Journal of Magneti sm and Magnetic Materials 90 & 91 (1990) 229-230North-Holland

229

Proton nuclear magnetic relaxation in quasi-one-dimensional S = 1Heisenberg antiferromagnet Ni(C2HgN2) 2N02(CI04)

N. Fujiwara, T. Goto a, T. Kohmoto a and S. Maegawa a

Departm ent of Physics, Faculty of Science, Kyoto University, Kyoto 606, JapanQ Departm ent of Physics, College of Liberal Arts and Sciences, Kyoto Unicersity, Kyo 606, Japan

The proton spin-lattice relaxation time T, in the Haldane-gap system , Ni(C2H sN2hN02(CI04) was measured down to 0.5K. The development of anti ferroma gnet ic short range order was not found even at low temperatures. A relaxation process ofac tivation type with an energy gap of 11 K has been observed.

where A/(q) is a dipolar coupling constant and r/(q) isa damping factor of the spin correlation functions, andX(q) is q·dependent susceptibility. In NENP the aver-

TFig. 1. Temperature dependences of T,-I of III in NENP for110 II b-axis and lIo.L b-axis. The solid line repre sents the best

fit of eq. (1) to the data at high temperatures.

(1)

10 (K)

a a

o ."::1'...o ..

o :.o..•o..

gg-2

10

-110

(i=x, y , z ), .

• HI/ b, 11 MHza HI b,ll MHz• H /I b.34 MHz

10

action when the Ni 2+ spin system is in the excited stateand contributes to the relaxation mechanism which ischaracterized by a monotonous decrease with decreas­ing temperature. The relaxation rate TJ-

J for the latteris given by the usual treatment for a paramagneticinsulator as

TJ~I = ("y~jN)(knT) L LAi(q)xi(q)jri(q)i q

Recently there has been considerable interest jnHaldane's conjecture that the one-dimensional Heisen­berg antiferromagnet (lD-HAF) with integer spin hasan energy gap between the singlet ground state and thefirst excited state (1). Renard et al. (2) suggested that theS= 1 quasi ID-HAF, Ni(C2HgN2hN02(CI04) (ab­breviated as NENP) is a good candidate for examiningHaldane's conjecture. In this compound they obtainedresults consistent with the conjecture, using inelasticneutron scattering and measurements of susceptibilityand magnetization. The existence of the gap was alsoconfirmed from the magnetization measurements in highfield [3,4).

In the present investigation, we have measured theproton spin-lattice relaxation time TJ in NENP, using acoherent pulsed-NMR method in the temperature rangebetween 0.5 and 77 K. No indication of 3D.long-rangeorder was found even at 0.5 K from the NMR spectra,Fig. 1 shows the temperature dependence of the relaxa­tion rate TJ- t obtained at the frequencies of 11.0 and34.0 MHz with an external field H parallel and per­pendicular to the linear chain , the crystallographic b­axis. The relaxation rates between 0.5 and 77 K de­crease over more than five orders of magnitude withdecreasing temperature, though there is a peak around 3K corresponding to the appearence of another relaxa­tion process. The value of TJ-

J at the peak has atendency to decrease with increasing resonancefrequency.

The relaxation rate TJ-J is determined by the

fluctuations of the local field at the nuclear site via adipolar interaction with the Ni2+ spins. To interpretour experimental results in the whole temperature re­gion, we consider two kinds of fluctuations which arecharacterized by different time scales. One is a slowfluctuation which is caused by the magnetic excitationfrom the non-magnetic ground state and contributes torelaxation around the peak at about 3 K. The other is arapid fluctuation which is caused by the exchange inter-

0304-8853/90/S03.50 (1) 1990 - Elsevier Science Publishers B.V. (North-Holland) and Yamada Science Foundation

230 N. Fujiwara et al. / The proton spin-lattice relaxation in NENP

• HI/b. 11 MHz

..1. Parameters a, {3 and ..1 may be different for eachaxis, but we choose the same value for simplicity. Theneq. (1) is rewritten as

(3)

10.•-I1'; e.

