Absence of magnetic long range order in Ba$_3$ZnRu$_2$O$_9$: A spin-liquid candidate in the $S=3/2$ dimer lattice

0.56 MB·

by  Ichiro Terasaki

JournalofthePhysicalSocietyofJapan
Absence ofMagneticLong RangeOrderinBa ZnRu O :A Spin-Liquid Candidate
3 2 9
inthe S = 3/2 DimerLattice
IchiroTerasaki1∗,TaichiIgarashi1,TakayukiNagai1,KenjiTanabe1,HirokiTaniguchi1,TakuMatsushita1,
NobuoWada1,AtsushiTakata2,TakanoriKida2,MasayukiHagiwara2,KensukeKobayashi3,Hajime
Sagayama3,ReijiKumai3,HironoriNakao3,andYouichiMurakami3
7
1DepartmentofPhysics,NagoyaUniversity,Nagoya464-8602,Japan
1
2CenterforAdvancedHighMagneticFieldScience,GraduateSchoolofScience,OsakaUniversity,1-1
0
2 Machikaneyama,Toyonaka,Osaka560-0043,Japan
3CondensedMatterResearchCenterandPhotonFactory,InstituteofMaterialsStructureScience,HighEnergy
b
AcceleratorResearchOrganization,Tsukuba305-0801,Japan
e
F
Wehavediscovered anovel candidateforaspinliquidstateinarutheniumoxidecomposed ofdimersofS =3/2
8
spinsof Ru5+,Ba ZnRu O .Thiscompound lacksalongrangeorder downto37mK,whichisatemperature5000-
3 2 9
timeslowerthanthemagneticinteractionscaleofaround200K.PartialsubstitutionforZncancontinuouslyvarythe
]
l magnetic ground statefrom anantiferromagnetic order toaspin-gapped statethrough theliquid state.Thisindicates
e
- thatthespin-liquidstateemergesfromadelicatebalanceofinter-andintra-dimerinteractions,andthespinstateofthe
r dimerplaysavitalrole.Thisuniquefeatureshouldrealizeanewtypeofquantummagnetism.
t
s
.
t
a
m
- Since Anderson proposed the idea of a quantum spin liq- Polycrystallinesamplesof Ba MRu O (M = Zn, Co and
3 2 9
d
uid as a possible ground state for a spin-half (S = 1/2) Ca) were prepared with solid state reaction. Stoichiometric
n
antiferromagnetictriangular lattice1 with a suppressed long- mixtures of powdered oxide or carbonate sources (BaCO ,
o 3
c range magnetic ordering due to geometrical frustration and RuO2, Co3O4, ZnO, CaCO3) were ground in an agate mor-
[ quantum fluctuations of interacting spins, researchers have tar,andwerepre-sinteredinairat1273Kfor12h.Thepre-

sought this state of quantum matter.2 A quantum spin liq- sinteredpowderswerefinelyground,pressedintopellets,and
2
v uid should possess a ground state consisting of highly en- sinteredinairat1473Kfor72h.
7 tangled singlet-spin pairs and exotic excited states called Thesynchrotronx-raydiffractionwastakenatBL8A&8B,
5 spinons.3,4 Although several candidates have been reported Photon-Factory, KEK, Japan. The energy of the x-ray was
2
experimentally, none has been confirmed. Organic candi- adjusted to be 18 keV, which was carefully calibrated us-
2
dates consist of ill-defined localized magnetic moments ing a standard powder sample of CeO . Powder samples
0 2
. where the magnetic exchange interaction is comparable to were sealed in a silica-glass capillary of 0.1-mm diameter,
1
the charge gap.5–7 On the other hand, inorganic candidates and the capillary was rotated by an angle of 30 deg from
