Table Of ContentDouble phase transition in the triangular antiferromagnet Ba CoTa O
3 2 9
K. M. Ranjith, K. Brinda, U. Arjun, N. G. Hegde, and R. Nath∗
School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram-695016, India
(Dated: January 9, 2017)
Here,wereportthesynthesisandmagneticpropertiesofanewtriangularlatticeantiferromagnet
Ba CoTa O . The effective spin of Co2+ is found to be J = 1/2 at low temperatures due to the
3 2 9
combined effect of crystal field and spin-orbit coupling. Ba CoTa O undergoes two successive
3 2 9
magneticphasetransitionsatT (cid:39)0.70KandT (cid:39)0.57Kinzeroappliedfield,whichistypical
N1 N2
for triangular antiferromagnets with the easy-axis magnetic anisotropy. With increasing field, the
transition anomalies are found to shift toward low temperatures, confirming the antiferromagnetic
nature of the transitions. At higher fields, the transition peaks in the heat capacity data disappear
7
andgivewaytoabroadmaximum,whichcanbeascribedtoaSchottkyanomalyduetotheZeeman
1
splitting of spin levels. The H −T phase diagram of the compound shows three distinct phases.
0
The possible nature of these phases is discussed.
2
n PACSnumbers: 75.10.Jm,75.30.Et,75.30.Kz,75.50.Ee
a
J
6 I. INTRODUCTION tive phase transitions, Ba3CoSb2O9 has only one tran-
sition in zero field, likely due to the easy-axis and easy-
] planetypeanisotropies,respectively.16,23 Ba CoSb O is
i Magnetic frustration and the rich variety of phases 3 2 9
c reported to display magnetization plateaus at interme-
driven by competing magnetic couplings have attracted
s diate fields below the saturation field.14 Because of such
- a lot of attention in present-day condensed matter
l non-trivialandexoticproperties,Co2+ basedTLAFsare
r physics.1 Two dimensional (2D) triangular lattice anti-
t paid a great deal of attention both experimentally and
m ferromagnet (TLAF) is the simplest example of a geo-
theoretically.
metrically frustrated quantum system, where lattice ge-
. Inthispaper,wereportthemagneticbehaviorofanew
t ometryprecludessimultaneousminimizationofexchange
a compound of this family, Ba CoTa O . It crystallizes in
m interaction energy on different bonds, thus leading to ahexagonalstructure25with3thespa2ce9groupP¯3m1. Fig-
a highly degenerate classical ground state.2–4 Quantum
- ure 1 shows the crystal structure of Ba CoTa O , which
d fluctuations,whicharemostpronouncedinsystemswith 3 2 9
canberepresentedasaframeworkconsistingofCoO oc-
n reduced dimensionality and low spin values, lift the clas- 6
o sical degeneracy and stabilize a variety of exotic phases, tahedra sharing corners with dimers of TaO6 octahedra.
c including quantum spin liquid (QSL),5–8 spin ice,9 and TheCo2+ ions,whichoccupythe1bsite,formtriangular
[ lattices parallel to the ab−plane (see the bottom panel
field-induced states manifesting themselves by plateau
of Fig. 1) and are separated by non-magnetic Ba atoms.
1 featuresinthemagnetization.10,11Inaquasi-2Disotropic
v Heisenberg TLAF, the spins order antiferromagnetically A weak inter-layer coupling still can be envisaged via
6 ina120◦structureatzerofield. Underexternalmagnetic an extended Co2+-O2−-Ta5+-O2−-Co2+ pathway. Our
8 magnetic measurements reveal two magnetic phase tran-
field this 120◦ ordered state evolves to an ‘up-up-down’
5 sitionsatT (cid:39)0.70KandT (cid:39)0.57Kwithacomplex
(uud) state showing a plateau at the 1/3 of the satu- N1 N2
1
H −T phase diagram.
