Magic-angle spinning electron paramagnetic resonance spectroscopy

Magic-angle spinning electron paramagnetic resonance spectroscopy

18 July 1997 CHEMICAL PHYSICS LETTERS ELSEVIER Chemical Physics Letters 273 (1997) 259-264 Magic-angle spinning electron paramagnetic resonance sp...

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18 July 1997



Chemical Physics Letters 273 (1997) 259-264

Magic-angle spinning electron paramagnetic resonance spectroscopy M. Hubrich, C. Bauer, H.W.


Mar-Planck-lnstitutfiir Polymerforschung, Posffa('h 3148, D-55021 Mainz, German)

Received 3 April 1997; in final form 7 May 1997


Pulsed electron paramagnetic resonance (EPR) has been combined with magic-angle spinning (MAS) to extract highly-resolved isotropic EPR signals from anisotropic powder spectra. With a self-built probe head, pulsed EPR

experiments are performed during sample rotation with a spinning speed of almost 17 kHz. Analogous to the ultra-slow MAS experiment in NMR, in the MAS-EPR experiment transverse magnetization evolves at selected rotor positions, leading to an averaging of anisotropic contributions. The MAS-EPR spectrum of E'~ centers in y-irradiated silica has been recorded, where averaging of the anisotropic g-factor leads to an isotropic resonance line of 1 MHz spectral width, comparable to EPR lines in low viscous liquids. © 1997 Elsevier Science B.V.

1. Introduction

Orientation dependent interactions of unpaired electron spins with their environments lead to inhomogeneously broadened EPR spectra in disordered systems. Therefore, detailed information about the molecular structure and dynamics of paramagnetic compounds are often difficult to obtain in solid materials. Pulsed EPR methods are particularly suited to separating various interactions in order to obtain information, usually hidden in the signal[l,2]. For instance, electron-electron interactions can de studied separately, with pulsed double resonance methods[3-5]. Furthermore, electron-nuclear hyperfine interactions are investigated with enhanced resolution by electron-nuclear double resonance (ENDOR) or electron-spin-echo envelope modulation (ESEEM) experiments[6-9]. Nevertheless, all these advanced

pulse techniques suffer from the anisotropy occurring in solid-state systems and therefore important information remains unobserved. Recently, higher spectral resolution has been achieved by a magnetic field-jump technique[10] and by sample rotation perpendicular to the magnetic field with detection during small changes of sample orientation[ 11,12]. These techniques exploit the fact that the first-order orientation dependence of the EPR signal vanishes if the magnetic field is along the principal axes of the second rank tensors describing the anisotropic interaction. Therefore, the spectral resolution at these points is improved significantly. Such methods are particularly useful for highly anisotropic couplings, often encountered in transition metal compounds. For the application of EPR to solids or highly viscous liquids, it is of interest to achieve high-reso-

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M. Hubrich et al. / Chemical Physics Letters 273 (1997) 259-264

lution spectra, similar to what is found for many paramagnetic centers in liquids. In solid-state NMR the concept of magic-angle spinning (MAS) has successfully been applied to suppress the contributions of anisotropic interactions [ 13-16]. Nowadays MAS is indispensable in solid-state NMR and a wide number of techniques are based on this concept [17-19]. Three regimes of MAS are distinguished, depending on the ratio between the spinning angular velocity tarot and the strength of the anisotropic interaction 3. For tarot/t~ > ~> 1 the anisotropic coupling is averaged and a single line as in liquids is observed. If tarot and 6 are similar in magnitude, this line is flanked by spinning side bands at multiples of tarot" For Wrot/6<< 1 the spectrum approaches the static-powder spectrum. However, if one superimposes the evolution of the spins at three equally spaced positions of the rotor, i.e. at 0 °, 120 ° and 240 °, an isotropic signal is observed. This has been performed in the NMR magic-angle hopping technique[20]. Recently it has been realized for ~3C NMR that such an averaging can also be performed under continuous rotation if the rotor period is so slow that the rotor appears quasi-static during the detection of the NMR signals[21]. This regime is denoted as ultra-slow MAS. The achievable mechanical spinning frequencies are limited to about tarot _~<2 7r • 50 kHz, whereas in EPR, the anisotropic couplings are typically 6 >_ 2 7r • 10 MHz. Thus, ta~ot/6 < 1 and the classical MAS approach cannot be applied. However, ultra-slow MAS might be feasible. The purpose of this Letter is to show that, with the high-speed spinners now available, MAS-EPR spectroscopy can indeed be achieved and narrow isotropic lines can be recorded.

