Stabilization of the high-spin state of Co$^{3+}$ in LaCo$_{1-x}$Rh$_{x}$O$_3$

0.92 MB·English

by  K. Knížek

Stabilization of the high-spin state of Co3+ in LaCo Rh O .
1−x x 3
K. Kn´ıˇzek,1,∗ J. Hejtm´anek,1 M. Maryˇsko,1 Z. Jir´ak,1 and J. Burˇs´ık2
1 Institute of Physics ASCR, Cukrovarnicka´ 10, 162 00 Prague 6, Czech Republic.
2 Institute of Inorganic Chemistry ASCR, 250 68 Rˇeˇz near Prague, Czech Republic.
TherhodiumdopingintheLaCo1−xRhxO3 perovskiteseries(x=0.02−0.5) hasbeenstudiedby
X-ray diffraction, electric transport and magnetization measurements, complemented by electronic
structure GGA+U calculations in supercell for different concentration regimes. No charge transfer
between Co3+ and Rh3+ is evidenced. The diamagnetic ground state of LaCoO3, based on Co3+
2 in low-spin (LS) state, is disturbed even by a small doping of Rh. The driving force is the elastic
1 energy connected with incorporation of a large Rh3+ cation into the matrix of small LS Co3+
0 cations, which is relaxed by formation of large Co3+ in high-spin (HS) state in the next-nearest
2 sites to the inserted Rh atom. With increasing temperature, the population of Co3+ in HS state

n increasesthroughthermalexcitation,andasaturatedphaseisobtainedclosetoroom temperature,
a consisting of a nearest-neighbor correlation of small (LS Co3+) and large (HS Co3+ and LS Rh3+)
J cationsinakindofdoubleperovskitestructure. Thestabilizingroleofelasticandelectronicenergy
4 contributions is demonstrated in supercell calculations for dilute Rh concentration compared to
1 otherdopants with various trivalent ionic radius.

] PACSnumbers: 75.30.Wx;71.15.Mb
ci Keywords: LaCoO3;Rhdoping;spintransitions;GGA+U
s
-
rl I. INTRODUCTION to a crossover. Such behavior finds a strong support in
t GGA+U calculations [3] and also the limiting HS popu-
m
lation of about 45% can be naturally explained.
. The cobalt perovskites LnCoO (Ln = La, Y,
t 3
a rare-earths) show various anomalous behaviors that are Anuncertaintyexists alsoconcerningthe formationof
m metallic phase at around 535 K. The gradual course of
associatedwith changes of the spin state of octahedrally
- coordinated Co3+ ions of 3d6 configuration. According this process, which is in striking contrast with standard
d I-M transition, has been modeled as a thermal excita-
to recent interpretation in the frame of LS-LS/HS-IS
n tion to IS states [5]. However, it is worth mentioning
model, the process can be understood as a local exci-
o
c tation of Co3+ ions from the diamagnetic LS (low spin, that the two-step transitions in LaCoO3 does not neces-
[ t6 )groundstate to closelylying paramagneticHS(high sarily require an existence of three close lying ionic con-
2g figurations (LS, HS and IS). A reference can be done to
spin, t4 e2) states, followed at higher temperature by a
1 2g g phenomenological model of Bari and Sivardi`ere, who in-
v formation of a metallic-like phase of IS character (inter-
0 mediatespin,t52gσ∗)-seee.g. [1–3]. InLaCoO3thesetwo vexesctitigeadteHdStshteataesctiinvcaltuiodningfrothme tmhaegLneStogerloaustnidc csotuatpelintog
5 stepsarewellseparated(Tmagn =70K,TI−M =535K). betweenthetwospecies[6]. Dependingonthemodelpa-
0 The experiments show that the HS population, after a
3 rameters, they obtained a succession of three phases in
steep increase at T , tends quickly to a saturation,
. magn coherencewithexperimentalfindings-the mixedLS/HS
1 reaching 40-50% in maximum - see e.g. the combined
states with gradually increasing HS weight at low tem-
0 analysis of susceptibility and anomalous expansion data
2 peratures,thedisproportionationofHS-poorandHS-rich
in [4]. To account for such behavior, two formal ap-
1 sitesintheintermediaterange,andare-enteredhomoge-
proaches have been used. In the first one, Kyˆomen et
: neous phase of LS/HS admixed states at high tempera-
v al. treat the excitations as locally independent events
tures. Veryrecentlythisscenarioofspin-statetransitions
i obeyingBoltzmannstatisticsandrelatetheactualcourse
X in LaCoO based on two states only was supported in a
of the diamagnetic-paramagnetictransition to lattice ef- 3
r study of a two-orbital Hubbard model with crystal-field
a fects. An activationenergyincreasingprogressivelywith
splitting using DMFT calculation by Kuneˇs and Kˇr´apek
HS population is obtained [1]. An alternative approach
[7]. They demonstrated that the existence of dispro-
is based on original idea of Goodenough that the sta-
portionated phase and subsequent homogenization com-
bilization of HS state is conditioned by presence of LS
bined with closing of the charge gap can be understood
states in the neighborhood. As shown by Kn´ıˇzek et al.
