Orbital fluctuations and orbital order below the Jahn-Teller transition in Sr3Cr2O8
Zhe Wang, M. Schmidt, A. Günther, S. Schaile, N. Pascher, F. Mayr, Y. Goncharov, D. L. Quintero-Castro, A. T. M. N. Islam, B. Lake, H.-A. Krug von Nidda, A. Loidl, J. Deisenhofer
aa r X i v : . [ c ond - m a t . s t r- e l ] J un Orbital fluctuations and orbital order below the Jahn-Teller transition in Sr Cr O Zhe Wang, M. Schmidt, A. G¨unther, S. Schaile, N. Pascher, F. Mayr, Y. Goncharov,
1, 2
D. L.Quintero-Castro,
A. T. M. N. Islam, B. Lake,
3, 4
H.-A. Krug von Nidda, A. Loidl, and J. Deisenhofer Experimental Physics V, Center for Electronic Correlations and Magnetism,Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany Institute of General Physics, Russian Academy of Sciences, 119991 Moscow, Russia Helmholtz-Zentrum Berlin f¨ur Materialien und Energie, D-14109 Berlin, Germany Institut f¨ur Festk¨orperphysik, Technische Universit¨at Berlin, D-10623 Berlin, Germany (Dated: September 18, 2018)We report on the magnetic and phononic excitation spectrum of Sr Cr O determined by THz andinfrared (IR) spectroscopy, and electron spin resonance (ESR) measurements across the Jahn-Tellertransition, which is detected by specific-heat measurements to occur at T JT = 285 K. We identifythe singlet-triplet excitations in the dimerized ground state and estimate the exchange couplings inthe system. ESR absorptions were observed up to T ∗ = 120 K with a linewidth ∝ exp ( − ∆ /k B T )and ∆ /k B = 388 K indicating a phonon-mediated spin relaxation via the excited orbital state of theCr e doublet in the orbitally ordered state. Upon entering the low-symmetry Jahn-Teller distortedphase below T JT , we find an extended regime T ∗ < T < T JT where the IR active phonons changeonly gradually with decreasing temperature. This regime is associated with strong fluctuations inthe orbital and lattice degrees of freedom in agreement with the loss of the ESR signal above T ∗ .Using the measured magnetic and phononic excitation spectrum we model the orbital contributionto the specific heat and find the persistence of strong fluctuations far below T JT . PACS numbers: 78.30.-j,71.70.-d,76.30.-v,78.20.-e
Orbital degrees of freedom (DOF) and their couplingto other DOF play an important role in understandingthe physics in many transition-metal compounds includ-ing colossal magnetoresistive manganites, vanadates, andiron-based superconductors.
Orbital ordering (OO)mechanisms, collective orbital excitations, and frustra-tion effects in the orbital sector have attracted consid-erable attention and formed the research field of orbitalphysics . Exotic ground states such as orbital and spin-orbital liquids have been explored both experimentallyand theoretically. Orbital fluctuations play an importantrole in the formation of these states and may even inducea dimerization of spins via magnetoelastic coupling. Here we investigate the OO transition in the spin-gapped dimerized system Sr Cr O . This compound hascome into focus due to the occurrence of a field-inducedmagnon condensation. The room temperature crystalstructure of Sr Cr O was determined to be hexagonalwith space group R ¯3 m . Each Cr ion with spin S =1/2 is surrounded by an oxygen tetrahedron and cou-ples antiferromagnetically to adjacent Cr ions along c direction, forming a spin singlet ground state at lowtemperatures. The tetrahedral crystal field splits the 3 d levels into lower-lying doubly-degenerated e and triply-degenerated t orbitals. Thus, the Cr ions are Jahn-Teller (JT) active and a JT transition to a monoclinicstructure with three twinned domains and space group C