ISSN 00824798 Ser. A No. 3507 September 1999 ¥ O l '--" __ I Direct Evidence for the Localized Single-Triplet Excitations and the Dispersive Multiple-Triplets Excitations in SrCu,(B03)2 by Hiroshi Kageyama, Masakazu Nishi, Naofumi Aso, Kenzo Onizuka, Tomoyuki Yoshihama, Katsuyuki Nukui, Katsuaki Kodama, Kazuhisa Kakurai and Yutaka Ueda Technical Report of ISSP is aperiodica11y pub1ished in the fo11owing two Series： Series A：This series contains preprints of papers intended for publication in a journa1or proceedings． Series B：This series contains va1uab1e research notes （1ec− ture notes，technical or instrument訓 information）㎜d numerica1tab1es etc．，which are not intended to be published e1sewhere．They must not be repro− duced without the permission of the author（s）： SrCu2(B03)2 crystallizes in a tetragonal structure and consists of alternately stacked Sr- and CuB03-layers [1]. Tue Direct Evidence for the Localized Single- magnetrc Cu2. rons m the latter laycr orgamze an S=1/2 Triplet Excitations and the Dispersive two-dimensional (2D) Iinkage of orthogonally arranged dimers. Figure I (b) shows a fundamental unit of the orthogonal dimers Multiple-Triplets Excitations in oricnted either parallcl to [1. Ij or [1 . - I], indicating in-plane S rC u2(B03)2 interactions which act within the dimers J and between the dimers J '. Our prcvious expcri ments [2-71 togcther with scvcral theoretical works [8- 10] on this cuprate has revcaled following H. Kageyamal, *, M. Nishi2. N. As02, K. nontrivial aspects, all originating from this peculiar spin Onizukal, T. Yoshihama2, K. Nukui2. K. arrangement. Solvable Ground Stale SrCu2(B03)2 is idcntified as a Kodama3 K. Kakurai2 and Y. Ucdal 2D spin gap system with an exact dimcr ground state, realizing the Shastry-Sutherland model [8-10], Measurements such as magnetic susceptibility [2,3] , magnetization curves [2] , specif ic l Material Design and Characterizalion Laboratory, heat [61, nuclear magnetic resonancc (NMR) [2, 7], elcctron Institutefor Solid State Physics, University of Totyo, spin resonancc (ESR) [41 and Paman scattering [5] have Roppongi, Minato-ku, Tokyo 106-8666, Japan confirmed the spin gapped nature of this material , consistently giving rise to A =3.0 meV as an energy gap between the 2 Neutron Scattering Laboratory, Institutefor Solid State exact dimer ground state and the lowest triplet excited state. Physics, University of Tokyo, 106-1 Slliralata, Toh7i, Furthennore, ESR and Raman scattering rcvealed highcr-cncrgy lbaraki 3]9-1]06, Japan magnetic excitations associated with two-triplets bound states [4, 5]. 3 Division of New Materials Science, Institute for Solid Spin Frustration: It turned out that the isolated dimer State P/1ysics,- University of Tolyo, Roppongi, Minato-ku, model considering nothing but J completely failcd to reproducc Tokyo I 06-8666, Japan our experimental data of, e,g., magnetic susccptibility [2]. Therefore J', which brings a spin frustration into the system. PACS numbers: 75.40.Cx, 75.40.Gb no doubt plays a crucial role in achieving the spin-singlet AB STl CT (a) k (b) Wc pcrfomlcd inclastic ncutron scattcring on thc 2D Shastry3 li Suthcrland systcm Sl(]u2( B03)2 with an exact dimcr ground state. 