0 ration magnetization, through quantum and/or thermal
1. fluctuations, as in the S = 1/2 compounds Cs2CuBr4
and Ba CoSb O .12–14 At very high fields, the uud state
0 3 2 9
becomes unstable leading to canted spin states. Ground II. EXPERIMENTAL DETAILS
7
1 states of TLAFs are also sensitive to inter-layer coupling
: and exchange anisotropy which often lead to even more Polycrystalline sample of Ba CoTa O was prepared
v 3 2 9
i complex phases.3,15 by a conventional solid-state reaction technique using
X Recently, a family of TLAFs, Ba MM(cid:48)O (M = Co, BaCO (99.999%, Aldrich), CoO (99.99%, Aldrich), and
3 2 9 3
r Ni, Cu, Mn and M(cid:48) = Sb and Nb), has been studied ex- Ta O (99.99%, Aldrich) as starting materials. Stoichio-
a 2 5
tensively. Thesestudiesunveiledaplethoraofinteresting metric mixture of the starting materials was intimately
properties.14,16–24 The S =1/2 compound Ba CuSb O ground, pressed into pellets, and fired at 900 ◦C for
3 2 9
shows features of a QSL, such as the absence of mag- 8 hours and then at 1200 ◦C for 48 hours in air with
netic long-range ordering (LRO) down to 0.2 K despite intermediate grindings and pelletizations. Phase purity
the large Curie-Weiss temperature θ , and the lin- of the sample was confirmed by recording powder x-ray
CW
ear temperature dependence of the heat capacity at low diffraction (XRD) pattern using the PANalytical pow-
temperatures.20Owingtotheoctahedralcrystalfieldand der diffractometer (CuK radiation, λ = 1.5406 ˚A) at
α ave
thespin-orbitcoupling,theCo2+ioninBa CoSb O and room temperature. Le-bail fit of the observed XRD pat-
3 2 9
Ba CoNb O features an effective spin S = 1/2 at low tern was performed using FULLPROF package26 for which
3 2 9
temperatures. While Ba CoNb O shows two consecu- the initial parameters were taken from Ref. 25. Figure 2
3 2 9
2
Ba3CoTa2O9 Iobs
)
nits Ical
b. u Iobs - Iobs
r
a Bragg positions
(
y
sit
n
e
nt
I
10 20 30 40 50 60 70
2 (degree)
FIG. 2: Powder XRD data for Ba CoTa O collected at
3 2 9
roomtemperature. ThesolidlinerepresentstheLe-bailfitof
the data. The Bragg peak positions are indicated by green
verticalbars,andthebottomsolidbluelineindicatesthedif-
ference between the experimental and calculated intensities.
III. RESULTS AND DISCUSSION
A. Magnetization
Temperature-dependent magnetic susceptibility
χ(T) (≡M/H) measured at applied fields of H =0.5 T,
1 T, and 3 T are shown in the upper panel of Fig. 3.
With decreasing T, χ(T) increases in a Curie-Weiss
(CW) manner as expected in the paramagnetic regime.
No indication of a magnetic LRO was observed down
to 2 K. As shown in the lower panel of Fig. 3, 1/χ
varies linearly with T in the high-T regime and a change
FIG. 1: Upper panel: Schematic crystal structure of
of slope is observed at low temperatures. In order to
Ba CoTa O . Lower panel: Triangular layer of Co2+ ions
3 2 9
extract the magnetic parameters, χ(T) measured at
formedbythecornersharingofCoO andTaO octahedrain
6 6
the ab−plane. H =1Tinthehigh-T regimewasfittedbythefollowing
expression:
C
χ(T)=χ + , (1)
0 (T +θ )
CW
shows the room temperature powder XRD pattern for
Ba3CoTa2O9 along with its Le-bail fit. All the peaks in where χ0 is the temperature-independent contribution
the XRD pattern could be indexed based on the space consistingofcorediamagnetismofthecoreelectronshells
group P¯3m1 (No. 164). The lattice parameters ob- (χ )andVan-Vleckparamagnetism(χ )oftheopen
core VV
tained from the Le-bail fit [a = b = 5.7748(6) ˚A and shellsoftheCo2+ ionspresentinthesample. Thesecond
c = 7.0908(1) ˚A] are comparable to the previous report term in Eq. (1) is the CW law with the CW tempera-
[a=b=5.7750 ˚A and c=7.0960 ˚A].25 The goodness of ture (θ ) and Curie constant C = N µ2 /3k , where
CW A eff B
fit parameter was obtained to be χ2 (cid:39)4.58. N is Avogadro’s number, k is Boltzmann constant,
A B
(cid:112)
Magnetization (M) measurements were performed as µeff = g S(S+1)µB is the effective magnetic moment,
afunctionoftemperatureT andappliedfieldH usingvi- g is the Land´e g-factor, and S is the spin quantum num-
brating sample magnetometer (VSM) attachment to the ber.
