Table Of ContentIncommensurate structure of the spin-Peierls compound TiOCl
A. Krimmel1, J. Strempfer2, B. Bohnenbuck2, B. Keimer2, M. Hoinkis3,4, M.
Klemm3, S. Horn3, A. Loidl1, M. Sing4, R. Claessen4, M. v. Zimmermann5
1 Experimentalphysik V, Elektronische Korrelationen und Magnetismus,
Universit¨at Augsburg, D - 86159 Augsburg, Germany
2 Max-Planck-Institut fu¨r Festk¨orperforschung, Heisenbergstr. 1, D-70569 Stuttgart, Germany
3 Experimentalphysik II, Institut fu¨r Physik, Universit¨at Augsburg, D - 86159 Augsburg, Germany
6 4 Experimentelle Physik 4, Universit¨at Wu¨rzburg, D-97074 Wuerzburg, Germany
0 5 Hamburger Synhrotron Strahlungslabor (HASYLAB) at Deutsches
0 Elektronen-Synchrotron (DESY), Notkestr. 85, 22603 Hamburg, Germany ∗
2 (Dated: February 4, 2008)
n
We report on a detailed single crystal x-ray diffraction study of the unconventional spin-Peierls
a
compoundTiOCl. Theintermediatephaseof TiOCl ischaracterized byan incommensuratemodu-
J
lation which is virtually identical to that recently found in the homologue compound TiOBr. The
4 first order phase transition between the spin-Peierls ground state and the incommensurate phase
revealsthesamekindofthermalhysteresisinboth,itscrystalstructureandmagneticsusceptibility.
]
l A weak, but significant magnetic field effect is found for this phase transition with a field induced
e shift of the transition temperature of ∆Tc1 = −0.13 K for an applied field of B = 10 T along the
-
chain direction. The field induced changes of theincommensurate crystal structure are compatible
r
t with a scenario of competing intra- and inter-chain interactions.
s
.
at PACSnumbers: 61.10.Nz,61.44.Fw,61.50.Ks,75.10.Pa
m Keywords: X-raydiffraction,low-dimensionalquantum magnets,incommensuratestructures
-
d
I. INTRODUCTION dencedby correspondingsuperlattice reflectionsshowing
n
a doubling of the unit cell along the b-axis10. Infrared6
o
c and Raman spectroscopy7, as well as electron spin reso-
[ Stronglycorrelatedlowdimensionalspinsystems have nance(ESR)5andNMRexperiments4corroboratedthese
attracted great interest due to a large variety of fasci- results and revealeda spin excitation gap of ∆=430 K.
1
nating physical properties. The reduced dimensionality
v However, a conventional spin-Peierls scenario is insuffi-
often allows for a description by exactly solvable theo-
9 cient to account for the physical behaviour of TiOCl. A
retical models which may clarify fundamental quantum
7 wealthofexperimentalresultshaveestablishedafirstor-
0 mechanicalaspectsofsolids,includingphenomenaofsig- der phase transition from the spin-Peierls ground state
1 nificanttechnologicalpotentiallikehigh-Tc superconduc- into a second, intermediate phase at Tc1 = 67 K, which
0 tivity. Moreover,the complex interplay between the dif-
extends up to T = 91 K where a second order phase
6 ferent microscopic degrees of freedom (charge, spin, or- c2
transitionseparatestheintermediatephasefromthenor-
0
bitalandlatticedegreesoffreedom)isattheheartofnu-
/ mal paramagnetic state at high temperatures. The na-
t merousphasetransitionsleadingtoexoticgroundstates.
a tureoftheintermediatephaseofTiOClhasnotyetbeen
Considering a one-dimensional (1D) antiferromagnetic
m clarified. Based on the temperature dependence of the
(AFM)S =1/2spinchain,acouplingtothe latticemay g-factors and line width in ESR experiments5 and, in
-
d result in a spin-Peierls transition with a non-magnetic, particular,onphononanomaliesfoundinRamanandIR
n dimerized ground state. The first example of an inor- spectroscopy6,7 ithasbeenproposedthatorbitalfluctua-
o ganicspin-PeierlscompoundisCuGeO 1. Morecomplex
3 tionsplayanessentialroleandmayextendwellaboveT
c physicsisobtainedifthespinsareadditionallycoupledto c2
up to 130 K. This interpretation has been further sup-
:
v charge or orbital degrees of freedom, as manifested i. e. portedby recentspecific heatmeasurements8 andis also
Xi in a metal-to-insulator transition (MIT) in Na1/3V2O52. in agreement with electronic structure calculations3,20.
