Vesignieite BaCu3V2O8(OH)2 as a Candidate Spin-1/2 Kagome Antiferromagnet

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by  Yoshihiko Okamoto

Vesignieite BaCu3V2O8(OH)2 as a Candidate Spin-1/2 Kagome Antiferromagnet
Yoshihiko Okamoto, Hiroyuki Yoshida and Zenji Hiroi
Institute for Solid State Physics, University of Tokyo,
Kashiwa, Chiba 277-8581, Japan
(Dated: January 15, 2009)
ApolycrystallinesampleofvesignieiteBaCu3V2O8(OH)2comprisinganearlyidealkagomelattice
composed of Cu2+ ions carrying spin 1/2 has been synthesized and studied by magnetization and
heat capacity measurements. Magnetic susceptibility shows a neither long range order, a spin
glass transition nor a spin gap down to 2 K, in spite of a moderately strong antiferromagnetic
9
0 interactionofJ/kB=53Kbetweennearest-neighborspins. Abroadpeakobservedatatemperature
0 corresponding to 0.4J in intrinsic magnetic susceptibility indicates a marked development of the
2 short-rangeorder. Thegroundstateofvesignieiteisprobablyagaplessspinliquidorisaccompanied
bya very small gap less than ∼ J/30.
n
a
J
Spin-1/2 kagome antiferromagnets (KAFMs) with these extrinsic contributions has made it difficult to
5
strongquantum fluctuations are one ofthe mostintrigu- determine the intrinsic ground state of the kagome
1
ing playgrounds in the field of highly frustrated mag- lattice in herbertsmithite.

netism. In spite of numerous theoretical and experimen-
] Another model system is volborthite
el tal studies in the last decade, the nature of the ground Cu3V2O7(OH)2·2H2O, which crystallizes in a mon-
- state of the spin-1/2 KAFM remains an open question. oclinic structure with the space group C2/m [7]. There
r
One of the most possible ground state proposed by ex-
t are two Cu sites, namely, Cu1 and Cu2, in the kagome
s act diagonalization studies is a nonmagnetic spin-liquid
. plane. Thus, the kagome lattice is slightly distorted,
t state with a small spin gap estimated to be on the order
a consisting of corner-sharedisosceles Cu1-Cu2-Cu2trian-
m ofJ/20,whichisfilledwithacontinuumofsingletexcita- gles,wherethe distances betweentwoCuatoms are3.03
- tions,whereJ isthe nearest-neighborexchangecoupling ˚A (Cu1-Cu2) and 2.94 ˚A (Cu2-Cu2) [7]. This structural
d constant[1]. Ontheotherhand,weneedexperimentson distortion should give rise to spatial anisotropy in J in
n an actual material to realize the spin-1/2 KAFM. How-
the kagome lattice, resulting in a J -J kagome system
o ever, only a few model systems are known at present, 1 2
rather than in a uniform one. The magnitude of the
c
where some extrinsic factors like three-dimensionality,
[ anisotropyhasnotyetbeendeterminedthusfar,butwas
disorder effects, and lattice distortion have prevented us estimatedtobe lessthan20%bytheoreticalanalysis[8].
1 from deducing the intrinsic properties of the KAFM at
The kagome layers in volborthite are well separated by
v low temperatures.
theV O groupandwatermolecules,resultinginagood
7 2 7
3 Two Cu2+ minerals, namely, herbert- two-dimensionality. Unlike herbertsmithite, volborthite
2 smithite ZnCu3(OH)6Cl2 [2] and volborthite doesnotsufferfromsuchantisitedisorderbetweenCu2+
2 Cu V O (OH) ·2H O [3], are known as model sys- and Zn2+ ions, because V5+ ions cannot replace Cu2+
3 2 7 2 2
. tems for the spin-1/2 KAFM. They have slightly ions: a mutual exchange between Cu2+ and V5+ ions
1
0 different kagome lattices of Cu2+ ions. Herbertsmithite is unfavorable in terms of ionic radius and Madelung
9 crystallizes in a rhombohedral structure with the space energy. In spite of the strong antiferromagnetic inter-
0 group R¯3m, comprising an ideal arrangement of Cu2+ actions revealed by the large negative θ = −115 K,
W
: ions in the kagome geometry, so as to be named a volborthite shows no long-range magnetic order down
v
i “structurally perfect kagome compound” [2]. Intensive to 60 mK, but exhibits a small spin glass transition at
X
experiments have established the absence of long-range 1.1 K, which is likely caused by impurity spins [9, 10].
