Table Of ContentHeat capacity of the quantum magnet TiOCl
J. Hemberger1, M. Hoinkis2, M. Klemm2, M. Sing2, R. Claessen2, S. Horn2, and A. Loidl1
1Experimentalphysik V, Center for Electronic Correlations and Magnetism,
Universit¨at Augsburg, D-86135 Augsburg, Germany
2 Experimentalphysik II, Institut fu¨r Physik, Universit¨at Augsburg, D-86135 Augsburg, Germany
Measurements of the heat capacity C(T,H) of the one-dimensional quantum magnet TiOCl are
5 presented for temperatures 2 K < T < 300 K and magnetic fields up to 5 T. Distinct anomalies
0
at 91 K and 67 K signal two subsequent phase transitions. The lower of these transitions clearly
0
is of first order and seems to be related to the spin degrees of freedom. The transition at 92 K
2
probablyinvolvesthelatticeand/ororbitalmoments. Adetailedanalysisofthedatarevealsthatthe
n entropychange∆Sthroughbothtransitionsissurprisinglysmall(∼0.1R),pointingtotheexistence
a strongfluctuationswell intothenon-orderedhigh-temperaturephase. Nosignificant magnetic field
J dependencewas detected.
1
2 PACSnumbers: 71.30.+h,72.80.Ga,65.40.Ba
]
el I. INTRODUCTION resonance9,infraredandRamanspectroscopy10,11 aswell
- asNMRmeasurements12 substantiatedtheseresultsand
r
t The discovery of high-Tc superconductivity in the established a spin gap of the order of 430 K. The ori-
s
. cupratesandofcolossalmagneto-resistanceinmanganite gin of the gap has been identified as due to a first order
at perovskitesgeneratedanenormousinterestintransition- spin-Peierls transition at Tc1, as evidenced by the obser-
m metal oxides (TMOs). TMOs are characterized by an vationofTidimerizationintemperature-dependentx-ray
- intimate coupling of spin, charge, orbital and lattice de- diffraction.13 The nature of a second transition at Tc2 is
d grees of freedom which is the origin of a number of com- still unclear. While a broadening of the NMR lineshape
n plex and exotic ground states. The discovery of a num- into a wide continuum below Tc2 has been attributed to
o ber of new low-dimensional spin 1/2 quantum magnets a possible incommensurate (orbital) ordering12, no cor-
c
[ was another result of this renewed interest. After the responding superlattice reflections could be observed in
first experimental observation of a spin-Peierls scenario x-ray scattering,13 though there is some evidence for a
1 in the organic compound TTF-CuBDT1 more than 30 structuralsymmetryloweringfromthehigh-temperature
v years ago, CuGeO 2 was the first inorganic spin-Peierls phase. ClosetoT∗ ≈135Ktheopeningofaspinpseudo
7 3
1 system. AnotherparamountexampleisNaV2O5,3 aspin gapasdetectedinNMR12 andtheonsetofgiantphonon
5 ladder with mixed-valent vanadium ions undergoing a anomalies in infrared and Raman spectroscopy11 indi-
1 chargeorderingtransition4. Furtherinterestintheselow- cated the presence of strong spin fluctuations and a pro-
0 dimensional quantum magnets comes from the fact that nouncedcoupling to the lattice,respectively,fortemper-
5 upon doping they may undergo metal-to-insulator tran- atures up to T∗ ≈135 K.
0 sitionsandpossiblyrevealsuperconductivity. Duringthe Electronically, TiOCl is a Mott insulator with nomi-
/
t lastdecadeTiOClhasbeenadistinguishedcandidatefor nallytrivalentTi. Electronicstructurecalculationsusing
ma aresonating-valencebondgroundstate5andhasemerged the LDA+U predict a Ti 3d1xy ground state,6,14 how-
asafurtherquantum-spinmagnetwithagappedground ever,couplingtoopticalphononmodescanleadtostrong
d- state5,6. orbitalfluctuations within the t2g crystalfield multiplet.
n Titanium-oxochloride has first been synthesized by Theimportanceofcorrelationeffectshasbeenelucidated
o Friedel andGuerin in 1876.7 The first detailed reporton in LDA+DMFT15,16 studies.
c growth and characterization has been given by Scha¨fer In this brief experimental report we provide detailed
:
v et al.8 almost 50 years ago. TiOCl crystallizes in the measurements of the heat capacity of TiOCl to further
i orthorhombic FeOCl structure, consisting of Ti-O bilay- unravel the nature of the two phase transitions.