c has been reported by neutron experiments to oc-cur at 275 K. Primarily associated with the antifer-rodistortive displacement of the apical oxygen ions thistransition is suggested to be accompanied by the split-ting of the e doublet into a lower-lying d z − r and ex-cited d x − y orbital, and an antiferro-orbital ordering of d z − r orbitals. In addition, this ordering report-edly changes the magnetic exchange paths and leads tospatially anisotropic exchange couplings. Recent abinitio calculations showed that correlation effects withinCr-3 d orbitals can account for both the structural phasetransition and the singlet ground state. We present a combined study using THz and infrared(IR) spectroscopy, electron spin resonance (ESR) andspecific heat. We directly observe the singlet-triplet ex-citations in the ground state and derive the splitting ofthe e -orbitals from the ESR spin relaxation below 120 K.Above 120 K strong fluctuations are found to influenceboth the IR active lattice vibrations and the spin relax-ation up to the JT transition at 285 K.Single crystals grown by the floating-zone method were orientated by Laue diffraction and cut along an a h c h -plane, where the subscript h stands for hexagonaland a subscript m for monoclinic in the following. Heatcapacity was measured in a Quantum Design physicalproperties measurement system from 1.8 to 300 K. Sus-ceptibility was measured using a SQUID magnetometer(Quantum Design). Polarization-dependent reflectivitywas measured from 20 to 300 K in the far- and mid-IR range using the Bruker Fourier-transform IR spec-trometers IFS 113v and IFS 66v/S with a He-flow cryo-stat (Cryovac). THz transmission experiments were per-formed in Voigt configuration using a Mach-Zehnder-typeinterferometer with backward-wave oscillators coveringthe frequency range 115 GHz - 1.4 THz and a magneto-optical cryostat (Oxford/Spectromag) with applied mag-netic fields up to 7 T. ESR measurements were performedin a Bruker ELEXSYS E500 CW-spectrometer at X-bandfrequency of 9.48 GHz from 4 to 300 K.The results of all THz transmission spectra measuredwith different frequencies for H k c h and H k a h aresummarized in Fig. 1(d). Absorptions labeled 1, 1’, and3’ in Fig. 1(b) correspond to excitations from the sin-glet ground state to the excited triplet states Zeeman-split by the external magnetic field H , while absorp-tion 2 corresponds to the intra-triplet excitations as il-lustrated in Fig. 1(a). The excitation spectrum agreeswith the one reported for Ba Cr O by Kofu et al. ex-cept for mode 3’ not having been observed for Ba Cr O .Modes 3’ and 1’ can be described in terms of a lin-ear Zeeman splitting following hν = hν ± gµ B H with ν opt = 1 .
24 THz ∼ = 5 .
13 meV and an effective g -factorof about 1.92(3) in agreement with the value of 1.94 ofmode 2, with ESR data discussed below and reportedvalues for Ba Cr O and Sr Cr O . For mode 1 wecould observe the lower branch within the available fre-quency range and found ν aco = 1 .
47 THz ∼ = 6 .
08 meVwhich corresponds well to the magnetic excitation energyreported by neutron scattering at the Γ-point. Follow-ing Ref. 15 we assign modes 1 and 1’ to the cooperativeacoustic ( n = 0) and optical modes ( n = ±
1) of thecoupled dimers of different bilayers with eigenfrequencies hν ≃ p J + J γ where γ = 2[( J ′ + J ′′ + J ′′′ ) cos( nπ )+( J ′ + J ′′ + J ′′′ )+( J ′ + J ′′ + J ′′′ ) cos( nπ )]. Here J denotesthe intradimer interaction, J s, J s, and J s are the in-terdimer interactions (see Fig. 1(c)). Using the values ofexchange couplings determined from neutron scattering we find hν aco = 5 .
92 meV and hν opt = 5 .
