Origin of Ferromagnetism and its pressure and doping dependence in Tl$_{2}$Mn$_{2}$O$_{7}$

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by  T. Saha-Dasgupta

Origin of Ferromagnetism and its pressure and doping dependence in Tl Mn O
2 2 7
T. Saha-Dasgupta1, Molly De Raychaudhury1 and D. D. Sarma2,∗
1 S.N. Bose National Centre for Basic Sciences, Kolkata 700098, India and
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2 Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore - 560012, India
0
(Dated: February 5, 2008)
0
2
UsingNMTO-downfoldingtechnique,weexploreandestablishtheoriginofferromagnetisminthe

n pyrochlore system, Tl2Mn2O7. It is found to be driven by hybridization induced spin-polarization
a of the delocalized charge carriers derived from Tl-s and O-p states. The mean-field estimate of the
J ferromagnetictransitiontemperature,Tc,estimatedusingcomputedexchangeintegralsarefoundto

5 bein good agreement with themeasurements. Wefindan enhancementof Tc for moderate doping
2 withnonmagneticSbandasuppressionofTc uponapplicationofpressure,bothinagreementwith
experimental findings.

]
i
c
s A range of compounds, mostly perovskites based on has been used to explain the ferromagnetism in low Tc
- manganese oxide, have been found with astoundingly pyrochlorematerials,makingthecaseofTl Mn O with
l 2 2 7
r large negative magnetoresistance (MR). The search is a much larger T even more intriguing. Mishra and
t c
m on for materials with better MR properties, either in Satpathy proposed13a mechanism which is a combina-
. theformofcolossalmagnetoresistance(CMR)ortunnel- tion of negative Hund’s rule energy (JH) driven double
t
a ingmagnetoresistance(TMR).Examplesincludesystems exchange mechanism, antiferromagnetic super-exchange
m such as double perovskites,1 pyrochlores,2 FeCr S and mechanismandanindirectexchangemechanism,though
2 4
Fe Cu Cr S chalcospinels,3 layeredrare-earthiodide lackingrigorousmicroscopicjustificationfor these mech-
- 0.5 0.5 2 4
d GdI .4 While work in 1950s and 1960s uncovered5 the anisms. In view of the enhancement of the ferromag-
2
n role of double-exchange (DEX) mechanism in providing neticcouplinginSbsubstitutedTl Mn O ,amoreexotic
2 2 7
o
a qualitative understanding of stabilization of the fer- scenario10 has also been suggested with antiferromag-
c
[ romagnetic (FM) phase in perovskite manganites, the netic(AFM)couplingbetweennearest-neighbor(NN)Mn
underlying driving mechanism for the magnetic order in ions dominatedby longer-rangedFMinteractions due to

1
diverse class of magnetoresistive materials need not be the frustration of the former in the pyrochlore lattice.
v
the same. Our work6 on Sr FeMoO in the past has
3 2 6 Given the diversity of disparate mechanisms for ferro-
shown that driving mechanism acting in Sr FeMoO is
6 2 6 magnetism,weconsidereditworthwhiletostudytheun-
5 neithertheconventionaldouble-exchangemechanismnor
derlyingelectronic structure model, responsiblefor mag-
1 thesuper-exchange,insteadanovelkineticenergydriven
netism within a rigorous and microscopic ab-initio the-
0 mechanism explains its unusual electronic and magnetic
ory of Tl Mn O . For this purpose, we have analyzed
6 behavior. In the present communication, we focus on a 2 2 7
0 pyrochlore manganite Tl Mn O , which has a number the electronic structure of Tl2Mn2O7, pristine, doped
/ 2 2 7 withSbandunderpressure,computedwithintheframe-
t of contrasting properties compared to perovskite man-
a workoflocalspindensityapproximation(LSDA)ofden-
ganites. For example, Tl Mn O does not have mixed
m 2 2 7 sity functional theory (DFT) in terms of muffin-tin or-
Mn3+-Mn4+ valences, they do not exhibit Jahn-Teller
- bital (MTO) based NMTO-downfolding technique. We
d distortionsintheMnO6octahedra,andinspiteofsimilar have also computed the magnetic exchange interaction
n CMR effect observed,both the ferro- and para-magnetic
strengths from ab-initio DFT calculations.
