Magnetic Frustration in a Mn Honeycomb Lattice Induced by Mn-O-O-Mn Pathways

0.18 MB·English

by  H. Wadati

Magnetic Frustration in a Mn Honeycomb Lattice Induced by Mn-O-O-Mn Pathways
H. Wadati,1,2,∗ K. Kato,3 Y. Wakisaka,3 T. Sudayama,3 D. G. Hawthorn,4 T. Z. Regier,5
N. Onishi,6 M. Azuma,6,† Y. Shimakawa,6 T. Mizokawa,3 A. Tanaka,7 and G. A. Sawatzky2
1Department of Applied Physics and Quantum-Phase Electronics Center (QPEC),
University of Tokyo, Hongo, Tokyo 113-8656, Japan
2Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
3Department of Physics and Department of Complexity Science and Engineering,
University of Tokyo, Kashiwa, Chiba 277-8561, Japan
4Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
5Canadian Light Source, University of Saskatchewan, Saskatoon, Saskatchewan S7N 0X4, Canada
1
6Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan
1
7Department of Quantum Matters, ADSM, Hiroshima University, Hiroshima 739-8530, Japan
0
(Dated: January 17, 2011)
2

n We investigated the electronic structure of layered Mn oxide Bi3Mn4O12(NO3) with a Mn hon-
a eycomb lattice by x-ray absorption spectroscopy. The valence of Mn was determined to be 4+
J with a small charge-transfer energy. We estimated the values of superexchange interactions up to
4 the fourth nearest neighbors (J1, J2, J3, and J4) by unrestricted Hartree-Fock calculations and a
1 perturbation method. We found that the absolute values of J1 through J4 are similar with pos-
itive (antiferromagnetic) J1 and J4, and negative (ferromagnetic) J2 and J3, due to Mn-O-O-Mn

] pathways activated by the smallness of charge-transfer energy. The negative J3 provides magnetic
l
e frustration in thehoneycomb lattice to preventlong-range ordering.
-
r PACSnumbers: 71.30.+h,71.28.+d,79.60.Dp,73.61.-r
t
s
.
t
a Since the resonating valence bond state in geometri-
m
callyfrustratedmagnetshasbeenproposedbyAnderson
z
- [1], spin-disordered ground states in Mott insulators on
d
frustrated lattices have been attracting great interest in J
n Mn1 1
condensed-matterphysics. TheexchangeinteractionJ in O1
o
c a Mott insulatoris roughlygivenby −2t2/Eg, where t is J O2 x y
[ the transfer integral between the two localized orbitals 3 J2 Mn2
and E is the excitation energy across the Mott gap. O3
1 g
v In Mott insulatorsonfrustratedlattices, spin-disordered O4
7 systems including organic and inorganic materials [2–6] Mn3
4 allhaverelativelysmallE ,suggestingthatthesmallness
g J
8 of E or the closeness to the Mott transition would be 4 Mn
g
2 important to realize the spin-disordered ground states. O
.
1
Various insulating transition-metal oxides are known
0
as Mott insulators and can be classified into (i) the
1
Mott-Hubbard type insulators where the Mott gap E
1 g FIG.1: (Coloronline): NetworkofMnO6 octahedronsinthe
: is mainly determined by the Coulomb interaction U be- honeycomb lattice with the definitions of interactions in the
v
i tweenthetransition-metaldelectronsand(ii)thecharge- nearest-neighborJ1,thesecondnearest-neighborJ2,thethird
X transfer type insulators where Eg is determined by the nearest-neighbor J3, and thefourth nearest neighbor J4.
charge-transfer energy ∆ from the oxygen p state to the
r
a transition-metal d state [7]. Therefore, the smallness of
E canbe obtainedintransition-metaloxideswithsmall
g
U or small ∆. In the small U case, theoretical stud- the higher order terms, the exchange pathways through
ies on triangular-lattice Hubbard models proved that a the oxygen p state may give unexpectedly long ranged
spin-disordered phase is realized near the Mott transi- exchange terms and may affect the spin disordering.
