Theoretical study of doped-Tl$_{2}$Mn$_{2}$O$_{7}$ and Tl$_{2}$Mn$_{2}$O$_{7}$ under pressure

0.46 MB·English

by  Molly De Raychaudhury

Theoretical study of doped-Tl Mn O and Tl Mn O under pressure
2 2 7 2 2 7
Molly De Raychaudhury1, T. Saha-Dasgupta1 and D. D. Sarma2,3,∗
1 S.N. Bose National Centre for Basic Sciences, Kolkata 700098, India
7 2 Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India and
0 3 Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-560012, India
0 (Dated: February 6, 2008)
2
Usingfirst-principlesdensityfunctionalbasedcalculations,westudytheeffectofdopingandpres-
n
sure in manganese based pyrochlore compound,Tl2Mn2O7 that exhibits colossal magneto-resistive
a
behavior. The theoretical study is motivated by the counter-intuitive experimental observation of
J
suppression of ferromagnetic transition temperature upon application of pressure and its enhance-
2
ment upon substitution of Mn by moderate amount of nonmagnetic Sb ion. We also attempt to

resolve theissue related to crystal structurechanges that may occur upon application of pressure.
]
i
c
s
I. INTRODUCTION In the present paper, we give a detail account of the
-
l doping effect and the pressure effect from the electronic
r
t structurepointofview,whichlendfurthersupporttothe
m
Manganese-based pyrochlore compounds such as existence of the proposed kinetic energy driven mech-
t. Tl2Mn2O7,formaninterestingclassofcompoundswhich anism in these compounds. While the changes that
a despite having similar colossal magneto-resistive (CMR) happen in the crystal structure upon doping is clear,
m
effect exhibit markedly different features compared to the situation is rather ambiguous in case of application
- that of manganites. In contrast to manganites, these of pressure. The initial measurement hinted to a de-
d
n compoundsarenotmixed-valent,donothaveanyappre- crease in Mn-O-Mn bond angle6,14 alongwith the com-
o ciableJahn-Tellerdistortion1 andseeminglyshowmetal- pression of Mn-O bondlength. However the subsequent
c lic behavior2 both below and above the magnetic transi- measurement15 indicated an increase in Mn-O-Mn bond
[ tion temperature T (≈ 140K). Concerningthe metallic angle which was used in terms of super exchange mech-
c
2 behavioraboveTc though,itisnottotallyclearwhether anism to explain the decrease in Tc. In view of these
v itisagoodmetalormorelikeabadmetaloraninsulator- conflicting claims, we also take the opportunity to theo-
5 like compound which arises due to difficulties related to reticallyaddresstheeffectofpressureonthestructureof
4 sample preparation and defects present in the paramag- Tl2Mn2O7 andits implication onmagnetismby detailed
2 netic phase. Though the original data by Shimakawa electronicstructure calculationstogether withstructural
2
et. al.2 suggests the metallic behavior above T , the relaxations under pressure.
1 c
optical conductivity data3 and and photoemission and Therestofthepaperisorganizedinthefollowingway.
6
0 x-ray absorption4 near edge spectroscopy point towards Section II deals with various methodologies that have
/ an insulator-like behavior in the paramagnetic regime. been employed to compute the crystallographic struc-
t
a These non-manganite like features rule out the gener- ture (in case of Tl2Mn2O7 under pressure) and to com-
m ally applicable double exchange mechanism or polaronic pute and analyze the subsequent electronic structure of
- mechanism as the driving mechanism of ferromagnetism Tl2Mn2O7 under doping and pressure. In section III,
d in this class of compound, and remained a mystery for we present our results. This section is divided into sev-
n quite some time. In absence of double exchange mech- eralsubsections. InsectionIIIA,the electronicstructure
o
c anism, a strong contestant for the driving mechanism is of pristine Tl2Mn2O7 is presented and the proposed ki-
: the Mn-O-Mn mediated superexchange mechanism, par- netic energy driven mechanism is introduced as a refer-
v ticularly since Mn-O-Mn form an angle5 of 133o, signif- ence,whichwillformthebasisofdiscussioninthefollow-
i
X icantly smaller than 180o. This is however contradicted ing. SectionIIIBisdevotedtoTl2Mn2O7 underpressure
r by the experimental findings that the ferromagnetic Tc ,whilesectionIIICisdevotedtoSb-dopedTl2Mn2O7. Fi-
a gets suppressed by application of pressure6 and gets en- nally, we conclude the paper with a summary presented
hanced by moderate amount of introduction of nonmag- in section IV.
