1 H-NMR Study of the Random Bond Effect in the Quantum Spin System (CH 3 ) 2 CHNH 3 Cu(Cl x Br 1−x ) 3
aa r X i v : . [ c ond - m a t . s t r- e l ] J un Typeset with jpsj2.cls < ver.1.2 > Letter H-NMR Study of the Random Bond Effect in the Quantum Spin System(CH ) CHNH Cu(Cl x Br − x ) Tomoya
Adachi , Keishi
Kanada , Takehiro
Saito , Akira
Oosawa and Takayuki
Goto
Department of Physics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan (Received November 30, 2018)
The spin-lattice relaxation rate T − of H-NMR has been measured in(CH ) CHNH Cu(Cl x Br − x ) with x = 0 .
88, which is reportedly a gapped system witha singlet ground state from the previous macroscopic magnetization and specific heat mea-surements, in order to investigate the bond randomness effect microscopically in the gappedcomposite Haldane system (CH ) CHNH CuCl . It was discovered that the spin-lattice relax-ation rate T − in the present system includes both fast and slow relaxation parts indicativeof the gapless magnetic ground state and the gapped singlet ground state, respectively. Wediscuss the obtained results with the previous macroscopic magnetization and specific heatmeasurements together with the microscopic µ SR experiments.
KEYWORDS: (CH ) CHNH Cu(Cl x Br − x ) , quantum spin system, spin gap, bond randomness, H-NMR,spin-lattice relaxation rate T − The bond randomness effects in spin gap systemsyield a rich variety of novel phases such as theimpurity-induced magnetic ordered phase, the Bose-glass phase, and the random-dimer phase. The title compound (CH ) CHNH Cu(Cl x Br − x ) (abbreviated as IPACu(Cl x Br − x ) ) shows the impurity-induced antiferromagnetic ordered phase. Both parentcompounds IPACuCl and IPACuBr are the spin gapsystems. The magnitude of the excitation gap ∆ be-tween the singlet ground state and the triplet excitedstates in IPACuCl was estimated as 17.1 ∼ Fromthe viewpoint of the crystal structure of IPACuCl , theorigin of the spin gap was expected to be the S = ferromagnetic-antiferromagnetic alternating chain alongthe c -axis. However, recently, it was suggested thatIPACuCl should be characterized as the spin ladderalong the a -axis with the strongly coupled ferromag-netic rungs, namely, the antiferromagnetic chain withan effective S = 1 ”composite Haldane chain,” and theexcitation gap was re-estimated as 13.6 K by meansof neutron inelastic scattering experiments. Mean-while, IPACuBr has been characterized as the S = antiferromagnetic-antiferromagnetic alternating chainwith a singlet dimer ground state and an excitation gap∆ = 98 K. However, IPACuBr may also be rechar-acterized as the spin ladder system when the neutroninelastic scattering experiments will be carried out, inthe same manner as IPACuCl .The mixed system IPACu(Cl x Br − x ) was studied bymeans of the magnetization and specific heat measure-ments, and it was reported that the bond-randomness-induced antiferromagnetic ordered phase with T N =13 ∼
17 K emerges in the region 0 . < x < . x ≥ x ≤
13, 14 and that the phaseboundaries between these phases are of the first order.Quite recently, the present authors microscopically stud-ied the mixed system IPACu(Cl x Br − x ) by means of NMR
15, 16 and µ SR measurements. Microscopic evi-dence of the impurity-induced antiferromagnetic orderedphase, such as the clear splitting of the H-NMR spec-tra and the clear rotation of the µ SR time spectra below T N , was observed in IPACu(Cl x Br − x ) with x = 0 . x Br − x ) with x = 0 .
95 and observed ananomalous enhancement of the relaxation rate indicativeof the existence of magnetic fluctuations at low temper-atures, in spite of the singlet Haldane phase.As mentioned above, based on the previous magneti-zation measurements, it was concluded that the groundstate is the singlet Haldane phase in x ≥ .
87, whilefrom the recent µ SR measurements, it was concludedthat magnetic fluctuations exist in the ground state of x = 0 .