tion [8–11], which could be related to the higher order
Very recently, a spin-disordered ground state is re-
exchange terms. As for the small ∆ case, in addition to
ported in a layered Mn oxide Bi Mn O (NO ) with
3 4 12 3
a Mn honeycomb lattice in which the exchange inter-
action between second neighbor Mn sites introduces a
kind of frustration in the honeycomb lattice [12]. In
∗Electronic address: [email protected];
this material, there is a network of MnO octahedrons
URL:http://www.geocities.jp/qxbqd097/index2.htm 6
†Present address: Materials and Structures Laboratory Tokyo In- and Fig. 1 shows the definitions of interactions in the
stituteofTechnology,4259Nagatsuta,Yokohama226-8503,Japan nearest-neighborJ1, the secondnearest-neighborJ2, the
2
third nearest-neighbor J , and the fourth nearest neigh-
3
bor J . The exchange interaction J between second
4 2
neighbor sites could be derived from the Mn-O-O-Mn Hd = ǫdd+k,mσdk,mσ
exchangepathwayswhichbecomesimportantinsmall∆ kX,mσ
sbyostthemths.eoTrehtiecavlalylue[1s3o]fatnhdeseexipnetreirmacetnitoanllsywbeyreinsteuladsiteidc + Vkd,dmm′d+k,mσdk,m′σ+H.c.
k,mX>m′,σ
neutron scattering [14]. In these studies, only J and J
1 2
are considered by assuming that the values of J3 and J4 + u d+i,m↑di,m↑d+i,m↓di,m↓
aresmallenoughto be neglected. However,since the ex- Xi,m
cahlsaondgeeriinvteedrafrcotmionthJe3Mbent-wOe-eOn-Mthneethxcirhdanngeeigphabtohrwsaityess,iist + u′ d+i,m↑di,m↑d+i,m′↓di,m′↓
i,mX6=m′
isnotatrivialquestionwhetherJ isnegligiblecompared
3
to J or not. In this context, it is very interesting and
2
important to study the electronic structure of the Mn
oxide, especially the values of interactions J1 - J4, us- + (u′−j′) d+i,mσdi,mσd+i,m′σdi,m′σ
ingspectroscopicmethods andto revealthe originofthe i,mX>m′,σ
sppoiinn-td.isInortdheirsepdasptaert,ewfreominvtehsetieglaetcetdrotnhiecesltercutcrtounriaclsvtireuwc-- + j′ d+i,m↑di,m′↑d+i,m↓di,m′↓
i,mX6=m′
ture of this material by x-ray absorption spectroscopy
(XAS), and also estimated the values of magnetic inter- + j d+i,m↑di,m′↑d+i,m′↓di,m↓,
actions. Unrestricted Hartree-Fock calculations and a i,mX6=m′
perturbation method revealed that the nearest neighbor
andfourthnearestneighborJ andJ arepositive(anti-
1 4
ferromagnetic), and the next nearest neighbor and third H = Vpd d+ p +H.c.
pd k,lm k,mσ k,lσ
nearestneighborJ2 andJ3 arenegative(ferromagnetic). k,Xm,l,σ
In the present analysis, the ferromagnetic J does not
2
introducemagneticfrustrationinthe honeycomblattice. Here, d+ are creation operators for the Mn 3d elec-
i,mσ
We conclude that the ferromagnetic J3 is the origin of tronsatsite i. d+ andp+ arecreationoperatorsfor
magnetic frustration and the absence of long-range or- k,mσ k,lσ
Blochelectronswithmomentumk whichareconstructed
dering in this material.
fromthem-thcomponentoftheMn3dorbitalsandfrom
the l-th component of the O 2p orbitals, respectively.
The synthesis of Bi Mn O (NO ) polycrystalline
3 4 12 3
The intra-atomic Coulomb interaction between the Mn
powderisdescribedinRef.[12]. X-rayabsorptionexper-
3d electrons is expressed using Kanamori parameters, u,
iments were performed at 11ID-1 (SGM) of the Cana-
u′, j and j′ satisfying the relations u = u′+j +j′ and
dian Light Source. The spectra were measured in the
j =j′. The transfer integrals between the Mn 3d and O
total-electron-yield(TEY) mode. The total energy reso-
lutionwassetto100meV.Allthespectraweremeasured 2p orbitals Vkp,dlm are given in terms of Slater-Koster pa-
at room temperature. The obtained spectrum is ana- rameters (pdσ) and (pdπ). The parameters determined
lyzed by standard cluster-model calculations [15] to ob- by the cluster-model calculationare used as input of the
tainelectronicparameters. Theparametersinthismodel unrestricted Hartree-Fock analysis.
