Journal of the Korean Physical Society, Vol. 63, No. 3, August 2013, pp. 333∼336

Anisotropic Spin Excitations in Spin-Peierls CuGeO3

Kazuhiko Ikeuchi∗ and Ryoichi Kajimoto

Research Center for Neutron Science and Technology,Comprehensive Research Organization for Science and Society (CROSS), Tokai, Ibaraki 319-1106, Japan

Fumio Mizuno

Department of Physics, Tohoku University, Sendai 980-8578, Japan

Masaki Fujita

Institute for Material Research, Tohoku University, Sendai 980-8577, Japan

Yasuhiro Inamura, Mitsutaka Nakamura, Kenji Nakajima, Kazuya Aizawa and Masatoshi Arai

Neutron Science Section, J-PARC Center, Tokai, Ibaraki 319-1195, Japan

(Received 31 May 2012, in final form 15 October 2012)

We report on the investigation of spin excitations in CuGeO3 at a low temperature by usinginelastic neutron scattering on a pulsed source with a time-of-flight analysis. By observing thedispersion relation of spin excitations not only along the chain direction but also along the interchain direction, we studied spin correlations in the S = 1/2 Heisenberg chains, as well as between thechains, in detail. The results show a clear anisotropy of the magnetic excitations at a temperaturebelow the spin-Peierls transition temperature.

PACS numbers: 68.37.Ef, 82.20.-w, 68.43.-hKeywords: CuGeO3, One-dimensional quantum spin system, Inter-chain interaction, Inelastic neutron scat-tering experimentDOI: 10.3938/jkps.63.333

I. INTRODUCTION

The one-dimensional S = 1/2 Heisenberg model in-cluding the second-neighbor interaction has providedvarious results for the ground state and the dynami-cal properties in the dimerization state of a quantumspin system [1–3]. In addition, the effect of the super-exchange interaction between spin chains has attractedwide attention because it causes magnetic frustration inthe quantum spin state [4,5]. Further investigation ofthe inter-chain coupling has been an important subjectfor understanding a quantum spin liquid in modern con-densed matter physics.

Since Hase et al. reported magnetic properties ofCuGeO3 [6], it has been a well-known inorganic one-dimensional quantum spin system that shows a magnetictransition to a dimerized state with a spontaneous latticedistortion at temperatures below a transition tempera-ture of Tc = 14 K. Nevertheless, it is not clear whether itis an archetypal material of a spin-Peierls system. In fact,neutron scattering experiment has not yet succeeded in

∗E-mail: k˙ikeuchi@cross.or.jp

assigning a soft phonon mode along the spin chain di-rection accompanied by the magnetic transition. Al-though by using inelastic neutron scattering (INS) witha triple axis spectrometer, Lorenzo et al. discovered alarge spontaneous distortion at temperatures below Tc,it appears along the b-axis which is perpendicular tothe spin chain along the c-axis [7, 8]. On the otherhand, with a slight doping of Zn by 0.1 % into the Cusite, three-dimensional antiferromagnetic long-range or-der was induced in the ground state [9–12]. Actually,due to an antiferromagnetic coupling between neighbor-ing spin chains, the dimerization state in the spin chainis near a three-dimensional state. Thus it is a systemin which we should consider the inter-chain coupling ex-plicitly.

In the present work, in order to further understandthe inter-chain coupling, we studied the momentum de-pendence of INS spectrum along the b-axis, as well asalong the c-axis, in detail. By observing the dispersivestructure on intensity-maps in a four-dimensional (mo-mentum: Q, energy: ω) space by using a direct geom-etry neutron chopper spectrometer, we have elucidatedthe anisotropic magnetic couplings.

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II. EXPERIMENTS AND DISCUSSION

In order to perform an INS experiment by using apulsed source with a time-of-flight (TOF) analysis, weprepared eight rods of single-crystal samples of CuGeO3

which were grown using the traveling-solvent floating-zone method. The total sample amount was 17.2 g. Asshown in Fig.1, these single crystals were co-aligned witheach other by using the conventional Laue method of x-ray diffraction. In our experiments, we defined the or-thorhombic lattice of CuGeO3 with these lattice param-eters of a = 4.81 A, b = 8.47 A, and c = 2.941 A atroom temperature [8]. The spin chains were along thec-direction and were aligned along the b-direction. Thelayered structures in the b-c plane formed alternatinglayers with the GeO4 block layers along the a-direction.The a-, b-, and c-axis component of momentum trans-fer were denoted by H, K, and L of Q = (H,K,L) inreciprocal lattice unit.

The TOF-INS experiments were carried out on thechopper spectrometer 4SEASONS in the Materials andLif Science Experimental Facility (MLF) of Japan Ac-celerator Research Complex (J-PARC) [13]. The powerof the spallation neutron source was 200 kW. In orderto reduce the background coming from around the sam-ples, we mounted the samples on a candleholder-typealuminum holder, which is formed from top and bot-tom plates connected by only one pillar. Furthermore,we wrapped the gluing parts between the samples andthe holder with cadomium plates. The monochromatingchopper, a Fermi chopper, was tuned to an incident en-ergy (Ei) of 45 meV. The rotation speed of the Fermichopper was 200 Hz. It realized an energy resolutionof about 6% of the incident energy at the elastic posi-tion. We aligned the a-axis of the sample vertically andthe b-axis with the incident beam (ki || K in a momen-tum expression). We set this position as the originalrotating position of the sample. Usually, the magneticexcitations of this system are measured as a projectiononto the chain direction by assuming that the spin cor-relations are one-dimensional. In this study, in order toobserve the dispersion relation not only along the chaindirection but also along the inter-chain direction, we ro-tated the sample around the a-axis from –90 degrees to0 degrees (ψ = –90 to 0) with a 2.5-degree step. Themeasurements were carried out at T = 6 K.