considering the on-site interactions of valence electrons
[4] using a simple probabilistic model, when nearest HS
and their itinerancy. This suggests that the physics of
neighbors are forbidden, the activation energy found by
LaCoO is primarilyof electronic(fermionic) origin,and
thefithasanoppositetrend-itdecreaseswithtempera- 3
elastic interactions between different spin-state species
ture (or equivalently with HS population) leading finally
have just a stabilizing effect.
The present study is undertaken with an aim to re-
solve by experimental and theoretical means the role of
∗correspondingauthor:[email protected] electronic and elastic interactions in the stabilization of
K. Kn´ıˇzek et al., Stabilization of the high-spin state of Co3+ in LaCo1−xRhxO3. 2
variousCo3+ spinstatesintheLaCoO typerelatedsys- tector, 2θ range 20o - 150o) was employed to determine
3
tems, in particular in LaCoO -LaRhO solutions. The thephasecompositionsandlatticeandstructuralparam-
3 3
studies on Rh-containing compounds were not frequent eters. The diffraction patterns were analyzed with the
in the past, mainly due to high cost of rhodium, which Rietveld method using the FULLPROF program[11].
limits potential applications. Nevertheless, since Rh3+ Themagnetic propertiesweremeasuredbymeansofa
of4d6 configurationisisoelectronicwithCo3+ asregards SQUID magnetometer MPMS-7 (Quantum Design) over
thevalenceelectrons,andisexclusivelyinlow-spinstate, thetemperaturerange4.2 300Kandamagnetosuscep-
−
thesubstitutionishelpfulinthefundamentalresearchof tometer DSM 10 (Manics) at elevated temperatures up
cobalt spin states and experienced an increased interest to 800 K.
inthelastyears. CompleteLaCo1−xRhxO3solidsolution Thermal conductivity, thermoelectric power and elec-
was recently studied in Ref. [8] with focus on transport trical resistivity were measured using a four-probe
propertiesathightemperatureandinRef.[9]withfocus method with a parallelepiped sample cut from the sin-
on magnetic properties. Influence of smallRh doping on tered pellet. The electrical current density varied de-
thespinstatetransitioninLaCoO3waspresentedin[10]. pending on the sample resistivity between 10−1 A/cm2
Our work revisits this system, focusing to composi- (metallic state) and 10−7 A/cm2 (insulating state). The
tions with small doping of Rh (x = 0 0.08), includ- measurementsweredoneonsamplecoolingandwarming
−
ing for completeness also the x = 0.2 and 0.5 samples. using a close-cycle cryostat working down to 3 K.
The experiments are complemented with GGA+U elec-
tronicstructurecalculationsusingthesupercellwithreg-
ularorderingsofCoandRhionscorrespondingtodoping III. METHOD OF CALCULATION
x=1/16=0.0625, 1/2 and 15/16=0.9375. The method
applied allows us to investigate not only various valence
ThecalculationsweredonewiththeWIEN2kprogram
and spin states in the model structures but also to op-
[12]. This program is based on the density functional
timize local bond lengths and angles that stabilize the
theory (DFT) and uses the full-potential linearized aug-
givenconfiguration. Theroleoftemperatureissimulated
mented plane wave (FP LAPW) method with the dual
by a change of unit cell volume. In agreement with the
basis set. The core states were defined as an electronic
experimental findings, the calculations support the sig-
configuration (Kr, 4d10) for La, (Ar, 3d10) for Rh, (Ne,
nificantHSpopulationspreservedintheLaCo1−xRhxO3 3s2) for Co and as (He) for O atoms. The valence states
systems down to the lowest temperature, and suggest
included3p,3dand4sorbitalsforCo,and4s,4p,4dand
thatthestabilizationofHSCo3+ statescomparedtoun-
5s for Rh.
doped LaCoO is to much extent due to elastic interac-
3 All calculations were spin-polarized. For the exchange
tions. Namely, the low-energy configurations are based
correlation potential the GGA form was adopted [13].
on a nearest neighbor correlations of LS Co3+ states of
The radii of the atomic spheres were taken 2.3 a.u. for
smallersizeandHSCo3+ orLSRh3+ statesoflargersize
′ La, 2.05 a.u. for Rh, 1.95 a.u. for Co and 1.55 a.u.
in a kind of the double perovskite A BB O structure.