netic ion like Sb in place of Mn7. Employing N-th or-
der muffin tin orbital (MTO) based NMTO-downfolding
technique8, we have recently established9 that driving II. METHODOLOGY
mechanismofferromagnetisminthis classofcompounds
is neither super-exchange or double-exchange, nor any We have investigated the electronic structure of
exotic mechanism with nearest neighbor (NN) antifer- pure Tl Mn O , Tl Mn Sb O and Tl Mn O under
2 2 7 2 2−x x 7 2 2 7
romagnetic (AFM) coupling dominated by long-ranged pressure by the tight-binding linear muffin-tin orbital
ferromagnetic (FM) interaction10, but a kinetic energy (LMTO)16 method, computed within the framework of
assisted mechanism similar to that of double perovskite the localspindensity approximation(LSDA) ofthe den-
compounds like Sr FeMoO , Sr FeReO 11,12 and Mn- sity functional theory (DFT). The employed basis set,
2 6 2 6
doped GaAs13. consisted of Tl-6s, 6p and 5d states, Mn-4s, 4p and 3d
2
states,and O-2sand2p states. Three differentclassesof and S = 3. k is the Boltzman constant and z ,z ,z
2 B 1 2 3
empty spheres were used to fill up the space. The self- are the number of NN, 2NN and 3NN Mn pairs. For un-
consistent calculations were performed on a BZ mesh of dopedTl Mn O ,z =6,z =12andz =12. However,
2 2 7 1 2 3
12×12×12. thesenumberschangeincaseofdopedcalculationswhere
The computed band structures were analyzed and in- some of the Mn atoms gets replacedby the nonmagnetic
terpreted in terms of NMTO-downfolding technique8. Sbion andthereforedo not contribute inthe calculation
The NMTO technique, introduced and implemented in of magnetic energy. The application of mean-field the-
recent years, goes beyond the scope of standard LMTO ory is naturally expected to overestimate the T . Use of
c
techniquebydefininganenergeticallyaccuratebasiswith Monte Carlo simulation17 or Green Function method18
consistent description throughout the space involving can give better estimates and agreements with experi-
both the MT spheres and the interstitial. As important mentally measured values. One needs to keep this in
feature of this technique is the energy-selective down- mind when comparisons are being made with the mea-
folding procedure where one integrates out degrees of sured T in the following sections.
c
freedom and keeps only few degrees of freedom active Tl Mn O occurs in cubic, face-centered lattice with
2 2 7
to define a few-orbital, low-energy Hamiltonian. The ef- Fd−3m space group and two formula unit in the cell.5
fective NMTOs defining such Hamiltonian, serve as the There are two types of oxygen, O’ and O. While O oxy-
Wannier or Wannier-like function corresponding to the gen provide the octahedral surrounding of the Mn atom
selected low-energy bands. which corner share to give rise to a geometry of a closed
For the calculation of the exchange interaction ringorcage,O’atomsformnearestneighborbonds with
strengths, J, a supercell involving a sixteen Mn atoms TlgivingrisetoTl2O’complexrunningthroughthecage
was constructedwhichamounts to enlargingthe original like geometry as shown in left panel of Fig. 1. The
unit cell by four times. This was achieved by replacing structuralparametersforthepristineTl2Mn2O7,andSb-
theoriginalfacecenteredcubic(FCC)latticebythesim- doped Tl2Mn2O7 have been taken as the experimentally
ple cubic lattice with four times as many atoms as that determined structure published in literature7,19. How-
inFCC.ThebasicstructuralunitofMnsublatticeisthe ever, as mentioned already, the structural information
Mn4 tetrahedra which share corners to form an infinite for Tl2Mn2O7 under pressure is somewhat controversial
3D lattice. We calculated the LSDA total energies by whichcallsforstructuraloptimization. Forthispurpose,
consideringdifferentmagneticconfigurationsofthis sub- wehaveadoptedthepseudopotentialmethod20 asimple-
lattice. Intotal,sixspinconfigurationshavebeenchosen. mentedintheVASP21code. Wehaveemployedthepseu-
One of the six configurations was FM and the other five dopotentialsgeneratedbytheprojector-augmentedwave
were AFM. The details of the spin configurationschosen (PAW)22 method. Wavefunctionshavebeenexpandedin
are as given in Table I in ref9. The total energies are terms of plane waves with a cut off energy of 400 eV.