'l'hrce cncrgy lcvcls at around 3, 5 and 9 mcV wcre _l ¥' "Jb 2 J observed at 1.7 K. The lowest excitation at 3.0 meV is almost dispcrsionlcss with a banctwidth of 0.2 mcV, showing J 1 a significant constraint on a single-triplet hopping owing to thc orthogonality of thc dimcrs. In contrast, the correlated o IA 2 D3 two-triplets excitations at 5 meV exhibit morc dispersive behavior. Fig. l: (a) The reciprocal latticc (h, k, O) of the nuclear unit cell. The Brillouin 7_one used in this study is given by the broken lines. Along thc lines A-C and D-F, the dispersion relations of band I, and bands 11 and HI, respectively, have been studied. (b) The fundamental unit of the orthogonal submitted to Phys. Rev. Lett. dimers . - I - ground state. Indeed, the exchange intcractions wcrc dctcnnined vector of Q=(2. O) . An abrupt growth in intcnsity below 2 as J= 100 K and J'=68 K [9]. The ratio of the exchange meV is due to the elastic incoherent scattering from thc eonstants J'/J=0.68 is, intercstingly cnough, just bclow thc samplc. Thc I .7 K spectrum consists of tluec peaks centcred critical boundary ((J '/J).=0.70 [9] or 0.69 1 [lO]) beyond which at 3.0 meV, 5.0 meV and 9.7 mcV (transitions I, 11 and 111, the system is expected to have a N6cl ordercd ground state. respcctively), while that for 24 K no longer has any appreciablc Localized Triplel Ercitalions: Mlyahara and Uedia pcak, indicating that all excitations are of magnetic origin. As theoretically showed that the wave ftmctions of thc triplct alrcady confirmed by other measurements [2-7], transition I at excitations are extremely localized [9]: Thc perturbation A=3.0 meV is the excitation of a single triplet from thc calculations of thc fifth order or less prohibit a single triplet singlct ground state. As shown in Fig. 2(b), the pcak intcnsities from propagating in the (a, b) plane. They argucd that this of transitions 1-III start to decrcase with increasing temperature localized character accounts for the crystalli7 ltion of thc triplets and disappear at about 13 K. We can derive from this similar observed at particular values of magnetization in high magnetic tempcrature dependencc that transitions ll and 111 arise from ficlds [2, 9]. multiplc-triplcts cxcitations, which will bc discusscd in dctails In this Letter, we investigate the s pin dynarnical properties l atcr . of SrCu2Q303)2 by mcans of inelastic ncutron scattcring using bulk single crystals . Almost dis persi onless magnctic excitations at 3 meV were observcd, rcflecting thc cxtremcly localized nature of the single-triplet hopping in the orthogonal dimer system. Magnetic excitations at higher energies were also .c_ investigated and discusscd i n tcnns of corrclatcd mul ti pl c-tri plcts v' EI (') E 500 1 400 excitations. c ann Eo ('vv Inelastic neutron scattering expcriments werc carried out e Oo 200 on ISSP-PONTA spectromcter installed at 5G bcam port of o o] ¥tl' 100 the Japan Research Reactor 3M (JRR-3M) in Japan Atomic IZII::III X I X: I 11 Ill c :: Energy Research Institute, Tokai Establishment. The o O 5 10 U O spectrometcr was opcrated in the unpolarizcd neutron mode with pyrolytic graphite Q?G) monochromator and analyzer. 15 E (meV) 1 .5 The inelastic scans were porformed with fixed final energy Er 14.7 meV (kf2.67 A-1) and horizontal collimations of x >t i^ (/'c I .O open(40' )40' -sample-80'-80' . A PG filter was placed aftcr thc o c IJ sample to suppress the higher order contaminations . In ordcr A e : E-3.15 meV e¥.X¥ X x: AE-S.15 meV : E-10.65 meV tL Al x 1) ,L, 'N 0.5 75 to minimize the neutron absorption by the natural abundance 'e ¥ X A ee x E L o of roB, IIB-enriched (99.6%) bulk single crystals of Z SrCu2(lIB03)2 wcre prcpared by the traveling solvent floating zone mcthod using LilIB02 flux [1 1]. The ncutron scattering a X*^A A _e_ 0,0 o sample consisted of two single cryst als with a total volume 5 10 T (K) of - 1.5 cm3 aligned witlrin 20' and it was orientcd with its ,_ 'L _ 1 5 20 25 a- and b-axes in the scattcring plane. For convenience, we use a Brillouin zonc at (h, k. O) Fig. 2: (a) Energy scans at Q=(2, O) obtaincd at T=1.7 K plane as givcn in Fig. I , where we do not distinguish between (circlcs) and 24 K (triangles). The peaks are labeled at the thc dimers lying along [1, l] and [1, -ll･ In this casc, thc bottom of thc figurc. The soiid curve is the fit to the data, as space lattice vectors are transferred toa a-b)/2 and b* a+b)/2, describcd in the text. (b) The temperature variation of the which correspond to the reciprocal space given by the lattice normaliz d intensities atE=3 . 