2 6 for O. To improve the description of Co 3d and Rh 4d
electrons we used the GGA+U method, which corre-
spondstoLDA+U methoddescribedin[14,15]withthe
II. EXPERIMENTAL
GGAcorrelationpotentialinsteadofLDA. Thevaluesof
Coulomb and exchange parameters were used the same
Polycrystalline samples LaCo1−xRhxO3 with x = 0, as in the previous studies, U = 2.7 eV and J = 0 eV,
0.02, 0.04, 0.08, 0.2 and 0.5, were prepared according for both Co and Rh [3, 4]. The atom positions were op-
to the following procedure. Hot water solution of metal timized by minimization of the calculated forces on the
ions prepared by decomposition/dissolution of La O , nuclei [16].
2 3
RhCl3.H2O, and Co(NO3)2.6H2O in 30% HNO3 was The calculations were performed in order to test two
mixed with in advance prepared citric acid (CA) - di- specific cases - small doping of Rh in LaCoO (and sim-
3
ethylenglycol (EG) water solution. The molar ratio ilarly small doping of Co in LaRhO ) and x = 0.5. For
3
CA:EGwas1:1andthemolarratio(CA+EG):metalions thefirstcase,anorderedarrangementof1Rhand15Co
was also 1:1. Clear, transparent and voluminous aerogel atoms was constructed (x = 1/16), simulating a rather
was obtained after evaporation of water at 140oC. The isolated Rh atom in Co matrix. The model is charac-
gel was pulverised in a mortar, dried, pyrolyzed, and or- terized by intersected Rh-Co-Co-Co-Rh-... chains run-
ganiccarbonresiduewereremovedbyproperheattreat- ning along three pseudocubic axes, and a body centered
ment at temperatures 180-450oC in a chamber furnace supercell 2√2a 2√2a 4a is used in order to in-
p p p
× ×
under static air atmosphere. After careful mixing and clude the octahedral tilting (a is a lattice parameter of
p
grinding,the finalcrystallizationofLaCo1−xRhxO3 per- the cubic perovskite cell). An analogical model struc-
ovskite phase has been done by annealing at 1200oC for ture for half doping x = 1/2 is of double perovskite
100 hours in air atmosphere. typewith1:1rock-saltarrangementofCoandRhionsin
X-ray powder diffraction using a Bruker D8 diffrac- the √2a √2a 2a cell, characterizedby intersected
p p p
× ×
tometer (CuKα radiation, SOL-X energy dispersive de- Rh-Co-Rh-... chains. Theinversionsymmetryoperation
K. Kn´ıˇzek et al., Stabilization of the high-spin state of Co3+ in LaCo1−xRhxO3. 3

3Cell volume per f.u. (Å) 55666802 a) WResistivity (m cm) 111110000013579 a) E (eV)A0000 ....0246200 400 600 800
Co,Rh - O (Å) 122...900505 b) 111155660505 Co,Rh - O - Co,Rh (deg) -1mThermoelectric power (V K) 1--24684200000000000000000 200 b4)00 600 8xxxxx0 =====0 00000....0005248 1000

Temperature (K)
0.0 0.2 x 0(R.5h) 1.0 -1m) 8
-1K 6 c)
FIG. 1: (Color online) (a) Unit cell volume per formula unit W
(oefrrLoarCboa1−rsxRarhexOsm3a(l⋄le)r. tThhane sstyrmaibgholt sdizaes)heddepliennediesncaelionneaxr uctivity ( 4
interpolation between x = 0 and 1. (b) Average Co,Rh-O d
n 2
bondlengths((cid:3))andCo,Rh-O-Co,Rhangles(◦)dependence co
on x. Corresponding values determined in Ref. [8] are shown mal
for comparison (×). her 00 50 100 150 200 250 300
T
Temperature (K)
was only retained in both cells. FIG. 2: (Color online) Resistivity, thermoelectric power
and thermal conductivity dependence on temperature of
LaCo1−xRhxO3.