then mapped on to an effective Heisenberg Hamiltonian A k-mesh of 6×6×6 was employed to perform the self-
formed by the Mn+4 spins. The Hamiltonian considered consistent calculations. In Tl2Mn2O7, Tl, Mn, O’ and
till the 3NN(third nearest neighbor) interactions is: O atoms occupy the Wyckoff positions, 16d, 16c,8b and
48frespectively. Amongtheseonlythepositionsgivenby
H =J S .S +J S .S +J S .S (1) 48f contain the internal parameter,u. This parameter u
1 i j 2 i j 3 i j
definesthe6 Mn-O-Mn(seerightpanelofFig.1). Asuin-
nn 2nn 3nn
X X X
creases, the 6 Mn-O-Mn decreases and vice versa. When
whereSi denotedthespin-3/2operatorcorrespondingto pressure is applied, it needs to be investigated whether
theMn+4 spinsatthesitei,andJ1,J2 andJ3denotethe the u parameter also varies along with the reduction in
NN, 2NN(second nearest neighbor) and 3NN magnetic the bondlengths. If at all it changes, it has to be ascer-
exchange interaction strengths. Since we have restricted tained in what way it does so. In our calculation, the
ourselvestoonlyfiveAFMconfigurationsamongstmany O position is relaxed by varying u, in order to find out
possible AFM configurations, we computed seven differ- the variation of total energy with angle formed between
entestimatesoftheseJ’salongwiththeirstandarddevia- Mn, O and Mn atoms. In orderto obtainthe theoretical
tionsemployingsetofthreeenergydifferenceschosenout ground state, cohesive properties and estimate the pres-
of total five different energy differences. This limitation sure, Murnaghan23 equation of state has been employed
can be overcome by taking as many AFM spin configu- tofittheLSDAtotalenergies. TheMurnaghanequation
rations as practically possible. The mean-field estimate of state is given by
of T is given by
c
′
Tcmf = S(S3k+1)J0 (2) E(V)=E0+ BB0.0′V "(VB00/′V−)1B0 +1#− BB0′0.−V01 (4)
B
whereV is the equilibriumvolume,B is the bulk mod-
where J , is the net effective magnetic exchange interac- 0 0
0 ulus and is given by B = −V(δP/δV) evaluated at
tion, given by 0 T
′
volume V . B is the pressure derivative of B also eval-
0 0 0
′
J =z J +z J +z J (3) uated at volume V . B provides a measure of stiffness
0 1 1 2 2 3 3 0 0
3
Mn
Mn
u = 0.3 2 4 5
u = 0.3 5
Tl
Tl O
O’
O
FIG.1: (color on-line)Left panel: TheTl2Mn2O7 structureconsisting oftheringformed byMnO6 octahedrawith Tl-O’rods
passingthroughtheholesoftherings. Rightpanel: Backboneofthestructurerealizedbytheringlikestructureformedbythe
Mn-O-Mnnetwork (theTl-O’rod network is not shown for clarity). Gold, green and black orcyan spheresdenotetheTl, Mn
and O atoms. Black and cyan spheres correspond to oxygen (O) atoms with two different oxygen (O) position parameter u.
of the material upon increasing pressure. Typical val- crossing the Fermi level, E , as seen in lower, left panel
F
′
ues for the parameter B are between 4 and 7. Pressure, of Fig.2. This hints to a large spin-splitting at the Tl
0
P, corresponding to volume, V, occupied by a cell of a site. This is unusual in the sense, one would normally
particular lattice parameter is given by expect Tl to be essentially nonmagnetic with tiny spin
splitting. This unusual feature plays the key role in pro-
P(V)= B0 (V /V)B0′ −1 (5) viding the understanding of the driving mechanism of
B′ 0 ferromagnetism in Tl Mn O . This has been explained
0 (cid:20) (cid:21) 2 2 7
in detail in ref9. As has been shown in ref9, the unhy-
bridizedeffectiveTl-O’levelispositionedinbetweenthe
III. RESULTS spin-splitMnt statesandonturning onthe hybridiza-
2g
tion, it induces a renormalized spin-splitting within the
A. FM Electronic Structure of Pristine Tl2Mn2O7 Tl-O’levelwhichis directedinaoppositewaycompared
and the Underlying Mechanism tothe spin-splittingatthe Mnsite. Thishappens dueto
pushing up of the Tl-O’ spin-up state and pushing down
TheLSDAelectronicstructureofferromagneticallyor- of the Tl-O’ spin-down states, driven by coupling with
dered Tl2Mn2O7, computed with TB-LMTO method is theMnt2g statesofthesamesymmetry. Theenergygain
shown in Fig.2. This figure shows both the band struc- contributed by this hybridization induced negative spin
ture and the orbital projected density of states (DOS). polarizationoftheotherwisenonmagneticelement,isthe
Consistent with the nominal valence of O2− and Mn4+, central concept in this novel mechanism. This mecha-
oxygen dominated states are totally occupied, while the nism ensures a specific spin orientation between the lo-
crystalfieldsplitMnt2g statesareoccupiedinthemajor- calizedMnt2g spinsandthemobilecarrierformedbythe
ity spin channel and close to empty in the minority spin hybridized renormalized state, which in turn aligns the
channel. Mn e states consistent with 3d3 configuration spins in Mn sublattice. This is a generalmechanismand
g
ofMn,remainemptyinboththespinchannels. Tlbands, found to be operative in case of a number of compounds
consistentwithTl3+ nominalvalencealsoremainalmost likeSr2FeMoO6,Sr2FeReO611,12,Mn-dopedGaAs13 and
empty. However,interestinglyinthemajorityspinchan- CuCr2S425 etc.
nel,the Tl-6sstate mixedwith O’-2pstatesoverlapwith Inthefollowingsubsections,wewillpresentadetailac-
Mn e manifold spanning an energy range of about 2-4 count of the changes in the electronic structure and the
g
eV24, while in the minority spin channel, they overlap variationinT ofTl Mn O withdopingandunderpres-
c 2 2 7
with nearly empty Mn t dominated states, which give sure. We will argue that the counter-intuitive variation
2g
risetohighlydispersivebandinbottomofthismanifold, in T has its origin in the modified electronic structure
c
4
purpose, we have carried out a series of structural op-
6
timization calculations with pseudopotential method20.