1 5 meV and Q ( I .5, 0,5) (circles), vectors a* a -b and b E=5.15 meV and Q (2, O) (crosses), and E=10.65 meV and a +b . Shown in Fig. 2(a) are typical energy scans obtained at I .7 K and 24 K for a scattering Q=(2, O) (triangles). The broken line is a guide to the eye. -2- 'nle Q dcpendcnce of transition I was incasured at I .7 K along the lincs A, B and C, and that of transitions 11 and 111 III 12 along D. F. and F indicated by arrows in h ig. l(a). It was found that, indepcndcnt of Q, the obtained profilc for tr,ansition I at I .7 K is rcsolution limited, whereas the transitions 11 and 10 III show intrinsic line widths. Accordingly, the 1.7 K profile was fitted to a combination of a delta function for transition I and two damped hannonic oscillators for transitions 11 and 111, the solid line in Fig. 2(a) includes the temperature independent >8 E term of incoherent scattering around energy zero. Lu convoluted with the instrumental rcsolution. It is noted that , , The dispersion relation of band I is shown in Fig. 3. 6 F E D II Most importantly, the excitation energies arc almost Q f indepcndent. Namely, the magnitudc of the dispersion, the diff erencebctwecn themaximurn and minimum of the excitation 4 energy, is AE=0.2 meV. This width is significantly small in contrast to conventional low-dimensional quantum spin systems. Experimentally, strong dis persions of the singl e-tri plet IC A B 2 excitations wcre observed in the ID spin-Peierls material (0,0) (1c,o) (1 t,1 ,) (0,0) CuGc03 (AE=14 meV) along the chain ,axis [12], and in the 2D plaquettc system CaV409 (AE=7 meV) parallel to thc Fig. 3: Q-depcndence of the excitation energies of bands I, H plaquette plane [13]. On the contrary, well-isolated clusters of and 111 obtained at I .7 K. The arrows represcnt the encrgy exchange-coupled paramagnetic ions, whcre intercluster resolutions of the instrument (hWIIM). The solid curves are interactions are rarely important, evidently exhibit flat guides to the eye. The bars represent the intrinsic line width dispersions in the spin excitation spectrum. Tlris has been (FWHM) of bands 11 and 111. The thcoretical dispersion curve experimentally shown by the neutron scattering measurements for the single-triplet excitations [10] is given by the broken on the isolated dimer systems Cs3Cr2Br9 (AE=1.8 meV) [14] line. and BaCuSi206 (AE=0.7 meV) [15], and the four-spin system Cu2P04 (AE=3 meV) [161･ In SrCu2(B03)2' the physical situation is completely different because the dimers within the Recent NMR mcasurement by Kodama et al. [7] has also (a, b) plane arc not isolatcd but strongly intcracting and disclosed cvidencc to support the localization of thc single moreovcr the system is located in thc vicinity of the N6cl tri plet. ordcred state. As thcoretlcally shown by Miyahara and Ueda Let us take a closer look at the Q-dependencc of band I, [9], thc key to the dispcrsionlcss band in SrClb(B03)2 Iies not see Fig. 3. Thc disporsion curve reachcs a maximwn (2.90 in the spatial isolation of the spin clusters but in the meV) at the so-called (7c, O), a second maximum (3.00 meV) orthogonality of the neighboring dimers: They proved that a at (1c/2, 1(:12), and minima (3.10 meV) at (O. O) and the hopping of thc single triplct from one sitc to another within equivalent point (1c, 7c). Using the scries expansion method each