1 / 2 system, with an anisotropic Zeeman interaction. Extension to an electron-spin hyperfine-coupled to many surrounding nuclear spins is straightforward. The electron Zeeman Hamiltonian H = / 3 e ~ e f f 0 is described by the eigenvalues gx, gy and gz of the ge tensor. Alternatively, it can be described by the isotropic frequency taiso = ( / 3 J h ) B 0 (gx + gy + gz)/3, the anisotropic frequency 6 = ( ~ J h ) B o gz wi~o and the a s y m m e t r y p a r a m e t e r r/ = (/3e/h)Bo(gy - gx)/6. The corresponding electron Zeeman frequency of an electron sp~, with polar coordinates (0, ~b) of the laboratory B 0 field direction in the tensor principal axis system is then given by

to(d), O) = 6/2(3cos20 - 1 - ~/. sin20 cos(2~b)) q'- taiso '


Summation over all orientations (0, ~b) gives the powder spectrum. Note that the isotropic frequency does not depend on the tensor orientation. Therefore, it has been stated, that the ultimate g-factor is the isotropic one[22]. Our aim is to average angular dependent contributions by sample rotation to obtain highly-resolved isotropic spectra• The rotation is described conveniently in the rotor frame, where the z~f axis is chosen in the rotor axis direction, see Fig. l a. The electron Zeeman tensor in the rotor frame ~RF= R - l ( a , / 3 , y ) ~ e R ( ~ , / 3 , y ) is characterized by the relative orientation of the principal axes system and the rotor frame, with Euler angles ( a , /3, 7). The sample rotation induces a time-dependent frequency shift, which can be written as ta(t) = taiso + ½(3c°sZ0rot- 1)C0 + CI >(COS(T + tarott) + C2cos(Zy + 2 tO~ott)

2. Concepts For the reader's convenience we will briefly refresh the concepts of ultra-slow MAS spectroscopy. Angular dependences of the resonance frequencies result from the anisotropic nature of the corresponding interactions• The following description is valid for all second-rank tensor-type interactions, which is a good approximation in most paramagnetic systems. The concept of the presented MAS-EPR experiment is exemplified for a single electron spin S =

+ Slsin(7 + tarott) + S2sin(23, + 2 Wrott) • (2) The time independent coefficients C 0, C 1, C2, S 1 and S z are functions of the Euler angles c~, /3 and the tensor values 6 and "r/, for more details see the textbook of Mehring[17]. Note that the time dependence in the four trigonometric functions is only influenced by the molecular orientation-angle y and the rotor phase tarott, which both correspond to rotations around the rotor axis•

M. Hubrich et al. / Chemical Physics Letters 273 (1997) 259-264



y + 240 ° of the sample relative to the /~0 field. The corresponding M A S - E P R pulse-sequence is shown in Fig. lb. It consists of three evolution time intervals at starting angles y, y + 120 ° and y + 240 °. After the first and second time interval with length tl/3 the magnetization is stored along the z direction. In the third evolution interval after the 5th microwave ~r/2-pulse at time t 2 = tl/3 the acquired phase values are






b) rd2 re2






rd2 rd2 *'~'



y ' + 120 ° ) + t o ( y + y ' + 240°)]

= toi~otl

c) •



~rd2 rt/2




rd2 rd2


b ~



x+t i/3 -.......~




Fig. 1. (a) Schematic representation of the magic-angle spinning experiment. Evolution at the three rotor positions, indicated by arrows, leads to vanishing anisotropy. (b) Pulse sequence of the electron paramagnetic resonance magic-angle spinning (MASEPR) experiment. (c) Pulse sequence of the refocused electron paramagnetic resonance magic-angle spinning (refocused MASEPR) experiment.

and a rotational echo occurs with a time domain shape in the t 2 dimension, which corresponds to the anisotropic spectrum. However, this rotational echo is modulated in t I with the isotropic EPR frequency toiso- Therefore, a Fourier transform of the t~ time domain signal yields the isotropic spectrum. During the two time delays T6 longitudinal relaxation and spectral diffusion can lead to signal losses, but the M A S - E P R experiment should be applicable, if a stimulated electron spin echo (ESE) can be measured after a time interval of T240 o = 2/(3Vrot). In the past,

From the trigonometric structure of the time dependence one gets the identity

, [°]

t o ( y ) + t o ( y + 120 ° ) + t o ( y + 240 ° ) --- 3toi~o + 3(3cos20,ot- 1)C 0









for any value C 0, C 1, C 2, S 1, S 2. Eq. (3) shows that it is indeed possible to average any anisotropic second rank tensor interactions by the summation of frequencies at three equally spaced rotor positions (see Fig. I a). If the sample rotation is performed about an axis aligned along the magic angle of 0to t = 0 m : = a r c c o s ( ~ - / 3 ) = 54.74 ° to the B 0 field, the (3cosZ0rot- 1) term vanishes and the sum of the three frequencies equals 3 toiso[19]. This is the basis o f the N M R magic-angle hopping experiment,[20] or, under continuous rotation in the N M R ultra-slow M A S experiment[21]. The anisotropy is averaged to zero by allowing the transverse magnetization to evolve at three orientations y, y + 120 °,








T¢ [gs] Fig. 2. MAS-EPR experiment, applied to y-irradiated fused silica, with incremented storing time intervals T4, corresponding to orientation changes 4~. Rotational echo is observed for ~ = 120°. The signal at ~ = 180° corresponds to a stimulated echo with longitudinal magnetization stored during one rotor period. The parameters are t I / 3 = 240 ns, vrot = 16.79 kHz, t.~/2= 32 ns.