95. In order to investigate these two conflictingconclusions, we measured the spin-lattice relaxation rate T − of H-NMR in IPACu(Cl x Br − x ) with x = 0 . both fluctuations indicative of the gappedsinglet ground state and the gapless magnetic one. In thisletter, we report and discuss the results.Single crystals of IPACu(Cl x Br − x ) with x = 0 . ± . ◦ C, in an atmosphereof flowing nitrogen gas during the entire period of crys-tal growth, which was approximately two months. Crys-tals with three orthogonal surfaces were obtained. Thesethree planes were termed A-, B-, and C-planes. The def-inition of these planes is given in ref. 10. The typical sizeof the obtained crystals was around 2 × × witha rectangular shape, as reported in a previous paper. The content of Cl, x = 0 .
88, was determined using theinductively coupled plasma spectrometry for three tinyfragments chipped off from different points of the crystal.
Letter
Tomoya
Adachi et al.
The spin-lattice relaxation rate T − of H-NMR with ν = 118 MHz was measured by the saturation-recoverymethod with a pulse train using a 4 K cryogen-free refrig-erator set in a 6 T cryogen-free superconducting magnet.Relaxation curves were traced until the difference be-tween the nuclear magnetization and its saturation valuewas 1 %. There are ten inequivalent proton sites in theunit cell of the present system. Each inequivalent protonsite has different distances such that it is exposed to dif-ferent hyperfine fields from the nearest magnetic Cu site.Since the nuclear spin-spin interactions between inequiv-alent protons result in a small hyperfine field, the finestructure of H-NMR spectra produced by inequivalentprotons were smeared and overlapped broad peaks wereobserved. In the present experiments, we measured thespin-lattice relaxation rate T − of the overlapped broadpeaks. We confirmed that there was no significant differ-ence in T − at any position of the spectrum.Figure 1 shows the nuclear magnetization recovery of H-NMR at various temperatures for the H ⊥ C-plane inIPACu(Cl . Br . ) . As shown in Fig. 1, nuclear mag-netization exhibits fast recovery at high temperatures.However, with a decrease in temperature, we can clearlyobserve that the recovery of the nuclear magnetizationbecomes slower and does not obey the single exponentialfunction. Based on the assumption that the spin-latticerelaxation includes fast and slow relaxation parts, we fit-ted the obtained results by the following equation1 − M ( τ ) M sat = a exp (cid:20) − τ ( T ) fast (cid:21) + b exp (cid:20) − τ ( T ) slow (cid:21) . (1)Reasonable fits can be obtained, as shown in Fig. 1,and the spin-lattice relaxation rate T − for both parts isobtained for each temperature. In this fitting, the ratiosof the two relaxation parts a and b are assumed to betemperature independent and are estimated to be 0.2and 0.8, respectively.Figure 2 shows the temperature dependence of thefast and slow relaxation parts of the spin-lattice relax-ation rate T − of H-NMR for the H ⊥ C-plane inIPACu(Cl . Br . ) . At high temperatures, both T − show a similar decrease with decreasing temperature dueto the development of antiferromagnetic correlations, asobserved in the previous magnetic susceptibility mea-surements. However, below T ∼
10 K, each T − exhibitsdifferent behavior, namely ( T − ) fast becomes constant,while ( T − ) slow decreases more rapidly on decreasing thetemperature. We fitted the temperature dependence of( T − ) slow at a low temperature by the following equa-tion 1( T ) slow ∝ √ T exp (cid:18) − ∆ k B T (cid:19) , (2)which indicates the existence of the excitation gapfrom the singlet ground state and was used for the esti-mation of the excitation gap ∆ in the previous magneticsusceptibility and specific heat measurements. The ex-citation gap ∆ was estimated as 11(1) K, as indicated bythe solid line in Fig. 2. -223456789 -123456789 - M ( τ ) / M s a t τ (s) T=2.2 K2.5 K3.0 K4.0 K6.0 K8.0 K10.0 K13.0 K18.0 K
IPACu(Cl Br ) H ⊥ C-plane
Fig. 1. Nuclear magnetization recovery of H-NMR at varioustemperatures for the H ⊥ C-plane in IPACu(Cl . Br . ) .Solid lines denote the results of fitting by eq. (1). Herein, we discuss the obtained results. First, it isnoted that there exists a correspondence between themagnitudes of ( T − ) fast and ( T − ) slow within the errorbars above T ∼
10 K, as shown in Fig. 2; therefore, thenuclear magnetization recovery observed above T ∼
10 Kcan also be fitted by the single exponential function. Inthe present experiment, we discovered that nuclear mag-netization recovery below T ∼
10 K cannot be expressedas a single exponential function, that the spin-lattice re-laxation rate T − consists of fast and slow relaxationparts, and that the slow part of T − at low tempera-tures exhibits gapped behavior with ∆ = 11(1) K inIPACu(Cl . Br . ) . As mentioned above, it has beenreported that the ground state of IPACu(Cl . Br . ) isthe singlet Haldane phase with an excitation gap ∆ ∼ in the previous magnetization and specificheat measurements.