0
7 suffer from unwanted disorder/impurity/nonstoichiometry. the sample-stage axis during measurement. The diffraction
1 Na Ir O 8 shows a spin-glass-like transition near 6–7 K,9,10 patterns were analyzed using the Rietveld refinement with
4 3 8
: whereas ZnCu (OH) Cl 11 and Ba CuSb O 12 include a Rietan-FPcode.17 Themagneticsusceptibilitywasmeasured
v 3 6 2 3 2 9
i considerable intermixture of cations. BaCu3V2O8(OH)213 withacommercialsusceptometer(QuantumDesignMPMS)
X and6H-BBa NiSb O 14 havea substantiallow-temperature above 2 K, and with a home-made probe equipped with a
3 2 9
r Curie tail due to unwanted impurities. In the case of SQUID sensor in a dilution refrigerator down to 37 mK in
a
BaCu V O (OH) , an inhomogeneous magnetic order has various external fields up to 7 mT. The signal of the sensor
3 2 8 2
been detected through NMR measurements around 9 K, be- wascalibratedwiththemeasureddatausingMPMSfrom2to
lowwhichtheunwantedCurietailgrowsrapidly.15,16 4K.Themagnetizationat1.4Kupto50Twasmeasuredin
We have discovered the absense of magnetic long range pulsedfieldsbyaninductionmethodatCenterforAdvanced
order in a hexagonallattice of Ru5+ dimers in Ba ZnRu O High Magnetic Field Science in Osaka University. The spe-
3 2 9
down to 37 mK, where neither Curie tail nor glassy behav- cificheatwasmeasuredwithacommercialmeasurementsys-
iorisdetected.Themagneticspecificheatshowsnoanomaly tem (Quantum Design PPMS). The ac resistivity was mea-
below 80 K, and is found to be linear in temperature below suredwithanLCRmeter(AgilentE4980A)withafrequency
around 5 K. These thermodynamic measurements suggest a of10kHz.
spin-liquidlikegroundstate inthisoxide.TheRu5+ ionacts Figure 1(a) schematically shows the crystal structure of
asawell-localizedS =3/2spin,andthespinliquidistotally Ba MRu O .18 Thetwoface-sharedRuO octahedra(Ru O
3 2 9 6 2 9
unprecedentedinsuchalargespin. dimerblock)formalayeredstructure,andareinterconnected
through the MO octahedron along the c-axis in a corner-
6
∗[email protected]
1
J.Phys.Soc.Jpn.
,*(cid:12) -(cid:29)., (cid:24)(cid:19)(cid:3)-(cid:26)(cid:23)(cid:2)(cid:27)(cid:28) (cid:8)(cid:19)(cid:12)
(
(cid:23)%(cid:0)(cid:1)(cid:1)(cid:22)(cid:1) (cid:0)/
(
(cid:10)
(cid:4)
+(cid:1) -(cid:29)(cid:25)(cid:14)
(cid:0)
(cid:18)(cid:7)(cid:8) (cid:0)(cid:1)(cid:22)(cid:1)
(cid:21)(cid:17)*(cid:17)(cid:15) -(cid:29)
"(cid:15)(cid:17) (cid:25)(cid:14)(cid:1)(cid:22)(cid:3).(cid:19)(cid:1)(cid:22)#
(cid:10)
(cid:14)(cid:17)(cid:15)(cid:16)(cid:12) (cid:24)(cid:0)(cid:1)(cid:22)(cid:7)(cid:19)(cid:6)(cid:29)(cid:3)(cid:30)(cid:7)(cid:25)(cid:30)(cid:30)(cid:14)(cid:1)(cid:6)(cid:26)(cid:7)(cid:3)(cid:31)(cid:23)(cid:7) (cid:2)(cid:27)(cid:28) (cid:8)$(cid:12) )(cid:23)(cid:16)$ (cid:0)(cid:22)(cid:1) (cid:5) (cid:0)(cid:1) (cid:5)(cid:1) (cid:0)(cid:1)(cid:1)(cid:0)(cid:1)(cid:0)(cid:29)(cid:0)(cid:22)(cid:1)(cid:7)’ (cid:5)(cid:1)(cid:1)
