Magnetic resonance on single nuclei

14 March

1997

CHEMICAL PHYSICS LETTERS

ELSEVIER

Chemical

Physics

Letters

267 (1997)

I79-

I85

Magnetic resonance on single nuclei J. Wrachtrup, A. Gruber, L. Fleury, C. von Borczyskowski TU Chrmnit:. lnsritutr ofPhysics. Received

5 August

1996;

in final

Chemnit;. Grrmuny form

8 January

1997

Abstract The magnetic resonance signal of individual hydrogen nuclei has been detected. The experiments have been performed on a single pentacene molecule with the aid of optically detected electron nuclear double resonance. Two nuclear magnetic resonance lines of 30 kHz width have been observed as a 3% change in the fluorescence intensity of a single molecule. The results can be reproduced by a spin Hamilton operator describing the interaction of a single electron spin with two hydrogen nuclei.

1. Introduction Optical single molecule spectroscopy has attracted considerable attention [1,2]. The detection of single molecules has been successful under ambient conditions with the aid of near-field [3] and confocal microscopy [4] on surfaces as well as in highly diluted solutions by photon burst detection [S]. At low temperature single molecules have been detected in solid matrices via narrow band laser excitation [6,7]. Due to the high photostability and large absorption cross section under these conditions one can usually perform time-consuming highly sensitive experiments. One of these is optically detected magnetic resonance (ODMR) [8,9]. This approach opened a pathway to the detection of a single molecular triplet electron spin. Recent studies include pulsed and time resolved ODMR experiments on single electron spins [lo] as well as investigations on the hyperfine interaction with individual nuclei [ 1I]. All previous investigations have been carried out in the realm of electron spin resonance (ESR). In this Letter we present for the first time a magnetic 0009-2614/97/$17.00

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1997 Elsevier

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resonance investigation on individual hydrogen nuclei. The experiment, which enabled us to detect the magnetic resonance signal of two hydrogen nuclei, is based on optically detected electron nuclear double resonance (ENDOR) on single molecules. The principles of low temperature single molecule spectroscopy have been reviewed recently [1,2]. In short, the isolation of individual molecules is achieved by narrow band laser excitation at low temperature in highly diluted samples of organic dye molecules embedded in a solid matrix. Under these conditions the fluorescence excitation lines of single molecules show up as individual peaks in the inhomogeneously broadened vibrationless zero phonon absorption origin. Upon tuning the excitation laser to the absorption frequency of an individual chromophore the molecule is excited from the singlet ground state ‘S, to its lowest excited singlet state ‘S, (see Fig. la). Usually, the relaxation from this state to one of the vibrationally excited levels of the ground state IS,, takes place via the emission of a fluorescence photon. However, there is also a chance to undergo intersystem crossing (ISC) to the lowest All rights

reserved.

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J. Wrachtrup et al./ Chemical Physics Letters 267 (1997) 179-185

4

decay time of 40 ps, whereas the Z level hardly shows any population probability and has a lifetime of 1 ms. Microwave irradiation in resonance with the X-Z transition increases the population probability of the long-lived Z level concomitant with a reduction in the fluorescence intensity owing to a longer average duration of the dark intervals when the molecule is in 3T,. Following standard schemes of fluorescence detected magnetic resonance [ 121 one thus is able to detect the ESR signal of a single molecule.

LASER

2. Experimental

Z

I

X

Fig. I. (a) Energy level scheme of the lowest excited electronic states of pentacene. The diagram shows only the vibrationless zero phonon levels in the ground and excited states. The lowest excited triplet state 3T, is split into three sublevels labelled X, Y and Z. The splitting is 120 MHz between the X and Y levels and 1360 MHz between the Y and Z levels. The population probability of the sublevels via ISC is such that the X level has the highest population probability and shortest lifetime (40 us) whereas the Z sublevel is hardly populated and has a lifetime of roughly I ms [9]. (b) Doubly protonated pentacene molecule used for the ENDOR experiments. The molecule is embedded in a single crystal of fully protonated p-terphenyl molecules. The axis system denotes the molecular symmetry axis for pentacene referred to in the text.