At first the cohesive properties were calculated within
4 Mn−e LSDA. Following the recent claim27 that application of
+ g
on-site U can also influence the cohesive properties of
Tl−6s−
2 transition metal oxides, we have repeated our calcula-
O’−2p
V) tions also with LSDA+U functional.
e
y ( 0
erg Mn−t2 g -158 Fitted (EOS) - LSDA -155
n
E LSDA
-2
Fitted (EOS) -LSDA+U
LSDA+U
O−2p -158.5 -155.5
-4 ) )
V V
e e
( (
y y
-6 rg rg
e -159 -156 e
n n
E E
-8 al al
6 ot ot
T T
Mn−e
-159.5 -156.5
+ g
4 Tl−6s−
O’−2p
2 -160 -157
900 950 1000 1050
y (eV) 0 Mn−t2 g Volume of c e l l ( A 0 3 )
g
r
ne FIG. 3: Total energy vs. volume of the unitcell calculations
E
-2 within LSDA and LSDA+U. The symbols denote the DFT
total energies and the solid and dashed lines depict the total
energies obtained from fittingwith Murnaghan23 equation of
O−2p
-4 state (EOS).
-6
LSDA total energy vs volume calculation, shown in
Fig.3, has a minimum corresponding to lattice constant
-8 L Γ X W L K Γ 5 10 15 20 of9.881˚A. Consideringtheexperimentalvalueofthelat-
DOS (States/eV) tice constant is 9.892 ˚A, this gives a deviation of about
0.1 %, which is within the limit of LSDA overbinding.
FIG. 2: (color on-line) Left panels show the spin-polarized The value of the bulk modulus, obtained by fitting the
band structure computed within LSDA for Tl2Mn2O7 . The total energy vs volume curve with Murnagahan equa-
zerooftheenergyissetattheLSDAFermienergy,EF. Right tion of state23 is 230.6 GPa, which is of the same order
panels give the spin-polarized total (black), Tl-6s (red), Mn- as the experimentally measured value of ≈200 GPa in
3d (green), O-2p(orange) and O’-2p(blue) densityof states. Tl Cd Mn O 15. B′ is +4.84,muchhigher than that
Upper and the lower figures correspond to the majority and 1.8 0.2 2 7 0
in Cd doped Tl Mn O but within the expected limit.
minority spin contributions respectively in both the panels. 2 2 7
Applying anon-siteCoulombinteractionofU=2eVand
Bars on the right signify the energy range for which various
J=0.7eV onthe Mn site leads to a slightly better agree-
characters dominate.
ment with the experimental values. The lattice param-
eter changes to 9.888 ˚A, B and B′ remain unaltered.
0 0
In view of the slightly improved results of LSDA+U, we
and follows naturally from the framework of proposed
′
have used the B and B as estimated by LSDA+U cal-
hybridization induced mechanism of ferromagnetism as 0 0
was established in ref9 and reviewed in the above. culations to compute the pressure as given by Eq.(5).
Tillnowwehaveconsideredthe experimental6 Mn-O-
Mnastheoneforthetheoreticalgroundstate. Oneneeds
torelaxthisangleinordertoobtainthetruetheoretically
B. Tl2Mn2O7 under pressure predictedgroundstate. Theco-ordinateofOatominthe
basisisgivenby(u,.125,.125). Theuparameterwillpush
As explained before, to investigate Tl Mn O under O atomin or out depending on its value, thereby chang-
2 2 7
pressure one needs to first settle the issues related to ingtheangleformedbetweenMn,OandMnatoms. The
crystalstructure. Tobeprecise,doesappliedpressurein- u parameter is relaxed in the subsequent calculations,
creaseordecreaseornotalterthe 6 Mn-O-Mn? Forthis andtheLSDA(for9.881˚A)andLSDA+Utotalenergies
5
-154
LDA LSDA+U EXPT.
P= Ambient
a(˚A) 9.881 9.888 9.892 P= 16.28 GPa
-154
u 0.3214 0.3227 0.3254 P= 3.04 GPa
Mn-O (˚A) 1.886 1.890 1.901
6 Mn−O−Mn(deg) 136.01 135.29 133.8 ) )
V -155V
B0 (GPa) 230.6 230.7 (e (e
′ y -155 y
B0 +4.84 +4.85 rg rg
e e
n n
E E
TTAl2BMLnE2OI7: CwailtchuinlatLedSDgArouanndd sLtSatDeAs+trUuctcuormalpapraerdamweittehrsthoef tal tal
experimental5 data at ambient condition. To -156To
-156
(for9.888˚A)arecomputedvaryingtheuparameter. The
minimum in the E vs u curve (see Fig.4) is obtained for
u=0.3214and0.3227respectively. The6 Mn-O-Mninthe -157 -157
00..3311 00..3322 00..3333 00..3344
groundstateobtainedwithinLSDAandLSDA+Uframe- Oxygen position parameter u
work are given in Table I along with the corresponding
experimental values. Slightly better results are obtained FIG.5: Totalenergyvsu,i. e. relaxationoftheOxygen(O)
for the LSDA+U calculations, a trend already observed positionparameteruatambientconditionandunderpressure
incalculationforequilibriumlatticeconstant. Theresult of 3.04 and 16.28 GPa within LSDA+U in Tl2Mn2O7. The
matchwithexperimentalvaluesuptothe seconddecimal symbolsaretheDFTtotalenergiesandthesolid,dashedand
point for u and within 1.5o for Mn-O-Mn angle. dashed-dottedlines are cubic spline interpolated.