(cid:21)(cid:22)(cid:7)(cid:23) (cid:26)!"(cid:7)(cid:29)(cid:7)#(cid:22)(cid:5)(cid:4)(cid:5) ’(cid:10)("(cid:10)(cid:20)(cid:19)(cid:15)(cid:23)(cid:20)(cid:10)(cid:7)(cid:8)(cid:31)(cid:12)
(cid:18)(cid:7)(cid:8)(cid:19)(cid:20) ,*(cid:12) (cid:0)(cid:5) (cid:24)(cid:19)(cid:3)(cid:25)(cid:14)(cid:26)(cid:23)(cid:2)(cid:27)(cid:28) (cid:8)(cid:21)(cid:12)
(cid:16)(cid:17)(cid:15) (
(cid:10)(cid:14) (cid:23)%
(cid:14)(cid:15) (
(cid:13)
(cid:4)(cid:10) (cid:0)(cid:1) (cid:1)(cid:22)(cid:1)(cid:30)
(cid:0)(cid:1) (cid:2)(cid:1) (cid:3)(cid:1) (cid:4)(cid:1) (cid:5)(cid:1) (cid:6)(cid:1) +(cid:1)
(cid:2)(cid:0)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12) (cid:8)(cid:0) (cid:23)(cid:12)(cid:1)(cid:22)(cid:1)(cid:6)
(cid:18)(cid:7) (cid:26)
(cid:16)(cid:17)(cid:15)(cid:18)(cid:7)(cid:8)(cid:19)(cid:20)(cid:21)(cid:22)(cid:7)(cid:23)(cid:14)(cid:17)(cid:15)(cid:16)(cid:12) (cid:8)(cid:0)(cid:0)%(cid:3)&(cid:8)(cid:2)(cid:3)%(cid:3)&(cid:8)(cid:0)(cid:9)&(cid:3)&(cid:12)(cid:6)(cid:12)(cid:12) (cid:8)(cid:0)(cid:1)%(cid:3)&(cid:4)%(cid:3)&(cid:3)(cid:12) (cid:8)(cid:10)(cid:12) )(cid:23)(cid:16)$(cid:10)"(cid:15)(cid:17)(cid:21)(cid:17)*(cid:17)(cid:15) (cid:1)(cid:5)(cid:0)(cid:1)(cid:1)+(cid:7)(cid:8)%(cid:0)(cid:2)(cid:24)(cid:1)(cid:1)(cid:22)(cid:22)(cid:1)(cid:1)(cid:1)(cid:2)(cid:4)(cid:1)(cid:0)(cid:1)(cid:0)+(cid:1)(cid:0) (cid:0)(cid:2)(cid:1)(cid:1)(cid:0)(cid:7)(cid:3)(cid:8)(cid:0)(cid:0)’(cid:1)(cid:22)(cid:1)(cid:12)(cid:4)(cid:4)(cid:1)(cid:7)(cid:31)(cid:1) (cid:5)(cid:1) (cid:0)(cid:1)(cid:0)
(cid:10)(cid:14) ’(cid:10)("(cid:10)(cid:20)(cid:19)(cid:15)(cid:23)(cid:20)(cid:10)(cid:7)(cid:8)(cid:31)(cid:12)
(cid:14)(cid:15)
(cid:13)
Fig. 2. (Color online) (a)Magnetic susceptibility of Ba3MRu2O9 above
(cid:3)(cid:3)(cid:22)(cid:2) (cid:3)(cid:3)(cid:22)(cid:4) (cid:3)(cid:3)(cid:22)(cid:6) (cid:3)(cid:4) (cid:3)(cid:5) 4 K. Upturn toward low temperatures for M = Zn0.3Ca0.7 is due to the
(cid:2)(cid:0)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12) (cid:2)(cid:0)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12) 0.1% contribution of unwanted magnetic impurities. Solid curve denotes
the intrinsic susceptibility of M = Zn0.3Ca0.7 obtained by subtracting of
Fig. 1. (Coloronline)CrystalstructureofBa3MRu2O9.(a)Layeredstruc- thelow-temperatureCurieterm.(b)Magneticsusceptibilitybelow10Kfor
turewherethetwoface-sharedRuO6 octahedra(theRu2O9 dimer)andthe Ba3ZnRu2O9.Nosignofaphasetransitionisdetecteddownto37mK.The
MO6 octahedronarealternately stackedalongthec-axis.(b)Theabplane insetshowsthemagnetization Mplottedasafunctionofexternalfieldµ0H
layerwheretheRu2O9dimerandMO6formanedge-sharednetworktocon- at1.4K.
structahexagonaldimerlatticeofRu5+.(c)Thesynchrotronx-raydiffrac-
tionpatternandtheRietveldrefinementofBa3ZnRu2O9at80K.(d)(e)The
magnifiedviewofthediffractionpattern.Thearrowindicatesapositionof
possiblesuperlatticereflectiontoprobeinter-cationmixtureofZnandRu.