physical property measurement system (PPMS, Quan- OurCWfitinthehigh-temperaturerange(T >65K)
tum Design). Heat capacity Cp as a function of T and yieldsχ0 (cid:39)−6.91×10−4 cm3/mol,C (cid:39)3.96cm3K/mol,
H was measured on a pressed pellet using the relaxation and θCW (cid:39) 50.1 K. From this value of C, the effective
(cid:112)
technique in a PPMS. The low temperature (T ≤ 2 K) moment was calculated to be µeff [= 3kBC/NA] (cid:39)
Cp measurements were carried out using an additional 5.63 µB/Co. This value of µeff is close to the value of
(cid:112)
3He attachment. ∼ 6 µ [= g S(S+1)µ ] expected for the high-spin
B B
3
3.0
0.4 1.5
Ba3CoTa2O9 2.5 12)M (B Van-Vleck lMin e(arB )fit 01..50 dM/dH Ba3CoTa2O9
mol) 0.3 HH == 01. 5T T 2)B.0 00 2 H 4(T) dM6/dH 8 0.0 2.1 K
3 m/ H = 3 T 1M ( .5
c 0.2 5 K
(
1.0
10 K
0.1
0.5
50 K
0.0 0.0
1 10 100 0 2 4 6 8
T (K)
H (T)
120 1/ FIG. 4: Magnetization isotherm (M vs H) of Ba CoTa O
3 2 9
Eq. (1) (T > 65 K) measured at different temperatures. Inset: M vs H (left
1
- l) Eq. (1) (T < 20 K) y−axis) at 2.1 K showing a nearly linear increase above Hs
o duetoVan-Vleckparamagnetism. dM/dH vsH isalsoplot-
m80
/ ted in the right y−axis.
3 m
c
(
1/40
H = 1 T ACoB3 (A = Cs, Rb and B = Cl, Br).28
Inordertoobtainfurtherinsightintotheground-state
0 properties, we measured M(H) isotherms at different
0 100 200 300 temperatures T =2.1 K, 5 K, 10 K, and 50 K, as shown
T (K) in Fig. 4. At higher temperatures (T >50 K), M varies
almost linearly with H, as expected for AFM materi-
FIG. 3: Upper panel: χ(T) of Ba CoTa O measured at dif- als with a large exchange coupling. For T < 50 K, it
3 2 9
ferentappliedmagneticfields. Lowerpanel: Inversemagnetic develops a curvature, which is more pronounced at low
susceptibility (1/χ) of Ba3CoTa2O9 as a function of temper- temperatures. At T =2.1 K, the Co2+ spins saturate at
ature measured at 1 T along with the fits by Eq. (1). H (cid:39) 3 T, above which M increases linearly, but with a
s
much smaller slope.
The inset of Fig. 4 shows the magnetic isotherm (M
vs H) and its derivative dM vs H at T = 2.1 K in
state (S = 3/2) of Co2+ taking g (cid:39) 3.1, obtained from dH
the left and right y−axes, respectively. The derivative
the magnetization data (discussed later).
