Multiple spin-echoes in a photo-excited triplet state

Volume 21, number 3

1 September

CHEMICAL PHYSICS LETTERS

MULTIPLE

SPIN-ECHOES

IN A PHOTO-EXCETED

C.A. VAN ‘T HOF, J. SCHMIDT,

P.J.F. VERBEEK

Kom.crlingl~ Omrsr Labomtorium,

Lriderr,

1973

TRIPLET STATE

and J.H. VAN DER WAALS Tile Netherlondr

Received 15 June 1973

A Carr-Purcell multiple spin-echo, as modified by Meiboom and Gill, is desnibed for the 3598 MHz zero-field transition of phosphorescent quinoline CgND7 in a durene host. The results show that the dephaing of the electron spins through spectral diffusion may be lxgcly eliminated by the multiple echo technique.

1. Introduction: stat es

coherence

in photoexcited

triplet

V,ISJ,ITJ = -CT,ISyITx) = i

The coherent interaction of photo-excited triplet states with resonant microwave fields is a subject of current interest. Theoretical aspects of this problem were first considered by Harris [I] and a number of experiments have been reported: the modulation of phosphorescence by microwave irradiation [2], the formation of a spin-echo from a photo-excited triplet state [3] and, quite recently, the optical detection of rotary echoes [4]. An elegant way to visualize the resonant interaction of two spin components of a triplet state with a coherent microwave field is provided by the geometrical model

of Feynman

et al. [5]. From

this model

it fol-

the behaviour of the triplet system in the course of time may be described by equations identical to the Bloch equations for the familiar S = l/2 system [6]. As in previous publications we take the deuterated quinoline molecule as an example. The three spin components of its phosphorescent triplet state are labelled T,, Tr, T, in order of increasing energy, see fig. 1 of ref. [2]. In zero external field the mapetic moment of the triplet state is “quenched”: the diagonal matrix elements of the spin angular momentum all vanish

lows that

(TUISITII) = 0 but on the other

(U = x,y,z) hand

,

(1)

(ii = 1) ,

C-7)

etc., by cyclic permutation of the indices in (2). In the experiments to be described we are concerned with the TX-T, transition occurring at 3598 h1H.z in a durene host. We represent the wavefunction related to this transition by ‘P(r) = a(t&

+ b(t)T,

(3)

and assume the time-dependent term v(f) in the hamiltonian to represent a resonant rf magnetic field of amplitude HI along the moleculary axis, .

V(r) = ~HISY coscJot In the Bloch picture coherence

effects

(4) to be used for visuaLzing

we label the laboratory

the axes by e I,

e2, e3, suppose the static field to be along c3 and denote the magnetization by ~1. ks explained in section 3 of ref. [2] the “translation” between the two systems afforded I-ry Feynman et al.? theory now is as FoUows. (I) Bloch’s longitudinal magnetization has to be identified with the population difference of the two trip. let levels: p3/y corresponds

to ~a* - bb* and thus to N, - .Nz; (5)

(II) Bloch’s transverse component prz, because of (2), in the triplet system also represents a transverse magnetization: ~,/7

corresponds

to i(ub*-o*b)

and hence to G,?. (6) 437

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(The third component p1 does not correspond to a sia:ple observable in the triplet system 2nd we need not consider it here.) In the quino!ine molecule the top level T, has a high rate of radiative decay whereas the two lower levels are almost non-radiative; this is reflected in the correspondi;lg lifetimes ‘i-- = 0.95, rY = 14.5, 7X = 14.7 set of CgND7 in a durene host at liquid helium temperature [7]. The striking difference in behaviour of the levels, which is a common feature of photo-excited triplet states, can be put to advantage in coherence experiments. Suppose we choose the moment the timedependent term V(t) is switched on as the origin of time, then prior to that the quinoline systelil may be prepared in the following way. First the sample is illuminated for a while and a steady-state distribution over the three levels established. Then at r = -5 set the exciting light is GUI out. Since the molecules in TZ decay much more rapidly than those in T, and T?,, a situation is created at t = 0 where the ‘KSlevel is virtually empty, q = 0, while the other two levels still carry substantial populations, flX, A$. Hence, relative to the Tz-T, transition one has established the equivalent of a large longitudinai magnetization p3 = p” in the Bloch situation (the same would be true for the T, Ty transition at 1001 MHz [2,3] which we shall not consider here). Now the beauty of the Feynman picture [S] is, that what happens to our system in a spinecho type of experiment can be literally “translated”

from the familiar description in a rotating frame of the corresponding nuclear magnetic resonance experiment, as for instance given in chapter 3 of Abragam’s