excited triplet state ‘T,, which is paramagnetic with a total electron spin angular momentum S = 1. The threefold degeneracy of this state is lifted owing to the anisotropic dipolar interaction of the two unpaired electron spins (zero field splitting: ZFS) and the Zeeman interaction in an external magnetic field (B,). The three resulting electron spin sublevels will be termed X, Y and Z throughout the present work. Owing to symmetry selection rules of the ISC the population and depopulation characteristics of the three levels is highly selective. For the present system, pentacene in a p-terphenyl single crystal, the X level has the highest population probability and a

Details of our experimental apparatus have been described elsewhere [13]. In short, we used a singlemode ring dye laser (Coherent 699-29) as an excitation light source for single molecule spectroscopy. The emission of the laser is spatially filtered, amplitude stabilised and coupled into a single mode optical fibre. The thin sublimation grown crystals containing the chromophores are attached to the end of this fibre which is placed in the focus of a parabolic mirror, used for efficient fluorescence collection. The probe head is immersed in liquid helium. The fluorescence collimated by the mirror is projected through a holographic notch and red pass filter onto a photomultiplier tube. The microwaves are generated by a synthesizer (HP 83752 B), amplified by a 20 W TWT and coupled to the sample by means of a one-turn short cut loop directly wrapped around the sample (diameter 2 mm). The radio frequency is generated by an additional synthesizer (HP 8660 Cl amplified by an EN1 420 L amplifier and coupled to the sample by a three-turn loop (diameter: 16 mm) oriented perpendicular to the microwave loop. As an example to demonstrate the feasibility of an ENDOR experiment on single nuclei we choose an isotopically labeled pentacene molecule where all except for the central two positions are deuterated (see Fig. lb). The chromophores are embedded in a fully protonated p-terphenyl single crystal. The system has been chosen because the observation of the hyperfine splitting in the ESR line facilitates the detection of the electron nuclear double resonance signals.

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et uI./Chemicul

3. Results and discussion

Physics

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267 (1997)

181

179-185

2400

The ESR and ENDOR spectra in 3T, are described by the following spin Hamilton operator

Here ? is the electron spin operator and 6 is the zero-field splitting tensor. g, and p, are the electron g-factor and Bohr magneton. The sum is over all nuclei interacting with the electron spin, where A^; is the hyperfine tensor of the nucleus represented by <, and g,;, /3, are the g-factor of this nucleus and the nuclear magneton. The first term in Eq. (11 represents the zero field splitting in 3T,, the second term the electron Zeeman interaction, the third describes the hyperfine interaction of the electron and nuclear spins and the last term is the nuclear Zeeman interaction, In the description of our magnetic resonance spectra we neglect all interactions between the nuclei. Fig. 2 shows one of the ESR lines (X-Z) ’ of an individual pentacene molecule recorded at a B, of 8 mT. The direction of B, is chosen to be parallel to the molecular Z axis (see Fig. lb). A threefold hyperfine splitting of the ESR line is visible. An analytical solution of Eq. (1) to describe the spectrum in Fig. 2 becomes difficult since at B, = 8 mT the zero-field splitting and the electron Zeeman interaction (see Eq. (1)) are of the same order of magnitude and the Zeeman interaction is non-diagonal in a basis diagonalising the zero field terms. However, a numerical solution of Eq. (1) shows that for the orientation of B, chosen in this experiment a field of 8 mT is already sufficient to allow a qualitative description of the shape of the ESR line in Fig. 2 in terms of the high field approximation. In this approximation one assumes that the electron spin is quantised along the direction of the external magnetic field such that the simplified energy level diagram shown in Fig. 2 results. Owing to the selection rules for magnetic dipole transitions in ESR spectroscopy to first order the transitions with Am, = _t 1 (m,:electron spin quantum number) and Am, = 0 (m,: nuclear spin quantum number) can be detected. The two hydrogen nuclei at the pentacene molecule assume four different relative spin configu-

1800 1480

1500

Microwave

1520

Frequency

1540

(MHz)

Fig. 2. Optically detected ESR spectrum of an individual pentacene molecule in an external B, field of 8 mT oriented along the out-of-plane (Z) axis of pentacene. The inset shows the splitting of the electronic levels due to the HFC of the electron spin with the two hydrogen nuclear spins.