are 3d - 3d and 3d - 2p Coulomb interactions (U and Figure 2 shows the Mn 2p XAS spectrum of
dd
Udc, respectively), charge-transfer energy from O 2p to Bi3Mn4O12(NO3). There are two structures, Mn 2p3/2
Mn 3d states ∆, hopping integrals between Mn 3d and → 3d absorption at 640 - 650 eV and Mn 2p1/2 → 3d
O 2p molecular states [V(t ) and V(e )], and crystal absorption at 650 - 660 eV. The experimental spectrum
2g g
field parameter 10Dq. The superexchange interactions has a sharp peak at ∼ 641.5 eV characteristic of Mn4+,
areevaluatedusingunrestrictedHartree-Fockcalculation concludedbycomparingwiththereferencedataofMn2+
with a multi-band d−p Hamiltonian with Mn 3d and O (MnO), Mn3+ (LaMnO3), and Mn4+ (EuCo0.5Mn0.5O3
2p states [16]. The Hamiltonian is given by and SrMnO3) from Ref. [17]. This indicates that the va-
lence of Mn is 4+ in Bi Mn O (NO ), consistent with
3 4 12 3
the valance state of Bi3+Mn4+O2−(NO )− obtained in
3 4 12 3
H =H +H +H , Ref. [12]. We performed configuration-interaction (CI)
p d pd
cluster-model calculations [15] to obtain electronic pa-
rameters. Here we fixed the following values U = 6.0
dd
eV, U = 7.5 eV, V(e ) = 3.0 eV, and 10Dq = 1.3 eV
dc g
and changed the value of ∆ from 0.0 eV to 4.0 eV, as
shown in Fig. 2 (a). The calculated spectra do not de-
pendonthevalueof∆somuch,butthesmall∆valuesof
Hp =kX,l,σǫpkp+k,lσpk,lσ+k,lX>l′,σVkp,pll′p+k,lσpk,l′σ+H.c., 1fr.o0m±a1.p0eeaVk artep∼ro6d4u1c.e5tehVeaexnpdeMrimne2npt1m/2ossttrusuctcuceresssf.ully
3
for Mn4+ specifically ∆=ǫ −ǫ +3U.
Mn 2p BiMnO (NO) d p
2p 3 3 12 3
3/2
2p
1/2
Experiment
nits) TEY With this parameter set, the lowest energy state is
u
y (arb. CD I= t h0e.0o reyV fwohuenrde tthoebfierstthenecigohnbvoernitniognsailteasnatirfeeraronmtifaegrnroemticagsnteattie-
sit D callycoupled. Intheantiferromagneticgroundstate,the
en = 1.0 eV
Int D second,third,andforthneighboringsitsareferromagnet-
= 2.0 eV ically, antiferromagnetically, and antiferromagnetically
D coupled,respectively. We havecalculatedenergiesoffer-
= 4.0 eV
romagnetic state as well as modified antiferromagnetic
635 640 645 650 655 660 665
states which are obtained by exchanging spins of some
Photon Energy (eV)
neighboring sites in the ground state. As expected, the
ferromagnetic state is very much higher in energy than
FIG. 2: (Color online): Mn 2p XAS spectra of
the antiferromagnetic ground state. However, some of
Bi3Mn4O12(NO3) and comparison with theCI theory.
themodifiedantiferromagneticstateswerefoundtohave
energies very close to that of the ground state. By map-
ping the Hartree-Fock energies to the Heisenberg model
eg Mn 3d Bi3Mn3O12(NO3) with J1, J2, J3, and J4, the obtained values are:
s) eg
nit O 1s
u Bi 6p
b. Mn 4sp
ar TEY
y (
sit
n e
e e t g
nt g 2g
I
calculation
J = 9.15 meV
1
525 530 535 540 545 550 555 J2 = −5.32 meV (1)
Photon Energy (eV) J3 = −4.80 meV
J = 5.77 meV
4
FIG. 3: (Color online): O 1s XAS spectra of
Bi3Mn4O12(NO3) together with the calculated O 1s partial
density of states by unrestricted Hartree-Fock calculations.