13, 14
Hence, we can expect that thegapped behavior of the slow relaxation part of T − in-dicates the existence of the gapped singlet ground state,as observed in the macroscopic magnetization and spe-cific heat measurements.
13, 14
In addition, the fast re-laxation part of T − was also observed in the presentexperiments. Since the fast relaxation part of T − be-comes constant with a decrease in temperature, we can . Phys. Soc. Jpn. Letter
Tomoya
Adachi et al. T - ( s - ) -1 (K -1 ) ∆ = 11(1) K (T ) fast (T ) slow IPACu(Cl Br ) H ⊥ C-plane
Fig. 2. Temperature dependence of fast and slow relaxation partsof the spin-lattice relaxation rate T − of H-NMR for the H ⊥ C-plane in IPACu(Cl . Br . ) . The solid line denotes the resultof fitting by eq. (2) for the slow relaxation part of T − . Thedashed line is the guide for the eyes. expect that the fast part of T − indicates that there is themagnetic ground state composed of localized moments,in contrast with the slow relaxation part. In the previ-ous µ SR experiments for IPACu(Cl . Br . ) , muonspin relaxation with two components was observed at T = 0 .
33 K, as observed in the present NMR experimentsfor IPACu(Cl . Br . ) ; further, it was concluded thatone of the two components indicates the existence of themagnetic instability in the ground state. Hence, we canexpect that the fast part of the spin-lattice relaxationrate ( T − ) fast observed in the present NMR experimentscorresponds to the observed muon spin relaxation indi-cating the magnetic instability and also supports the ex-istence of magnetic fluctuations in the ground state. Theother of two components observed in the µ SR experi-ments was also concluded to originate due to the qua-sistatic nuclear spin part, that is, a part of the muonswas unaffected by the magnetic fluctuation of electronicmoment at the Cu sites. We infer that this componentobserved in the µ SR experiments reflects the gapped sin-glet ground state, as observed in the present NMR ex-periments.That the two spin-lattice relaxation components orig-inate due to the macroscopic phase separation can beruled out on the basis of the following discussions. Forone, no diverging behavior indicative of magnetic or-dering above T = 2 K was observed in ( T − ) fast . Ithas been reported that the magnetic ground state onlyexists in the impurity-induced magnetic ordered phasewith T N = 13 ∼
17 K for the region 0 . < x < .
87 inIPACu(Cl x Br − x ) and that the diverging behaviorof the spin-lattice relaxation rate T − of H-NMR in-dicative of the impurity-induced magnetic ordering wasactually observed in IPACu(Cl x Br − x ) with x = 0 .
85 at T N = 13 . therefore, we can safely conclude that theobserved ( T − ) fast does not reflect the magnetic orderedphase of 0 . < x < .