planc is possible only from the sixth order in the up to the fifteenth order, Weihong, Hamer and Oitinan obtained perturbation calculations, Ieading to exceedingly weak the single-triplet excitation spectrum [10]. They argued that dispersions of band I. It is noted that the appearancc of the the bandwidth is quite small as anticipatcd, but increases as quantized plateaux in the magnetization curve [2, 9] and the J'/J approaches (J'/J).. For a comparison, thc calculated multiple magnctic resonanccs in ESR [4] indicatc the localized dispersion curve is shown by the brokeil line in Fig. 3, where character of multiple-triplcts cxcitations. Our neutron scattering we assumed J=100 K. J'=68 K and A=3.0 meV. From the study, however, provides for the first thne a direct proof of qualitative point of view, the calculated Q dependence of the the significant constraint on the single-triplet excitations. cxcitation energies nicely reproduces our experimcut 1 data -3- Howcver, the calculated bandwidth of 0.7 meV is (relatively discrcte energi es. We suppose the excitations are also delocalizcd narrow but) much widcr than thc obscrved onc. To add to tlris, owing to the correlation of the multiple triplets as in the case their theory yields a slightly smaller value of A=2.0 meV at of transition 11 though, at present, thc very wcak peak intensity (O. O) and (1 . 7c). A possiblc explanation for the quantitative and broad nature of transition 111 do not allow a reliablc discrepancies is that thc perturbative approach bccomes no discussion of the dispersion relation. longer appropriate when we discuss thc phenomena of the F･inally, wc discuss the Q dependcnce of the intensities of excitation I. The intensities at T= I .7 K and E=3.0 meV system near thc critical boundary (J '/J).. The ncxt argument concems transition 11 which occurs were mcasured over various Q-points. As typical examples, at energy transfer of about 5 meV. This excitation has bccn the data taken along three directions in the rcciprocal latticc already observcd by ESR [5] and Raman scattering [6] (at 4.7 arc shown in Fig. 4. The observed periodic intensity modulation meV), and thc magnetic field depcndencc of the ESR frequcncy was compared with the dynamical structure factor which can has identified this mode as the second triplct state [5]. As be obtained by calculating the transition probability from the discusscd in Rcfs. [51 and [6], transition 11 is undcrstood basod singlct ground state to the lowcst triplct cxcited statc. For on two triplets coupled by J,(>0): If J,=0, the corrcsponding simplicity, Ict us considcr a non-interacting pair of orthogonal transition occurs on]y at 2A=6.0 meV. But when J* is finitc, dimers (J'=0) with the intradimer dist,ancc 2.905 A. Thcn, the one expects a separation of the transition into tlucc energy intcnsity at Q ll, k) is given by the superposed form, sin[a(h- levels at E0=2A-2J, for the singlet state. El=2A-J, for the k)]2+sin[a(h+k)]2 (a=0.717), where the Q dependence of thc triplet state, and E2=2A+J, for the quintct statc. Using /"I=4'7 magnetic fonn factor is not includcd, bccausc it docs not meV [5. 6] and Eo=-3'7 mcV [6]. J* is detcrntincd to be I . I - affcct the rcsult considcrably in the limited Q-range studied. l.3 mcV. Includcd in Fig. 4 are thc theorctical curvcs, which achicve Figure 3 shows that the Q dcpendence of band 11 is close conforrnity with the experimental ones in spitc of the qualitatively idcntical to that of band I. The striking difference unrealistic assumphon about J'. This fact reflects thc spin betwecn bands I and 11 is that the latter shows more dispersive frustration bctween the dimers. A slight deviation bctween the behavior w:ith a bandwidth