Asshowninthefigure,therefinementissatisfactory,andwe
haveverifiedthecrystalstructureshowninFigs.1(a)and1(b)
(SpacegroupP63/mmc(No.194),a=5.7576Å,c=14.1424
Å).Wealsoemphasizethatnotraceofimpurityphasesisde-
sharedarrangement.TheRu5+ ionwithanelectronicconfig-
tected,andthesampleispureenoughtodiscussthethermo-
uration of (4d)3 acts as a local moment of S = 3/2 and is
dynamicpropertiesofthe main phase.Figures1(d)and 1(e)
responsibleforthemagnetismofBa MRu O .
3 2 9 show the magnified view of the diffraction pattern. The ar-
Figure1(b)depictsthein-layerarrangementoftheRu O
2 9 row indicates a position of possible superlattice reflections,
dimerblocks,whereeachblockisconnectedwiththreeneigh-
if an inter-mixture of Zn and Ru happened as in the case of
boringMO octahedratoformahexagonaldimerlattice.The
6 Ba CuSb O .12 No trace of such reflection peaks safely ex-
speciesof M determinesthemagneticgroundstate.For M = 3 2 9
cludesthepossibilityoftheZn-Ruinter-mixture.
Co,Ni,andCu,thesystemexhibitsanantiferromagneticor-
Figure 2(a) plots the magnetic susceptibility of
der below aroundT = 100 K.18–20 The nearly identical T
N N Ba MRu O forM =Co,Zn,andZn Ca onalogarithmic
for the differentspecies of M impliesthat the magneticmo- 3 2 9 0.3 0.7
scale. Although an antiferromagnetic transition occurs for
mentofthe M ionsplaysasecondaryrole.For M = Ca and
the M =Cosampleasakinkaround100K,amuchsmaller
Sr, the ground state is a nonmagnetic spin-gapped state, in
susceptibility is observed for the M = Zn Ca sample.
whichthetwolocalizedspinsintheRu O dimerblockform 0.3 0.7
2 9 If the low-temperature Curie tail is subtracted by assuming
asingletpair.19,21,22
a tiny contribution (0.1 mol %) of an unwanted magnetic
Figure 1(c) shows the synchrotron x-ray diffraction pat-
impurity, the solid curve shows the intrinsic susceptibility.
tern and the Rietveld refinement of Ba ZnRu O at 80 K.
3 2 9 The curve gives a nearly temperature-independent value of
2
J.Phys.Soc.Jpn.
(cid:0)(cid:1)(cid:0)(cid:1) (cid:24)(cid:19) (cid:25)(cid:14)(cid:26)(cid:23) (cid:27) (cid:0)(cid:1)(cid:2) (cid:31)(cid:12)
(cid:3) (cid:2) (cid:28) (cid:7) Figure 3 shows the resistivity and specific heat of
$((cid:12)(cid:0)(cid:1)(cid:30) (cid:0)(cid:1)(cid:0) 3%(,* tBeam3pZenrRatuu2rOe,9.aTndheinrecsreisatsiveistyupistaos1h0ig8hΩacsm10a3tΩ1c0m0 Kat.rToohmis
(cid:0) (cid:8)
(cid:8) (cid:1)(cid:7) highly insulating behavior eliminates the possibility that the
(cid:15)(cid:18)(cid:7) (cid:0)(cid:1)(cid:1) (cid:15)(cid:7) susceptibility of this oxide is due to simple Pauli paramag-
(cid:16)(cid:17)(cid:16)(cid:15)(cid:17)0(cid:17)(cid:0)(cid:1)(cid:6) (cid:2)(,*(cid:31)(cid:12)(cid:0)(cid:2)(cid:1)(cid:1) (cid:0)(cid:1)+(cid:0)$(cid:7)2(cid:10)(cid:19) ntheetiascmti.vTathieonteemnepregryatiusraerdoeupnedn2d0e0n0ceKn,ewahri3c0h0gKreaimtlypleixecsetehdast
(cid:26)(cid:10)(cid:0)(cid:1)(cid:4) (3% $(cid:17)1(cid:17) Jintra =150–240K.Theseobservationsindicatethattheelec-
(cid:1)(cid:2)(cid:0)(cid:7)(cid:8) (cid:1)(cid:1) (cid:0)(cid:0)(cid:1)(cid:2)(cid:7)(cid:8)(cid:31)(cid:2)(cid:2)(cid:1)(cid:12) (cid:3)(cid:1) (cid:0)(cid:1)+(cid:2))"(cid:10) tmroangsneatriecwmeollmleonctasliazreedrienspthoinssoibxliedefo,rjuthsteifmyianggntehtaistmlo.calized