In Fig. 2, we show a scattering intensity map on L−ωspace as a color contour. All of the data from ψ = –90 to 0 are accumulated and projected onto the L − ωplane after integration over the H and the K directions.With Ei = 45 meV, we can cover 3 sets of the entireBrillouin zone (BZ) of CuGeO3. First of all, we cansee clear magnetic excitation of a one-dimensional S =1/2 Heisenberg chain which is composed of a singlet-triplet excitation, the so-called des Cloizeaux Pearsonmode (dCP mode), at the lower boundary and a twospinon excitation that exists as a continuum up to the

Fig. 1. (Color online) Photograph of coaligned singlecrystals of CuGeO3 mounted on a candleholder-type sampleholder, which is a conventional sample holder of 4SEASONS.

Fig. 2. (Color online) Spin and phonon excitations onCuGeO3 at T = 6 K. This color map is a projection of thedata from ψ = –90 to 0 on the L direction. Integration rangesalong H and K are shown at the bottom of the figure, andfully covered the measured momentum region.

upper boundary.Additionally, a high-energy region just above the S =

1/2 Heisenberg spin excitation exhibits several charac-teristic optical phonons. Especially at the high |Q| re-gion at around L = 1.5, we can see more intense phonon

Anisotropic Spin Excitations in Spin-Peierls CuGeO3 – Kazuhiko Ikeuchi et al. -335-

branches because intensity of a magnetic excitation de-creases due to the magnetic form factor and that of aphonon becomes stronger due to the |Q|2 factor.

Also, we show the intensity map on K−L space cut atan energy transfer of ω = 5 meV in Fig. 3. Because wealso confirmed an almost dispersion-less structure alongthe H direction, we can integrate along the H directionin many cases. The small red spots at momentum posi-tions ofK = integer and L = integer which correspond tonuclear Brillouin zone centers (ZC’s) and the broad redspots at K = odd and L = half integer which correspondto magnetic ZC’s are acoustic phonons and low-energyparts of the dCP mode, respectively. In principle, if thespins were correlated only along the L direction, the ex-citation would appear as uniform red bands along the Kdirection. The modulation in intensity reflects a three-dimensional structure of the spin excitation in the low-energy region. Overall structures of these excitations areconsistent with the former TOF-INS results on CuGeO3

reported by Arai et al. in 1996 [14]. However, in thepresent work, we can demonstrate more detailed char-acters of the excitations. The reason is that the map isexhibited using an integral of the four-dimensional dis-tribution of the intensity over the entire BZ instead ofthe projection by assuming that the magnetic correlationis one-dimensional along the L direction.

The dispersion curve of the dCP mode determined byusing a triple axis spectrometer has been reported byNishi et al. [15]. They estimated a coupling energy of Jc

= 10.4 meV in the L direction for a maximum energy ofthe mode of 16.3 meV. They also estimated the exchangeenergies in the H and the K direction as Jb = 0.1 Jc andJa = –0.01 Jc, respectively. The anisotropic structuresin our measurement are consistent with their results.

A recent theoretical work proposed a new kind of spinphonon coupling in this system. They calculated the dy-namical spin correlation function and phonon spectrumby using the dynamical density-matrix renormalization-group method [16]. The coupling induced a new phononmode below the spin gap. Concomitantly with that, aninduced magnetic mode appearred above the S = 1/2Heisenberg excitation. Because we succeeded in mea-surements over a wide four-dimensional Q − ω range,we will be able to make a comprehensive study on spin-phonon coupling in CuGeO3 with data including bothspin and phonon excitations. Such a study should clar-ify the detailed structure of the spin excitation in a sys-tem even including frustration affected by the inter-chaincorrelation.

III. CONCLUSIONS

To summarize, we report on an investigation of spinexcitations in CuGeO3 at a low temperature by usinginelastic neutron scattering on a pulsed source with thetime-of-flight analysis. By observing the dispersion re-

Fig. 3. (Color online) Color contour map of the excitationson the K − L plane at ω = 5 meV. White ellipsoidal linesin the map come from gaps in the detector arrays of thespectrometer. Integration ranges along H and ω are shownat the bottom of the figure.

lation of spin excitations along the inter-chain direction,we studied the inter-chain interactions of S = 1/2 Heisen-berg chains. The results show a clear anisotropy of themagnetic excitations at a temperature below the spin-Peierls transition temperature by rotating the sample. Inaddition, we succeeded in observing the precise phononstructures and the magnetic excitations. The data pre-sented here should be a complete set of excitations onthis system at a low temperature, then, a further analysiswill lead to the detailed physics of a spin-Peierls-relatedsystem.

ACKNOWLEDGMENTS

The authors would like to thank Dr. T. Sugimotoand Dr. T. Tohyama for helpful discussions. The workat Japan Accelerator Research Complex (J-PARC) wascarried out under Proposal No. 2009A0093 and ProjectNo. 2009A0087. This work was supported by a Grant-in-Aid for Special Promote Reaseach (No. 17001001) fromthe Ministry of Education, Culture, Sports, Science andTechnology of Japan.

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