of 1.5 meV. This observation may theory and experiment may bc corrected by including the indicate that the propagation of correlated two Uiplets is much interdimer interactions. casier than that of the single triplet. Very recently, preliminary consideration of the two-triplets excitations by Miyahara and 500 Q=(h,O) 400 II 300 200 Ueda indicates that two triplets sitting on the nearest neighbor sites can propagate within the fourth-order perturbation calculations [17J. Considering the instrumental energy resolution, the full width at half maximurn (IWHM) of band II for any Q points is obtained to be approximately 0.7 meV. . The finite width possibly indicates a spin continuum and/or a Lr) ? short lifetime of the coupled two triplets. One of the remaining co problems regarding this mode is to detennine thc distance E J, OO to O1 ¥ between a particular pair of the triplets. This may be possible if one analyses the Q and intensity variations of this mode, 1 OO o Il l i o interpreted within the framework of correlated three triplets or 1 OO the transition 111 is considerably broad (see Figs. 2(a) and 3). O U Transition 111 wlrich appears at 8-12 meV may be Illl 1 oo more. Compared with the transition II. the observed profile of =0 Q-(h,h) (b) 200 400 300 200 which will be our future work. (a) l : I (C) l f 11 Q*(h,2-h) h which may result from a much wider spin continuum and/or a much shorter lifetime of the bound state. Or one might think Fig. 4: Observed and calculated Q iependcnce of the scattering the case of several excited states lying at nearly degenerated intensity for excitation I. -4- Imsu㎜町，wepe㎡om由ime1ぷclleu甘㎝sc汕ed㎎ Mod，㎜d N．Nis阯，J．Phys．S㏄．Jpn．“，793（1997）。・・p・hm・・t・㎝S・C・。（IlBO。）。t・n・仙・・m・即・O…dt・d…．口4】B．Leuenberger，A．S屹b1er，H．U．GOde1，A．F㎜Ter，R． The1owestex・M㎝from血・gmmds側ew㎜obs・wed・t Fei1e，‘㎜d Jl K．Kj’㎝1s，Phys．Rev．B，30．6300（1984）一 3．0meV，inagreem㎝twiulo此m㎝surcm㎝ts．Weobs6ned 血e a1most dispersio血ess cu〃e fo“he firs“me in s血ong1y ooπc1atω1−3D spin systems，ohgimting fmm伽e p㏄u1i町 ○汕10gon刮dimcr1letwork mt from血e iso1adon or血e sp㎞口5］Y．Sasago，K．Uc肚mk山ra，A．Zheludev，‘㎜d G．S㎞r三㎜e， Phys．Rev−B55．8357（1997）．〔161M．Hase，K．M．S．E此r出ge，S−J．Hwu，K．㎜m血，md G．S阯rme，Phys．Rev．B56．3231（1997）．［1刀S．Miyah町a㎜dK．Ueda，pdva蛇oo㎜㎜icaOons． cluslers．mlcs㏄ond㎞plαmode虹aromd5meVis㎜derstood to the nrst approxim汕on by血e localized model o〔he coπe1atωユwo trip1cts，but its exci胞don sp㏄血㎜n is more dispersive血al1血atof血e3meV mωc．Likewise，血ehighest− en町gy mode煎9meV wo血d㎞serrom血e ooπe1ated此㏄or m…φα…d胞d㎝干・ The au血ors胴帥tcr山o H．N句iH，P．レmn㎝s，M、丁批gawa，S．Miy㎞蛆a㎝dK．U剣aforsdm此d㎎discussion． T11is work w㎜supP011．cd by a Grmレin−Aid forEhoourag㎝1e1lt Yo㎜1g Sciendsts from The Mi㎡s岬of Educadon，Scien㏄， Spo111s∼md Cu1111肥． 1−6圧01r611CeS ＊Elec血o皿ic address：kage＠issp．u−tokyo．acjp 凹R，W．Smith md D．A，Kes加r，J．So1id State Chem． 93，430（1991）．【2】H．Kagey㎜a，K．Yoshimm，R．S屹m，N．V．Mus㎞㎡kov， K．0nizu由，M．㎏to，K．Kosuge，C．P．Slichter，T． G伽o，…㎜d Y．Ue由，Phys．Rev．Leu．82．3168（1999）．固H．Kageyama，K．0㎡zuka，T．Yamauchi，Y．Ueda，S． Hl㎜e，H．Miレ㎜㎜a，T．G伽o，Kl Yos肚mura，ε㎜d K． Kosuge，J．Phys．Soc．Jpn．68．1821（1999）．凹H．N句iri，H、胞gcy㎜a，K．0㎡zuka，Y．Ueda，㎜d M． Motokawa，to aP畔町in J．Phys．Soc．Jpn．固P．Le㎜ens，M．Grove，M．Fisher，G．G舳em砒，H． Kageyama，K．Onizuka，md Y．Ueda，to be published。〔6】甘尽ageyama，H．Su刎ki，M．Noh〃a，K．0㎡z此a，H． Takagi，alld Y．Ucda，to app㎝r in Physi㎝B． r1】K．Kod㎜a，Y．K刎o，M。丁批gawa，H．Kagcy㎜1a，K． 0此㎜ka，md Y．U地，㎜published．エ8】B．S．Shas甘y md B．Su血eH㎜d，Physica108B，1069 （1981）．圧9】S，Miyah肛a aI1d K−U耐a，Phys．Rev．Le肚．82．3701 （19”）．エ10］Z．Weih㎝g，C．J．H㎜er，㎜d J．Oi㎞㎜，Phys．Rev．B 60．6608（1999）．［11］H．Kageyωna，K．0㎡zuka，T．Ymauchi，ξ㎜d Y．Ueda， to apP㎝r in J．C町sωGmw血．口2】M．NisM，0．珂i胞，㎜d J．A㎞㎜i舳，Phys．Rev．B5g， 6508（1994）．［13］K．K砒ma，H．H趾as阯m，H．Sas舳，Y．Kobay困肚，M． K㎜㎡，S．T㎜i馴chi，Y．Yaslli，M．Sato，K．K水urai，T．一5一