shows a gradual change of slope with increasing field,
Since a change in slope was observed at low temper- andabove∼3Tthechangeisalmostnegligiblesuggest-
atures for 1/χ, the data were fitted separately using ing that the saturation field H is close to 3 T. This
s
Eq.(1)forT <20K,whichyieldsχ0 (cid:39)0.0355cm3/mol, small value of Hs is comparable to that reported for
C (cid:39) 1.2 cm3K/mol, and θCW (cid:39) 1 K. From this value Ba3CoNb2O917 but much smaller than Hs (cid:39) 32 T in
of C, the effective moment was calculated to be µeff (cid:39) Ba3CoSb2O9.14 Above Hs, there isa slow linear increase
3.1 µB/Co, which is reminiscent of an effective S = 12 inM,usuallyattributedtothetemperature-independent
state with the same g (cid:39) 3.1 (the value of µeff = 2.7 µB Van-Vleckparamagneticcontribution,typicalforaCo2+
wouldbeexpected). Thereductioninµeff uponcoolingis ioninanoctahedralenvironment.29,30 Similarscenariois
indeedexpectedforCo2+ intheoctahedralenvironment, also reported for Ba CoNb O and Ba CoSb O .14,17,27
3 2 9 3 2 9
because spin-orbit coupling λ splits the lowest orbital A linear fit of the data above H gives a slope of ∼
s
triplet into six Kramers doublets. When the tempera- 6.4 ×10−2 µ /T, which corresponds to the Van-Vleck
B
ture is low enough such that T (cid:28) λ/kB, magnetic be- susceptibilityχVV (cid:39)3.7×10−2 cm3/mol. Thisisinclose
haviorisdeterminedbythelowestKramersdoubletwith agreement with the value χ (cid:39)3.4×10−2 cm3/mol re-
VV
J = 1,whereJ standsforthefullangularmomentum,as ported for the TLAF compound Ba CoNb O .17 From
2 3 2 9
opposedtothespinangularmomentumS. InCo2+ com- theinterceptofthelinearfitaboveH onthey−axis,the
s
pounds,|λ|/k (cid:39)250K27andhenceatlowtemperatures saturationmagnetizationwasobtainedasM (cid:39)1.55µ .
B s B
Ba CoTa O isexpectedtoproduceaneffectivespin-1/2 This value of M (M = gJµ ) corresponds to an aver-
3 2 9 s s B
behavior. The effective spin-1/2 ground state is also re- age g−value of g (cid:39) 3.1 for J = 1/2, and the deviation
ported for other TLAFs with the octahedral coordinates from the free-electron g-value of 2.0 is due to the spin-
Co2+ sites, such as Ba CoM O (M = Sb, Nb)22,23 and orbit coupling. Such a large value of g is also reported
3 2 9
4
Fig. 5 shows C data as a function of T in zero applied
p
6 fieldandthefit(solidline)byEq.(2)withc =3,c =1,
1 2
)
2 9 R ln2 c = 2, and c = 9. Here, c , c , c , and c represent
K 3 4 1 2 3 4
ol the number of Ba, Co, Ta, and O atoms per formula
C/T (J/m36mag 12C (J/mol K)p0000 24 (J/mol K)mag uitdθshDniffe2ittehlf,raoeerrrngenCtesupoDmde2i+ecbffbt,eeiyvrareeenonldytfce.θemasDtTp3oinehmfroetasrhtsOeupure2mae−rtso.:fomoFfθriimDccnn1aumllfelaaoyqs,rusuteaBhnslei,sat3wh.t+ioegBhau1e-ns5Tced,adfiuwTttsahhew3ric+aeohesf,
S extrapolateddownto2KandC (T)wasestimatedby
mag
0 subtracting C (T) from C (T). C (T)/T is plotted
0 50 100 150 ph p mag
T (K) as a function of T in Fig. 5.
0 0 To cross-check the reliability of the fitting procedure,
1 10
T (K) we calculated the total magnetic entropy (Smag) by inte-
gratingC (T)/T between2.1Kandhightemperatures
FIG. 5: C /T (left y-axis) and S (right y-axis) as a mag
mag mag
as
function of T in the low temperature regime. The downward
arrows indicate the two transition anomalies. The horizon- (cid:90) T C (T(cid:48))
tal dashed line corresponds to Rln2. Inset: Temperature- Smag(T)= maTg(cid:48) dT(cid:48). (3)
dependent heat capacity C (T) of Ba CoTa O measured at 2.1K
p 3 2 9
zero applied field along with the calculated Cph(T) (solid The obtained Smag is plotted on the right y−axis of
line). Fig. 5. It reaches the value of S (cid:39) 5.1 J/mol K at
mag
around 16 K. This value is only slightly smaller than
the expected theoretical value [S = Rln(2J +1)] of
mag
5.76 J/mol K for J = 1/2. This indeed is a strong ev-
for Ba CoNb O and Ba CoSb O 14,17. The high and
3 2 9 3 2 9 idence for the formation of the J = 1/2 state at low
anisotropic g-values are expected for Co2+ compounds
temperatures.