o phases show a metal-like behavior.
c Sincethe discoveryofCMReffectinTl Mn O ,ithas The pyrochlore structure of general stoichiometry
: 2 2 7 ′
v been recognized as a class of compounds that does not A2B2O6O canbe describedastwointerpenetratingnet-
i fitwithintheDEXframework. Nevertheless,nocommon works. The smaller B cations (Mn) are octahedrally co-
X
consensushasemergedconcerningthedrivingmechanism ordinatedbyO-typeofoxygens,withtheBO6 octahedra
ar in this interesting class of compounds. Considering the sharing corners to give rise to a BO3 network compo-
fact that Mn-O-Mnbond angle in Tl Mn O is substan- sition. The cage-like hole of this network (cf. Fig. 3)
2 2 7 ′
tially reduced7 from 180o to ≈ 133o, a value that falls in containsthesecondnetworkcomprisingofA(Tl)andO -
′ ′
therangewhereasignchangeoftheexchangeinteraction type oxygens forming A-O chains with a formula A O .
2
from antiferromagnetic to ferromagnetic is expected ac- Self-consistent calculations were carried out within the
cordingtoGoodenough-Kanamorirule,8 aferromagnetic framework of tight-binding LMTO14, for Tl Mn O in
2 2 7
superexchangepicturewasproposedoriginally.9Lateron Fd3m symmetry. The calculation yields a net spin mo-
this interpretation has been questioned in view of the ment of 2.90 µ per Mn atom, consistent with the the
B
fact that ferromagnetic T is enhanced by introduction measured values (2.74 µ and 2.59 µ 2,15) and the pre-
c B B
ofmoderateamountofnonmagneticcationlikeSbinthe viousband-structurecalculations.13,16 EachMnsitewith
Mn sublattice10 and gets suppressed by application of a radius of 1.2 ˚A contributes 2.57 µ , while each 1.0 ˚A
B
pressure,11 contrary to the expectation based on super- O′ sphere and each 1.5 ˚A Tl sphere contribute 0.24 and
exchange. Theextendedversionofsuper-exchangeidea12 0.08 µ , respectively.
B
2
Mn−eg Mn−t2g Tl−s O’−p ≈ 1 eV. In the minority spin channel the t manifold of
6 thecrystalfieldsplitFe-dbands,stronglyhy2gbridizedwith
4 Mo-t2g (and O-p), cross the Fermi level. These band-
2 structureaspectssuggestastrongrenormalizationofthe
spin-splitting of the Mo-t bands (or more precisely the
0 2g
Mo-t2g −O-phybridizedstates)overitsbarevalue,since
-2
Mois usually nonmagneticwith0.1- 0.2eVintrinsic ex-
-4 change splitting. This was explained6 in terms of the
)
ev -6 large spin splitting at the Fe site and the presence of
(
rgy -8 sautibosntamntaiyalbheodpipriencgtlbyectowmeepnarFeedawnidthMtohastiteosf.TTlhMisnsitOu-
e 6 2 2 7
En with half-filled t2g 3d3 state of Mn in Tl2Mn2O7 playing
4
the role of half-filled 3d5 state of Fe in Sr FeMoO and
2 6
2 the hybridizedTl-O′ state playingthe roleofdelocalized
0 Mo-O state in Sr FeMoO .
2 6

-2 In the following we attempt to unravel the ex-
-4 changemechanismbyapplicationofNMTO-downfolding
technique.17 NMTO-downfolding technique provides a
-6
useful way17 to derive few-orbital Hamiltonians starting
-8
Γ X W Γ X W Γ X W Γ X W from a full LDA/LSDA Hamiltonian by integrating out
degrees of freedom that are not of interest. This proce-
FIG. 1: Spin-polarized LDA band-structure of Tl2Mn2O7. durenaturallytakesintoaccountthe renormalizationef-
Theupperpanelscorrespondtoup-spinchannelandthelower fectduetotheintegrated-outorbitalsbydefiningenergy-
panels correspond to down-spin channel. The fatness associ- selective, effective orbitals which serve as the Wannier
ated with the bands in each panel is proportional to the or- or Wannier-like orbitals for the few-orbitalHamiltonian.