-158 -155 AMBIENT 3.04 GPa 16.28 GPa
LSDA u 0.3227 0.3230 0.3234
LSDA+U Mn-O(˚A) 1.890 1.883 1.854
-158.5 -155.5 6 Mn−O−Mn (deg) 135.29 135.18 134.90
) )
V V
e e
( ( TABLE II: Structural parameters obtained within LSDA+U
y y
g g atambientandtwodifferentpressuresuponrelaxationofthe
r r
ne -159 -156 ne Oxygen(O)position parameter u in Tl2Mn2O7.
E E
al al
t t
o o
T T establishthat,regardlessofkindofDFT oneisusing,on
-159.5 -156.5
applying pressure 6 Mn-O-Mn does not increase rather
decreases though almost insignificantly. The major ef-
fects comes from reduction in the bondlengths. In the
-160 -157 following calculations, we have therefore kept the 6 Mn-
0.31 0.315 0.32 0.325 0.33 0.335
Oxygen position parameter u O-Mn unchanged upon application of pressure.
WehavecarriedoutLSDAtotalenergycalculationsfor
FIG.4: Relaxation of theOxygen-Oposition parameter uat various spin arrangements of Mn atoms as explained in
ambientconditionwithinLSDAandLSDA+UinTl2Mn2O7. section II. The relative LSDA total energies, as given in
The symbols are the DFT total energies and the solid and TableIIIaremappedontoEq. (1)inordertoextractthe
dashed lines are cubic spline interpolated. J’s. Themagneticexchangeinteractionstrengthsarecal-
culated and shown in Table IV for almost 2 % reduction
Having established the ground state, in the next step in experimental lattice parameter, amounting to a pres-
we relax the O position for lattice parameters a=9.846 sure of 16.28 GPa. Considering pressure of 16.28 GPa,
and9.69˚A(LSDA+U)whichamounttoapplyingapres- we observe a substantial decrease in the NN FM inter-
sureof3.04GPaand16.28GPa. Thiswillclarifywhether action. The 2 and 3 NN interactions remain almost the
theMn-O-Mnanglealsochangeswiththedecreaseinthe same. Thisleadstoamean-fieldT ofabout140K,lead-
c
interatomic distances. The minimum obtained from the ing to a decrease of about 41 K. The gradient is about
totalenergyvs. uplots,ashowninFig. 5arelistedinTa- -2.5 K/GPa. The gradient calculated from another set
ble II. We findthat onapplicationofpressure,the 6 Mn- of calculations at 3.04 GPa is about -2.3 K/GPa. One
O-Mn reduces insignificantly, by about 0.1o and 0.4o can approximate a linear relation between T and ap-
c
for pressure of 3.04 GPa and 16.28 GPa respectively. A plied pressure. Thus the average gradient is about -2.4
reduction of the angle by about 0.60 occurs for the same K/GPa. This is not an unreasonable estimate consider-
applied pressure (16.28 GPa) within LSDA. We thereby ing the mean-field overestimation. The ratio of exact T
c
6
∆E(meV) 20
Mn − t2g Mn − eg
Normal 3.04 GPa 16.28 GPa +
FM 0 0 0 Tl−s + O’−p Tl−s + O’−p
AFM1 9.55 9.18 7.36
O − p
AFM2 13.98 14.17 13.05 10
AFM3 12.24 11.49 8.82
AFM4 17.59 22.5 16.24
AFM5 18.39 17.7 14.04
)
V
TABLEIII:RelativeLSDAenergiesperMnioninmeVinFM e 0
and five AFM spin configurations for Tl2Mn2O7 at normal, s /
3.04GPaand16.28GPapressures. Allenergiesareconverged te
a
upto0.01 meV perMn ion. St
(
S
O -10
andTmf isestimatedas0.79and0.81forBCCandFCC D O − p
c
Tl−s + O’−p
lattice with coordination 8 and 12 respectively. Consid-
Mn − eg
ering the average coordination of 10 for Mn sublattice
Energy (eV)
ibpneerTaimbl2oeMnuttna2-l1Ov.97a,luKoe/nsG,ewPwhao.iuchlTdhaeirsxepi-se1c.a6tbKtiht/eGlagPrrgaae6driaetnnhdtanianbthoTuectetx-o1- -20 States/eV)-0.-10.4 -0.2 0 0.2 0.4 Mn +− t2g
K/GPa15 . A plausible explanation for this somewhat S (
O Tl−s + O’−p
overestimationmay be due to computational limitations D-0.2
imposed by the number of spin configurations. A better
-30
estimate of the gradient might have been reached had -8 -6 -4 -2 0 2 4 6
all the possible spin configurations been considered for Energy (eV)
calculation of the J’s. Therefore one can conclude that
within the limitationofourmethod, we haveestablished FIG.6: (coloron-line)Spin-polarizeddensityofstatesatam-
the trend in ferromagnetism of Tl Mn O with applied bientcondition(black)and16.28GPa(red)calculatedwithin
2 2 7
pressure correctly. LSDA for Tl2Mn2O7. The upper (lower) panel corresponds
to the majority (minority) spin. The negative of density of
states has been plotted in the lower panel for clarity. Inset
Pressure Appl. J1 J2 J3 J0 Tmc f shows minority spin channel density of states for the energy
(GPa) (meV) (meV) (meV) (meV) (K) region nearFermilevelat ambient and16.28 GPa. Thesolid
0 -2.52 -0.11 +0.33 12.48 181 and dashed lines show the contribution from Mn - 3d and
Tl-6s+O’-2p states respectively within LSDA.