(cid:0)(cid:1)(cid:2) Thespecificheatdoesnotshowananomalyfrom80down
(cid:5) (cid:0)(cid:1) (cid:5)(cid:1) (cid:0)(cid:1)(cid:1)
to 2 K, indicating the absence of a thermodynamic phase
’(cid:10)("(cid:10)(cid:20)(cid:19)(cid:15)(cid:23)(cid:20)(cid:10)(cid:7)(cid:0)(cid:7)(cid:8)(cid:31)(cid:12)
transition. The inset shows the existence of a temperature-
linear contribution in the specific heat, which is evaluated
Fig. 3. (Coloronline)ResistivityandspecificheatofBa3ZnRu2O9plotted to be 4 mJ/mol K2 for T → 0. The specific heat does not
asafunctionoftemperatureT.InsetplotsC/TasafunctionofT2wherethe
exhibit a Schottky anomaly above 2 K, which is consistent
gaplessT−linearcontributionofCisevaluatedtobe4mJ/molK2.Thesmall
withtheabsenceofaCurietailinthesusceptibility.Thelin-
dotteddatarepresentthespecificheatofanon-magneticreferencematerial
Ba3ZnSb2O9takenfromRef..14 ear dependence is most likely from spinons and not simple
magnons. The magnitude is on the same order as the elec-
tronspecificheatcoefficientofalkalinemetals,providingev-
idence of gapless excitations in the spin sector. In order to
10−5emu/molbelow20K,whichcanbeassignedtotheVan examinethe magneticcontribution,we plotthe specific heat
VlecksusceptibilityoftheRuions. of Ba3ZnSb2O9 taken from Ref.14 as a non-magnetic refer-
The M =Znsampleshowsamagneticsusceptibilityinter- encematerial.Asisclearlyseen,thespecificheatofthetwo
mediatebetweenthe M =CoandZn Ca samples,which samplesisalmostidenticalabove10K,andthemagneticcon-
0.3 0.7
isroughlyconsistentwithaveryrecentreport.23Thissample tributionofRuishiddenintheoverwhelmingmajorcontribu-
shows a weakly temperature-dependentsusceptibility with a tionfromthelattice.Theinsetshowsthatthespecificheatof
broadmaximumaround400Kwithoutanytraceofacuspor Ba3ZnSb2O9hastheidenticalT3termwithoutT-linearterm.
discontinuitydownto 37 mK (Fig. 2(b)).A Curie tail is not This indicates that the magnetic contributionis proportional
visiblethroughoutthemeasuredtemperatureranges,whereas toT inBa3ZnRu2O9atlowtemperatures.
thesusceptibilityweaklyincreaseswithdecreasingtempera- A unique feature of Ba3MRu2O9 is that the magnetic
ture below1 K. The insetof Fig. 2(b)showsthe magnetiza- ground state can be finely tuned from the antiferromag-
tion plotted as a function of external field up to 50 T at 1.4 netic order to the non-magnetic spin-gapped state through
K.Thelinearandreversiblebehaviourindicatesanantiferro- the gapless quantum spin-liquid state. Figures 4(a) and (b)
magenticinteractionlargerthan50T.Ifmagneticimpurities show the magneticsusceptibilityof Ba3Zn1−xCoxRu2O9 and
were present, the magnetizationcurve should be convexup- Ba3Zn1−yCayRu2O9, respectively. The susceptibility at 120
ward as can be explained with the Brillouin function. If the K systematically increases with the Co concentration x, be-
systemwereinaglassystateasseeninBaCu V O (OH) ,13 cause the magnetic Co2+ ion contributes to the susceptibil-
3 2 8 2
thenonlinearsusceptibility(i.e.themagnetizationdevidedby ityinBa3Zn1−xCoxRu2O9.Simultaneously,theantiferromag-
externalfield)shoulddecreasewithincreasingexternalfield. netic transition temperature systematically increases with x.