bitalcharactercorrespondingtothatindicatedontopofeach We employ the NMTO-downfolding technique to con-
panel. structthereal-spaceHamiltonianintheNMTO-Wannier
functionbasisforSr FeMoO andTl Mn O . TheOde-
2 6 2 2 7
′
grees of freedom for Sr FeMoO and O degrees of free-
2 6
The well-studied13,16 band-structure of Tl Mn O , dom in case of Tl Mn O are downfolded to define ef-
2 2 7 2 2 7
′
shown in Fig. 1, may be summarized as follows. The d- fective Mo-O and Tl-O states respectively. The on-site
p hybridized band-structure extends in an energy range matrixelementsofthesereal-spaceHamiltoniansgivethe
from about - 6 eV to 6 eV with the zero of energy set at estimate of various energy level positions in absence of
the LSDAFermilevel,EF. Theoccupiedband-structure the hybridization between the localized magnetic (Fe or
in both spin channels are dominated by O-p contribu- Mn) and the delocalized non-magnetic (effective Mo-O
tions (not shown in the figure). In the majority or up or effective Tl-O′) states. As illustrated in Fig. 2, the
spin channel the upper part of the occupied manifold, ′
essentially non-magnetic Mo-O or Tl-O states with a
startingfrom≈-2eV isalsostronglycontributedby the tiny exchange splitting (≤ 0.2 eV)18 appear in between
Mn-t2g states. The crystal field split Mn-eg states span the exchange split Fe-d or Mn-t states19, respectively.
2g
anenergyrangefrom1.5eVto4eVoverlappingwiththe
On switching on the hybridization, as depicted in the
Tl-s−O′-phybridbands. The almostfullMn-t bands
2g right hand side of the level diagram in Fig. 2, the Mo-
separated by a gap from Mn-e bands produce tiny hole ′
g O or Tl-O levels get pushed up in the up-spin chan-
pockets in the majorityspinchannelformed outof three
nel and pushed down in the down-spin channel resulting
almostflatbands. Inthe minorityordownspinchannel,
into a large, renormalized negative spin-polarization of
theexchangesplitMn-dbandsareshiftedupinenergyby
the mobile electron due to purely hopping interactions.
≈ 2 eV, thereby making the Mn-d states close to empty ′
The renormalized spin-splittings of the Mo-O or Tl-O
in the down-spin channel. The noticeable feature is the
states, after switching on the hybridization, have been
highly dispersive Mn-t band hybridized with Tl-s and
2g estimated by massive downfolding calculations. In these
′
tOhe-pmtihnaotritcyrosspseins EchFa,nnperol.duTchineguannuseulaelcltyrolnargpeocTkle−tOin′ ckaelpctualacttiiovnesa,nodnalyllotthheerMdoe-gtr2egesoorfTfrle-esdsotmat,eisnchluadveingbeFeen-
′
hybridization produces Tl-O bonding like states at the d or Mn-t , have been downfolded to take into account
2g
bottom of the spectrum at both spin channels spanning the hybridization induced renormalization effect. Fig. 3
the energy from ≈ -7 eV to -6 eV. shows the Wannier orbitals corresponding to massively
Theband-structureofTl Mn O showsastrikingsim- downfolded NMTO Hamiltonian in the down-spin chan-
2 2 7
ilarity with that of Sr FeMoO over the low to medium nel for Sr FeMoO and Tl Mn O . The central Mo site
2 6 2 6 2 2 7
energyscale. IncaseofSr FeMoO ,Fe-dstatesarecom- (Sr FeMoO ) or Tl site (Tl Mn O ) shows the expected
2 6 2 6 2 2 7
pletelyfullinthemajorityspinchannel,whilecompletely Mo-t or Tl-s character,while the tail ofthe orbitalsit-
2g
emptyMo-dstatesappearseparatedfromE byagapof ting at the Fe and O sites (Sr FeMoO ) or Mn, O and
F 2 6
3
Sr FeMoO Tl Mn O