LETTERS

1 September

1973

and, since the intensity of phosphorescence is proportional to N,, the emission is modulated at a frequency YH, /27r. An ex::mple of this analogue of a transient nutation is shown in fig. 1 for the T, - TX transition of quinoline CgND7 in a durene host at 1.2%. At r = 0 the radiative level is empty and no li&t is detected, at t =Z 0.55 Psec the population is almost completely reversed causing a maximum in the emission, and at t Z= 1.10 qsec the cycle is completed. Apparently the rf field that produces the modulation in the present instance has an amplitude of 0.33 G, corresponding to a nutation frequency yH1/2n of about 0.9 MHz. Further ii follows from fig. 1 that the modulation disappears with a characteristic time constant of the order of 2.5 psec and we shall see later what is the main source of the dephasing. A second type ofesperiment is the equivalent of Hahn’s spin-echo in nuclear resonance (6,5]. By the application of an rf pulse for which rfll 7 = n/3 the initial magnetization p” is first brought along the e; axis in Bloch’s rotating frame. For an observer, looking along the fixed e2 axis in the laboratory this then gives rise to a transverse magnetization pZ oscillating at the resonance frequency wo. As we know, this transverse magnetization decays owing to the dephasing of the spins in the ensemble, but the dephasing can be partially reversed by means of a n-refocusing pulse that causes a fractjon of the initial transverse magnetization to reappear as an “echo”. Because of the physical equivalence of the two

book [6]. The simplest experiment is lhat in which a continuous rf field is applied from f = 0 onwards. In the NMR situation this causes a “transient nutation” of p” tibout the effective field Ei, in the rotating frame, which manifests itself as an oscillation of the longitudinal magnetization in the laboratory /JJ = &osyH1

t.

The equivalent

in a photo-excited

(7) triplet

state of the

transient nutztion experiment is the modulation of phosphorescence by an rf field, first observed for quinoline [2]. Via (5) it follows from (7) that r(t) 438

= +A$( 1 - cos@Y1 t)

Fig. 1. Modulation

of the phosphorescence (“transient C9ND7 in a durcne host produed microwave tield resonant with the T, -TX transition MHz. Horizontal 1 psec per division. T= 1.2%.

tion”) of quinoline

(8)

nutiby a at 3598

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quantities ~12 and rcS,.) that replace one another according to (6) in the equation of motion describing the two systems, a spin-echo experiment also is feasible in a photo-excited triplet state, even though the magnetization is quenched in the stationary state. Such an experimellt, which in contradistinction to the previous one, involves a microwave detection system, has been realized in this laboratory and “T?‘‘-values were derived from the spin-echo attenuation as a function of the delay between the two pulses for the T, -T? transition of a number of aza-naphthalenes [3]. We have repeated the experiment for the Tg- T, transition of quinoline C9ND, in a durene host at 4.2”K and observed a not quite exponential attenuation of the echo that can approximately be described by “T2” = 18.5 psec. The significance of the quantity “T?” thus measured gave rise to speculation: is it an electronic spinspin relaxation time, or is it affected by spectral diffusion within the inhomogeneously broadened line [9]‘! From the study of nuclear spin-echoes in liquids it is known that diffusion effects may be (partly) eliminated by using a multiple spin-echo train as first suggested by Carr and Purcell [IO], who refer to it as a “type B” echo as distinct from the “type A“ echo of Hahn (see also Abragam [6]). Although there has

1973

mate!y constant, which is taken to indicate that the dephasing in fig. 1 is caused by a variation of the effectivc HI over the sample and not by the circumstance that the rf nrnpli tude is not large compared ivith the linewidth (” 0.6 MHz). The variation of H, may arise in two ways: by an inhomogeneity of the rf magnetic field over the specimen in the cavity, or by an imperfect alignment of the crystal which cau~s the two sites in the durene host to be subject to slightly different components of 11, along the molecular )f axes. Because of the above variation of H, the nominal “n-pulses” in the train will not be felt as such by a11 molecules! but there will be a spread around this m
been a profound study of spectral diffusion in inhomogeneously broadened ESR lines [9] and its influence on free precession decay and the “type A” echo, to our knowledge nc Carr-Purcell pulse sequences have been realized in electron resonance. In the Carr-Purcell experiment the sample is subjected to a resonant n/2 pulse at t = 0 and then to a series of z-pulses at times 7, 3r, 57 . . . . which give rise to the formation of echoes at times 2~, 4r, 67 . . . . Since our triplet system may be described by the same Bloch equation a similar multiple echo experiment should be feasible and the present paper gives an account of such an experiment. In designing the experiment a complicating feature had to be taken into consideration. The “transient nutation” signal of fig. 1 decays with a time constant of about 2.5 Irsec, which is far shorter thiin the time “Tz” derived from the spin-echo