in the octahedral environment due to the large orbital
The C (T) measured at different applied fields from
contribution.31 The ESR experiment on the analogous p
0 T to 1.5 T in the low temperature regime is shown
compound Ba CoSb O indeed reports the high values
3 2 9 in the upper panel of Fig. 6. In zero field, it exhibits
of g (cid:39)3.84 (for H (cid:107)ab) and g (cid:39)3.87 (for H (cid:107)c).14
two anomalies suggesting two successive magnetic tran-
In contrast to Ba CoNb O and Ba CoSb O , the
3 2 9 3 2 9 sitions at T (cid:39) 0.70 K and T (cid:39) 0.57 K. Below T ,
N1 N2 N2
anomaly in the M vs H curve at Hs (cid:39) 3 T is not very the C (T) data were fitted using a power law C ∝ Tα
sharp.14,17 Theshapeofthisanomalydependsonvarious p p
with the exponent α (cid:39) 2.05 (inset of the upper panel of
factors such as the g-tensor anisotropy. In powder sam-
Fig. 6). A quadratic temperature dependence of C in
p
ples, thisanisotropysmearstheanomalyout. Therefore, the ordered state is expected for 2D lattices.34 With in-
thefactthatourM vsH curvedoesnotshowanysharp
creasing field, the transition peaks get smeared and shift
anomaly at H is possibly indicating at an anisotropic
s towards lower temperatures before they completely dis-
g-value.
appear at H ≥ 1.5 T. With increasing field, a broad
feature appears at about T =2 K for H =1.5 T, which
can be identified as the Schottky anomaly arising due
B. Heat capacity to the Zeeman splitting of the J = 1/2 energy levels at
low temperatures (lower panel of Fig. 6). As the field
Heat capacity C (T) for magnetic insulators has two increases, the Schottky anomaly is observed to shift to-
p
major contributions: phononic (C ) and magnetic wards higher temperatures. It is to be noted that, al-
ph
(C ) parts. At high temperatures, C (T) is mainly though the peak positions and their heights at the mag-
mag p
dominatedbyC ,whileatlowtemperaturesitismostly netic transition as well as Schottky anomaly regimes are
ph
of magnetic origin. In order to estimate the phonon part changing with magnetic field, the value of S at 16 K
mag
oftheheatcapacity,theC (T)dataathightemperature remains close to 5.76 J/mol K, irrespective of the mag-
p
were fitted by the sum of Debye functions nitude of the applied field. For H = 2 T, a theoretical
curve was simulated using the Schottky expression,
C (T)=9R(cid:88)4 c (cid:18) T (cid:19)3(cid:90) θDTn x4ex dx, (2) (cid:18)gµ H(cid:19)2 1
ph n θ (ex−1)2 C =N k B . (4)
n=1 Dn 0 Sch A B 2kBT cosh2(gµBH/2kBT)
whereθ arethecharacteristicDebyetemperaturesand ThisexpressionrepresentstheSchottkyspecificheatdue
Dn
c aretheintegercoefficientsindicatingthecontributions to the Zeeman splitting of the J = 1/2 state without
n
of different atoms (or group of atoms) to C (T). Similar exchange interactions between the spins. As shown in
p
procedure has been adopted in various other compounds Fig.6,thelowtemperaturedatamatchwellwiththesim-
to estimate the phonon contribution.32,33 The inset of ulated curve with g (cid:39) 3.1, further confirming the large
5
0 T 2 K)8 Ba3CoTa2O9
ol K) 6 001.. 57T 5T T C/T (J/mol p246 Cp/T 2.0 TTNN12
J/m 4 1.5 T 0.0 0.2 Li0n.4ear fi0t.6 0.8 1.0 T) 1.5
C (p T (K) H (
2 1.0
Ba3CoTa2O9
0 0.5
0.3 0.6 0.9 1.2
T ( K) I II III
0.0
3 Ba3CoTa2O9 1.5 T 0.0 0.2 0.4 0.6 0.8
2 T
)
K 3 T T (K)
ol Schottky fit
m 2 FIG. 7: The H−T phase diagram for Ba3CoTa2O9 showing
J/ three distinct phase regimes. The dotted lines represent the
(
p power law behavior.