r Recently,thetitanium-basedoxohalidesTiOX(X=Cl, Withindensityfunctionaltheoryemployingthe LDA+U
a Br)havebeendiscussedasnewunconventionalinorganic approximation,the electronic groundstate configuration
spin-Peierls systems3,4,5,6,7,8,9,10,11,12,13,14,16. They crys- 3d1xy oftheTi3+ ionscancoupletoopticalphononmodes
tallize in an orthorhombic structure with Ti-O bilay- thatinturnmayleadtostrongorbitalfluctuationswithin
ers within the ab-plane well separated by Cl/Br ions19. the t2g crystal field multiplet3,20. Moreover, the impor-
Quasi-1DS=1/2spinchainsalongthecrystallographicb- tanceofcorrelationeffectshasbeenrevealedbycombined
axis are formed via orbital ordering giving rise to strong LDA+DMFT studies11,21.
direct exchange with an exchange constant of J/k ≈ In contrast, ARPES measurements could not detect
B
660 K3. For TiOCl, the low temperature spin-Peierls any evidence for phonon assisted orbital fluctuations11.
state is established by a steep decrease of the magnetic Moreover, recent polarization dependent optical mea-
susceptibility below T = 67 K3, accompanied by a si- surements in combination with cluster calculations pro-
c1
multaneous lattice dimerization of the Ti3+ ions, as evi- vide evidence that the orbital degrees of freedom are ac-
2
tually quenched12. Alternatively, it has been proposed 0.8
thatinter-chaininteractionswithinthebilayersleadtoan
(0 1.5 0) − reflection H = 10T
incommensurate spin-Peierls state below T that locks-
in in a conventional commensurate dimerizce2d phase be- nits) H = 0T
low Tc112. b. u 0.6
In fact, such a behaviour has been observedin the ho- ar
mtaTmsThhncioeeo2Odnlwo=Btsgsearwuxam4hesi7ttehihbwcoKoieowtaml.fesosTcpslitpdtomhwriuonesionuln-alPdpporeecwhTiropaesnisrthtOfieelrysmugBstcugirprctrra1aeuoan6rlrut.aseinipottaudnrTioloroiesnpOantsenapgBrtdahttertiah1ecs5aesTer,.n1cyb61do-s.atfL=axTTRilikisiO2eeOsic7tnCerBTnKularitcgOhltayraauC,elnvsredlaoee-, Integrated Intensity ( 00..24 Integrated Intensity (arb. units) 0000....2468 ((−0 δ1 .25− 0ε) 0)
single crystal x-ray diffraction study on TiOBr revealed 0.0
0 10 20 30 40 50 60 70 80 90 100
anincommensuratemodulatedstructurefortheinterme- T (K)
diatephase16,inaccordancewithopticaldataandcluster 0.0
62 63 64 65 66 67 68
calculations. T (K)
Here we report on a detailed x-ray diffraction study
on single crystalline TiOCl to elucidate the nature of FIG. 1: (Color online) Temperature dependence of the in-
the intermediate phase and to investigate any magnetic tensity of the (0, 1.5, 0) superlattice reflection of TiOCl in
field effectofthe phase transitions. This is motivated by the vicinity of the first phase transition around Tc1 = 67 K.
Shownaremeasurementsinzerofield(opencircles)andinan
a large magnetic field dependence of the incommensu-
externalfieldofB=10T(fullcircles),respectively. Theinset
rate structure observedabove a threshold magnetic field
showsintensitiesofbothcommensurateandincommensurate
in other spin-Peierls compounds such as TTF-CuBDT17
reflections over thewhole temperature range.
and CuGeO 18.
3
surementsinzerofieldandB =10Tareobservedwitha
II. EXPERIMENTAL RESULTS marginalpossibleerrorofthetemperaturebelow0.01K.
Cycling the temperature reveals a pronounced thermal
Single crystals of TiOCl were prepared by chemical hysteresis of the intensity of the (0,1.5,0) reflection.