Figure 3 shows the O 1s XAS spectrum of
Bi Mn O (NO ) and the calculated O 1s partial den-
3 4 12 3
sity of states by unrestricted Hartree-Fock calculations.
There are two structures in the O 2p - Mn 3d hybridized
states, assigned as majority-spin eg states (eg↑) and While the antiferromagnetic J1 and ferromagnetic J2,
minority-spin eg states (eg↓), and another structure in andantiferromagneticJ4 areconsistentwith the antifer-
the O 2p - Bi 6p states as shown in Fig. 3. There is a romagneticgroundstate,the ferromagneticJ canintro-
3
higher intensity at eg↓ states in the experiment than in duce frustration effect on it. Since the magnitude of the
the calculation, indicating that there is a substantial Bi ferromagneticJ is comparable to those of the antiferro-
3
6pcontributionalsointhisstructure. Theseassignments magnetic J and ferromagnetic J , the ferromagnetic J
1 2 3
areconsistentwiththeMn4+ (d3)state,wheremajority- bythe Mn-O-O-Mnsuperexchangepathwaysisresponsi-
spin t2g states are occupied by electrons. ble for the absence of long-range ordering in the present
In order to obtain the values of magnetic interactions, honeycomb system.
wehaveperformedunrestrictedHartree-Fockanalysison
the multiband d−p Hamiltonian with the Mn 3d and O
2p orbitals. ∆, U, and (pdσ) were set to be 1.0, 6.0, and
−1.8 eV, respectively, on the basis of the cluster model Let us also examine the sign of J by considering su-
3
analysis. The ratio (pdσ)/(pdπ) is −2.16. Remaining perexchange pathways in Bi Mn O (NO ) using a per-
3 4 12 3
transfer integrals expressed by (ppσ), (ppπ), (ddσ), and turbation method based on the electronic structure pa-
(ddπ) are fixed at −0.6,0.15, −0.3, and 0.15 eV, respec- rameters obtained from the analysis of the Mn 2p XAS
tively, for the honeycomb lattice with the regular MnO spectrum. Here, we will use Slater-Koster parameters,
6
octahedron. Here ∆ denotes the charge-transfer energy (ppσ), (pdσ), (ddσ), and so on [18].
4
J is given as Hereweconsideredthemolecularorbitalsmadefromtwo
3
oxygensites. The first and second terms proportionalto
(pdπ)4 (pdπ)4 are given by the pathway from the Mn t states
J = + 2g
3 (cid:18)[∆−(ppσ)/2+(ppπ)/2]2 to the O 2p molecularorbitals to the Mn t2g states. The
(pdπ)4 1 1 third and fourth terms proportionalto (pdσ)2(pdπ)2 are
+
[∆+(ppσ)/2−(ppπ)/2]2(cid:19)(cid:18)∆+up u(cid:19) given by the pathway from the Mn eg states to the O
+ 2(pdπ)4 ×2p molecular orbitals to the Mn t2g states. J3 is dom-
[∆−(ppσ)/2+(ppπ)/2][∆+(ppσ)/2−(ppπ)/2] inated by the negative third term and causes ferromag-
1 1 1 netic interactions, which is consistent with the result of
(cid:18)∆+u + u − ∆+u −j (cid:19) the unrestricted Hartree Fock calculations.
p p p
(pdσ)2(pdπ)2
− + Fromtheneutronmeasurements,itwasfoundthatthe
(cid:18)[∆−(ppσ)/2−(ppπ)/2]2 values of interlayerinteractions (J ) are also comparable
(pdσ)2(pdπ)2 c
× to J1 [14]. This is consistent with our result because Jc
[∆+(ppσ)/2+(ppπ)/2]2(cid:19) is also determined by Mn-O-O-Mn pathways.
1 1 1
+ −
(cid:18)∆+u u−3j u−2j(cid:19) We investigated the electronic structure of
p
− 2(pdσ)2(pdπ)2 ×Bi3Mn4O12(NO3) by XAS. The valence of Mn was
[∆−(ppσ)/2−(ppπ)/2][∆+(ppσ)/2+(ppπ)/2] determined to be 4+, and from CI theory we found
1 1 1 1 that a charge-transfer energy is small in this material.
(cid:18)∆+u + u−3j − ∆+u −j − u−2j(cid:19) Then we estimated the values of J1,2,3,4 by unrestricted
p p p
Hartree-Fock calculations and a perturbation method.