C
1
0 (∼0.18)seeninBa3CoTa2O9 suggeststhattheeasy-axis
0 4 8 12 anisotropy is significantly smaller than the intra-layer
T (K) coupling.
The H − T phase diagram derived from the field-
FIG. 6: Upper panel: C (T) measured at different applied
p dependent C (T) measurements is shown in Fig. 7. It
magneticfieldsinthelow-temperatureregion. Inset: C /T vs p
p
exhibits three distinct phases denoted by I, II, and III.
T withalinearfitbelowT . Lowerpanel: C (T)measured
N2 p
at higher applied fields. The solid line is the simulated curve RegionIIIcorresponds tothe paramagneticphase, while
using Schottky expression Eq. (4). regionsIIandIareexpectedtobethecollinearand120◦
spin states, respectively, in line with the theoretical pre-
dictions and the subsequent experimental realizations in
Ba CoNb O and RbMn(MoO ) .17,37,42,43
3 2 9 4 3
valueofginferredfromthemagnetizationmeasurements. The data points in Fig. 7 are fitted by a power law,
The deviations between the simulated curve and experi-
mentaldataathighertemperaturesareattributedtothe (cid:18) T (cid:19)β
H =H 1− , (5)
phonon contribution of the heat capacity. c T
N
where the critical field H , T , and critical exponent
c N
IV. DISCUSSION β are the fitting parameters. The β value reflects the
universality class and dimensionality of the spin system.
Ba3CoTa2O9 shows two successive magnetic phase The values obtained for TN are consistent with the tran-
transitions at low temperatures. It has been theoreti- sition temperatures at zero applied field and the value of
cally predicted that double magnetic transitions can oc- β (cid:39) 0.31 (for TN2) and 0.38 (for TN1) are close to the
cur in TLAFs when the magnetic anisotropy is of the value of β = 1/3 predicted by the mean-field theory for
easy-axis type, while a single transition is expected for three dimensional (3D) spin systems.44
easy-planetypeanisotropy.35,36 InTLAFswiththeeasy-
axis anisotropy, the 120◦ state is often preceded by a
collinear state. Our zero-field measurements show two V. CONCLUSION
transitionsthatcanbethusassociatedwiththecollinear
state below T and the 120◦ state below T < T . Magnetic properties of the triangular antiferromag-
N1 N2 N1
Theputativeeasy-axisanisotropyinBa CoTa O issim- net Ba CoTa O were investigated. At low tempera-
3 2 9 3 2 9
ilar to that reported for other TLAFs, Ba CoNb O , tures, it undergoes two successive AFM transitions at
3 2 9
RbMn(MoO ) , CsMnI , and CsNiCl .17,37–41 The tem- T (cid:39) 0.70 K and T (cid:39) 0.57 K with a narrow inter-
4 3 3 3 N1 N2
perature range of the intermediate phase can be used mediate phase, which is due to weak easy-axis magnetic
to obtain (T −T )/T that roughly quantifies the anisotropy. Co2+ adopts the J = 1/2 state at low tem-
N1 N2 N1
sizeoftheeasy-axisanisotropywithrespecttotheintra- peratures, whereas at higher temperatures the S = 3/2
layer exchange coupling. The narrow intermediate phase state is observed. The magnetization saturates already
6
at H (cid:39) 3 T suggesting weak magnetic interactions in Acknowledgments
s
thesystem. TheH−T phasediagramdeducedfromthe
heatcapacitymeasurementsshowsthreedistinctphases.
TheabovepeculiarfeaturesrenderBa CoTa O amodel
3 2 9
TLAF compound for further experimental and theoreti-
cal studies. We thank Alexander Tsirlin for fruitful discussions.
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