r order or spin glass transition down to 50 mK, in spite Magnetic susceptibility exhibits a broad maximum at T
a
of the presence of strong antiferromagnetic interactions ∼ 0.25J/k , indicative of the development of a short
B
betweenCu spins, asevidenced by the largeCurie-Weiss range order, and approaches a large finite value at 60
constant θ = −300 K [4]. However, a neutron diffrac- mK, suggesting a gapless or a very small spin-gapped
W
tion study revealed that ∼ 10% of Cu2+ sites in the (less than J/1500) ground state [10]. Very recently,
kagomeplane areoccupiedbyZn2+ ions[5]. This means a polycrystalline sample with much better quality has
that 30% of Zn sites bridging the kagome layers are been prepared, and an intriguing phenomenon called
occupiedby Cu2+ ions, whichcause nearlyfree impurity “magnetization steps” was observed in magnetization
spins with weak magnetic interactions. The existence curves at low temperatures [10]. However, it is still
of these impurity spins has also been supported by unclearwhether these resultsonvolborthite areintrinsic
the observations of a large Shottky-type contribution to the spin-1/2 KAFM or related to deviations from
in heat capacity, divergent magnetic susceptibility the ideal model. Therefore, it is necessary to search for
towardT = 0,andmagnetizationcurveswithdownward alternative, more ideal kagome compounds in nature. In
curvatures at low temperatures [6]. The presence of this letter, we report that vesignieite BaCu V O (OH)
3 2 8 2
2
(a) Cu (a)
Ba 1.0 3)u) CW
z OVH CxuC2uy1 -31mmol-Cu)mu/mol Cu) 00..86 CWc -1-1(mol-Cu cm(mol Cu/em642000000 pqefWf== 1 -.9787 mKB
(b) -22c0e 0.4 cc- 00 100 200
I (arb. unit) 001_110111_002112_311310112__221222221 113_222B423a004_C330224u_3223V6222O8(OH)2 c-c (10(1 00..200 c 5cb0uimlkp 100HTS1E50 2T00 (K)250 300
T (K)
10 20 30 40 50 60 70 80 (b)
2 q (deg.) 1.0
)
)1 BaCu V O (OH)
-uu 3 2 8 2
FviIeGw.e1d:a(alo)nCgrythstealastarxuicstu(rleefto)fvaensdignpieeritpeenBdaiCcuul3aVr2tOo8t(hOeHa)2b mol Col-C 0.8 m 0H= 01. 1T T
plane (right). (b) Powder XRD pattern of a polycrystalline u/m 3 T
m3 5 T
saarmegpilveeonfbvyesaigsnsuiemitientgaakemnoantorcoloinmicteumniptecrealtluorfea. P=ea1k0.i2n7d3ic˚Aes, -20e2cm 0.6 7 T
b = 5.907 ˚A, c = 7.721 ˚A and β = 116.29◦. -(10
1 0.4
c ( 0 5 10 15 20
c T (K)
can be a suitable compound for realizing spin-1/2
KAFMs. The thermodynamic properties of vesignieite FIG.2: (a)Temperaturedependenceofmagneticsusceptibil-
are studied and compared with those of the previous ity χ of vesignieite BaCu3V2O8(OH)2 polycrystalline sample
kagome compounds. measured on heating at a magnetic field of 0.1 T. The filled
circles, open circles, and broken line represent χ, χ , and
Vesignieite BaCu V O (OH) is a natural mineral re- bulk
ported about a half3ce2ntu8ry ago2 [11]. It crystallizes in a χimp, respectively. The solid curve on the χ data between 2
and10KrepresentsaCurie-Weiss(CW)fit,andthatbetween
monoclinic structure of the space group C2/m with lat-
150 and 300 K represents a fit to the kagome lattice model
ticeparametersofa=10.271˚A,b=5.911˚A,c=7.711˚A, obtained by high-temperature series expansion (HTSE) [13],
β =116.42◦ [12]. ThisstructureconsistsofCu3O6(OH)2 which yields J/kB = 53 K and g = 2.16. The inset shows
