordering.The entropy associated with the 22 K transition inNa . CoO and the 8 K transition in Na . CoO are estimated to be △ S ∼
170 mJ/mol K and △ S ∼ △ S and the transition width character, these re-sults indicate that the magnetic moments order better inNa . CoO than in Na . CoO . The relatively poorordering of stage-2 for x=0.820 (T N =22K) than thatof stage-5 x=0.833 (T N =8K) is interestingly in agree-ment with the alternating T-Q stacking requirement asdescribed by the x=0.71 superstructure model before, i.e., tri-vacancy is not favorable in the even-layer withinP6 /mmc symmetry and there must exist mixing stagesof 1 and 3 for x=0.820. The △ S value for x=0.833 ismore than 10 times larger than that reported in Ref. [10],which suggests a nearly single 8 K phase in the presentsample. On the other hand, these measured △ S valuesare only about 20% of the entropy estimated from thecomplete ordering of fully localized spin-1/2 Co ions.This discrepancy might indicate the failure of the simpleionic Co -Co picture.Since all samples with x > ∼ √ ∼ √ ×√ ×
3c superstructure.
Butwhat kind of mechanism is responsible for these discreteT N ’s of △ x only 1-3% apart? The secret lies in the stackordering of 2D hexagonal superlattices. From our previ-ous studies on the structure of 0.71 and 0.84, the idealsuperlattice has a 3c periodicity. The 3c periodicity forx=0.820 is once again confirmed by electron diffractionpatterns on single domain crystals as shown in Fig. 6.Although [001] p diffraction pattern cannot tell the peri-odicity along c-direction, perfect indexing for diffractionpatterns with transmitted beam along primitive [101] p and [201] p can only be achieved with the help of 3c peri-odicity assignment. When one and two more Na defectsper 3c unit (i.e., six layers of Na) are introduced into theperfectly ordered original 0.846 = 11/13 superstructure, two additional stoichiometries of 0.833 = 0.846 − × and 0.820 = 0.846 − × can be introduced, as verifiedby our X-ray and magnetic measurement results shownabove. When magnetic ordering occurs, spins from itiner- !"" %& !"" !" "!" !" "!" !"" ! %& "!" !" $ !"! !" "!" !!! $ !’" %& "!" !" $ !!% !" "!" !"% $ FIG. 6: (color online) ) Electron diffraction patterns of sin-gle domain Na . CoO for transmitted e-beam along [001] p ,[101] p , and [201] p projections (p, denoting the primitive lat-tice). The superlattice spots surrounding the intense primi-tive cell reflections in the ab-plane projection, [001] p , indicatethe superlattice ordering of √ ×√
13a without c-axis infor-mation. In the azimuthal projections of [101] p and [201] p , thesuperlattice reflections suggests 3c ordering, i.e. can only beindexed correctly with √ ×√ ×
3c superlattice. ant electron or localized electrons near Co ions are certainto be affected by the rearrangement of Na multi-vacancyclusters in the nearby layers. In fact the in-plane inter-vacancy cluster distance √
13a is nearly twice the interCoO distance. Since every one extra Na vacancy in-troduced into the ideal 3c unit would convert the orig-inal layer of di-vacancy formed 2D superstructure intotri-vacancy, we can thus simplify the stacking probleminto stack ordering between the di-vacancy (D) and tri-vacancy (T) layers along the c-direction. We propose anew staging model as shown in Fig. 1 to explain suchstack ordering, which shows strong resemblance to thestaging phenomenon often observed in the 2D interca-lated graphite compounds. The x=0.833 phase whichhas only one Na defect introduced could have a stage-5construction, while x=0.820 phase of two Na defects per3c unit must have a stage-2 construction, i.e., there arefive and two D-layers sandwiched in between T-layers.We can now use the staging picture to interpret thevariety of magnetic ordering temperatures observed inthe range 0.82 < ∼ x < ∼ the di-vacancy may localize a carrier on the adjacent Colayer, leaving a low density hole gas of density , whichis unstable to Stoner ferromagnetism. This may be the origin of the ferromagnetic layers which then order anti-ferromagnetically between layers to form the A type AFordering. Here we suggest that the driving force for in-terlayer coupling may lie in the T-layer. The tri-vacancyhas one extra negative charge which lowers the tunnelingbarrier between the localized holes on the adjacent layersand enhances the antiferromagnetic spin correlation be-tween them. Thus the T-layer may form the nucleationlayers to drive the three dimensional AF order. This pic-ture explains why T N is 22K for x=0.820 vs. T N is8K for x=0.833 where the spacing between T-layers ismuch larger. Upon rapid cooling, some stage 4 and stage6 states may form. The stage 4 meta-stable phase maybe responsible for the intermediate T N of 16K. The hys-teretic behavior observed below T N (see Fig. 4) couldalso be explained by either the in-plane FM domain ef-fect or by uncanceled A-type AF moments along the c-axis as a result of mixed staging. The phase separationobserved near 0.83-0.86 can also be explained using thesame stage model. Since 0.859=0.846+ × , i.e., onemore Na ion (not vacancy) is introduced into the originalideal x=0.846 phase of √ ×√ ×
3c superstructure,the di-vacancy is converted to a mono-vacancy (M) form-ing a stage 5 stacking. The hole density on either side ofthe M-layer is now reduced by × and we may expectan even strong tendency toward Stoner ferromagnetism.The higher transition temperature of the Co layers adja-cent to the M-layer may explain the higher T N = 29Kfor x=0.859. IV. CONCLUSIONS
In conclusion, we have revised Na x CoO phase dia-gram in the range of 0.71-0.86 using electrochemicallyfine tuned single crystal samples. The puzzling and in-consistent measurement results in this range before havebeen clarified and interpreted as a result of phase separa-tion and staging phenomena. A direct link between thehigh temperature Na ion (vacancy) ordering and the lowtemperature magnetic properties have been established.The highly correlated ion, magnetic and charge orderingsin layered Na x CoO can provide invaluable informationto the study of strongly correlated electron low dimen-sional system which has itinerant electrons on a triangu-lar lattice. Acknowledgment
FCC acknowledges the support from National ScienceCouncil of Taiwan under project number NSC 97-3114-M-002. PAL acknowledges support by the DOE grantnumber DE-FG02-03ER46076. ∗ Electronic address: [email protected] M. L. Foo, Y. Wang, S. Watauchi, H. W. Zandbergen,
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