vapourtransport19fromthestartingmaterialsTiCl and
3
TiO . The samples were characterizedby magnetization
2 2400
measurements employing a SQUID magnetometer and
T = 66.84K H = 0T
the magnetic properties were found in excellent agree-
T = 67.29K
ment with published results. Magnetic field dependent
T = 68.23K
single crystal x-ray diffraction measurements employing
T = 70.35K
synchrotronradiationhavebeenperformedatthe beam-
line BW5 of HASYLAB (DESY, Hamburg). An inci- ps)1600 T = 76.97K
c
dent photon energy of 100 keV was used. The sample y ( T = 85.89K
was mounted in a cryomagnetallowing for temperatures nsit T = 90.31K
e
1.6≤T ≤300KinhorizontalfieldsuptoB =10T.The nt
I
samplewithasizeof1x1x0.01mm3wasorientedwiththe 800
bc-planeinthehorizontalscatteringplane. Themagnetic
fieldwasorientedalongthescatteringvectorinthechain
direction. This geometry was possible due to the small
scattering angles at high photon energies. By tilting the
cryomagnet,alsosmallvaluesinhwereaccessible. Atlow 0
temperatures(T =10K),anumberofsuperlatticereflec- −0.10 −0.05 0.00 0.05 0.10
h (r.l.u.)
tions along the chain direction (0,k+0.5,0),k = 0,1,2
have been recorded. The strongest intensity was found
FIG. 2: (Color online) Evolution of the (0, 1.5, 0) superlat-
for (0,1.5,0). tice reflection of TiOCl for various temperatures on passing
Fig.1showsthe temperaturedependence oftheinten- through the first phase transition from the dimerized spin-
sityofthe(0,1.5,0)reflectionaroundthefirstphasetran- Peierlsgroundstateintotheintermediatephaseinzerofield.
sitionatT =67.5Kinzerofieldandinanexternalfield The peak splitting indicates an incommensurate modulation
c1
ofB =10T.AsevidentfromFig.1,theintensityremains of the intermediate phase.
virtually constant at low temperatures, starts to steeply
decrease at 66.5 K and vanishes at 67.5 K. Within the Fig. 2 shows the evolution of the low temperature
experimental accuracy, no differences between the mea- (0,1.5,0)reflectionforincreasingtemperatures,covering
3
essentiallythetemperaturerangeofthesecond,interme- the modulations along the h- and k-direction appear to
diate phase 67.5 K = T ≤ T ≤ T = 92.5 K. At T be slightly different. A scan along k at T = 67.52 K
c1 c2 c1
the (0,1.5,0) reflection splits into two incommensurate shows a single peak at k = 1.5015 whereas a scan along
satellites which also show an additionalincommensurate h showsapeak splitting with δ =±0.03atT =67.54K.
component along k. Moreover, also the intensities of the satellite reflections
exhibit slight changes thus confirming a small field
induced modification of the incommensurate crystal
0.505
structure.
(a)
0.500
0.500 H = 10T
0.498 III. DISCUSSION AND CONCLUSION
H = 0T
u.)
ε (r.l.0.495 0.496 diffWraecthioanvestpuedryforomf etdheaspdinet-aPieleiedrlssincogmlepcoruynsdtalTixO-rCaly.
66.5 67.5 68.5
However, it should be noted that the present investiga-
0.490 tion does not represent a complete crystal structure de-
termination. Due to geometric restrictions by use of a
(δ 2−ε 0) − reflection
large cryomagnet, only reflections of type (0,k,0) were
0.485 explored in detail for their temperature dependence and
(b) possible field effects. Therefore, the focus was on the
phase transitions in order to elucidate the nature of the
0.05
0.05 intermediate phase of TiOCl and its relation to the un-
conventionalspin-Peierls transition.
u.) H = 10T The temperature dependence of the (0,1.5,0) reflec-
δ (r.l. 0.00 0.00 H = 0T tion is characteristic for a doubling of the unit cell
alongthe b-axisduetothe dimerizedspin-Peierlsground
−0.05 state10. A sudden decrease of the intensity is observed
−0.05
66.5 67.5 68.5 at T = 67.5 K which confirms that the transition is of
c1
firstorder. Moreover,acorrespondingthermalhysteresis
ofthe intensityofthis superlattice reflectionis observed.
