Spin lattice relaxation in triplet states of naphthalene crystals at very high magnetic fields

Volume

52, nun~ber

1

CHKMICAL

I’IIYSICS

LPITLRS

15

November 1977

SPIN LATTICE RELAXATION IN TRIPLET STATES OF NAPHTHALENE CRYSTALS AT VERY HIGH MAGNETIC FIELDS *

Received

25 July 1977

Spm Lttttcc reiaxdtmn times of rnetact:iblc trq&!t states in dn org:mic molcfular crystal were mcabured at hq$~ magnetic fields up to energy level splitttngs &E near the Debyc acoustx limit. By an opticai method we Sound that the drrcct-process relaxation of the r?r = +1 Zceman state is domixttcd by Am = 2 phonon trantitions. TIE Am = L?relaxation 1s weakly anisotropic and much &tcr thin the highly nnisotroplc Am = I relaxdon of tiw m = 0 state. The relaxation tlmC5 Wry with ti-’ up to AK - 31 cm-’ at 18 tesla.

RcIaxation time meazuremcnts are reported for electron spin states that have e~lcrgy lcvcl splittings in the range of high density of states of acoustic phonons. &cause orgnnic r&ocular crystals have low Debyc temperatures t!c use of Iligll magnetic fieIds a!tows obtaining Zecman splittings close to the acoustic limit of low laying acoustic phonon bmnchcs, even for spin states with g-values of the free e!ectron. Of special interest are triplet states III orgzlnic mo!ccular crystafs: at low crysta! temperature the coupling between tfle electron spins and the phonon system is cxtrcmcly weak, the spin lattlcc relaxation times arc relatively long and, therefore, directly treasurable. Spin lattice relaxation times in triplet states of orgame crystals have been measured at magnetic fields up to about 5 tcsl:l by optical and spin resonance tcchmques f t -41. The experiments, especia!ly on nap!tthalene doped with q~inoxaIine, indicate that at very low temperatures (T< 2 K) the relaxation occurs by * Work supported by the Ucuts&c I‘orscRungr~c~ncinscll.rft. r On lcave from Institut fiir An~~~v,~ndte Physik. University, 8400 Regcn\butg, W.-Germany. iPcrmancnt address: Physikaliwiw Institut, University, 7000 Stuttgart, W.-Germany; present address: Max-Planck-

Imtitut ftir l’estkbrperforschung, W.-Germany. I Presant address’ 8400 Rcgensburg,

98

7000 Stuttgart,

Institut fdr An~~~valldt~ Physzk, University, W.-Germany.

direct processes in the magnetic field region 3 tcda to 5 tesla [3j. It is tllc purpose of this paper to study the direct-process relaxation between the Z&man states m = 1, nz = 0 and tn = -1 up to much higher fields and to determine tfte ~~nli~nt channel for the relaxation of the upper of the three states. T!zis state can relax by a Am = 1 phonon transition (m = 1 --) tn = 0 transition) or by a 5~2 = 2 phonon transition (nr = 1 + 112= - 1 transition) as illustrated in fig. 1. We made our measurements on sing!e crystals of perdeuterated napl~tl~alcno C,,D, doped with quinoxaline C8N2116 (1 wt % in tllc melt) because this system is well investigated at the lower fields and has a weak spin lattice coupling for the direct process as indicated by the long relaxation time in the order of 10m2 s at 5 tesla [3]. The method for our measurements is illustrated in fig. I. The 337 nm ~diation of a nitrogen laser is absorbed in the region of the quinoxa!inc singlet states. Fast internal conversion and intersystem crossing lead to population of the Zeeman states of the lowest triplet state. We measured the time dependence of the phosphorescence radiation from the m = I and M = 0 states. The crystal (4 X 5 X 5 tnm3) is immersed in liquid helium at a temperature of 1.7 K and is located in the field of a 10 Mur Bitter magnet. The laser radiation (with 1 MW pulse power, 3 ns duration and a repeti-

CHI:MKXL

Volume 52, number 1

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PHYSICS LCTTIXS

I5 November

1977

m

D

Fig. 1, Method of the IWaCUremCnt of the spin lattice r~laxatroll times T1 and Tf . Population of the Zecman states m = 1, m = 0 and m = -1 of the lowest triplet state IS obtained after optic‘81 ~urnp~n~ at 337 nm to higher sin&x states (SE). Time dcpcndencc of phosphorescence from tlrc m i 0 and m - 1 staCe$ is observed. At high magnetic fields the energy spWing IS aEt =g&I for the An1 f 1 transltion and &72 = grlgf for the Am = 2 transition with g = 2.