3.04 -2.48 -0.16 +0.40 12.06 174
16.28 -1.99 -0.16 +0.35 9.66 140
TABLE IV: NN, 2NN, 3NN and effective exchange interac- pressure. Since the underlying mechanism of ferromag-
tion strengths and mean-field Curie Temperature calculated netism is based on the Mn-Tl-O’ hybridization, weaken-
withinLSDAatambientconditionandat3.04and16.28GPa ingofsuchhybridizationwouldcauseadecreaseinTc as
for Tl2Mn2O7. supportedbythedetailcalculationpresentedabove. The
changeinthehybridizationisproportionaltothechange
In Fig.6 we show the density of states of Tl Mn O in the hopping interaction strength, t and inversely to
2 2 7
under 16.28 GPa pressure alongwith that of Tl Mn O the change in the energy level separation ∆. Applica-
2 2 7
under ambient pressure for comparison. Upon applica- tion of pressure causes shortening of bondlength, hence
tionofpressure,thebondlengthsshortenwhichenhances one would expect hopping to increase and in turn the
theMn-OandTl-O’interactionandasaresultnetband- hybridization to increase, opposite to what is observed
width expands and t -e splitting enhances. However in the calculation. For this we performed the NMTO-
2g g
the key effect is seen in the inset, where we show the downfolding calculation keeping Mn-3d, Tl-6s and O-2p
Mn-d and Tl-s projected density of states in an energy degrees of freedom active and integrating out the rest,
windowclosetoE insolidanddashedlinesrespectively. including O’ degrees of freedom to define a Tl-O’ effec-
F
They are shown in two different colors,corresponding to tive level. The real-space representation of that down-
ambient and 16.28 GPa pressure. We notice that the folded Hamiltonian in the NMTO-Wannier function ba-
relative proportionof Tl-O’in the hybridized, dispersive sis for Tl Mn O under application of 16.28 GPa pres-
2 2 7
band has reduced significantly upon application of pres- sure shows the Tl-O’ effective level to shift down by 0.3
sure. It has reduced from 45 % in case of ambient pres- eV compared to that under ambient pressure. This in-
sureto36%incaseof16.28GPapressure. Thisindicates creases the ∆ and substantially reduces the Tl-O’-Mn
reductionof Mn-Tl-O’hybridizationupon applicationof hybridization, substantial enough to compensate the in-
7
crease in t hopping interaction between Mn-t and atoms in the unit cell for two cases. In one case, two Sb
sdσ 2g
the effective Tl-s orbital and to produce a net negative atoms were chosen as NN pairs while in the second case
contribution to the hybridization.This is an interesting, they have been chosen as 3NN pairs. The respective co-
counter-intuitive situation which can only be unraveled ordinationnumbersat12.5%dopingare5.14,10.28and
byadetailanalysisoftheunderlyingelectronicstructure 10.86for 3NN substitution and 5.28, 10.28and 10.28 for
as has been done in the present study. NN substitution. In all the three cases, i.e for x=0.125,
0.25 (NN) and 0.25 (3NN), the ground state is found to
be FM.
C. Sb-doped Tl2Mn2O7
doping J1 J2 J3 J0 D(EF) Tcmf
conc. (meV) (meV) (meV) (meV) (States/eV) (K)
To mimic the doping effect, we have carried out cal-
culations using supercell containing sixteen Mn atoms. x=0.0 -2.52 -0.11 +0.33 -12.48 0.2 181
Constructionofsuchsupercellhasbeendescribedinsec- x=0.125 -3.65 -0.12 -0.41 -26.38 1.0 382
tion II. Out of these, sixteen Mn atoms, some are sub- x=0.25(3NN) -2.72 -0.57 -0.85 -29.08 1.4 422
stituted by Sb to simulate the effect of doping. There x=0.25(NN) -2.74 -0.56 -0.87 -29.30 1.44 423
aretwodopinglevelsthathavebeeninvestigated. Inone
case, one of the Mn atom is substituted by an Sb atom, TABLE VI: Exchange interaction strengths J1 (NN), J2
and in another case, two of the Mn atoms are replaced (2NN)andJ3(3NN)andeffectiveexchangecouplingstrength
by two Sb atoms. The former amounts to doping level J0 in meV, total density of states at Fermi level, D(EF)
ofx=0.125or6.25%andthe latteramountstodopingof andmean-fieldCurieTemperature,Tcmf forTl2Mn2−xSbxO7,
x=0.0, 0.125 and 0.25.