layers, made up of edge-shared CuO4(OH)2 octahedra χ−1,wherethesolid linebetween200and300Krepresentsa
and separated by VO4 tetrahedra and Ba2+ ions (Fig. CWfit,whichgivesθW =−77Kandpeff =1.98µB/Cu. (b)
1 (a)). Cu2+ ions form a nearly perfect kagome lattice, Temperaturedependenceoffield-cooled andzero-field-cooled
though there are two crystallographic sites for them, as χ measured in various magnetic fields up to 5 T.
in volborthite. The distortion of a Cu triangle from the
regular one is negligible (∼ 0.2%) with the distances be-
tweentwoCuatomsbeing 2.962˚A(Cu1-Cu2)and2.956 in MPMS and PPMS (Quantum Design). All the peaks
˚A (Cu2-Cu2) [12]. Thus, the spatial anisotropy in J observedinthepowderXRDpatternwereindexedtore-
may be much smaller than that in volborthite. More- flectionsbasedonamonoclinicstructurewiththelattice
over, vesignieite is expected to be free of antisite disor- constants a = 10.273 ˚A, b = 5.907 ˚A, c = 7.721 ˚A, β
der, the same as volborthite, because it contains no ions = 116.29◦ (Fig. 1 (b)), confirming that our sample is
chemically similar to Cu2+. From these structural and single-phase vesignieite [11, 12]. The peaks are consider-
chemical features, we expect that vesignieite can be an ably broad, indicating a small particle size on the order
ideal model system for the spin-1/2 KAFM to be com- of a few nm estimated using the Scherrer equation.
pared with herbertsmithite and volborthite. Thetemperaturedependencesofmagneticsusceptibil-
A polycrystalline sample of BaCu V O (OH) was ity χ and inverse susceptibility χ−1 of vesignieite are
3 2 8 2
preparedby the hydrothermalmethod. 0.1g of the mix- shown in Fig. 2 (a). χ−1 exhibits a linear tempera-
ture of Cu(OH) and V O in 3:1 molar ratio and 0.3 turedependenceabove150K,interpretedasCurie-Weiss
2 2 5
g of Ba(CH COO) were put in a Teflon beaker placed magnetism. A Curie-Weiss fit to the data between 200
3 2
in a stainless-steel vessel. The vessel was filled up to 60 and 300 K yields a moderately large negativeθ = −77
W
volume % with H O, sealed and heated at 180 ◦C for K and an effective moment p = 1.98 µ /Cu, which
2 eff B
24 h. Sample characterizationwas performed by powder is slightly larger than the spin-only value expected for
x-raydiffraction(XRD) analysisusing Cu-Kα radiation. S = 1/2. The exchange coupling J and Lande g-factor
Magnetic and thermodynamic properties were measured g are estimated to be J/k = 53 K and g = 2.16, by
B
3
impurity spins is also evidenced in the large field depen-
600
1) BaCu V O (OH) dence of χ observed below 10 K (Fig. 2 (b)), as well as
-u 500 3 2 8 2 inthesmallbutfinitefielddependence ofC/T (theinset
C
mol- 400 -1Cu) T (K) olafrFgeigr.t3h)a.nT0h.0e7a%mofourntvoolfbiomrtphuirtietybsuptinsmsianllverestighnainei1te1%is
2 300 mol-2000 4 8 12 forherbertsmithite [10,15],whichwereestimatedbythe
-C / T (mJ K 210000 -2C / T (mJ K 1000 840 TTT nissmmaiempaituleelrapiitnsayarnltpyoihcstlaiescssleoesnoarorχrcb.rauyTltisehtmnaelasolipyrniiegnbisednleaooftecftcairtmtiseb.pduutnreeidtayrtostphuiennssiduinerfnavtceifiesiegod-f
0
0 50 100 150 200 By subtracting χimp from χ, we obtain the intrinsic
T (K) magnetic susceptibility χ , as shown in Fig. 2 (a).