87. Second, the changes in the tem-perature dependence of both ( T − ) slow and ( T − ) fast at T ∼
10 K occur simultaneously and therefore we expect that the changes are cooperative. Since it has been ob-served that the singlet formation commences at T ∼
10 Kin the parent compound IPACuCl ,
18, 19 we expect thatthe change in ( T − ) fast is also associated with the sin-glet formation together with the exponential decrease in( T − ) slow , as shown in Fig. 2.From the observation of ( T − ) slow and ( T − ) fast , itcan be considered that there are more than two Cu siteswith inequivalent magnetic properties because the spin-lattice relaxation process of H-NMR is caused by thefluctuation of the magnetic moment around the protons.It should be noted that the observed fast and slow partsdo not correspond to the relaxation processes of the in-equivalent protons in the unit cell of the present systembecause the spin-lattice relaxation rates of inequivalentprotons should exhibit the same temperature dependenceand should be scaled by the distance between each pro-ton and the magnetic moment at the Cu site. Non-singleexponential behavior of spin-lattice relaxation indicativeof the existence of some inequivalent magnetic sites hasalso been observed in the doped spin-Peierls systems(Cu − x Mg x )GeO and Cu(Ge − x Si x )O . This non-single exponential behavior has been expressed in thespatially nonuniform relaxation processes, as expressedby the stretched exponential form 1 − M ( τ ) /M sat ∝ exp[ − t/T − ( t/τ ) / ], indicating that there are ad-ditional dilute magnetic moments in the homogeneoushost. We tried to fit the present results using the abovestretched exponential form; however, we were unable toobtain suitable results. Hence, we conclude that eachmagnetic moment is not isolated dilutely, but forms is-lands in the singlet sea in the present system.From the above discussion, we expect that the groundstate of the present system can be expressed as a mi-croscopic mixture of singlets and localized magnetic mo-ment islands. The singlets correlate to the magnetic mo-ment islands because the Curie-law behavior indicativeof the existence of paramagnetic moments has not beenreported in the magnetic susceptibility measurements, and simultaneous changes in the spin-lattice relaxationrate below T ∼
10 K were observed, as mentioned above.Further, it was found that the spin-lattice relaxation be-havior of the present system is considerably differentfrom that of the parent compound IPACuCl , in whichthe nuclear magnetization recovery can be expressed asa single exponential function, and the spin-lattice re-laxation rate T − exhibits an exponential decrease in-dicative of the gapped singlet ground state. Hence,the present result indicates that the ground state of thepresent system is a new phase that is different from boththe singlet Haldane phase of IPACuCl , as opposed to theconclusion of the previous macroscopic experiments,
13, 14 and the impurity-induced magnetic ordered phase in theregion 0 . < x < .
87 of IPACu(Cl x Br − x ) . Spin-lattice relaxation measurements at lower temperaturesare required in order to investigate the ground state ofthe present system in a more detailed manner, especiallyto investigate whether the fast part of the spin-latticerelaxation rate ( T − ) fast exhibits diverging behavior orremains constant, which indicate the magnetic orderingand precursor phenomenon of the Bose-glass phase at J. Phys. Soc. Jpn.
Letter
Tomoya
Adachi et al. T = 0,
6, 7 respectively. This problem will be consideredin future studies.The observed nontrivial ground state composed ofboth the magnetic and nonmagnetic Cu sites is inducedby the bond randomness effect for the gapped singletHaldane phase of the parent compound IPACuCl and isrevealed for the first time from the observation of bothgapless magnetic and gapped nonmagnetic fluctuationsby the present H-NMR experiments.In conclusion, we have presented the results of thespin-lattice relaxation rate T − measurements of H-NMR in IPACu(Cl x Br − x ) with x = 0 .