X
ers separated by Cl layers. In this structure every Ti is
r
a surrounded by 4 oxygen and 2 chlorine ions forming a
distortedoctahedron. Originally,basedonananalysisof II. EXPERIMENTAL DETAILS
susceptibility data combined with band-structure calcu-
lations,ithasbeensuggestedthatthet orbitalsareor- Single crystals of TiOCl were prepared by chemical
2g
bitallyordered,producingone-dimensionalantiferromag- vapour transport from TiCl and TiO .8 The samples
3 2
netic S = 1/2 chains6. The high-temperature magnetic have been characterized using x-ray diffraction, SQUID
susceptibilitycouldwellbedescribedbyaBonner-Fisher andESRmeasurementsatX-bandfrequencies. Thecrys-
typeofbehaviorwithanexchangeconstantJ =660K.A tal symmetry was found to be orthorhombic with lat-
suddendropofthesusceptibilityalmosttozeroindicated tice parameters of a = 0.379 nm, b = 0.338 nm and
the opening of a spin gap at T =67 K, while a further c = 0.803 nm. The magnetic properties were found to
c1
anomalyhasbeendetectedatT ≈95K.6Electronspin be in excellent agreement with published results6,9. The
c2
2
phasetransitionsforbothzerofieldandanexternalmag-
netic field of 5 T measured on cooling together with a
TiOCl specialheating/coolingrunin the vicinity ofTc1 in zero-
2 K) field, which will be discussed later.
80 0.35 ol
m Concerning the magnetic field dependence we observe
J/
0.30 T ( no effects on the heat capacity within experimental un-
) 60 C/ certainties. The moderate magnetic fields used here nei-
K 0.25 ther shift the transition temperatures, nor do they seem
C (J/mol 40 60 T 8(0K) 100 2 mJ/molK) 1200 tO5o0naktffOheeec×totµthhBeer(eh≈natnr0do.0p,6itehsmeiesnVmv)oallivlseednneeignrgliytghiobeflypohusarmsfieaeltlldrcasonomsfiptoiarordneesdr.
20 C/T ( 0 H50 = k 0Oe tmoatthede ifnrotrminskiBcTmc1a,2gn(e5t.i8caennder7g.y9smcaelVe)oforTtihOeCelxacshaenstgie-
0 50 100 constant J (57 meV).
2 2
T (K)
In order to analyze the nature of the detected anoma-
0
0 100 200 300 liesintermsoffirstorsecondorderphasetransitions,we
performed heating/cooling cycles across the phase tran-
T (K)
sitions. As the experimental setup utilizes a relaxation
method, each data point is related to the average over a
FIG. 1: Heat capacity of TiOCl vs. temperature. The ver- temperature interval above the initially stabilized tem-
tical bars indicate experimental uncertainties and reveal the perature rather than to an exact temperature.17 This
scatter of C(T) in different measuring cycles with different means, that for the cooling sequence the temperature
temperature stimuli and using different samples. Upper in- is decreased between the data acquisition and increased
set: Magnified region of the two phase transitions. The heat
during the acquisition process itself. Thus, in the case
capacity measured at 5 T (stars) is compared to the heat
of hysteretic (i.e. first order) behavior, the actual tran-
capacity in zero external field (circles), both measured on
sition, together with the corresponding release of latent
cooling. The temperature region around the lower transi-
tion at Tc1 ≈ 66.7 K was remeasured (triangles) utilizing heat,only is fully capturedonly inthe heating branchof
a reduced relaxation amplitude of δT ≈ 0.5 K on heating the measuring sequence. Around Tc1 a significant differ-
and subsequent cooling. For clarity thesedata are shifted by encebetweenheatingandcoolingcanbedetected,point-
50 mJ/molK2 Lower inset: Low-temperature heat capacity ing towards a first order transition (shifted curve in the
plotted as C/T vs. T2. For the results in zero magnetic field inset of Fig. 1). No such feature could be found for the
a fit using a Debye-derived phonon contribution is indicated upper transition at T .
c2
as solid line.
The lower inset in Fig. 1 shows the low-temperature
heatcapacityplottedasC/T vs. T2tosearchforpossible
spincontributions. Inzeroexternalmagneticfield,C(T)
heat capacity measurements have been performed with
is fully determined by phonon contributions and from a
acommercialPPMSfromQuantumDesignfortempera- ′
linearfit(solidline)aDebyetemperatureofΘ =210K
tures 1.8 K <T < 300K andin externalmagnetic fields D
can be determined. The low-temperature heat capacity
up to 5 T.