14 meV in agree-ment with our experimental values. The observability ofthe singlet-triplet transitions 1, 1’, and 3’ implies an addi-tional anisotropic contribution to the spin Hamiltonian,which mixes singlet and triplet states and relaxes theselection rule ∆ S . The intensity of mode 2 increaseswith increasing temperature in agreement with the ther-mal population of the excited levels (see absorption linesat 4 K and 7 K in Fig. 1(b)) and corresponds to theexpected ESR signal which has been tracked with highsensitivity in a cavity-based setup at X-band frequency.Fig. 2(a) shows an ESR derivative absorption spectrummeasured at 30 K. The spectrum is well fitted by a deriva-tive Lorentzian line shape characterized by effective g fac-tor, peak-to-peak linewidth ∆ H , and double integratedintensity I ESR . The latter follows the temperature de-pendence of the dc susceptibility for T < T ∗ (= 120 K)(see Fig. 2(b)) as expected for an ESR signal originat-ing from the Cr dimers. Above T ∗ the ESR absorp-tion becomes extremely broadened and cannot be trackedany further. In Fig. 2(c) we show the temperature de-pendence of the linewidth ∆ H with the magnetic field H ⊥ a h . The effective g -factor of 1.93(1) is almostconstant below 70 K, and in good agreement with THztransmission spectra and previous reports. When ∆ H starts to increase strongly and reaches the order of mag-nitude of the resonance field above 70 K (see below), g -factor cannot be determined reliably anymore.The temperature dependence is described using ∆ H =∆ H + A exp ( − ∆ k B T ) with a residual ∆ H = 135 Oe, A = T r an s m i ss i on ( a r b . un i t s ) Magnetic field (T) (b) S z = -1S z = 0 E ne r g y H0h mode 1, 1’ singlet(S = 0)mode 2mode 2 mode 3’S z = 1 triplet(S = 1) (a) H || a h H || c h T = 4 K F r equen cy ( G H z ) Magnetic field (T)
Mode 2Mode 1’Mode 1 Mode 3’ opt0 =1.24 THz aco0 =1.47 THz (d)(c)
FIG. 1: (Color online) (a) Zeeman-splitting of triplet statesin a magnetic field. Modes 1, 1’, 2, and 3’ are described inthe text. (b) Transmission spectra measured at different fre-quencies at 4 K. The spectrum obtained at 170 GHz and 7 K(dashed line) is shifted for clarity. The spectra correspondingto mode 2 are measured with H k c h , while the spectra corre-sponding to modes 1, 1’ and 3’ are measured with H k a h . (c)Bilayer structure of Cr ions. (d) Magnetic field dependenceof the observed absorption frequencies at 4 K for H k c h and H k a h .
130 kOe, and a gap ∆ /k B = 388 K. The exponential in-crease of the ESR linewidth indicates that the relaxationof the excited spins occurs via an Orbach process, i.e.absorption of a phonon with energy ∆ to an excited or-bital state and emission of a phonon with energy ∆ + E Z where E Z is the Zeeman splitting of the lower-lying e or-bital as illustrated in the inset of Fig. 2(c). Thus, thespin dynamics are dominated by spin-lattice relaxationand we associate the gap with the energy splitting of theCr e -orbitals in the regime T < T ∗ where OO is com-plete but the system has not reached its non-magneticsinglet ground state yet. The splitting ∆ can be associ-ated with the interaction driving OO and will be impor-tant for a theoretical understanding of the energy scalesin Sr Cr O . The fact that ESR spectra cannot be ob-served above T ∗ is ascribed to a drastically increasedspin-lattice relaxation rate for T > T ∗ as a result ofstrong fluctuations in the orbital and lattice DOF.To study the lattice dynamics we performed IR reflec-tivity measurements with the electric field E k a h and E k c h . Normal mode analysis yields the irreducible rep-resentations of IR active modes 6 A u ( E k z ) + 7 E u ( E k ( x, y )) for the hexagonal R m (No. 166) structure. The room temperature spectra for E k c h (shown inFig. 3(a)) and E k a h (not shown) confirm this expecta-tion by exhibiting six modes with eigenfrequencies 192.8,200.6, 335.6, 734.7, 765.6, and 827.3 cm − , and seven d -r H ( k O e ) Temperature (K)