te2gg ~ 2.0 e~V0~.4 3 e.V1 eV2~0.2 eV 6 ~1.0 eV t2g ~0.5 eV2 ~02.2 eV7 ~ 1.5 eV 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sTMtLtiAaThnSntteBDheeiseLMrAoaunElnacsestsenIiitad:ooerncnMretgossoia.laeuigdsTnsmneshptetnheheteoirregcnwmiMusvnciumenonpsinebnefiitetrohtghrcnheiueenelrirlgmnaepftlooaimiacofrgttneintutvVshehreet.eeoi.cf
eg ~ 2.3 eV
~2.9 eV ~2.0 eV AFFMM1 ++1 +2- ++3 ++4 ++5 +6- ++7 ++8 ++9 1+-0 1++1 1++2 1++3 1+-4 1++5 1++6 ∆9.05E5
t2g
t2g FLee v3edls MEStfoaf(et tec 2 st gi)v −e O(p) RphSryteeabnstreoeisnrd mciizneaa lotiizfoend MLenvetl2sg TEStlfa(fsete)c st−iv Oe ’(p) RphSryteeabnstreoeisnrd mciizneaa lotiizfoend AAAFFFMMM234 +-- +-- +-- ++- +-- +++ ++- +-- ++- ++- --- --- +++ +-- --- --- 111273...259498
AFM5 - - + + - - + + - + - + + - + - 18.39
FIG. 2: Positioning of various energy levels as obtained by
NMTO-downfolding calculation before and after switching
on thehybridization between the magnetic and nonmagnetic mixing with Mn-O states which extends till the bottom
ions. of the spectra.16
We now turn to estimate quantitatively the exchange
Sr FeMoO Tl Mn O
2 6 2 2 7 a interactionstrengths,andthereforeTc. We compute the
exchange integrals by comparing the LSDA total ener-
b giesofdifferentspinconfigurationstothatofaneffective
a b
c Heisenberg Hamiltonian constructed out of Mn4+ spins.
O ThenetworkofMnionsinTl Mn O ,asshowninTable
Tl 2 2 7
Mn
Mo I,isaninfinitethree-dimensionallatticeofcorner-sharing
tetrahedra. Suchageometricalarrangementgivesriseto
a very high degree of frustration for AFM, NN interac-
Fe
O tions. Due to this frustration, it is not possible to sat-
isfy the antiferromagnetism completely, and the chosen
O’ AFM configurations invariably have net magnetic mo-
ments. The energy differences of all the AFM configura-
tions relative to FM configurationare positive, implying
FM state as the stable ground state consistent with ex-
FIG. 3: (Color on-line) Effective Mo-t2g like and Tl-s
like Wannier orbital corresponding to massively downfolded perimental findings.
NMTO Hamiltonian in the down spin channel. Shown are The effective Heisenberg Hamiltonian, considering till
the orbital shapes (constant-amplitude surfaces) with lobes 3NN interactions (six NN, twelve second NN and twelve
of opposite signs colored as red and blue. third NN), can be written as,
′ H =J1XSi.Sj +J2XSi.Sj +J3XSi.Sj (1)
O sites (Tl Mn O ) has appreciable weight shaped ac-
2 2 7 nn 2nn 3nn
′
cording to Fe-t , O-p or Mn-t , O-p, O -p symmetries
2g 2g
indicating the basic hybridization effect responsible for where Si denotes the spin-3/2 operator corresponding
the renormalization. This kinetic energy driven mecha- Mn4+ states at site i, and J1, J2, J3 denote the NN,
nism enforces a particular spin orientation of the mobile 2NN and 3NN magnetic exchange interaction strengths.
carrierswithrespectofthatofthelocalizedspin,thereby For the calculation of exchange couplings, the computed
providing a mechanism of ferromagnetic ordering at the LSDA energies were fitted to the mean-field Heisenberg
localized spin sub-lattice. This is a general mechanism model,whichcontainsIsingtermsofthefullHamiltonian
and will take place whenever the nonmagnetic, partially (1). A well-known limitation of this approach is that in
occupied level is placed within the exchange split energy some cases the result depends on the choice of spin con-
levels of the magnetic ion as was emphasized in ref.20. figurations. Toovercomethisweobtainedsevendifferent
The above exercise demonstrates beyond any doubt estimatesofJ1,J2andJ3employingvariousindependent
thatthehybridizationinducednegativespin-polarization combinations of five different energies listed in Table I.