experiment,

this is caused

perhaps

and one must

find out whether

by an instrumental

effect

that

interfere with the Carr-Purcell cycle. By varying the rf power over several decades it was found that the number of periods that can be discem-

witl

ed in the “transient

nutation”

signal remains approxi-

2. Experimental

arrangement

Except for the generation of the pulse train: the design of the experiment was similar to that used previously [.7,3]. A durene crystal containing quinoline C9ND7 as a guest is placed in a tunable re-entrant cavity suspended in a liquid helium dewar. The caystal is mounted against the end of a quartz light pipe and irradiated by a high pressul-e mercury arc through quartz windows in the bottom sf the dewar and a hole in the cavity. The phosphorescence of the ample can be monitored with a photo&ultiplier (EhiI95248) via the light pipe. The microwaves

are generated

later. For realizing the 90’ phase waves the output of the osci!lator

by a HP8690R

oscil-

shiFt in the microis switched by a

HP33006A switch to either of two pzrdlel coaxial lines in one of which a line stretcher is incorporated. The parailel branches are joined in a hybrid junction and the microwaves are then amplified by a Varian VTS 6055P 1 travelling wave tube amp!ifier and changed 439

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into a pulse train by a HP8732 B PIN modulator. The width and relative delay of the pulses, and the triggering of the switch between the first two pulses are controlled by a Bradley 176 B pulse generator. The pulses, with a maximum power of 340 mW, are fed through a circulator to the cavity. The reflccted driving pulses, together with the echoes generated in the cavity pass through a Watkins and Johnson low noise travelling wave tube amplifidl (WJ-269) for amplifying the echoes, while limiting the direct signal from the pulses. Detection takes place in a superheterodyne system with intermediate frequency of 30 MHz and a bandwidth of 8 MHz. When carrying out an experiment the proper duration of the pulses is first determined from the transient nutation of the phosphorescence signal; for the particular experiment of tig. 1 a rr/l-pulse lasts 0.275 psec and a n-pulse 0.5‘5 psec. Further, when defining the separation between the initial slopes of the r/1puise and the first ?r-pulse as 7, then the period of the ?r-pulses has to be adjusted to 2r. Since the 90” phase shift is performed behveelz the first two pulses, ihe actual switching does not affect till: experiment.

1973

Fig. 2. Multiple spin-echo signal of quinoline CgND7 in a durene host. The microwave pulses are resonant with the Tz-TX transition at 3598 MHz. Horizonral 4 usec per division. T = 4.2”K.

3. Results Experiments have been carried out both at 1.2 and at 4.2’K. At 1.2OK the sample is tirst irradiated during one minute and then S set after termination the excitation by a shutter, the pulse train is switched on. By this procedure one utilises the large population difference as described in section 1. At 4.1,“K the system is in Boltzmann equilibrium. This permits us to repeat the experiment with a repetition rate of SO0 Hz under continuous excitation. In fig. 2 an example is shown of the multiple echoes ai 4.2”K with 7 = 1 psec; the high narrow spikes are the driving pulses and the signals in between the echoes. Fig. 3 is a photograph of the same experiment on a longer time base; the echoes are no longer separately observable and the microwave pulses manifest themselves as a hazy background. Almost at the end of the time base the microwaves have been cut off in order to get an impression of the noise level. While from a “type A” sintie echo experiment at 4.2% we derived “T,” = 18.5 psec, the “type B” multiple echo experiment yields echoes during more than SO0 psec!