bulk
χ clearly exhibits a broad peak at 22 K ∼ 0.4J/k ,
bulk B
and a substantially large value of 2.6 × 10−3 cm3 mol-
FIG.3: Temperaturedependenceofheatcapacitydividedby Cu−1 atT =2K.Notethatthis broadpeak hasalready
temperature C/T of vesignieite BaCu3V2O8(OH)2 polycrys- appeared as a hump or a shoulder in χ and has been
talline sample measured at zero field. The inset expands the
observedbysubtractingtheextrinsiccontributionoffree
low-temperature part taken in various fieldsup to 8 T.
spins. The broad peak indicates that short-range order
developsremarkablybelow22K,andthatthelargefinite
value at the lowest temperature implies that the ground
fitting the data between 150 and 300 K to the calcula-
state is a gapless spin liquid, or, at least, that the gap is
tionforthespin-1/2KAFMusingthehigh-temperature-
much smaller than J/30.
seriesexpansion[13]. The g of vesignieiteis nearlyequal
to those of herbertsmithite (g = 2.33) [14] and volbor- Letusdiscussmagneticinteractionsinkagomelattices
thite (g = 2.205)[3], whichareslightly largerthan 2,re- of the three Cu compounds in terms of orbital arrange-
flecting a negative spin-orbitcoupling constantfor Cu2+ ments. It is common in all the three compounds that
ions. J smaller than those of herbertsmithite (J/kB = the degeneracy of the Cu 3d eg orbitals is lifted at room
170K)[14]andvolborthite(J/k =84K)[3]maybeas- temperature owing to the Jahn-Teller distortion. How-
B
cribed to the corresponding variation in Cu-O-Cu bond ever, the orbital arrangements are completely different
angle over the series: the smaller the bond angle, the from each other among the three compounds, as shown
larger the antiferromagnetic coupling. in Fig. 4, which can be deduced reasonably from the
Wehaveobservedneitheralong-rangeordernoraspin shape of octahedra around Cu2+ ions. The z2 orbital is
glass transition down to 2 K in spite of the moderately occupiedbyanunpairedelectronwhentwooppositeCu-
strong antiferromagnetic interaction. The temperature Obondsareshorterthantheotherfourbonds,whilethe
dependence of χ under various fields shows no kink-like x2 − y2 orbital is occupied when the two Cu-O bonds
anomaly or thermal hysteresis between field cooling and are longer than the others. In herbertsmithite, all the
zero-field cooling, as shown in Fig. 2 (b). The absence Cu2+ ions have their unpaired electrons in the x2 − y2
of long-rangeorder is also supported by heat capacityC orbital,whichareplacedsymmetricallyaroundthethree-
measurements showing no peak-like anomaly indicative fold axis, resulting in a structurally perfect kagome lat-
of a phase transition (Fig. 3). Thus, the geometrical tice [15]. In volborthite, on the other hand, the x2 − y2
frustration of the kagome lattice effectively suppresses orbitalisresponsiblefortheCu2site,whilethez2orbital
long-range order down to low temperatures much less fortheCu1site[15],whichcausesadisparitybetweenJ1
than J/kB. (Cu1-Cu2) and J2 (Cu2-Cu2). In contrast, a single or-
At low temperatures below J/k = 53 K, χ exhibits bitalmustbeselectedinvesignieite,asinthecaseofher-
B