The present magnetization curve excludes a possible exis- The 20%Co substitutedsample (x = 0.2)shows a tempera-
tence of free magnetic impurities and/or glassy states. Pre- ture hysteresis below approximately15 K, which can be as-
vious neutron diffraction studies have also reported no long signed to a glass transition. For x < 0.2, the system seems
rangeorder.18,23Therefore,theseresultsstronglyindicatethat to be in a spin-liquid state. For Ca substitution, the y = 0.2
thisparamagnetismisduetoaquantumspin-liquidstate. sample shows a finite paramagnetic contribution around 20
Letusevaluatethemagnitudeoftheintra-dimerexchange K and is still in the spin-liquidstate. The magnitudecontin-
energy. Darret et al.21 first analyzed the susceptibility of uouslydecreaseswithy,implyingamagneticallyinhomoge-
Ba MR O (M = Ca, Mg, Cd) assuming independent spin neousstatesuchasamixtureofspin-liquidandspin-gapped
3 2 9
dimers, and evaluated the intra-dimer interaction J to be states.
intra
around200K.LaterSennetal.evaluatedJ tobe240Kfor Here we discuss a possible microscopic mechanism to
intra
Ba3CaRu2O9.22 In an LDA+U calculationfor Ba3CoRu2O9, causevariousmagneticgroundstatesinBa3MRu2O9.Figure
Streltsov24theoreticallyevaluatedJ tobe150K.Thuswe 4 (c) plots the transition temperature as a function of the a-
intra
can conclude that magnetic phase transition is not detected axislength,orequivalently,theinter-dimerdistance.Thetwo
attemperatures5000timeslowerthantheinteractionenergy dotted lines represent the phase boundary determined from
scaleinBa ZnRu O . Figs. 4(a)and4(b).First ofall, we emphasizethatthe inter-
3 2 9
dimer interaction competes with the intra-dimer interaction
3
J.Phys.Soc.Jpn.
(cid:23)(cid:16) (cid:25)(cid:26)(cid:18) (cid:27)
(cid:24) (cid:1) (cid:28)
(cid:30)(cid:31) !, (cid:30)(cid:31) !(cid:16)
(cid:7) " " (cid:7) (cid:8) (cid:8) thefactthatthemagneticmomentiscomprisedofdimerized
,%(cid:22) (cid:1)(cid:0) (cid:20)(cid:16)(cid:22) "(cid:9)(cid:7)(cid:5)(cid:0) (cid:7)(cid:5)(cid:6) (cid:20)(cid:29)(cid:22) spins;thetwoS = 3/2spinscantakespinstatesofStot =0,
(cid:13) (cid:0)(cid:5)(cid:28) (cid:8)(cid:9)(cid:0) 1,2,or3.Anearlyneutronexperiment18 andfirst-principles
(cid:13)(cid:18)2 (cid:0)(cid:5)(cid:3) calculations24 suggestStot ∼2(1.5-2µBperRu)for M =Co,
(cid:24)(cid:19)(cid:12) (cid:7)(cid:5)(cid:0) (cid:0)(cid:5)(cid:7) butStot =0for M =Ca.22 Hence,weexpectthatthemagni-
(cid:0) (cid:0)(cid:5)(cid:2) tudeofS varies(perhapsdynamically)between0and2for
(cid:7) tot
(cid:8)(cid:19)(cid:20) (cid:7)(cid:0) M = Zn, causing a strong magnetic fluctuation, which sup-
(cid:29)#%#(cid:17) (cid:0)(cid:5)(cid:1) (cid:0)(cid:5)(cid:1) presses the magnetic ordering.A recenttheoreticalstudy by
(cid:14)(cid:17)# (cid:0)(cid:5)(cid:7) (cid:0)(cid:5)(cid:6) Watanabe et al.25 suggests that randomness in the exchange
(cid:12)
1 interactioncan inducespin-liquid-likebehavior.The present
$
.(cid:18) "(cid:9)(cid:0) (cid:0)(cid:5)(cid:0)(cid:6) (cid:0)(cid:5)(cid:10) oxidemayhaverandomnessnotin Jinter butinStot.Thisidea
can be examined by carefully analyzing the neutron diffrac-
(cid:0) (cid:0)
(cid:0) (cid:6)(cid:0) (cid:7)(cid:0)(cid:0) (cid:0) (cid:1)(cid:0) (cid:2)(cid:0) (cid:3)(cid:0) (cid:4)(cid:0) tionofBa3Zn1−xCoxRu2O9.