ESR OrbachrelaxationE z d x -y (c) H (kOe) d P / d H ( a r b . un i t s ) T = 30K = 9.48 GHz (a) I ESR dc I ES R ( a r b . un i t s ) T (K) (b) 369 d c ( - e m u / m o l ) FIG. 2: (Color online) (a) X-band ESR spectrum measuredat 30 K for H ⊥ a h fitted by a Lorentzian line. Temperaturedependence of (b) the ESR intensity I ESR together with the dc susceptibility χ dc measured at 3.4 kOe and (c) of the ESRlinewidth. The solid curve is a fit described in the text. Inset:sketch of the spin relaxation via an Orbach process. modes with eigenfrequencies 110.6, 115.6, 183.0, 758.8,805.0, 855.1, and 938.1 cm − , respectively. For the mon-oclinic C /c (No. 15b) structure below JT transition, thenumber of expected normal modes increases to 19 A u ( E k y )+20 B u ( E k ( x, z )). However, only the selection rule forthe 19 A u modes is determined by E k b m , because theunique monoclinic b m -axis coincides with a principal axisof the dielectric tensor. The dipole moments of the 20 B u modes are confined to the a m c m -plane, but their di-rections do not necessarily coincide with the crystal axes.Using the relations a h = ( a m − b m ), b h = − ( a m + b m ),and c h = c m − a m , it is clear that upon cooling below T JT with polarization E k a h we may expect to see atleast the 19 A u modes from the contribution of the mon-oclinic b m -axis plus possible additional B u modes due tothe projection of the polarization along a m . Similarly, for E k c h we can expect to probe the majority of the 20 B u modes confined to the a m c m -plane. The above transfor-mation corresponds to only one of three reported mono-clinic twins and, thus, the number of expected normalmodes may be even larger. Consequently, one would ex-pect a drastic increase in the number of IR active modesfor both measured polarizations when comparing spectrabelow and above the JT transition, e.g., at 250 K and295 K. However, as shown in Fig. 3(a) the IR spectra donot change dramatically across T JT = 285 K. Only oneadditional mode B u (16) is already visible at 250 K, whilethe expected 20 B u modes of the low-temperature struc-ture appear only gradually upon further cooling. This be-havior is illustrated in Fig. 3(b) where spectra at 150 K,100 K, and 20 K are compared. The modes present at20 K can be observed at 100 K, while in the phonon spec-trum at 150 K several modes are not resolved anymoreand appear to be strongly broadened. A similar behaviorhas also been observed for the IR spectra measured for E k a h . Previous structural diffraction studies clearly as-
200 500 8000.00.40.8 R e f l e c t i v i t y E || c h A (i) (i=1,...,6)
12 3 4 5 621 3 64 5
295 K250 K B u (16)
150 300 4500.10.50.9
Wave number (cm -1 )
121 823 5 6 7 91011 13 143 6 78 1513 161515
20 K100 K150 K B u (i) (i=1,...,20)
450 8500.10.6