rations. For an electron spin interacting with these two nuclei one thus observes three transitions with an intensity ratio of 1:2: 1 since two of the nuclear spin configurations are degenerate [ 141. The frequency splitting between these transitions is given by the hyperfine coupling (HFC) (see Eq. (111 [14] between the electron spin and the two hydrogen nuclear spins. The spectrum is dominated by this HFC because the HFC of the deuterons at the other positions in the molecule (see Fig. lb) is considerably smaller [ 151 such that they only contribute to the residual linewidth of the three hydrogen hyperfine components of the ESR line. For the direction of the B, field chosen the splitting in the Z level is below a few hundred kHz and the observed splitting in the ESR line is mainly due to the HFC in the X level (see inset in Fig. 2). From previous work [S-l 11 and from Fig. 2 it is apparent that the ESR transition of a single molecule is inhomogeneously broadened. The four possible

‘Theelectron spin energy sublevels are labeled X, Y and Z throughout the presentation although the labels correspond to the spin eigenfunction only for B, = 0 mT. However, since the experiments have been performed in a weak external field the labeling X, Y and Z is kept.

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configurations of the two hydrogen nuclei and thus the three lines in the ESR spectrum show up because of a spectral diffusion process which is changing the nuclear spin configuration in the course of the experiment [8-101. A similar lineshape is observed in a completely deuterated p-terphenyl crystal. The nuclear magnetic resonance signal is observed via electron-nuclear-double-resonance (ENDOR) [163. In such an experiment one observes a change in the ESR signal as a function of an applied radio frequency field as it is swept through the resonance of a nuclear magnetic resonance (NMR) transition. It is generally known that in standard continuous wave microwave-detected ENDOR experiments, the alteration of the ESR signal intensity is of the order of l-5% [ 161.Thus with regard to the signal-to-noise ratio of the ESR signal of a single molecule (see Fig. 21, such an experiment seems to be exceedingly difficult. Indeed, we did not succeed in detecting any ENDOR signal on a single pentacene molecule under continuous microwave and radio frequency irradiation. Fortunately, there has been a considerable development in pulsed ESR and ENDOR schemes during the past decade [17] which has allowed an increase in the ENDOR effect by almost an order of magnitude in certain cases. In our experiment we have chosen a two-pulse (Davies-type) microwave sequence consisting of a preparation and a detection pulse which selectively excite one of the hyperfine components of the ESR transition. The microwave pulses are applied at the central frequency of the ESR line at 15 12 MHz (see Fig. 2). The pulse length is chosen such that for the resonant ESR transitions an effective pulse length of n/2 results. The excitation bandwidth of the microwave pulse is N 7 MHz and is thus restricted to the central hyperfine component of the ESR line. A delay T between the microwave pulses of 50 ILS has been used which is shorter than the mean triplet lifetime of 100 p.s after a r/2 pulse [lo]. During this time interval a radio frequency pulse with a length of 50 us is applied. The ENDOR spectrum shown in Fig. 3 is recorded by sweeping the radio frequency between 5 and 20 MHz. In the frequency region between 1I .3 and 11.8 MHz two ENDOR signals are found which are separated by 120 kHz. The signals correspond to an increase in fluorescence intensity by about 3%,

Physics Letters 267 (1997)

5 3

13,4

“0 v

13-2

2

13,o

32

12.8

5

12,6

= LL

I 11,3

179-185

II,4

I’ II,5

I

I

II,6

II,7

Radio Frequency

(MHz)

.I 1

I,a

Fig. 3. ENDOR spectrum of a single molecule recorded with a microwave excitation at 15 12 MHz, corresponding to the central peak in the ESR spectrom in Fig. 2. 3500 scans with a duration of 0.8 s have been accumulated.

equivalent to a relative change in the ESR signal of 15%. The time needed to record the spectrum was around 50 min. The width (full-width half-maximum) of each signal is 30 kHz which is of the order of the homogeneous linewidth limited by the nuclear T,. Unfortunately, the present experimental accuracy does not allow a precise determination of the lineshape of the ENDOR signal. In contrast to the ESR line the ENDOR signal is detected as an increase in fluorescence intensity. In a qualitative picture a radio frequency pulse in resonance with one of the ENDOR transitions will cause a flip of one nucleus from being parallel with the other one to a situation where both are antiparallel or vice versa. Thus the ESR resonance frequency is shifted between the central hyperfine component in Fig. 2 and the satellite lines upon resonant radio frequency excitation. As has been discussed resonant microwave irradiation (ESR) causes a decrease in the fluorescence intensity. If no radio frequency is applied and no relaxation occurs during 7 both microwave pulses would result in a decrease in fluorescence intensity equivalent to a 7~ pulse [lo]. However, upon exciting an ENDOR transition the electron spin, marked by the preparation pulse, is detuned with respect to the detection pulse and a smaller reduction of the fluorescence intensity equivalent to a 7r/2 microwave pulse is obtained. Consequently, the fluorescence intensity is expected to increase upon resonant excitation of an ENDOR transition, as is found in the experiment.