becomesslightlyenhancedinmagneticfieldsof5Twhich
canbeexplainedbytheincreasingimportanceofnuclear
hyperfine contributions or the influence of paramagnetic
III. RESULTS AND DISCUSSION defects at the lowest temperatures. For comparison, the
low-temperature specific heat of the canonical organic
Fig.1showsthecentralresultofthisinvestigation,the spin-Peierlscompound(TMTTF)2PF618displaysbesides
heat capacity as function of temperature. The heat ca- the nuclear hyperfine and T3 phonon contributions an
pacityischaracteristicforathree-dimensionalsolidwith additional quasi-linear(∼T1.2) term which has been as-
a Debye temperature of order 200 K. Superimposed we cribed to low-energy excitations. A similar contribution
find two weak but distinct anomalies which are clearly certainly can be excluded for TiOCl.
related to the two subsequent phase transitions at T = In the following analysis we will decompose the heat
c1
67 K and T = 91 K. In recent NMR experiments12 capacity into phonon and spin (S = 1/2) contributions,
c2
slightly different temperatures, namely 94 K and 66 K, with the former dominating the latter for all tempera-
respectively, have been determined. The effects of the tures. Nevertheless, we are able to perform a straight-
phase transitions on the specific heat are remarkably forward analysis of the thermal properties of TiOCl and
weakandarealmostlostunderthe largephonon-derived wewillshowthatwearriveataratherconsistentdescrip-
heat-capacity contributions, and it is clear that the en- tion despite the large uncertainties mentioned above.
tropycoveredby the twoanomaliesiscomparablysmall. Fig. 2 shows the heat capacity for the complete tem-
The upper inset in Fig. 1 shows the heat capacity perature regime investigated, plotted as C/T vs. T. As-
(given as C/T vs. T) in the temperature region of the sumingaS =1/2spinchainthe contributionofthe spin
3
chain for T >67 K is modelled by a Bonner-Fisher type Debye- and two Einstein-type contributions, yielding a
of behavior19 taking into account an exchange coupling totalof5freeparameters,namely,themeanDebye(Θ )
D
J = 660 K. For the low-temperature regime, i.e. below and two Einstein temperatures (Θ ), and the ratio of
E1,2
the spin-Peierls transition at T = 67 K, the expected Debye to Einstein modes R , as well as the ratio be-
c1 D/E
exponentialdecreaseofthespinpartoftheheatcapacity tween the Einstein modes R . The number of de-
E1/E2
is simulated by a BCS-like mean-field treatment20 with greesoffreedom(N ),whichofcourseshouldbenineper
f
a temperature dependent gap, 2∆ = 3.5k T , and, at formula unit of TiOCl, was kept fixed. The experimen-
0 B c1
T , a heat capacity jump of 1.43 times the contribution tallydeterminedheat-capacityvaluesfor2K<T <65K
c1
of the spin-chain, as it was proposed for canonical spin- and 130 K<T < 300 K have been used for the fit of the
Peierls systems.1 Using this approach we can calculate heat capacity. For the fitting procedure we included the
the spin-derived heat capacity without any free parame- spincontributionswhichhavebeencalculatedparameter-
ter. The result (for representationmultiplied by a factor free as outlined above. The totalheat capacity,spinand
of 3) is shown as dash-dotted line in Fig. 2. We are phonon contributions are shown as solid line in Fig. 2.
awarethatthiscanonlybe averyroughanalysis,specif- The lattice derived heat capacity is indicated as dashed
icallyhavinginmindthattheactualgapinTiOClseems line. Despite this oversimplified model we arrive at an
to be much larger and has recently been determined as astonishingly good description of the heat capacity over
2∆ = 10 ∼ 15k T by NMR experiments12 and that the complete temperature range. The parameters as de-
B c1,c2
the transition actually is of first order. The disregard of termined by the best fit seem to be realistic: The char-
these experimental facts gives an underestimation of the acteristic temperatures, Θ = 188 K, Θ = 352 K,
D E1
jump height of the magnetic specific heat at the spin- and Θ = 614 K, with the ratios R = 0.30 and
E2 D/E
Peierls transition and a too broad decay below, leading R = 0.51 determining the relative weight of Debye
E1/E2
indeed to observable differences between the measured and Einstein modes, are reliable keeping in mind that
dataandourcalculationcloselybelowT . However,the the optical phonon modes in TiOCl range from approxi-
c1
overallentropybalanceisnotaffectedbytheseshortcom- mately100Kto700Kwithdominantmodesclosetoour
ings of our simple model. The total magnetic entropy at values for Θ .10,11 The small discrepancy of the De-
E1,2
high temperatures sums up to Rln2 as expected for a bye temperature obtained from this over-all fit to C(T),
spin 1/2 system. comparedto the valuederivedfromthe low-temperature
The phonon system has been fitted assuming one heat capacity only, can be explained by the presence of
relatively low lying optical modes.