2(pdπ)4 [(ppσ)/2−(ppπ)/2]2 1 WefoundantiferromagneticJ1 andferromagneticJ2 and
∼ 1− J , leading to the existence of magnetic frustration and
∆2 (cid:18) ∆2 (cid:19)∆+u 3
4(pdπ)4[(ppσ)/2−(ppπ)/2]2 1 j p the absence of long-range ordering, as experimentally
+ − p confirmed.
∆4 (cid:18)u (∆+u )2(cid:19)
p
−2(pdσ)2(pdπ)2 1− [(ppσ)/2+(ppπ)/2]2 1 The authors would like to thank Y. Motome for in-
∆2 (cid:18) ∆2 (cid:19)∆+u formative discussions. This research was made possible
p
4(pdσ)2(pdπ)2[(ppσ)/2+(ppπ)/2]2 withfinancialsupportfromtheCanadianfundingorgani-
− ×
∆2 zationsNSERC,CFI, andCIFAR.H.W. is supportedby
j − jp the Japan Society for the Promotion of Science (JSPS)
(cid:18)u2 (∆+u )2(cid:19) throughits Funding Programfor World-LeadingInnova-
p
(2) tiveR&DonScience andTechnology(FIRST Program).
[1] P.W. Anderson, Mater. Res. Bull. 8, 153 (1973). [10] T. Senthil,Phys. Rev.B 78, 045109 (2008).
[2] Y.Shimizu,K.Miyagawa, K.Kanoda, M. Maesato, and [11] S.-S. Lee and P. A. Lee, Phys. Rev. Lett. 95, 036403
G. Saito, Phys. Rev.Lett. 91, 107001 (2003). (2005).
[3] S. Nakatsuji, Y. Nambu, H. Tonomura, O. Sakai, S. [12] O. Smirnova, M. Azuma, N. Kumada, Y. Kusano, M.
Jonas, C. Broholm, H. Tsunetsugu, Y. Qiu, and Y. Matsuda, Y. Shimakawa, T. Takei, Y. Yonesaki, and N.
Maeno, Science309, 1697 (2005). Kinomura, J. Am.Chem. Soc. 131, 8313 (2009).
[4] S. Yamashita, Y. Nakazawa, M. Oguni, Y. Oshima, H. [13] S. Okumura,H.Kawamura, T. Okubo,and Y. Motome,
Nojiri,Y.Shimizu,K.Miyagawa,andK.Kanoda,Nature J. Phys.Soc. Jpn.79, 114705 (2010).
Phys.4, 459 (2008). [14] M. Matsuda, M. Azuma, M. Tokunaga, Y. Shimakawa,
[5] J.S.Helton,K.Matan,M.P.Shores,E.A.Nytko,B.M. and N.Kumada, Phys. Rev.Lett. 105, 187201 (2010).
Bartlett, Y. Yoshida, Y. Takano, A. Suslov, Y. Qiu, J.- [15] A. Tanaka, J. Phys. Soc. Jpn. 63, 2788 (1994).
H.Chung,D.G.Nocera,andY.S.Lee,Phys.Rev.Lett. [16] T. Mizokawa and A. Fujimori, Phys. Rev. B 54, 5368
98, 107204 (2007). (1996).
[6] Y. Okamoto, M. Nohara, H. Aruga-Katori, and H. Tak- [17] A. N. Vasiliev, O. S. Volkova, L. S. Lobanovskii, I. O.
agi, Phys.Rev.Lett. 99, 137207 (2007). Troyanchuk, Z. Hu, L. H. Tjeng, D. I. Khomskii, H.-J.
[7] J. Zaanen, G.A. Sawatzky,and J. W. Allen, Phys.Rev. Lin, C. T. Chen, N. Tristan, F. Kretzschmar, R. Klin-
Lett.55, 418 (1985). geler, and B. Buchner, Phys.Rev.B 77, 104442 (2008).
[8] H. Morita, S. Watanabe, and M. Imada, J. Phys. Soc. [18] J.C.SlaterandG.F.Koster,Phys.Rev.94,1498(1954).
Jpn.71, 2109 (2002).
[9] O.I. Motrunich, Phys.Rev. B 72, 045105 (2005).