IV. RESULTS
Thesymmetryoftheunitcellischangedfromrhombo- conducting state is observed above 400 K for small Rh
hedralR¯3cforsmalldopingx=0 0.08toorthorhombic dopings,manifestedbyapeakinapparentactivationen-
Pbnmforx=0.2 1inagreemen−twithpreviousstudies ergyaround500K,seeinsetofFig.2a. Forx=0.5,only
[8,9]. Theaverage−bonddistanceCo,Rh-Oincreasesand a broadhump is observedin the activation energy. High
average bond angle Co,Rh-O-Co,Rh decreases as more thermoelectric power at low temperature indicates a low
rhodium is inserted in the structure, i.e. the octahedral concentrationofcarriers,seeFig.2b. Theabsolutevalue
tilting is enhanced with increasing doping, see Fig. 1b. of Seebeck coefficient ranges from 400 to 800 µV/K. A
Theseobservationsareinagreementwithlargerionicra- decrease to a metallic-like value 30 µV/K is observed
∼
diusofRh3+ (0.665˚Ainsix-foldcoordination)compared above 400 K for small Rh doping. In contrast, the See-
to Co3+. Actually, the ionic radius of Co3+ significantly beck coefficient for x = 0.5 saturates at a higher value
depends on its spin state (0.545 ˚A in LS and 0.610 ˚A in of 100 µV/K. Thermal conductivity is decreasing and
∼
HS state), nevertheless Rh3+ is larger than Co3+ in any thephononicpeakatlowtemperatureissuppressedwith
spin state. increasing Rh content, see Fig. 2c.
ThestructuralevolutionofCo,RhO octahedraisman- MagneticsusceptibilitymeasuredinDCfieldof10kOe
6
ifestedinthe increaseofcellvolumewith Rhdoping,see is displayed in Fig. 3. The low-temperature transition
Fig.1a. Thedependenceshowsapositivedeviationfrom to LS state is shifted down in temperature by approx.
linearity in agreement with previous studies [8, 9]. This 35 K for x = 0.02 and it is suppressed for x = 0.04.
deviation could also be detected in the dependence of It means that inserting Rh into LaCoO destabilizes the
3
bond distances and angles, although it is mostly hidden purely LS ground state of Co. As can be deduced from
within error bars because the accuracy of these values is the slope of inverse magnetic susceptibility at the lowest
much lower, since X-ray diffraction is very accurate in temperatures, a nonzero HS population is present start-
determination of lattice parameters, but is not as much ing from x=0.04. The poulation of Co3+ in HS state is
sensitive to oxygen positions. estimated between 14 18% with maximum for x=0.2.
−
Electricresistivityhassemiconductingcharacteratlow Thecompositionx=0.2deservesspecialattention,since
temperatureforallx, seeFig.2a. Atransitiontoamore the sample shows clear signatures of magnetic ordering
K. Kn´ıˇzek et al., Stabilization of the high-spin state of Co3+ in LaCo1−xRhxO3. 4

of LaCo1−xRhxO3 in a more quantitative manner, let
a) x = 0 us discuss the results of the Curie-Weiss fit of inverse
-1Oe) 0.006 xx == 00..0024 susceptibility within 150−300K,which aresummarized
-1ol xx == 00..0280 in Table I. It is seen that the effective magnetic moment
m µ is enhanced for x = 0.02 compared to x = 0 and
u 0.004 x = 0.50 eff
m then it takes anopposite trend and is decreasingwith x.
e
c ( The number of Co3+ in HS state (pHS, S = 2) can be
calculatedfromthe µ presumingRh3+ andremaining
eff
0.002 Co3+ ions in the non-magnetic LS state. The calculated
p is reduced from 0.47 for x = 0.02 to 0.41 for 0.08
HS
while the number of Co3+ in LS state p is practically
LS
0.5 constantaround 0.51,as though Rh were predominantly
800 0.4
e) 0.3 pHS replacing Co3+ in HS state for the small doping range
ol O 600 0.2 pLS of x. On the other hand, the extrapolation to x = 0
m 0.00 0.25 0.50 givesp =0.49,whichisasomewhathighervaluethan
-1mu 400 x (Rh) pHS =H0S.46 actually determined for x=0. The origin of
(e this discontinuity can be rationalized as follows:
c1/ 200 b) In the frame of the LS/HS thermal excitation model
[1, 3, 17], the population of HS states in pure LaCoO is
3
0 limitedto50%,sinceprobabilityofnearestHSneighbors
0 100 200 300 400 500 600 700 800
is strongly suppressed. Because the excitations to HS
Temperature (K)
state are dynamic and only a short-rangecorrelated,the
actual limit should depend on the size of the correlated
FIG. 3: (Color online) Molar magnetic susceptibility and clusters of alternating HS-LS states (or rather on the
inverse susceptibility of LaCo1−xRhxO3. (The spurious in- size of disordered boundaries between the clusters with
creaseofsusceptibilityatlowtemperatureforx=0and0.02
Co ions in LS states), and should be somewhat lower
is aCurie term dueto minor impurity.) Theinset shows cal-
than 50%. Therefore µ corresponding to p 0.46
culated populations of HS and LS states. eff HS ∼
is observed. We suppose, that the clusters of alternating
HS-LS states, which are stabilized by dilute Rh dopants
representingimmobileelasticdefects,arelargerthanthe
TABLE I: The results of themagnetic susceptibility analysis
inthemiddletemperaturerange(150−300K):effectivemag- thermally induced dynamic clusters, hence the sum of
netic moment µeff, Weiss θ, and calculated ratio of the Co Rh3+ and HS Co3+ (x+pHS) may approach closer the
cations in HS state (p , S =2) and LS state (p , S =0). limit of 50%.