a slightly complicated temperature dependence. With bertsmithite, but it must be the z2 orbitalinstead ofthe
decreasing temperature, a small hump appears around x2−y2orbitalorbital,givingrisetoanessentiallyundis-
20 K, followed by a sharp rise below 10 K (Fig. 2 (a)). tortedkagomenetwork(Fig. 4). Nevertheless,theactual
The lattermustbe due tothe presenceofnearlyfreeim- crystal symmetry is not trigonal but monoclinic, which
purity spins. Thus, χ should contain two independent comes from a lateral shift in the stacking of the kagome
contributions: χ and χ from impurity and bulk layers through intervening layers containing Ba2+ ions
imp bulk
spins, respectively. The former may be given as χimp = andVO4 tetrahedra. Sincethe distortionofCutriangles
C /(T − θ ), and should increase enormously as T in vesignieite is negligible, only 0.2%, one can consider
imp imp
→ 0. In contrast, the T dependence of χ may be vesignieiteasanearlyidealkagomesystem,whichisbet-
bulk
weak, compared with χ , at low temperatures. Thus, ter than volborthite from a structuralpoint ofview, and
imp
we fit the χ data between 2 and 7 K, assuming a T- cleaner than herbertsmithite in terms of impurity spins.
independent term χ instead of χ (Fig. 2 (a)), we Finally, we compare the χ for the three kagome
0 bulk bulk
obtainC =0.028cm3 K−1 mol-Cu−1,θ =−1.7K, compounds, in order to deduce the general feature of
imp imp
andχ =2.8×10−3 cm3 mol-Cu−1. C indicatesthat the KAFM. The temperature dependence of χ nor-
0 imp bulk
7% of spins behave as impurity spins. The presence of malized by both J and g is shown in Fig. 5. At a
4
herbertsmithite volborthite vesignieite of herbertsmithite, it was found that local susceptibility
ZnCu(OH)Cl CuVO(OH)·2HO BaCuVO(OH) decided from shift measurements, which may be unaf-
3 6 2 3 2 7 2 2 3 2 8 2
fected by impurity spins or defects in the kagome plane,
J OH J1 J1 exhibits a similar broad maximum at around 0.4J [16].
Cu
J J Therefore,T ,aswellasthemagnitudeofχ ,arein
2 2 peak bulk
O
Cu1 z2 goodagreementbetweenvesignieiteandherbertsmithite,
Cl x 2–y2 Cu2 suggesting a general feature of the KAFM. In contrast,
the normalized χ of volborthite seems considerably
bulk
different from the others: T is lower, and the magni-
peak
FIG. 4: Schematic representations of the arrangement of
tudeofχ atT issignificantlylarger. Thisislikely
Cu2+ orbitals in the kagome plane for three kagome com- bulk peak
duetothespatialanisotropyinJ. Recenttheoreticalcal-
pounds. One of the two eg orbitals, dx2−y2 or dz2, carrying culationsofχ onaspin-1/2spatiallyanisotropicHeisen-
spin-1/2 is depicted on each Cu atom.
bergmodelonthekagomelatticesuccessfullyreproduced
these tendencies with increasing anisotropy [17].
0.15 Common to all the three compounds, χ seems
bulk
to approach a large finite value at T = 0, indicative
CuVO(OH)·2HO
3 2 7 2 2
of the absence of a spin gap having a realistic magni-
)
2 tude. Therefore, the intrinsic ground state of the spin-
B 0.10
2mg 1/2KAFM mustbe a gaplessspin liquid state ora state
A
N withagapmuchsmallerthantheoreticallypredicted[1].