J. Wruchtrup

et al./Chemicul

Physics Letters 267 (1997)

183

ZFS

Let us now discuss the ENDOR spectrum in Fig. 3. The shape and intensity distribution of the ESR line has been qualitatively interpreted in a high field approximation. In a conventional high field triplet state ENDOR spectrum one would expect a single ENDOR line per set of equivalent nuclei (described by the same hyperfine tensor A^ > [18]. In this approximation the ENDOR resonance frequencies for a specific nucleus are given by [ 181 ko=g,/3,B,+(?jG,

179-185 HFC a

(2)

where (s’> is the expectation value of the electron spin operator. Thus one ENDOR line is expected at the nuclear Zeeman frequency (when (S) = 0) and another one at the sum of the nuclear Zeeman and HFC frequency (when ( S) = f 1) [ 181. At B, = 8 mT the transition at the nuclear Zeeman frequency is expected at roughly 250 kHz and is thus invisible in our ENDOR experiment because this frequency is smaller than the excitation bandwidth of the microwave pulses [ 171. The second line should appear at the frequency of the HFC plus the nuclear Zeeman frequency, i.e. around 12 MHz as observed in the experiment. In the high field approximation one would thus expect a single ENDOR fine in the spectrum in Fig. 3. This clearly indicates that this approximation is invalid for the description of our ENDOR experiments in a weak external magnetic field. The discussion of the ENDOR spectra requires an exact treatment of the spin Hamiltonian in Eq. (1). Such a treatment has been applied to the present case, i.e. for a single electron spin interacting with two hydrogen nuclear spins. As a basis for the electron spin levels the zero field eigenfunctions X, Y, Z have been chosen and the four possible configurations of the two hydrogen nuclei are represented by the spin eigenfunctions (Y and l3 (i.e. a(~, pp, (YP, pa). The deuterons at the pentacene as well as the hydrogen nuclei in the matrix material have not been taken into account because of their small coupling to the electron spin. The hamilton operator in Eq. (1) thus reduces to a 12 X 12 matrix which is diagonalised numerically. In our calculation we used values for the hyperfine coupling of pentacene from Lin et al. [ 151. Fig. 4 and Table 1 show the results of the calculations. Since B, is parallel to the Z axis our calculation shows splittings in this state which

Fio 4. Energy level scheme as calculated from a numerical di&onalisation of Eq. (1) (see text) for the case of a single electron spin interacting with two hydrogen nuclei. The figure shows the ZFS of the electron spin levels and the splitting of the electronic levels due to the HFC with the two nuclei. The excitation bandwidth of the ESR pulse in the ENDOR experiment covers the central two energy levels (b, c) in the X and all of the hyperfine levels in the 2 state. The HFC in the Y level has not been included in the figure.

are below 500 kHz. This is smaller than the microwave excitation bandwidth and thus the splittings in the Z level do not show up in the ENDOR spectrum. In the X level four separate energy levels (a, b, c, d) are calculated, two of which are nearly degenerate (see Table 1). The situation closely resembles the high field case where an exact degeneracy of b and c would be found. Table 1 compares all calculated transition frequencies with those determined experimentally. Under consideration of the microwave excitation bandwidth four transitions should be observable. These four possible transitions form two pairs of transition (a-b, a-c and b-d, c-d), where the transitions a-b, a-c or b-d, c-d are

Table I Experimentally tions (MHZ)

and theoretically

4 /mT

7.8

transition calcvalue

a-b 11.68

exp. value

I 1.67

determined

ENDOR

line posi-

I .o a-c 11.66

b-d 11.56

I I .55

c-d II.54

a-b 5.15 5.17

a-c 5.18

b-d 7.16

c-d 7.13

7.23

Comparison of the calculated and experimentally determined ENDOR line positions for two different values of the external magnetic field B,,. The values for the HFC tensor have been taken from Ref. [ 151. A perfectly planar molecule with D,, symmetry has been assumed in the calculations.