HS LS
The decrease of µ with higher doping of Rh (x >
x(Rh) µ (µ ) θ(K) p p eff
eff B HS LS
0.08) is not so steep. In particular for x = 0.5, the cal-
0 3.31 -203 0.46 0.54
culated p only decreasesto 0.35,while p is reduced
0.02 3.35 -189 0.47 0.51 HS LS
down to 0.15. We suppose, that the reason is in cumu-
0.04 3.25 -140 0.44 0.52
lation of large Rh ions, which creates a positive lattice
0.08 3.14 -146 0.41 0.51 strain and thus supports HS state on nearby Co sites.
0.2 3.10 -159 0.40 0.40 This effect of Rh dopants for stabilizationof HS state at
0.5 2.89 -148 0.35 0.15 neighboring Co ions prevails for higher x 1, whereas
→
the previously mentioned effect of Rh ions replacing HS
Co ions in LS/HS ordered regions and supporting HS
below 10 K, including the finite remanentmagnetization state on the next neighbor Co sites dominates for lower
in measurements of hysteresis loops, in agreement with x 0. Nevertheless, in both cases the HS states stabi-
→
the recent paper of Asai et al. [9]. lizedbyRh,unlikethoseobtainedbythermalexcitation,
With increasing temperature, the slope of inverse sus- are preserved down to the lowest temperature.
ceptibility is changed as a result of the excitation of fur- The dependence of cell volume on x would be linear if
ther HS states and interactions among them. Finally, theroomtemperatureratiop :p remainedconstant
HS LS
practically linear behavior of inverse susceptibility is ob- at the original x = 0 value for all x. Since this ratio
served within the range 150 300 K. At a higher tem- becomes higher in the doping region x = 0.2 0.5 (and
− −
perature, the samples x = 0 0.2 exhibit a magnetic presumably also for x > 0.5), the observed cell volume
−
anomalyassociatedwiththe I-Mtransition. Itsextentis show a marked positive deviations, see Fig. 1a.
gradually diminished and shifted to slightly higher tem- The Weiss θ deducedfrom the susceptibility data over
perature with Rh doping, and for x= 0.5 the transition the range 150 300 K are negative for all x and the
−
completely vanishes, in agreement with the behavior of absolute values are approximately decreasing with p ,
HS
the anomaly in transport data in the inset of Fig. 2a. as expected regarding the antiferromagnetic interaction
In order to characterize the room-temperature phases between Co3+ in HS state.
K. Kn´ıˇzek et al., Stabilization of the high-spin state of Co3+ in LaCo1−xRhxO3. 5
FIGa.)4:HLHSS(SHCLHSSSolLRLSohSrHLHoSSSHnLHSSSlineb))ELHLxSSSLHaLSSSmHRHpShSleLHsLSSSLHLoSSSf Cco)spRRRhhhiRnRRhhhsRHtRhShatRReRhhhsRRRhhhconfigura- bilisation energy (meV / f.u.)relative to LS state --2468420000000 (LTa ~C› o0O K3) T( R ›~h -0d oKped)
a
tions considered in theGGA+U calculations. St 98 99 100
Relative cell volume V / VRT (%)
The previous GGA+U calculations evidenced, that
twomagnetic phasesmayexistinLaCoO perovskite,in FIG. 5: (Color online) Stabilization energy of LS/HS (full
3
addition to the non-magnetic LS ground state [3, 4, 18]. symbols)andIS(opensymbols)configurationsrelativetoLS
ThefirstoneisaresultofgradualpopulationofHSstates configuration of LaCo1−xRhxO3 for x=0 ((cid:3)) and x=1/16
(◦) in dependenceon cell volume byGGA+U calculation.