(cid:11)(cid:12)(cid:13)(cid:14)(cid:12)(cid:15)(cid:16)(cid:17)(cid:18)(cid:15)(cid:12)(cid:19)(cid:20)(cid:21)(cid:22) (cid:11)(cid:12)(cid:13)(cid:14)(cid:12)(cid:15)(cid:16)(cid:17)(cid:18)(cid:15)(cid:12)(cid:19)(cid:20)(cid:21)(cid:22)
In summary, we have discovered that no magnetic transi-
tions occur down to 37 mK in Ba ZnRu O . The T-linear
*+ -./ .0 3 2 9
magnetic specific heat and the paramagnetic susceptibility
(cid:30)(cid:31)(cid:7) "!," (cid:20)1(cid:22) stronglysuggestaquantumspinliquidstate.Consideringthat
(cid:7)(cid:0)(cid:0) "(cid:9)(cid:7)
the related oxides show the antiferromagnetic order or the
(cid:0)(cid:5)(cid:28)
spin-gapped nonmagnetic state, we suggest that competing
(cid:22) (cid:0)(cid:5)(cid:3)
(cid:21)
interactionbetweenintra-andinter-dimerinteractionsshould
(cid:20)
(cid:1)(cid:19)) (cid:6)(cid:0) stabilizethisspinliquidlikestate.
(cid:0)(cid:5)(cid:2)
The authors would like to thank Chisa Hotta and Yukio
(cid:30)(cid:31)(cid:7) (cid:8)!(cid:16)(cid:8) Yasui for fruitful discussion and useful advise. This work
"(cid:9)(cid:8)(cid:9)(cid:0) (cid:8)(cid:9)(cid:0)(cid:5)(cid:7) (cid:0)(cid:5)(cid:1) (cid:0)(cid:5)(cid:10)
was partially supported by Grant-in-Aid for Scientific Re-
(cid:0)
search and a Grant-in-Aid for JSPS Fellows, Japan Society
(cid:6)(cid:5)(cid:10)(cid:2) (cid:6)(cid:5)(cid:10)(cid:3) (cid:6)(cid:5)(cid:10)(cid:4) (cid:6)(cid:5)(cid:4) (cid:6)(cid:5)(cid:4)(cid:1) (cid:6)(cid:5)(cid:4)(cid:2)
forthePromotionofScience,Japan(KakenhiNos.25610091,
(cid:0) (cid:16)"#$(cid:19)%(cid:12)(cid:31)&(cid:17)’(cid:19)(cid:20)((cid:22)
26247060, 15J04615), and by Program for Leading Grad-
uate Schools “Integrative Graduate Education and Research
Fig. 4. (Coloronline)Magneticsusceptibility of(a)Ba3Zn1−xCoxRu2O9 in Green Natural Sciences”, MEXT, Japan. The synchrotron
and(b)Ba3Zn1−yCayRu2O9.(c)Transitiontemperatureplottedasafunction x-ray diffraction was performed under the approval of the
ofthea-axislength(theinter-dimerdistance).Dottedlinesindicatetheap-
proximatephaseboundariesdeterminedfrom(a)and(b).AF,QSL,andSG PhotonFactoryProgramAdvisoryCommittee(ProposalNos.
standforantiferromagnetically orderedstate,quantumspin-liquidstateand 2012G718and2012S2-005).
spin-gappedstate,respectively.
1) P.Anderson:Mater.Res.Bull.8(1973)153.
(J =150–240K) in this family,if the numberof the near- 2) L.Balents:Nature464(2010)199.
intra
3) S.-S.LeeandP.A.Lee:Phys.Rev.Lett.95(2005)036403.
est neighbor dimers (z = 6) is taken into account. Accord-
4) P.A.Lee,N.Nagaosa,andX.-G.Wen:Rev.Mod.Phys.78(2006)17.
ing to the LDA+U calculation,24 the interaction J along
inter 5) Y.Shimizu,K.Miyagawa,K.Kanoda,M.Maesato,andG.Saito:Phys.
theRu–O–O–Runetworkbetweentheneighboringdimersis Rev.Lett.91(2003)107001.
evaluatedtobe30–40K,andwearriveattheparticularcon- 6) T.Itou,A.Oyamada,S.Maegawa,M.Tamura,andR.Kato:Phys.Rev.