tion rate up to 20 Hz,) is focused on the sample. Phosphorescence radiation is collected with lenses and focused on the entrance slit of a monochxornator that selects the radiation from the m = 0 or m = 1 states and suppresses broad band fluorescence radiation arising from the fenses, the cryostat windows and the crystal. The radiation is detected with a photomultiplier. The photomuitipkr signals are recorded with a signal averaging transient recorder triggered synchronousIy to the nitrogen laser pulses. In our experiments we found strong phosphorescence radiation from the triplet states after a iaset pump pulse. At high magnetic fields radiation signals from the m = Oas welt as from the m = 1 state could be easily observed and showed exponential time dependences which give directly the relaxation times of these states. Fig. 2 shows experimental values for the relaxation time T1 of the m = 0 state and for the relaxation time Tf of the fn = 1 state at a constant magnetic field of 10 tcsla and a crystal temperature of 1.7 K for different crystal orientations with respect to the magnetic field. The crystal was rotated about the crystat &axis which was perpendicular to the mag-

Fig. 2. Experimental relaxation times Ti and Tr at d magnctlc field of H = 10 tesla for different crystal orientations. The crystal is rotated about the crystal b-axis by the angle p (see

in-&). For tp = 0 the projections X of the quinoxaI~n~ molecular long axes on the QCplane (daQed lines m the mset) are parallel to the magnetic field M Tg has large experimental errors (see error bars) IW.ITIf Ix’ and T,* near HllF for these orientations the optical transitions to the iinglct ground state are forbidden [S J. The angular accuracy of rpis about *SD.

netic field (see inset of fig. 2). Thus the two molecules of the crystal unit cell were magnetically equivalent. In fig. 2 the angle upis the angle between the magnetic field and the projection Z of the long molecule axes in the QCplane (see inset of fig. 2). Our experimental results show that the relaxation time T1 (upper curve in fig. 2) is highly anisotropic. T1 has a minimum value of 2 ms for the crystal orientation in which the F-direction is parallel to the magnetic field (compare inset of fig. 2). The maximum value of IO ms is obtained when the Sl-direction has an angle of 45” to the magnetic fletd. A second minimum occuts for x oriented perpendicular lo the magnetic field. A second maximum is found near the direction $02: 135” ($Q5%-45”). The relaxation time TT has a much less pronounced anisotropy (lower curve in fig. 2). With respect to the rotation angle a broad minimum (around cp= 3@) and a broad maximum (around up= loo*) have been found. Tr varies between 0.2 ms and 0.36 ms. WC found that Tr and T; have the same anisotropy behavior for 18 tesla as for 10 tesla. 99

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Our experiments

CHl hlICAL

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I’IlYSlcs

1977

show that the relaxation of the than that of orientation.

ttz = 1 state is eight to forty times faster the tn = 0 state depending on the crystal If the rclnx:ition of the 111= 1 state were a Anz = 1 transition (ttz = 1 -> ttz = 0) T{

don~inatcd

by

should be equal to 7; and Should show the same :~nlsotropy. Because Ti and Yi differ by ;UI order of magnitude and h;ivc different anisotropy (5cc fig. 2) we conclude that the relaxation of the m = 1 state is governed by a Attl = 2 translilon comicctctl with the emission of a phonon of energy AE, = 2gpBH. We would like to note that during our work the anisotropy of the direct-process relaxation has been studied for the sm-nc system with a similar optical method up to mngnctic fields of 5 tesla at the University of Stuttgart. The results Icad to the smc conclusions concerning the Anz = 2 transition [G]. Furthermorl:, we measured for fixed orientations the vnriatlon of the relaxation times with the magnetic !?eld. The upper curve of fig. 3 shows the experimental time Tl for the crystal orientation +J= 0. For high magnetic fields we found an 1P3 dependence for T,. For low magnetic fields the obsclved decay time for the n2 = 0 5tatc EilChCS a constant value of 7 = 0.08 S which corresponds to the hfctime of the riz = 0 state for (radiationless) transitions to the singlet ground state. The lower curve of fig. 3 shows T; for the oricntatiorl 0 = 90’. It is found that T; also valies proportional to H1-? up to OUI highest fiels. At ii = 18 tesla the AnI = 2 transition occurs by the C~~ISSIOI~ of a phonon at 34 cm--’ . This energy is close to the energy (39 cm-l) [7] for which the density of states of the phonons in nnphthalenc is cxpcctcd to have a peak value corresponding to the Debye acoustic limit of the lowest ilcoustic phonon branches. From the H- 3dcper~chcc of TI and T; we conclude that the density of sta!es of the pho~lons involved in the relaxation process mcreascs quadraticlilly up to uur largest cucrgy splitting.

Our curves of fig. 2 and fig. 3 were measured at 8 crystal temperature of 1.7 K. For the high field5 (B > 8 tesla) no tcrnperaturc dependence for T1 and 7’; has been found up to 4.2 K as expected for the relaxation by direct processes. For lower fields the relaxation times arc shorter at 4.2 K due to additional strongly temper:iture dependent relaxation processes 131. 100

15 November

Li3-Kl~s

MAGNETIC

FIELD

(TESLA)

1-1g.3. Vanation of the relavdtion tirncs Tl and T: wit11the nl:lgnctlc f~cld. The expcriment;d points follow an if-j slope (~11d lines). TI was meitsurcd for the orientation II[lXand

Tr for HJE; in these orientations only the m = 0 state and the 1)~- -61 status, rcyxctwcly, arc popul~tcd due to bclcctivc intcrsystem crossing [5 1. for low magnetic fields the obscrvcd time constant k dctcrmined by the lifetime 7 of the m = 0 st.!te for decay to the ground state.