conditioned by presence of the LS states at the nearest
Co sites. Nevertheless, some Co(HS) pairs do exist and
are responsible for prevailing antiferromagentic interac-
is related to temperature induced contraction and an-
tions. The HS state in LS matrix is further stabilized
other 1% is related with the reduction of the Co3+ size
if Co(HS) site is expanded (breathing-type) at the ex-
at the spin transition [20]. Since the spin transition
pense of neighboring Co(LS) sites. The mixed LS/HS
phase tends to a short-range ordered 1:1 arrangement, in LaCo1−xRhxO3 is incomplete, the maximum volume
contraction is expected between 1 2% in this case.
whose long-range formation is presumably prevented by
−
The relative cell volumes approximately corresponding
the entropyfactor. The secondphase consistsoflargeIS
to T = 0 K are indicated in the figure. In both cases,
clusters, which may exist within the LS/HS phase and
the lowest energy state at room temperature (volume
finally tend to a formation of uniform itinerant IS phase
V ) is LS/HS, but the stabilization energy, relative to
with ferromagnetic coupling. The cell volume expansion RT
LS state, is higher for Rh-doped compound. With the
destabilize the LS ground state and for certain critical
volumecontractionsimulatingthetemperaturedecrease,
volumes the energy of LS/HS phase or IS phase become
theLaCoO systemundergoesacrossoveratabout99.4%
lower. 3
volume to the LS ground state, while this crossover for
In the present GGA+U calculation, several spin
LaCo Rh O isaround98.7%volume,whichisal-
states configurations of Co were tested using the 15/16 1/16 3
most T 0 K in this case.
La Co RhO supercell (x=0.0625), namely:
16 15 48 →
ThesecalculationsthusevidencethattheLS/HSstate
1. All Co ions in LS state. is stabilized upon rhodium doping. The driving force of
this stabilization is the elastic energy. The ionic radius
2. All Co ions in IS state.
of Co3+ strongly depends on the spin state. This is con-
3. CoinLSandHSstatein1:1ratio,withthe6near- firmed by GGA+U structure optimization, which gives
estCoaroundRhinLSstate,seeFig.4adisplaying Co-O bond lengths 1.92 ˚A and 1.97 ˚A for LS and HS
thenearestneighbors(CoLS)andthenextnearest states, respectively. The optimized Rh-O bond length is
neighbors (Co HS). around2.02˚A.InsertingRhtoComatrixthereforebrings
about an increase of elastic energy, which is relaxed by
4. CoinLSandHSstatein1:1ratio,withthe6near-
keeping the nearest Co neighbors in LS state and excit-
est Co around Rh in HS state, see Fig. 4b.
ing the second nearest Co neighbors do HS state, cre-
Spin moment of Rh was allowed to vary, nevertheless it ating locally ordered cluster of large cations (Rh3+ and
alwaysconvergedtoLSvalue. Cellvolumeswereadopted HSCo3+)andsmallcations(LSCo3+), seeFig.4a. The
tovaluesexpectedforvariousdopingbyinterpolationbe- alternativeLS+HSstateconfiguration,seeFig.4b,isev-
tweenLaCoO andLaRhO . Atompositionsdetermined idently less favorable regarding the elastic energy, as it
3 3
at room temperature were used as the initial values and was confirmed by the calculations.
allrefinablecoordinateswereoptimized. Thecellvolume Calculation for the x=0.5 within the La4Co2Rh2O12
was also decreased by 1-2% to simulate the cell contrac- supercell suggests that the LS Co3+ state is stable for
tion with temperature (T 0 K). T 0, energies of HS and LS state become comparable
→ →
Fig. 5 shows a comparison of the calculated energies at around the room temperature, and HS state is stabi-
for the LS/HS configuration and homogenous IS phase lizedatelevatedtemperatures,i.e. uponfurtherincrease
relative to the LS phase, depending on the perovskite of the unit cell volume.