88. It was ob-served that the nuclear magnetization recovery of H-NMR exhibits non-single exponential behavior and canbe well expressed by the model that includes the fastand slow spin-lattice relaxation processes, as shown inFig. 1. It was also found that the obtained temperaturedependence of the fast and slow parts of the spin-latticerelaxation rate T − of H-NMR exhibit the simultaneouschanges below T ∼
10 K, that is, the fast part ( T − ) fast becomes constant indicative of the magnetic ground statecomposed of localized moments, while the slow part( T − ) slow decreases exponentially with ∆ = 11(1) K in-dicative of the gapped singlet ground state, as shown inFig. 2. From the discussions on the previous macroscopicmagnetization and specific heat measurements and themicroscopic µ SR experiments, we expect that the groundstate of the present system is a new phase in whichthe singlets and localized magnetic moment islands aremixed microscopically and both the singlets and mag-netic moment islands are correlated with one another;this new phase is different from both the singlet Hal-dane phase of IPACuCl and the impurity-induced mag-netic ordered phase in the region 0 . < x < .
87 ofIPACu(Cl x Br − x ) .We acknowledge H. Manaka and T. Suzuki for theiruseful suggestions in discussions. This work was sup-ported by Grants-in-Aid for Scientific Research on Pri-ority Areas ”High Field Spin Science in 100 T” from the Ministry of Education, Science, Sports and Culture ofJapan, the Saneyoshi Scholarship Foundation, and theKurata Memorial Hitachi Science and Technology Foun-dation.
1) L. P. Regnault, J. P. Renard, G. Dhalenne, and A. Revcolevschi:Europhys. Lett. (1995) 579.2) T. Waki, Y. Itoh, C. Michioka, K. Yoshimura, and M. Kato:Phys. Rev. B (2006) 064419.3) C. Yasuda, S. Todo, and H. Takayama: J. Phys. Soc. Jpn. (2006) 124704.4) A. Oosawa and H. Tanaka: Phys. Rev. B (2002) 184437.5) Y. Shindo and H. Tanaka: J. Phys. Soc. Jpn. (2004) 2642.6) T. Suzuki, I. Watanabe, A. Oosawa, T. Fujiwara, T. Goto, F.Yamada, and H. Tanaka: J. Phys. Soc. Jpn. (2006) 025001.7) T. Fujiwara, H. Inoue, A. Oosawa, R. Tsunoda, T. Goto, T.Suzuki, Y. Shindo, H. Tanaka, T. Sasaki, N. Kobayashi, S.Awaji, and K. Watanabe: J. Phys.: Conf. Ser. (2006) 199.8) M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher:Phys. Rev. B (1989) 546.9) R. A. Hyman, K. Yang, R. N. Bhatt, and S. M. Girvin: Phys.Rev. Lett. (1996) 839.10) H. Manaka, I. Yamada, and K. Yamaguchi: J. Phys. Soc. Jpn. (1997) 564.11) T. Masuda, A. Zheludev, H. Manaka, L.-P. Regnault, J.-H.Chung, and Y. Qiu: Phys. Rev. Lett. (2006) 047210.12) H. Manaka and I. Yamada: J. Phys. Soc. Jpn. (1997) 1908.13) H. Manaka, I. Yamada, and H. Aruga Katori: Phys. Rev. B (2001) 104408.14) H. Manaka, I. Yamada, H. Mitamura, and T. Goto: Phys. Rev.B (2002) 064402.15) K. Kanada, T. Saito, A. Oosawa, T. Goto, and T. Suzuki: J.Phys. Soc. Jpn. (2007) 064706.16) K. Kanada, T. Saito, A. Oosawa, T. Goto, T. Suzuki, and H.Manaka: QuBS2006 proceedings , to be published in Suppl. ofJ. Phys. Chem. Solids.17) T. Saito, A. Oosawa, T. Goto, T. Suzuki, and I. Watanabe:Phys. Rev. B (2006) 134423.18) H. Manaka and I. Yamada: Phys. Rev. B (2000) 014279.19) H. Manaka, I. Yamada, M. Hagiwara, and M. Tokunaga: Phys.Rev. B (2001) 144428.20) Y. Itoh, T. Machi, N. Koshizuka, T. Masuda, and K. Uchi-nokura: Phys. Rev. B (2002) 100406(R).21) J. Kikuchi, T. Matsuoka, K. Motoya, T. Yamauchi, and Y.Ueda: Phys. Rev. Lett.88