Comparing the model heat capacity to the measured
oneinFig.2wefindverygoodagreementforthesmooth
temperature evolution for low (T < T ) and high (T >
TiOCl T ) temperatures. As clearly seen, thce1main deviations
c2
arise in the temperature region between the two phase
0.3 transitions. The good agreement concerning the smooth
) phonons partoftheheatcapacitymayseemsurprisinginthelight
2 K of our simplified model. On the other hand, the phonon
mol 0.2 2 molK)40 S 0.12 R dpeasrctroipftoiounr Cin(vTol)v-minogdtehleistrrueeaspohnoanbolyncslpoescetrtouma raenadlistthiec
T (J/ T (mJ/20 sTphinusp,awrteobfetlhieevehetahtactaopuarcitmyobdeealrsyioenldlys aasrmelaiallbwleeiegshtti-.
C/ 0.1 C/ 0 mate of the regular part of the specific heat, allowing us
50 100 150 to separate out the anomalous contribution due to the
phase transitions at T and T . The inset of Fig. 2
spins 3 c1 c2
0.0 shows this extra heat capacity in a limited temperature
0 100 200 300
range from 50 to 150 K. The integral over this region
T (K) givesanestimate ofthe entropy∆S being releasedwhen
going through both transitions. ∆S is of the order of
0.12 R (±0.02 R) vanishingly small compared to Rln(2)
FIG. 2: Heat capacity of TiOCl plotted as C/T vs. T. The
expected for a spin S =1/2 system or an orbital doubly
S =1/2contributionincludingamean-fieldspin-Peierlstran-
degenerate state. The narrow peak at T corresponds
sitionasdescribedinthetextisindicatedasdash-dottedline. c1
to the latent heat released at the phase transition where
For representation purposes the calculated values have been
multiplied by a factor of 3. The fit to the phonon-derived according to magnetic measurements spin dimerisation
specific heat (see text) is indicated as dashed line. The sum appears. The larger fraction of the entropy is covered
ofboth contributionisdrawn assolid lineandrepresentsthe underthe phasetransitionatT extending upto 135K,
c2
best fit to the experimental results. The inset shows the dif- exactly the temperature where in NMR experiments the
ferencebetweencalculated andmeasuredheatcapacitiesina opening of a pseudo gap has been detected12. Assum-
limited temperature regime. ing that the phononand spin derivedheatcapacities are
4
correctly described, we are left with the orbital degrees spin-dimerizationsetsin,revealssignificanthysteresisef-
of freedom only. However, if the orbitals undergo an or- fectsandhenceisoffirstorder. Mostprobablytheorbital
dering transition at T the entropy again is much too degrees of freedom are involved in the phase transition
c2
low and orbitalfluctuations must extend to much higher at T , which shows no thermal hysteresis. The entropy
c2
∗
temperatures, even far above T , the characteristictem- below this anomaly is vanishingly small indicating that
perature of the opening of a pseudo gap. In this sense the largestfractionof entropyis releasedat considerable
our results are compatible with the strong fluctuation higher temperatures. The total heat capacity can sat-
effects observed in NMR12 and in Raman scattering11 isfactorily be explained describing the phonon spectrum
and with the results of density-functional calculations withDebyeandEinsteinmodesandthemagneticexcita-
suggesting that TiOCl may be subject to strong orbital tions by a Bonner-Fisher type heat capacity for T >T
c1
fluctuations14. ThisindicatesthatthephaseaboveT is andtheopeningofaspingapbelow. Atlowtemperatures
c1
characterizedbythepresenceofpronouncedfluctuations and zero external fields the heat capacity can satisfacto-
retaining some sort of short range order and thereby de- rily be described taking a phonon-derived T3 term into
layingthereleaseofthefullentropywithtemperature,as accountonly. Noindicationofcontributionoflow-energy
typical for one-dimensional systems. Unfortunately, our excitations can be detected.
specific heat data do not allow us to decide on the pre-
cise microscopic nature of the fluctuations (spin-Peierls
or orbital ordering).
Acknowledgments
IV. CONCLUSIONS We want to thank R. Valenti, J. Deisenhofer, and H.-
A. Krug von Nidda for helpful discussions. This work
Summarizing, we have measured the heat capacity of was partly supported by the Bundesministerium fu¨r Bil-
TiOCl for temperatures 2 K <T < 300 K and magnetic dung und Forschung (BMBF) via Grant No. VDI/EKM
fieldsupto5T.WeobservedtwoanomaliesatT =91K 13N6917-AandbytheDeutscheForschungsgemeinschaft
c1
and T = 67 K corresponding to two subsequent phase (Sonderforschungsbereich 484 in Augsburg and project
c2
transitions. The phase transition at 67 K, where strong CL 124/3-3).
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