cell volumes of LaCoO and LaCo Rh O . Thecalculationsimulatingtherhodium-richlimitx
3 15/16 1/16 3
→
ThecellvolumeofLaCoO at5Kisabout2%smaller 1, i.e. using the La CoRh O supercell (see Fig. 4c),
3 16 15 48
compared to room temperature [19], however only 1% shows that in this case the HS state of Co is more stable
K. Kn´ıˇzek et al., Stabilization of the high-spin state of Co3+ in LaCo1−xRhxO3. 6
Stabilisation energy (meV / f.u.)relative to LS state --244200000 Al Co0.6Ga Rh 0.7 I0n.8 DOS (eV cell)S (eV f.u.) --6336-202400000 Ctoo(tLaSl)
Ionic radius rM (Å) DO -4
4
FIG. 6: (Color online) Stabilization energy of LS/HS rel- u.) 2 Rh
AarMtli,veG(tathoeanLadSveIrcnao)gnefifogfruorrxaCt=ioon31+/o1fi6nLinLaCSdoea1p−nedxnMdHexSnOc3estao(Mtneio=isniuCcsoer,addRifuohrs, OS (eV f. -20
r ), by GGA+U calculation for room-temperature cell vol- D -4
Co
umeVRT((cid:3)), V/VRT =99% (◦) and V/VRT =98% (△). 4
u.) 2 O
eV f. 0
thanLSstate. Thisresultcanbeunderstoodconsidering S ( -2
thatisolatedLSCo3+ in the lattice ofmuchlargerRh3+ DO -4
ionswouldrepresentanelasticdefectoflargeenergycost.
-4 -2 0 2
The results of GGA+U calculations are in agreement
Energy (eV)
with magnetic susceptibility analysis. For small dop-
ing the Rh atoms stabilize the HS states of cobalt at
FIG. 7: Density of states for LS Co configuration of
the next-nearestsites due to the elastic energy,therefore
LaCo15/16Rh1/16O3.
the low-temperature transition to pure LS state is sup-
pressed. But at the same time, Rh ions actually occupy
places which would be otherwise available for HS Co3+,
thus the saturated number of Co in HS state is lowered
witAhctchoerddinopgintogaLnSd-LnSu/mHbSe-rISofmCoodienl,LtShsetahtieghistreemtapineerad-. cell) 3600 total
ture spin transition is based on formation of uniform IS eV 0
phase. Thus the destabilization of the IS state by Rh S ( -30
O
doping (Fig. 5) is in agreement with suppression of this D -60
transition evidenced by magnetic data. 4 Co(HS)
Inordertoinvestigatetherelativeroleofelasticenergy u.) 2 Co(LS)
associated with larger Rh3+ size and purely electronic eV f. 0
effects, additional simulations have been performed for S ( -2
O
x = 1/16 doping of other isovalent dopants with differ- D -4
ent ionic radii - Al3+ (r = 0.535), Ga3+ (r = 0.62)
Al Ga 4
and In3+ (rIn = 0.80). Cell volumes were adopted to u.) 2 Rh
expectedvaluesforx=1/16dopingbyinterpolationbe- eV f. 0
tween LaCoO3 and respective LaMO3. Atom positions S ( -2
determinedatroomtemperature wereusedas the initial O
D -4
values and allrefinable coordinates were optimized. The
4
ccseeenlllltevcdoonliuntmrFaecigtwi.oa6ns. wIatlistiohssdteeeemcnrpetahesraeatdttuhbreey.s1tTa-2bh%ielizrtaoetsiusoilnmtseunalareteregpytrhoee-f eV f.u.) 02 O
the LS/HS configuration with respect to pure LS phase S ( -2
O
is proportional to the ionic radius of the doping cation D -4
in the Al, Ga and In doped systems, but in the case of -4 -2 0 2
Rh there is an additional energy gain, obviously due to Energy (eV)
electrons of unfilled shell 4d and their covalency.
Total and atom projected density of states (DOS) of FIG. 8: (Color online) Density of states for LS/HS Co con-
LaCo1−xRhxO3 (x = 1/16) for LS spin configuration is figuration of LaCo15/16Rh1/16O3.