x=0.25 or 12.5 %. These are not exactly the doping lev-
els that has been investigated experimentally but close
to them (i.e. x = 0.1 and 0.2 respectively). Table VI gives the magnetic exchange interaction
Substitution of Mn4+ by larger cation Sb5+ does not strengths for all the three cases and their corresponding
cause any significant changes in the crystal structure, T ’s and density of states at E , D(E ). For compar-
c F F
other than the fact that lattice expands slightly keep- ison, we also quote the numbers corresponding to pure
ing the various angles unchanged. The lattice parame- Tl Mn O taken from ref9. Pristine Tl Mn O has a
2 2 7 2 2 7
ters corresponding to doping levels of x=0.125 and 0.25 very strong NN FM interaction, a weak 2NN FM inter-
are obtained by interpolation of the experimentally de- actionand a little stronger 3NN AFM interaction. With
termined lattice constants at various doping as shownin the introduction of doping, all the interactions became
the inset of Fig.1. in ref7. The lattice parameters for x FM and their strengths also increase. On further in-
=0.125and 0.25 are increased by 0.3% and 0.9% respec- crease of doping, the 2nd and 3NN FM interactions be-
tively, compared to undoped lattice constant. come stronger with a small decrease in the NN FM in-
To estimate the exchange interaction strengths for teraction. It is worth mentioning here that the results
Tl Mn Sb O with x=0.125and 0.25 we have carried for x=0.25 doping with two NN Mn atoms substituted,
2 2−x x 7
out LSDA total energy calculations for various spin ar- doesnotchangesignificantlycomparedtotheresultwhen
rangements of Mn atoms as explained in section II. The the two Mn ions substituted were 3NNs, proving that
relative LSDA total energies, as given in Table V are choiceofdisorderedconfigurationdoesnotalterthe gen-
mappedontoEq. (1)inordertoextracttheJ’s. At6.25 eral trend. Computation of T , using the values of J ,
c 1
J and J , listed in Table I, show rapid increase in T
2 3 c
onthe initialdopingwhichthenattainsakindofsatura-
∆E (meV)
tion on further doping, considering upto moderate level
x=0 x=0.125 x=0.25
of doping. This trend is in good agreement with experi-
FM 0 0 0
mental findings, but the quantitative values differ. This
AFM1 9.55 16.50 23.96 happens primarily because of the clustering effect not
AFM2 13.98 26.07 29.39 included in our calculation. To quote Alonso et. al.7,
AFM3 12.24 23.18 31.53 “ For low doping levels, we cannot disregard some type
AFM4 17.59 33.30 35.69 ofmagneticclusteringwithalmost pureTl2Mn2O7 (Tc =
AFM5 18.39 34.39 40.11 135K) andSbrichregions”. Sucheffectsareboundtore-
ducetheglobalT measuredexperimentally. Alsolattice
c
TABLEV:RelativeLSDAenergiesperMnioninmeVinFM relaxation effect could be important. Although experi-
and five AFM spin configurations for doped Tl2Mn2O7. All mentallymeasuredcrystalstructuredatashowsthesame
energies are converged upto 0.01 meV per Mn ion. space group symmetry as that of the undoped one with
little variation in the internal u parameter, the substitu-
% doping the average coordination numbers change to tion of Mn ion by a larger cation will probably change
5.6,11.2and11.2respectively. Inordertocheckwhether the structure locally. Therefore structural relaxations of
the chosendisorderedconfigurationhas any influence on the doped compounds, which is beyond the scope of our
the trend, we have repeated the calculation with two Sb presentcomputationalcapacity,areneededtoresolvethe
8
issue completely. highly dispersive Tl-O’-Mn-t hybrid state in the mi-
2g
nority spin channel. Because of the highly dispersive
nature of this band, the density of state in the minor-
20 ity spin channel close to E rises fast after the tail part
F
Tl−s + O’−p Mn − t2g whichthen attains a kindof smallplateaubefore attain-
Mn − e inghighlypeakedvaluescorrespondingtoweaklydisper-
g
O − p + sive Mn t dominated states between 1-2 eV. This is
2g
Tl−s + O’−p
shown in the inset of Fig.7. With introduction of first
)
eV 10 Sb atom, the doped extra electrons while populating the
tes/ dispersive minority spin band increases D(EF) substan-
ta tially. UponincreasingthenumberofSbatomsfromone
S
s ( to two, the Fermi level shifts towards right to accommo-
te date more electrons, but since it has almost crossed the
a
St 0 highly dispersive region and falls within the plateau-like
y of structure, D(EF) does not change significantly. This is
sit evidentbyquantitativeestimatesofD(EF)showninTa-
n ble I. In Fig.7, we have shown only the case of x=0.25