-1

10

-210

V 'l

/ \ "/ (a)" '\

--.....\"\

\\(b)

\

In regard to the contribution from the slow fluctuationcaused by the excitation from the ground state, weassume. that the Ni 2

+ spin system remains in the groundstate for an average time TO and in the excited state fora lifetime TI, during which an effective transverse localfield h.L appears at the nuclear sites. Then TIl isexpressed as [6]

TI-I

= (YNh.L)2/( TO + T1)(w~ + l/T2)

(liT = liTo + 1fTI)·

-1 1.0T

Fig. 2. Temperature dependences of TI-1 of I H in NENP for

lIo II b-axis. The broken lines (a) and (b) represent the best fitsof eqs. (2) and (3), respectively. The solid line is the sum of

them.

ages of Ai(q) at eight non-equivalent sites of I H arealmost q-independent, and are calculated as AX(q) ==AY(q) =:: 4.0 X 10 45 cm- 6 and A'(q) =:: 1.3 X 1045 cm- 6•

At first, we analyze the experimental results at tem­peratures above about 6 K. Since it is expected that theNiH spin system remains for longer time in the excitedstate than in the ground state, only the rapid fluctuationwould contribute to TI-

I• As discussed in the previous

paper [5], we assume that P(q)=P'(q)=T'(q)=::constant and X(q) =:: X(O), and then apply the experi­mental results [2] of the static susceptibility to X(q) ineq. (1). We obtained the solid line in fig. 1 by choosingT =:: 2.6 X 1012 s-I. The good agreement beteen the the­oretical curve and our experimental results shows thatour assumption X(q) =:: X(O) is valid. This means thatthe antiferromagnetic short range order or q = orrstaggered mode is not developed.

Next, we analyze the experimental results at temper­atures below about 6 K shown in fig. 2. We have toconsider the contributions from both of two fluctua­tions. In regard to the contribution from the rapidfluctuation, we assume X(q) == X(O) in eq. (1) as men­tioned above and X(O) = n exp( -..1lknT) + {3, which isexpected in the Haldane-gap system with an energy gap

We assume this mechanism to be an activation-typeprocess, thus we set liTo = B exp( -..1lknT) and l/TI= A (temperature independent). In fig. 2 the brokenlines (a) and (b) represent the best-fit curves obtainedfrom eqs.. (2) and (3), respectively, with fitting parame­ters n, {3, A, B, h.L and ..1. The solid line represents thesum of them. As is seen, the experimental results can beexplained consistently by the contributions from therapid' and slow fluctuations. The value of the energy gapin X(O) and TO was obtained to be ..1lkn = 11 K.

The values of the energy gaps obtained from thesusceptibility measurement [2] are reported to be ..1ll/kn= 11 K'for H II b-axis and ..1.L Ik n = 17 K for H .l. b-axis.Our value of ..d is the same as that of ..111 • This agreementindicates that the activation-type process with thesmalIer energy gap has the dominant contribution toT I-

I at low temperatures.

References

[1) F.D.M. Haldane, Phys. Rev. Lett. 50 (1983) 1153.[2) J.P. Renard, M. Verdaguer, L.P. Regnault, W.A.C. Erke­

lens, J. Rossat-Mignod and W.O. Stirling, Europhys. Lett.3 (1987) 94.

(3) K. Katsumata, H. Hori, T. Takeuchi, M. Date, A. Yama­guchi and J.P. Renard, Phys. Rev. Lett. 63 (1989) 86.

(4) Y. Ajiro, T. Goto, H, Kikuchi, T. Sakakibara and T. Inami,Phys. Rev. Lett. 63 (1989) 1424.

(5) T. Ooto, N. Fujiwara, T. Kohmoto and S. Maegawa, J.Phys. Soc. Jpn. 59 (1990) 1135.

(6) O.E.O. Hardeman, N.J. Poulis and W. v.d. Lugt, Physica22 (1956) 57.