( BaCu V O (OH)
J / 3 2 8 2 This unusual ground state seems to be robust to the
k 0.05
bul ZnCu3(OH)6Cl2 spatial anisotropy of the kagome lattice, as observed in
c volborthite. It is important to determine whether the
anomalous magnetization steps that have recently been
0.00 observed in the high-quality sample of volborthite [10]
0.0 0.5 1.0 1.5 2.0 2.5 3.0
are general features of the KAFM and are also observed
k T / J
B in vesignieite. To answer this question, a higher-quality
sample with fewer impurity spins is required, and an ef-
FIG. 5: Temperature dependence of normalized fort to improve sample quality is in progress.
χbulk for vesignieite BaCu3V2O8(OH)2, volborthite In conclusion, we have demonstrated that vesignieite
Cu3V2O7(OH)2·2H2O and herbertsmithite ZnCu3(OH)6Cl2.
BaCu V O (OH) is a spin-1/2 antiferromagnet on a
The J/kB and g used are 53 K and 2.16 for vesignieite, 3 2 8 2
nearly idealkagome lattice. The kagome lattice in vesig-
84 K and 2.21 for volborthite [3], and 199 K and 2.23 for
herbertsmithite [15], respectively. nieiteismorespatiallyisotropicthanthatinvolborthite,
and contain fewer impurity spins than that in herbert-
smithite. The χ of vesignieite shows a broad peak at
bulk
high temperature, all the curves tend to merge, as ex- ∼ 0.4J/kB due to short-rangeorderingand a large finite
pected from the mean-field picture. However, they sep- value as T → 0, without a long-range order, a spin glass
arate from each other on cooling below T ∼ 1.5J/k transition and a spin gap down to J/30. These features
B
andshowbroadpeaksatT = 0.4J/k forvesignieite arecommontootherkagomecompounds,suggestingthat
peak B
and 0.25J/k for volborthite, indicative of the forma- the ground state of the spin-1/2 KAFM is a very small
B
tion of short range order. Although the presence of such gapped or gapless spin liquid.
a broad peak is not discernible for herbertsmithite, this This workwas partly supported by a Grant-in-Aid for
may be because of the experimental ambiguity in esti- Scientific Research on Priority Areas “Novel States of
matingalargeχ inχ. Infact,inarecentNMRstudy Matter Induced by Frustration” (No. 19052003).
imp
[1] Ch. Waldtmann et al.: Eur. Phys. J. B 2 (1998) 501; P. [10] H. Yoshidaet al.: submitted toJ. Phys.Soc. Jpn.
Sindzingreet al.: Phys. Rev.Lett. 84 (2000) 2953. [11] C. Guillemin: Compt. Rendus 240 (1955) 2331; C.
[2] M.P.Shoresetal.: J.Am.Chem.Soc.127(2005)13462. GuilleminandZ.Johan: Compt.RendusAcad.Sc.Paris
[3] Z. Hiroi et al.: J. Phys. Soc. Jpn. 70 (2001) 3377. D 282 (1976) 803.
[4] P.Mendels et al.: Phys.Rev.Lett. 98 (2007) 077204. [12] M. Zheshenget al.: Dizhi Xuebao64 (1990) 302.
[5] S.-H.Lee et al.: Nat.Mater. 6 (2007) 853. [13] N. Elstner et al.: Phys. Rev.B 50 (1994) 6871.
[6] F. Bert et al.: Phys. Rev. B 76 (2007) 132411; J. S. [14] M. P. Rigol et al.: Phys. Rev.Lett. 98 (2007) 207204.
Helton et al.: Phys. Rev.Lett. 98 (2007) 107204. [15] Z. Hiroi et al.: J. Phys.: Conf. Series, in press.
[7] M. A. Lafontaine et al.: J. Solid State Chem. 85 (1990) [16] A. Olariu et al.: Phys. Rev.Lett. 100 (2008) 087202.
220. [17] F. Wanget al.: Phys. Rev.B 76 (2007) 094421.
[8] P.Sindzingre: arXiv: 0707.4264.
[9] F. Bert et al.: Phys.Rev.Lett. 95 (2005) 087203.