FIG. 3: (Color online) Reflectivity spectra of Sr Cr O with E k c h (a) at 295 K and 250 K, and (b) at 150 K, 100 Kand 20 K. The spectra are shifted with respect to the ones at150 K and 295 K in order to clearly illustrate the evolutionof phonon modes with temperature. sign the monoclinic symmetry to be realized just below T JT . Consequently, we interpret our results as a sig-nature of strong fluctuations which dominate the latticedynamics and lead to a strong damping and broadeningof phonons in the temperature range T ∗ < T < T JT with100 K < T ∗ <
150 K in agreement with the ESR results.Having identified the magnetic and phononic excita-tions we turn to the specific heat (see Fig. 4). A peakwithout any thermal hysteresis, which had not been de-tected in a previous specific-heat study, is clearly vis-ible at T JT = 285 K, indicating an order-disorder phasetransition at 285 K. We associate this anomaly with theOO transition reported to occur at 275 K. Moreover,an additional broad shoulder is discernible around 20 K(see Fig. 4). We assume that the total heat capacityoriginates from three different parts, a magnetic contri-bution C mag corresponding to the thermal population ofthe excited dimer states, a lattice contribution C latt dueto phonons, and an electronic contribution reflecting theorbital DOF. We approximate the magnetic contributionby C mag ( T ) = N ∂E∂T using E = Z P i =0 g i ǫ i e − βǫ i withthe partition function Z = P i =0 g i e − βǫ i , the excitationenergies ǫ , , = 0 , hν opt , hν aco as observed in the THztransmission experiment, degeneracies g , , = 1 , , β ≡ /k B T . The resulting magnetic specific heat(dashed line in Fig. 4) accounts well for the shoulder at20 K. Using the gap ∆ determined by ESR we can fixthe orbital contribution C oo in the completely orbitallyordered phase below T ∗ by a two-level system with split-ting ∆ as shown in the upper inset of Fig. 4.The lattice contribution can be described by a sum ofone isotropic Debye ( D ) and four isotropic Einstein terms( E , , , ). The ratio between these terms was fixed to D : E : E : E : E = 1 : 3 : 4 : 3 : 2 to account forthe 39 DOF per formula unit. The resulting contributionto the specific heat shown as a dash-dotted line in Fig. 4has been obtained with the Debye and Einstein temper-atures θ D = 135 . θ E = 153 . θ E = 306 . θ E = 541 . θ E = 1360 K consistent with the fre-
50 150 2500.000.050.1050 150 25008
T*=120K C mag /T C latt /T C / T ( J m o l - K - ) Temperature (K) T JT T JT =285K20K T*C OO /T C res /T S OO S res S ( J m o l - K - ) S = R ln4 T JT FIG. 4: (Color online) Specific heat divided by tempera-ture
C/T vs T . Solid line is a superposition of the modeledmagnetic (dashed line) and phonon contribution (dash-dottedline) as described in the text. Upper and lower insets showthe temperature dependence of orbital-related specific heatand entropy, respectively. quency ranges where IR active phonons of the hexagonalstructure occur. Within these constraints the lattice con-tribution was modeled in such a way that no discontinuityoccurs between the Schottky-like term for T < T ∗ andthe residual specific heat C res = C − C mag − C latt − C oo for T > T ∗ . In the upper inset of Fig. 4, C oo and C res are shown together. One can clearly recognize a λ -shaped anomaly at the JT transition at 285 K and abroad hump-like contribution below the transition fol-lowed by the Schottky-like contribution for T < T ∗ . Theentropy ∆ S = S oo + S res = R T dϑ ( C oo + C res ) /ϑ associ-ated with the orbital DOF reaches a value slightly higherthan the expected ∆ S = R ln 4 (lower inset of Fig. 4).We interpret this observation as due to persistent fluctu-ations of the orbital and lattice DOF in the temperaturerange T ∗ < T < T JT in agreement with the