e
D -10 O − p (NN),buttheDOScorrespondingtox=0.25(3NN)isnot
Tl−s + O’−p very different and D(EF) changes only marginally. Fol-
Mn − e lowingtheperturbativetreatmentintermsofthetransfer
Energy (eV) g
-2 -1 0 1 2 integral26,t,betweenthemagneticandnonmagneticsite,
-20 S (States/eV)-2 TlM−sn ++ − O t’2−gp ttehhrgeeyeaxvdcerhrivaaegnnegesecncheoerumgpyelisniesgp,gaiJrv,aewtnioibtnhyi,bnte4ttDwhee(eEpnrFot)ph/oe∆sme2d,awgknihneeetrtiecic∆aennids-
O-4
D nonmagnetic level and D(E ) is the density of states at
F
Fermi level introduced in the above. The real space rep-
-30
-8 -6 -4 -2 0 2 4 6 resentation of NMTO-downfolded Hamiltonian keeping
Energy (eV) Tl-6s, Mn -3d and O-2p states active and downfolding
the rest shows that the Tl-Mn hopping integral, t’s and
FIG. 7: (color on-line) Spin-decomposed density of states theirenergylevelseparationchangesonlyslightlyfor0.3
for x=0.0 (black), 0.125 (red) and 0.25 (blue) doping in % and 0.9% expansion of the lattice upon x=0.125 and
Tl2Mn2−xSbxO7. Zeroof theenergy isset at theFermilevel 0.25 doping. The major changes come from the sharp
of the undoped Tl2Mn2O7 compound. The upper (lower) increaseinD(E )whichexplainstheenhancementofJ’s
F
panel corresponds to the majority (minority) spin. The neg-
and T ’s in turn.
ative of density of states has been plotted in the lower panel c
for clarity. Inset shows the density of states in minority spin
channel at the same doping levels for theenergy region close
to Fermi level. The dashed lines in the inset correspond to
therespective Fermi levels.
IV. CONCLUSIONS
One needs to examine the electronic structure upon
dopingto understandthe microscopicoriginofthe strik-
ingeffectdescribedabove. InFig. 7weshowthe density
of states corresponding to Sb-doped Tl Mn O for dop-
2 2 7
ing levelofx=0.125and0.25. To appreciatethe changes We presented a detailed study of Tl2Mn2O7 under
in the electronic structure upon doping, we also show pressure and Sb-doped Tl2Mn2O7 using first-principles
the density ofstatesforpure Tl Mn O . Comparingthe electronic structure calculations. The analysis of the
2 2 7
various density of states, we observe slight shrinking of computed electronic structure shows that the counter-
the overallband-width due to the smallexpansionofthe intuitive experimental observation of suppression of fer-
lattice. The t2g-eg splitting at the Mn site decreasesdue romagnetic Tc upon application of pressure and its en-
to expansion of the Mn-O bondlength. Smearing of the hancement upon moderate amount of doping by Sb in
DOS, compared to pure case is also observed due to the Mn sublattice is naturally explained in terms of the hy-
effect of disordering. The Sb ions in the 5+ state have bridization induced mechanism proposed earlier9. Ap-
completely filled 4d shell which are essentially core-like plication of pressure reduces the hybridization between
′
while 5s and 5p states remain more or less empty with localized Mn t2g level and the delocalized Tl-O effec-
′
no contribution to the states close to E . The most im- tive state due to the shifting of the position of the Tl-O
F
portant effect is that of electron doping. Replacement effective level, which weakens the driving mechanism of
of Mn4+ by Sb5+ introduces additional electrons in the ferromagnetism and thereby reduces the strength of ex-
system which have no other option but to populate the change coupling and the T .
c
9
In case of doping,on the other hand, the enhancement decrease is only marginal and for all practical purposes,
of T is induced by the charge-carrierdoping of the sys- it may be assumed to remain same as that of Tl Mn O
c 2 2 7
tem by Sb. This enhances the value of density of states in ambient condition. This rules out the use of angle
at the Fermi energy significantly, thereby enhancing the variation argument to explain the reduction of T .
c
exchangecouplingandtheT . Ourconclusionsweresub-
c
stantiated by the explicit calculation of the J’s and the
T ’s.
c
In case of Tl Mn O under pressure , we resolved the Acknowledgements
2 2 7
issue related to the change in Mn-O-Mn angle. We car-
riedoutstructuralrelaxationbymeansofaccuratepseu-
dopotentialbasedtotalenergycalculations. Ourtheoret-
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the original suggestion by Sushko et. al.6. However the collaboration.
* Also at Jawaharlal Nehru Center for Advanced Scientific 14 Y. Shimakawa, Private Communication, 6 Mn-O-Mn de-
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