displayed in Fig. 7. The character of DOS is insulating
K. Kn´ıˇzek et al., Stabilization of the high-spin state of Co3+ in LaCo1−xRhxO3. 7
withagapabout0.8eV.Thenarrowstates0 0.25eVbe- that the transition metal ions in the LaCo1−xRhxO3
−
lowE correspondtoRh(t ),whereasCo(t )andO(p) solid solutions remain in trivalent states. The GGA+U
F 2g 2g
states are situated lower in energy between 0.25 1 eV. calculations suggest that the elastic coupling of the
−
The states just above Fermi level are mainly of Co char- nearest and next-nearest cobalt neighbors of the in-
acter. DOS of LS/HS spin configuration is displayed in serted Rh dopant is important in stabilization of the
Fig. 8. The insulating character of DOS is retained with spin-state configurations. The Rh3+ ions are always in
aslightlydecreasedgapabout0.5eV.The narrowstates the non-magnetic LS configuration, while the Co3+ ions
correspondingtoRh(t )arealsowithintheenergyrange may vary, depending on composition and temperature,
2g
0 0.25 eV below E , and the states of Co-LS(t ) and between the non-magnetic LS and paramagnetic HS lo-
F 2g
−
O(p)couldbefoundlowerinenergybetween0.25 1eV. cal configurations. In distinction to pure LaCoO , in
3
A sharp peak above Fermi level belongs to Co-H−S(t ) whichHSCo3+ statesonlyappearatincreasedtempera-
2g
band. ture througha thermalactivationprocess,the Rhdoped
Itwasassumedinthepreviousdiscussion,thatthereis systems starting from x = 0.04 exhibit certain number
nochargetransferbetweenCo3+ andRh3+. Toestimate of stable HS Co3+ species already in the ground state
quantitatively charge equilibria in our GGA+U calcula- (up to 18% for x = 0.2). The HS population increases
tions we use Atoms InMolecule (AIM) concept ofBader graduallywithincreasingtemperatureandreachesasat-
[21]. Inthisapproachtheunitcellisdividedintoregions uration above 150 K, similarly to what is observed in
by surfaces that run through the minima in the charge undoped LaCoO . The resulting phases, based on the
3
density. The charge on a given site is obtained by inte- LS/HSdisproportionatedcobaltsites,persistatleastup
grating the electronic density within these regions. The toroomtemperature. Agradualtransformationtoauni-
advantage of this method is that the analysis is based formstatewithmetallic-likeconductivityisevidencedat
solely on the charge density, so it is independent on the elevated temperatures for samples with x<0.5.
basis set and atomic spheres used.
The ionic charges calculated by the AIM method dif-
The main characteristics of the room-temperature
fer from the formal valencies due to hybridization be-
phase of LaCoO is the LS/HS population close to the
tween cations and oxygen. The ratio of the AIM and 3
1:1 ratio. This can be understood as a result of cooper-
ideal chargemay be regardedas the degree of hybridiza-
ative effects, which prefer a regular ordering of smaller
tion. Therefore, a different AIM charge of cations with
LS Co3+ ions and larger HS Co3+. Nevertheless, only
nominally equal valencies can be solely caused by a dif-
short-rangeLS/HScorrelationsareanticipatedconsider-
ferent degree of hybridization with oxygen, and cannot
ingthe entropyreasons. Similarorderingtendenciesalso
be directly considered as a charge transfer between the
exist in the doped systems but the mechanism is differ-
cations. Instead, we compare calculated AIM charge of
ent. The primary HS population arises from the elastic
Co in undoped and doped structures. The AIM charges
strain associatedwith presence of immobile Rh dopants.
of cobalt in LaCoO are within 1.40 1.64 depending
3
− The strain is released by stabilization of LS states on
on the its actual spin state, since the hybridization with
the nearest cobalt neighbors and HS states on the next
oxygen is predominantly based on e orbitals and thus
g nearestones. TheseclustersgrowasadditionalHSstates
depends strongly on their occupation, which is different
arethermallyactivatedandtendtoasaturationinwhich
for each spin state. Essentially the same AIM charges
smallLSCo3+ ionsalternatewithHSCo3+ andLSRh3+
of Co are obtained for doped structure LaCo1−xMxO3 ionsoflargersize. Thestabilityofsucharrangementcan
(x = 1/16), in spite of the various values calculated for
berelatedtotwofactors. Thefirstoneistheknownprop-
the substituting cations M, namely Rh (1.33), Al (1.98),
′
ertyofdoubleperovskitestructureA BB O toadaptto
Ga (1.94) and In (1.88). It means that the difference 2 6
′
very different radii of B and B cations. This is a kind
between AIM charge of nominally Co3+ and Rh3+ in
ofelastic energyoptimization,whichiseffective notonly
LaCo1−xRhxO3 solelyaccountforthe differentdegreeof fortherhodiumbutalsoforotherlargeisovalentdopants
hybridization of Rh and Co, but not present any ground
likeIn. Thesecondmechanismisofpurelyelectronicori-
for the charge transfer between Co and Rh.
ginandisassociatedwithincompletecharacterofthe3d
and 4d shells of Co and Rh ions.
V. CONCLUSION
Acknowledgments. This work was supported by
The present experiments supported by GGA+U elec- Project No. 202/09/0421 of the Grant Agency of the
tronic structure calculations provide strong arguments Czech Republic.
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