−0.10 Incombinationwiththe sametypeofhysteresisfoundin
65 70 75 80 85 90 95
T (K) the magnetic susceptibility, it is concludedthat the non-
magnetic,dimerizedgroundstateofTiOClisrealizedvia
FIG. 3: (Color online) Temperature dependence of the in- a first order spin-Peierls transition.
commensuratecomponentsǫ(a)andδ(b)ofthe(±δ,2−ǫ,0) Recently, the unconventional properties of TiOX
reflection of TiOCl in the intermediate phase in zero field (X=Cl, Br) have been interpreted in terms of frustrated
(open circles) and in an external field of B = 10 T (full cir- interchaininteractionswithinthebilayers12. Withinthis
cles). The insets show the incommensurate positions δ and ǫ scenario, the spin-Peierls mechanism would give rise to
in more detail around Tc1. an intermediate phase characterized by an incommensu-
rate order with a subsequent lock-in transition into the
The observed incommensurate reflections are commensuratedimerizedgroundstate12. Infact,suchan
(±δ,ǫ,0),(±δ,2 − ǫ,0) and (±δ,2 + ǫ,0) consistent incommensurate modulated structure has recently been
with space group Pmmn. The incommensurately observedinTiOBr16. TheintermediatephaseofTiOClis
modulated intermediate phase can be described by a alsocharacterizedbysuchanincommensuratestructural
propagationvectorq=(±δ,0.5+ǫ,0)with0≤δ ≤0.078 modulationwithapropagationvectorq=(±δ,0.5+ǫ,0)
and 0.4857 ≤ ǫ ≤ 0.5. The satellites can be monitored with0≤δ ≤0.078and0.4857≤ǫ≤0.5,asevidencedby
up to T = 92.5 K where the undistorted orthorhombic a corresponding peak splitting. The intermediate phase
structure of the paramagnetic phase is recovered. The of TiOCl exhibits a two dimensional (2D) modulation
temperature dependence of the two incommensurate within the Ti-O bilayers. The absolute values and the
components of the reflection (±δ,1.5+ǫ,0) is shown in temperature dependence of the modulation vector in Ti-
Fig.3. Fig.3a,showsthek-componentǫandFig.3b,the OCl are almost identical to those observed for TiOBr
h-component δ of the incommensurate satellite for zero (for TiOBr, the published temperature dependence of
field and in an applied field of B = 10 T. An expanded the modulation vector is restricted to the x-component
view around T is given in the corresponding insets. or δ)16. We therefore conclude that both, TiOCl and
c1
For both components, a small, but significant shift TiOBr exhibit the same kind of incommensurate modu-
∆T = −0.13 K of the phase transition temperature is lationintheirintermediatephase. Apartfromtheincom-
c1
observed in the external field of 10 T along the chain mensurability,thismodulationischaracterizedbyrather
direction. Remarkably, the transition temperatures for largedisplacementsalongtheb-axis(chaindirection)and
4
comparable small amplitudes along the a-axis16. The corresponding strong magneto-elastic coupling. The or-
intermediate phase can be interpreted as either due to bital ordering further gives rise to inter-chain π-bonding
frustrated spin-Peierls interactions12 or, alternatively,as with apredominantly ferromagneticexchange. Basedon
a phase with competing 1D spin-Peierls interactions and band structure calculations20, the inter-chain exchange
2Dmagneticinteractionswhicharecoupledtothelattice can be estimated to be one order of magnitude weaker
modulation16. than the principal exchange along the chains. The com-
A crucial test to identify a spin-Peierls state is its petition between these different exchange interactions
generic B−T-phase diagram22. Due to the large energy leadstofrustrationandanincommensuratelymodulated
scale in TiOCl with an exchange constant of J/k ≈ crystal structure12. The application of an external mag-
B
660 K no significant magnetic field effects are expected netic field then slightly shifts the equilibrium position of
within the accessible field range of conventional labora- these competing interactions. The small magnetic field
tory magnets. Our measurements in an external field of effect on the incommensurability confirms that the in-
B = 10 T could not observe any significant change of commensurate modulation is of fundamentally different
theprincipalsuperlatticereflectionsoftype(0,k+0.5,0) origin as the field-induced modulation observed in clas-
characterizingthe doubling of theb-axisdue to the com- sical spin-Peierls systems17,18. To conclude, we have de-
mensurately dimerized spin-Peierls ground state. How- termined the incommensurate modulation of the inter-
ever, a weak but significant field effect is found for the mediate phaseofTiOClandfind somesmall,but signifi-
phase transition into the incommensurate phase with cant changes upon the application of an external field of
a field induced shift of the transition temperature of B = 10 T along the chain direction. These results are
∆T = −0.13 K for B = 10 T. The negative temper- compatible with a frustrated spin-Peierls scenario.
c1
ature shift indicates a stabilization of the incommensu-
ratestructureandasuppressionoftheantiferromagnetic
spin singlet formation of the spin-Peierls ground state
Acknowledgments
by the external field. These observations may be ac-
counted for within the scenario of frustrated inter-chain
interactions that give rise to a second, incommensurate This work was supported by the German Bundesmin-
phase12. In TiOCl, the formation of spin chains along isterium fu¨r Bildung und Forschung under contract No.
the b-axis with a strong antiferromagnetic exchange re- VDI/EKM 13N6917 and by the Deutsche Forschungsge-
sults from orbital ordering of the xy-orbitals3,20 with a meinschaft DFG via SFB 484, Augsburg.