mechanismsimilarto Sr2FeMoO6 to be operativealsoin Our calculation gives the average estimate of J1, J2, J3
caseofTl Mn O . ThereasonthatincaseofTl Mn O , as -2.52 meV, -0.11 meV and 0.33 meV with a standard
2 2 7 2 2 7
Tlincontrastexhibits a netpositive momentasopposed deviation of 0.24 meV, 0.06 meV and 0.08 meV, respec-
to the ferrimagnetic spin alignment of Fe and Mo states tively. Substituting the estimated values of J1, J2, J3 in
in Sr2FeMoO6, is the unusual covalency of Tl-O′ and the mean-field estimate of Tc: Tcmf = S(S3+kB1)Jo, where
4
J , the net effective interaction is 6J + 12J + 12J , lengths are assumed to decrease. In the second set, we
o 1 2 3
S=3/2 and k is the Boltzmann constant, gives a T of also changed the Mn-O-Mn bond angle, taken according
B c
181 K. This is a very reasonable estimate considering to Fig. 2 of ref.23. Using the first set of calculations,
mean-field overestimation and experimentally measured themeanfieldestimateofT derivedfromourcomputed
c
value of 142 K.2 J′s, show a decrease of T by 40 K upon 2 % change
c
As mentioned in the beginning, magnetic properties in bond lengths. In second set of calculations, where we
of Tl Mn O exhibit interesting variations with Sb- alsochangedthe Mn-O-Mnbond angle,which according
2 2 7
substitution and under pressure. We have addressed to ref23 for 2% decreasein bond length, increasesby less
these issues within the present approach. We mention than 1o, the T is found to decrease further by 7 K24.
c
here only the salient points of our study, the details of From analysis of electronic structure, upon application
the calculation will be reported elsewhere.22 To mimic of pressure, the bond lengths shorten which in turn en-
′
theSb-substitution,wehavecarriedoutcalculationswith hances the Mn-O and Tl-O interactions resulting into
eight formula unit supercells, where 1 and 2 out of 16 the broadening of the net band width. The more im-
Mn atoms are replaced by Sb, corresponding to a dop- portant effect for the present issue, however, is that the
ing level of 6.25 % and 12.5 %, respectively. Due to the delocalized Tl-O′ effective levels are found to shift25. As
slightly larger size of Sb, lattice parameters and bond is evidentfrom the leveldiagramin Fig. 2, the strength
lengths increase by less than 1% with no appreciable of the hybridization between the magnetic and the non-
changeinbond angles.10 The computed electronicstruc- magnetic states depends crucially on the positioning of
tureshowstheoverallbandshapestoremainmoreorless the various energy levels. The movement of the energy
same withelectrondoping inthe stronglyhybridizedTl- levels causes changes in hybridization strengths, leading
s–O-p–Mn-t conductionbandinthedownspinchannel. tosuppressioninthekineticallydrivenmagneticinterac-
2g
This causes a substantial rise in the density of states of tions and hence in a reduction of T . The small increase
c
the conduction band at E , from 0.2 eV−1 for the un- ofMn-O-Mnbondangleinthesecondsetofcalculations,
F
dopedcaseto1.0eV−1 and1.4eV−1 for6.25%and12.5 which is a secondary effect on top of the former effect,
% doped cases, respectively. Within the framework of increasestheantiferromagneticsuper-exchangecontribu-
the proposed mechanism, this is expected to lead to a tion resulting into further suppression of ferromagnetic
strong enhancement of the magnetic coupling.21 This is T .