anomaloustemperature dependence of the IR phonons and the ESRspectra.In summary, the Zeeman splitting of singlet-triplet ex-citations at 5.13 and 6.08 meV was observed in Sr Cr O .The spin-relaxation is dominated by spin-lattice effectsand revealed the splitting ∆ /k B = 388 K of the low-lying e doublet of the Cr ions below 120 K. The broad-ening of spin resonances and polar phonons above 120 Kis ascribed to strong orbital fluctuations. The specificheat clearly marks the JT transition temperature at285 K and reveals an extended fluctuation regime be-low the JT transition. This indicates the competitionof e.g. spin-orbit coupling and electron-electron interac-tions with electron-phonon coupling.We want to thank V. Tsurkan and D. Vieweg for exper-imental support and P. Lemmens, D. Wulferding, K.-H.H¨ock, R.M. Eremina, T.P. Gavrilova, and M.V. Ereminfor stimulating discussions. We acknowledge partial sup-port by DFG via TRR 80 and FOR 960. Y. Tokura and N. Nagaosa, Science , 462 (2000). G. Khaliullin, Prog. Theor. Phys. Suppl. , 155 (2005). F. Kr¨uger, S. Kumar, J. Zaanen, and J. van den Brink,Phys. Rev. B , 054504 (2009). K. I. Kugel and D. I. Khomskii, Sov. Phys. Usp. , 231(1982). E. Saitoh, S. Okamoto, K. T. Takahashi, K. Tobe, K.Yamamoto, T. Kimura, S. Ishihara, S. Maekawa, and Y.Tokura, Nature , 180 (2001). G. Khaliullin and S. Maekawa, Phys. Rev. Lett. , 3950(2000); V. Fritsch, J. Hemberger, N. B¨uttgen, E.-W.Scheidt, H.-A. Krug von Nidda, A. Loidl, and V. Tsurkan,Phys. Rev. Lett. , 116401 (2004); V. Tsurkan, O. Za-harko, F. Schrettle, Ch. Kant, J. Deisenhofer, H.-A. Krugvon Nidda, V. Felea, P. Lemmens, J. R. Groza, D. V.Quach, F. Gozzo, and A. Loidl, Phys. Rev. B , 184426(2010); L. Balents, Nature , 199 (2010). L. F. Feiner, A. M. Ole´s, and J. Zaanen, Phys. Rev. Lett. , 2799 (1997); G. Jackeli and D. A. Ivanov, Phys. Rev.B, , 132407 (2007). T. Nikuni, M. Oshikawa, A. Oosawa, and H. Tanaka, Phys.Rev. Lett. , 5868 (2000). C. R¨uegg, N. Cavadini, A.Furrer, H.-U. G¨udel, K. Kr¨amer, H. Mutka, A. Wildes,K. Habicht, and P. Vorderwisch, Nature (London) , 62(2003); M. Jaime, V. F. Correa, N. Harrison, C. D. Batista,N. Kawashima, Y. Kazuma, G. A. Jorge, R. Stern, I. Hein-maa, S. A. Zvyagin, Y. Sasago, and K. Uchinokura, Phys.Rev. Lett. , 087203 (2004); T. Giamarchi, C. R¨uegg, and O. Tchernyshyov, Nature Physics , 198 (2008). A. A. Aczel, Y. Kohama, C. Marcenat, F. Weickert, M.Jaime, O. E. Ayala-Valenzuela, R. D. McDonald, S. D. Se-lesnic, H. A. Dabkowska, and G. M. Luke, Phys. Rev. Lett. , 207203 (2009). E. Cuno and H. M¨uller-Buschbaum, Z. Anorg. Allg. Chem. , 95 (1989). L. C. Chapon, C. Stock, P. G. Radaelli, and C. Martin,arXiv:0807.0877v2 (unpublished). D. L. Quintero-Castro, B. Lake, E. M. Wheeler, A. T. M.N. Islam, T. Guidi, K. C. Rule, Z. Izaola, M. Russina, K.Kiefer, and Y. Skourski, Phys. Rev. B , 014415 (2010). G. Radtke, A. Sa´ul, H. A. Dabkowska, G. M. Luke, andG. A. Botton, Phys. Rev. Lett. , 036401 (2010). A. T. M. Nazmul Islam, D. Quintero-Castro, Bella Lake, K.Siemensmeyer, K. Kiefer, Y. Skourski, and T. Herrmanns-dorfer, Crystal Growth & Design , 465 (2010). M. Kofu, H. Ueda, H. Nojiri, Y. Oshima, T. Zenmoto, K.C. Rule, S. Gerischer, B. Lake, C. D. Batista, Y. Ueda,and S.-H. Lee, Phys. Rev. Lett. , 177204 (2009). V. N. Glazkov, A. I. Smirnov, H. Tanaka, and A. Oosawa et al ., Phys. Rev. B , 184410 (2004); M. Matsumoto, T.Shoji, and M. Koga, J. Phys. Soc. Jpn. , 074712 (2008). A. Abragam and B. Bleaney,
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