∗
Electronicaddress: [email protected] Benthien,E.Jeckelmann,T.Saha-Dasgupta,L.Pisani,R.
1 M.Hase,I.Terasaki,andK.Uchinokura,Phys.Rev.Lett. Valent´i,andR.Claessen,Phys.Rev.B72,125127(2005).
70, 3651 (1993) 12 R. Ru¨ckamp, J. Baier, M. Kriener, M. W. Haverkort, T.
2 M. Heinrich, H.-A. Krug von Nidda, R. M. Eremina, A. Lorenz, G. S. Uhrig, L. Jongen, A. M¨oller, G. Meyer, and
Loidl, Ch. Helbig,G. Obermeier, andS.Horn,Phys.Rev. M. Gru¨ninger, Phys. Rev.Lett. 95, 097203 (2005).
Lett. 93, 116402 (2004). 13 C. Kato, Y. Kobayashi, and M. Sato, J. Phys. Soc. Jpn.
3 A.Seidel, C. A.Marianetti, F. C.Chou, G. Ceder,and P. 74, 473 (2005).
A. Lee, Phys. Rev.B 67, 020405(R) (2003). 14 P. Lemmens, K. Choi, R. Valent´i, T. Saha-Dasgupta, E.
4 S. T. Imai and F. C. Chou, cond-mat/0301425 (unpub- Abel, Y.Lee, and F. Chou, N. J. Phys., 7, 074 (2005).
lished). 15 T. Sasaki, M. Mizumaki, K. Kato, Y. Watabe, Y. Nishi-
5 V. Kataev, J. Baier, A. Moller, L. Jongen, G. Meyer, and hata, M. Takata, and J. Akimitsu, J. Phys. Soc. Jpn. 74,
A. Freimuth,Phys. Rev.B 68, 140405 (2003). 2185 (2005).
6 G. Caimi, L. Degiorgi, N. N. Kovaleva, P. Lemmens , and 16 S. van Smaalen, L. Palatinus, and A. Sch¨onleber, Phys.
F.C.Chou,Phys.Rev.B69,125108(2004); G.Caimi,L. Rev.B 72, 020105(R) (2005).
Degiorgi, P. Lemmens, and F. C. Chou, J. Phys.: Cond. 17 V. Kiryukhin, B. Keimer, and Moncton, Phys. Rev. Lett.
Matter 16, 5583 (2004). 74, 1669 (1995).
7 P. Lemmens, K. Y. Choi, G. Caimi, L. Degiorgi, N. N. 18 V.Kiryukhin,B.Keimer,J.P.Hill,andA.Vigliante,Phys.
Kovaleva, A. Seidel, and F. C. Chou, Phys. Rev. B 70, Rev. Lett. 76, 4608 (1996); V. Kiryukhin, B. Keimer, J.
134429 (2004). P. Hill, S. M. Coad, and D. McK. Paul, Phys. Rev. B 54,
8 J. Hemberger, M. Hoinkis, M. Klemm, M. Sing, R. 7269 (1996).
Claessen, S.Horn, and A.Loidl, Phys.Rev.B 72, 012420 19 H.Sch¨afer, F.Wartenpfuhl,andE.Weise,Z.Anorg.Allg.
(2005). Chem. 295, 268 (1958).
9 L. Pisani and R. Valent´i, Phys. Rev. B 71, 180409(R) 20 T. Saha-Dasgupta, R. Valent´i, H. Rosner, and C. Gros,
(2005). Europhys.Lett. 67, 63 (2004).
10 M. Shaz, S. van Smaalen, L. Palatinus, M. Hoinkis, M. 21 T. Saha-Dasgupta, A. Lichtenstein, and R. Valent´i, Phys.
Klemm, S. Horn, and R. Claessen, Phys. Rev. B 71, Rev.B 71, 153108 (2005).
100405(R) (2005). 22 M. C. Cross, Phys. Rev.B 20, 4606 (1979).
11 M. Hoinkis, M. Sing, J. Sch¨afer, M. Klemm, S. Horn, H.