ditionzJ ∼ J . We furthernote thattheinteractionbe- B77(2008)104413.
inter intra
7) T. Isono, H. Kamo, A. Ueda, K. Takahashi, M. Kimata, H. Tajima,
tweenCoandRuisevaluatedtobelessthan8K,beingmuch
S.Tsuchiya, T.Terashima, S.Uji,andH.Mori:Phys.Rev.Lett.112
smallerthan J .Thus,eventhoughthemagnetismofCo2+
inter (2014)177201.
ionscomplicatesthemagneticstructure,wemaysafelyignore 8) Y.Okamoto,M.Nohara,H.Aruga-Katori,andH.Takagi:Phys.Rev.
this in the lowest approximation. We expect that the a-axis Lett.99(2007)137207.
lengthchangesJ ;Forashorta,theconditionzJ > J 9) R.Dally,T.Hogan,A.Amato,H.Luetkens,C.Baines,J.Rodriguez-
inter inter intra
Rivera, M. J.Graf, and S. D.Wilson: Phys.Rev. Lett. 113 (2014)
stabilizes the antiferromagnetic order, wheres for a long a,
247601.
zJ < J favorsthespinsingletwithindimers.Weexpect
inter intra 10) A.C.Shockley,F.Bert,J.-C.Orain,Y.Okamoto,andP.Mendels:Phys.
thatthequantumspin-liquidstatecanemergefromadelicate Rev.Lett.115(2015)047201.
conditionofzJ ∼ J . 11) M.P.Shores,E.A.Nytko, B.M.Bartlett, andD.G.Nocera:J.Am.
inter intra
Inconventionaldimerspin lattices, thespin-liquidstate is Chem.Soc.127(2005)13462.
12) S.Nakatsuji,K.Kuga,K.Kimura,R.Satake,N.Katayama,E.Nishi-
expected to emerge just at the boundary between the spin-
bori,H.Sawa,R.Ishii,M.Hagiwara,F.Bridges,T.U.Ito,W.Hige-
gapped state and the antiferromagnetic state. In the present
moto, Y. Karaki, M.Halim, A. A.Nugroho, J.A.Rodriguez-Rivera,
system,incontrast,thespin-liquidstateseemstobestablein M.A.Green,andC.Broholm:Science336(2012)559.
a finite range of zJ /J . We think that this arises from 13) Y. Okamoto, H. Yoshida, and Z. Hiroi: J.Phys.Soc.Jpn.78 (2009)
inter intra
4
J.Phys.Soc.Jpn.
033701. 20) J.Rijssenbeek, Q.Huang,R.Erwin,H.Zandbergen, andR.Cava:J.
14) J.G.Cheng,G.Li,L.Balicas,J.S.Zhou,J.B.Goodenough,C.Xu, SolidStateChem.146(1999)65.
andH.D.Zhou:Phys.Rev.Lett.107(2011)197204. 21) J.Darriet,M.Drillon,G.Villeneuve,andP.Hagenmuller:J.SolidState
15) J. A.Quilliam, F. Bert, R. H.Colman, D. Boldrin, A. S.Wills, and Chem.19(1976)213.
P.Mendels:Phys.Rev.B84(2011)180401. 22) M.S.Senn,A.M.Arevalo-Lopez, T.Saito, Y.Shimakawa, andJ.P.
16) M.Yoshida,Y.Okamoto,M.Takigawa,andZ.Hiroi:J.Phys.Soc.Jpn. Attfield:J.Phys.:Condens.Mat.25(2013)496008.
82(2013)013702. 23) P.Beran,S.Ivanov,P.Nordblad,S.Middey,A.Nag,D.Sarma,S.Ray,
17) F.IzumiandF.Momma:SolidStatePhenom.130(2007)15. andR.Mathieu:SolidStateSci.50(2015)58.
18) P.LightfootandP.Battle:J.SolidStateChem.89(1990)174. 24) S.V.Streltsov:Phys.Rev.B88(2013)024429.
19) I.Fernandez,R.Greatrex,andN.N.Greenwood:J.SolidStateChem. 25) K.Watanabe,H.Kawamura,H.Nakano,andT.Sakai:J.Phys.Soc.Jpn.
34(1980)121. 83(2014)034714.
5