Fig. 3. The sune experiment 50 usec per division.

as shown

in fig. 2. Horizontal

To illustrate the power of the Meiboom-Gill “trick” it is worth mentioning that without the 90” phase shift a few echoes only could be observed. The decay of the echoes at 4.2”K has been reproduced in fig. 4 for several values of 7. Because of the recovery time of the receiver the interval T had a lower limit of 0.75 Psec. For the experiment at 1.2”K the shape of the decay curves 2nd the T-dependence are analogous to fig. 4, although the decay is systematically less rapid. The experimental material at present available is insufficient for a real discussion, but one conclusion already stands out. The remarkable lengthening of the phase coherence (up to hundreds of psec) in a multiple echo experiment as compared to a “Tl” = 18.5 gsec of the two-pulse echo indicates that spectral

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-75 115

I

‘0 time _ Oj2

0.4

I

0.6

I

I

0.8

ms

10

Fig 4. Decay of the echoes as a function of time for quinoline CgND, in a durene host. Transition: TZ - T, at 3598 MHz. T= 4.2”K. The repetition parameter of the pulses 5 is defined in the text.

diffusion within the ESR line occurs. As in Carr and Purcell’s original NhlR experiments on liquid water in a field gradient [IO], the loss of phase coherence of the triplet spins due to “diffusion” effects is gradually eliminated by making Q-shorter. But contrary to their results, the decay of our multiple echoes is not exponential. The present equipment does not permit us to work with a power fed into the cavity of more than 340 mW, and hence the amplitude of the rf magnetic field could not be made large compared to the linewidth. By varying the power over a wide range below 340 mW we have verified that the non-fulfilment of the condition rH, ia Aw must have contributed to the non-exponential decay in fig. 4. Clearly, future experiments are planned to eliminate this shortcoming. In the Carr-Purcell experiments there was one overriding phase-destroying effect: the spatial diffusion of the molecules in the inhomogeneous field. But in the present, complex situation, where the electron spins see different nuclei in the host and guest molecules, and also excitation diffusion may occur, one would expect the dephasing to occur with a spectrum of rates that may be probed by varying the repetition

1 September

1973

parameter T. Clearly, the present method holds a promise for following stochastic prccesses invoLving photo-excited triplet states, such as ener,qy migration in a crystal, changes of nuclear conformation, and relasation between closely spaced electronic states. While the present work was in progress, Harris, Pines and co-workers [4] have developed the analogue of Solomon’s rotary echo [6,12] to restore the loss of phase-coherence in an excited tripiet state. Their experiments, in which optical detection is used, roughly relate to the transient nutation phenomenon as the multiple echoes relate to a free precession decay. Whereas we follow the analogue of the transverse magnetization p2, they follow that of the longitudinal magnetization ~3. Both experiments seem to agree cn the importance of spectral diffusion for the dephasing of a triplet electron spin system that Interacts with a coherent microwave field.

Acknowledgement This work is part of the research programme of the Stichting voor Fundamentecl Onderzoek der Materie (F.O.M.), financially supported by the O!-ganisatie voor Zuiver Wetenschappelijk Onderzoek (Z.W.O.). References [I] C.B. Haxis, J. Chem. Phys. 54 (1971) 972. [Z] J. Schmidt, W.G. van Dorp and J.H. van der \!‘a&, Chem. Phys. Letters 8 (1971) 345. [3] J. Schmidt, Chcm. Phys. Letters i-! (1972) 411. [4] W.G. Breiland, C.B. Harris and A. P nrs, Phys. Rev. Letters 30 (1973) 158; C.B. Harris, R.L. Schlupp and H. S~huch, to be pnblished. [S] R.F. Fcynman, F.L. Vernon and R.W. Hellwxth, 5. Appl. Phys. 28 (1957) 49. [6] A. Abragam, The principles of nuclex msgnetism (Clarendon Press, Oxford, 1961). [7] J. Schmidt, Thesis, University of Leiden (1971); J. Schmidt, D.A. Antheunissnd J.H. van der WasIs, Mol. Phys. 22 (1971) 1. [S] E.L. Hahn, Phys. Rev. 80 (1950) 580. [9] B. Herzog and E.L. Hahn, Phys. Rev. 103 (1956) 148; W.B. Mims, K. Nassau and J.D. hic(;ee, Phys. Rev. 123 (1961) 2059; IX. Brown, J. Chem. Phys. 5.5 (1971) 2377. [lo] H.Y. Carr and EM. Purcell, Phys. Rev. 94 (1954) 650. [ 111 S. Meiboom and D. Gill, Rev. Sci. Insti. 29 (19.58) 688. [ 121 I. Solomon, Phys. Rev. Letters 2 (1959) 301. 441