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separated by only 20 kHz. We calculate a separation between the two sets of transitions of 100 kHz, close to the experimentally found splitting between the two ENDOR transitions of 120 kHz. In order to allow an additional comparison between experiment and theory we measured ENDOR spectra at still lower B, fields. In this case the splitting between the two ENDOR lines increases as it is reproduced by the calculations shown in Table 1.

4. Conclusion

and outlook

A pulsed Davies-type ENDOR sequence enabled us to detect the electron nuclear double resonance signal of two hydrogen nuclei. The ENDOR effect of 15% of the ESR signal is within what one would expect. Two ENDOR transitions separated by 120 kHz are found in the experiment. The width of both transitions is close to the homogeneous linewidth given by the nuclear T, as expected for Davies-type ENDOR experiments [ 171. A closer analysis however shows that each of the two ENDOR signals found is composed of two NMR transitions separated by only 20 kHz, which is of the same order of magnitude as the homogenous ENDOR linewidth and thus cannot be resolved. The finding of two ENDOR lines for a pentacene molecule with two equivalent hydrogen nuclei can be understood as an effect of the weak B, field used in the experiments. We did not succeed in detecting any ENDOR signals at B, = 0 mT or at a B, much larger than the field used in the present experiments, nor did we succeed in detecting ENDOR signals with continuous microwave and radio frequency irradiation. This is certainly not a principle limitation but indicates that under these conditions the sensitivity of the ENDOR experiment is lower, such that within a 50 min averaging period no ENDOR signal can be detected with sufficient accuracy. The experiments described in the present work demonstrate the feasibility of an electron nuclear double resonance experiment on individual nuclear spins in the solid state. Although promising approaches in magnetic force microscopy exist 1191the present approach is currently the only feasible way to achieve the demanded sensitivity. As compared to previous ESR investigations the ENDOR experi-

Physics Letters 267 (1997) I79- I85

ments on a single molecule yield an increase in spectral resolution by a factor of lo*, such that now a much more sensitive tool for the investigation of the interaction of a single molecule with its environment in the domain of magnetic resonance is at hand. Moreover, the rapidly developing field of double resonance techniques is now applicable to a single molecule and with the aid of more sophisticated pulse schemes [17] the sensitivity and resolution of the experiment may even be increased. From the spectroscopist’s point of view the application of the ENDOR technique to defect centres with a high degree of delocalisation of the electron spin wavefunction seems to be especially intriguing. In this case the analysis of the HFC would allow detailed spectroscopy on a truly local scale.

Acknowledgements The technical assistance of J. Schuster is acknowledged. H.M. Vieth, H. Zimmermann and C. Kryschi provided us with the sample material. The work has been financially supported by the DFG (Contract Bo 935/6- 1).

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[I31 A. Gruber, M. Vogel, J. Wrachtrup and C. von Borczyskowski, Chem. Phys. Lett. 242 (1995) 465. [14] A. Abragam. Principles of nuclear magnetism (Clarendon Press, Oxford, 1961)); C.P. Slichter, Principles of nuclear magnetic resonance (Springer, Berlin, 1990). [IS] T.T. Lin, J.L. Ong, D.J. Sloop and H.L. Yu, in: Pulsed EPR: A New Field of Applications, eds. C.P. Keijzers, E.J. Reijerse and J. Schmidt, (North Holland, Amsterdam, 1989) p. 191. [I61 L. Kevan and L.D. Kispert, Electron Spin Double Resonance Spectroscopy, (Wiley-Intersience, New York, 1976).

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[I71 C. Gemperle and A. Schweiger, Chem. Rev. 91 (1991) 1481; A. Gtupp, M. Mehring, in: Modem Pulsed and Continuous Wave Electron Spin Resonance, eds. L. Kevan and M.K. Bowman. (Wiley, New York, 1990) p. 195. [ I81 P. Ehret, Cl. Jesse and H.C. Wolf, Z. Naturforsch. 23a (I 968) 195. [I91 D. Rugar, 0. Zllger, S. Hoen, C.S. Yannoni, H.-M. Vieth, Science 264 (I 994) 1560.