It is Interesting that around p = 0 (H parallel to 3 the experimental ratio T, /T; = 8 (see fig. 2) corrcsponds to the simple estimate that the relaxation for an energy SCpilriltioIl AE, = 2AE occurs filster than for the energy geparation Al<, = AE by the factor (ti~/M~)~ = 8. Nearly the same ratio is obtained around cp = 90” (H perpendicular to x3. These results show that at y = 0 (and also at 9 = 90”) the relaxation times Tl and T; are equal for the same energy splittings (at the fields H and H/2, respectively). Under the assumption of an accidentally equal spin-phonon coupling for the Am = 1 and Am = 2 phonon transitions at cp= 0 (and also at ‘p = 90°) this result suggests that for q x 0 (and also for upx 90”) the density of states of the pliono~is involved in the Am = 1 relaxation (at the field H) is equal to the density of states of the phonons involved in the Am = 2 relaxation (at the field H/2). The coupling between the electron spin system and the phonons which give rise to the spin lattice relaxation in molecular crystals is not yet understood [3]. Qualitative reasons for the different behavior in the anisotropy of the two relaxation times may be found by symmetry arguments: if the crystal orientation is changed with respect to the magnetic tieid the wave-

Volunle 52,

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CHi-hlICAL PHYSICS LETTCRS

function of the m = 0 state changes differently than the wavcfunctions of the MZ= 1 and ?YZ = -1 states [S] _ The spin photon coupling of the m = 0 + m = - 1 transition has, therefore, a different anisotropy than the spin phonon coupling of the m = 1 -* m = - 1 transition resulting in a different anisotropy behavior of Tl and T,*. A further anisotropy effect is to be expected from the anisotropy of the density of states of the phononr which are involved in the relaxation pro-

15 November 1977

We thank K. Dransfeld for the support of this work, H.C. Wolf, M. Schwocrer and F. Dietz for stimulating discussions and N. Karl for crystal preparation. Very helpful assistance by the staff at the Hochfcld-Magnetlabor and by K. Lachncr is acknowledged.

References

WSSEi.

[ 11 h1.S. dc Croat. I.A.M. flcs~elnlann, J. Schmidt and J-11.

Our method of observing spin lattice relaxation times is applicable to other molecular crystals. Due to the specitk symmetry properties of different crystals these measurements should lead to a better understanding of spin lattice relaxation procesnes in molecular crystals. Our experimental results dcmonstratc that for large energy splittings spin lattice relaxation times of the triplet states in organic molecules can be more than four orders of magnitude longer than relaxation times of impurity states in auorganic crystals [S] . The triplet states in organic molecular crystals seem, furthermore, to be interesting systems for experiments with very high frequency phonons because of the occurrencc of the b?z = 2 phonon transitions. It should be possible to detect [9] and to geucratc [lo] phonons of variable frequency. Phonon experiments should make it posslblc to study the spin phonon interaction in molecular crystals in more detail and to study properties of large cl-vector phonons.

van dcr Waals, Mol. Cryst. 15 (1968) 17; J.P. Wolfe, Chcm. Phys. Letters 10 (1971) 212. [ 2 1 hf. Schwoercr, U. Konalmann and D. ZCilppcr,Chem. Phyr. Letters 13 (1972) 272; U. Konxlmann and Xl. Schwocrer, Chcm. I’hys. Lcttcrs 18 (1973) 143. 131 U. Konzelmann, I). Kilppcr and hl. Schwoercr, /.. NdturfOr\Ch. 30 (1975) 754. [41 D. Anthcunis, thesis, University of Leydcn (1974). I [51 M. Schwoercr and H. SIXI, Chcm. Phys. Letters 2 (1968)

14; A. Hammer, M. Schwocrcr and II. Siul, Chem. Phys. Letters 5 (I 970) 434. 161 F. Dictz, II. Port and M. Schwoerzr, Chem. Phys. Lcttcr\ 50 (1977) 26. I71 R. Ostertag, lhesis, University of Stuttgart (1972). [81 M. lIumc, R. Orbach, A. Kicl and S. Ce~h~md, Phys.

Rev. 139 (1964) A 314; G-1’. Imtrusch. S.R. Chmn and S. Geschwmd, Phys. Rev. 161 (1967) 295. [91 K.F. Rcnk and J. Dciscnhofer, Phys. RCV. Lcttcr\ 26 (1971) 764. IlO1 R.S. Meltxr and J.E. Rives, Phys. Rev. Lcttcrs 38 (1977) 421.

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