c
supported by our computed J’s fromLSDA total energy
Toconclude,wehaveshownbymeansofNMTObased
calculations, which necessarily includes the proposed ki-
downfolding studythatthe underlyingmechanismoffer-
neticenergydrivenexchange. Themeanfieldestimateof
romagnetism in Tl Mn O is a kinetic energy driven
T isfoundtobe382Kand420Kfor6.25%and12.5% 2 2 7
c mechanism originally proposed for Sr FeMoO . The
doping concentrations,respectively. Thoughthe trend is mean field T , estimated using compute2d J′s is6in good
in agreement with the experimental observations,10 the c
agreementwith experiments. For Tl Mn O moderately
enhancementisgrosslyoverestimated,presumablydueto 2 2 7
doped with Sb, we found an enhancement in T and on
clusteringanddisorderingeffects,nottakenintoaccount c
application of pressure, T is found to decrease, both
in the calculation. c
in agreement with experimental observations. The mi-
Existing proposals for structural changes under pres-
croscopic origin of these changes in T are found to be
sure are controversial. The first paper11 reported a de- c
dominantly due to changes in the magnetic interaction
creaseofMn-O-Mnbondangle,inadditiontoadecrease
strengths arising from the proposed kinetically-driven
of bond lengths. Subsequent measurements23 claim the
mechanism.
Mn-O-Mn bond angle to increase. In absence of a clear
consensus about the structural changes, we carried out TheresearchwasfundedbyDSTprojectSR/S2/CMP-
two sets of calculations. In the first set, the pressure ap- 42/2003. We thank MPG-partnergroupprogram for the
plied is assumed to be isotropic, so that only the bond collaboration.
* Also at Jawaharlal Nehru Center for Advanced Scientific 9 Y. Shimakawaet. al.,Phys. Rev.B 55 6399 (1997).
Research and Center for Condensed Matter Theory, IISc. 10 J. A. Alonoso et. al., Phys.Rev.B 60 R 15024 (1999).
1 K. I. Kobayashiet. al.,Nature(London),395, 677 (1998). 11 Yu.V.Sushkoet. al.,Physica B 259-261 831 (1999).
2 Y. Shimakawa et. al., Nature(London),379, 53 (1996). 12 M. D. Nu´n˜ez-Regueiro and G. Lacroix, Phys. Rev. B 63
3 A. Ramirez et. al.,Nature(London),386, 156 (1997). 014417 (2000).
4 C. Felser et. al. J. Solid State Chem 147 19 (1999). 13 S.K.MishraandS.Satpathy,Phys.Rev.B587585(1998).
5 P. W. Anderson and H. Hasegawa, Phys. Rev. 100 675 14 O. K. Andersen and O. Jepsen, Phys.Rev.Lett. 53 2571
(1955); P.-G. DeGennes, Phys. Rev. 118 141 1960). (1984).
6 D. D.Sarma et. al., Phys.Rev.Lett 85, 2549 (2000). 15 M. A. Subramanian et. al. Science 273, 81 (1996).
7 A.RamirezandM.Subramanian,Science277,546(1997). 16 D.J. Singh, Phys. Rev.B 55 313 (1997).
8 J. B. Goodenough, Phys.Rev. 100 564 (1995). 17 O. K. Andersen and T. Saha-Dasgupta, Phys. Rev. B 62
5
R16219 (2000); See references in O. K. Andersen et. al., tively,whichoverestimatestheexperimentalestimateof≈
Bull. Mater. Sci26 19 (2003). -1.6 – -1 K/GPa. However, it is necessary to clarify the
18 The tiny splitting comes from the electrostatic effect. experimentalscenario in termsof precisestructural deter-
19 Empty Mn-eg does not contributein themechanism. mination.IfMn-O-Mnbondangleindeeddecreasesaswas
20 D. D. Sarma, Current Opinion in Solid State & Materials suggested in the first paper, then the theoretical estimate
Science, 1 (2001) of dTc/dP will be closer to experimental value.
21 J.KanamoriandK.Terakura,J.Phys.Soc.Jpn.70,1433 25 The energy level positions obtained by NMTO-
′
(2001). downfolding technique show a shift of Tl-O derived
22 M.De Raychaudhuryet. al.,unpublished. states relative to Mn-t2g by +0.3 eV on applying the
23 P. Velasco et. al., Phys.Rev.B 67 104403 (2003). pressure.Thisenergyshift morethancompensatesforthe
24 Consideringtheexperimentalestimateofthepressurecor- slight increase in the hopping interaction due to the 0.07
responding to 2% bond length change and accounting for A compression in Mn-Tl bond length.
themean field overestimation, thetwo setsof calculations
lead to dTc/dP as -2.7 K/GPa and -3.2 K/GPa respec-