M. Hubrich et al. / Chemical Physics Letters 273 (1997) 259-264

M A S in N M R was mainly performed at spinning speeds below 3 kHz. At such spinning speeds, the condition T240o~ Tt is not fulfilled for most paramagnetic systems. Nowadays, however, spinning frequencies ~'rot> 15 kHz are almost routine. Thus, M A S - E P R is now feasible for systems with T~ >_ 20 i.t,s. Spectral lines are usually broad in solid-state EPR and transversal phase memory relaxation is usually relatively fast. Therefore, we have to take into account the deadtime of the receiver during which the EPR signal cannot be observed, due to cavity ringing after a high power microwave pulse. Therefore, we used for our M A S - E P R experiment a modified pulse sequence, shown in Fig. 2c. Here, the rotational echo in the detection period is refocused with a 11 pulse, leading to two rotational echoes at times "r+_ i l l 3 after the final microwave pulse. We neglect the influence of the rotation during the final ESE sequence. To overcome this limitation, more advanced pulse sequences with refocusing during each evolution time interval are currently beeing developed.

3. Experimental The experiments have been performed with a pulsed X-band EPR spectrometer Bruker-ESP 380 E. A home-built probe head was used, which allows for sample rotation within a microwave resonator. With a 4 m m M A S system (Standard Bloc BL 4, Bruker, Rheinstetten, Germany) rotation frequencies v,.o~= 3 - 2 0 kHz can be achieved. The rotor frequency exhibits a stability of _ 10 Hz at high spinning speed, which is checked by fiber optics. With a dielectric microwave resonator mounted into the stator, ~ / 2 - p u l s e lengths of t~/2 = 32 ns can be applied during rotation. A more detailed description of the probe head and the experimental apparatus will be published elsewhere. The experiments have been performed on glassy clear fused silica (SUPRASIL, Haereus, Hanau, Germany), which has been y-irradiated with a 6°Co source with a dose of 230 kGy. During irradiation the primary E'~ point defect center is produced, which is observed in glassy silica or in quartz crystal[23,24]. At room temperature a longitudinal relax-

ation time of T 1 = 200 ~ s and a phase memory time T2 = 4 txs are observed.

4. Results and discussions In order to check whether rotational echoes are indeed created, the storing time 7~, see Fig. l b, was incremented from 8 to 40 Ixs, corresponding to 4' = 48 ° to 240 ° at a spinning speed of almost 17 kHz. Fig. 2 shows the amplitude of the electron-spin signal of the M A S - E P R experiment applied to yirradiated fused silica as a function of T+. As expected, the rotational echo occurs at 4' = 120 ~'. A second echo occurs for 4' = 180°. It corresponds to the stimulated echo created by the first, second and final microwave pulse after a 360 ° rotation. Fig. 3a shows the rotational echo with the refocused M A S - E P R sequence (Fig. lc) in the t 2 domain at a rotor frequency Urot = 16.79 kHz, for an evolution time q / 3 = 200 ns, a -rr/2-pulse length t~/~ = 32 ns and a refocusing time interval of ~-= 200 ns. If the rotor angle is turned to Ofot = 35 ° we detect almost no signal, see Fig. 3b. This proves that the signal observed in Fig. 3a is indeed caused by rotation around the m a g i c angle, where the anisotropic part of the electron Zeeman interaction is averaged. Finally, we compare the EPR spectra of a static sample of fused silica with that recorded under MAS. The decay of the ESE signal of E't centers yielded an






t~ [Its]

Fig. 3. (a) Rotational echo of ~/-irradiated fused silica with a refocused MAS-EPR sequence. Experimental parameters are: Orot =54.7 ° 5:0.5°, t L/3=200 ns, Vot=16.79, Ti20o=19848 ns, t~/2 = 32 ns, ~"= 400 ns. (b) No rotational echo is observed at off-magic-angle rotation. 0tot = 35°.

M. Hubrich et al. / Chemical Physics Letters 273 (1997) 259-264



L, 0.0







t [~]




v [MHzl





spectral width of only 1 MHz. Furthermore, the center frequency at 3.5 MHz of the refocused MASEPR signal agrees well with the isotropic frequency position of the powder spectrum of Fig. 4b. Indeed, the MAS-EPR spectrum represents the isotropic EPR spectrum, where anisotropic contributions are averaged. The isotropic linewidth of 1 MHz obtained here is comparable to liquid EPR signals, demonstrating the capability of the MAS-EPR technique. However, the MAS-EPR linewidth is still considerably broader than the homogeneous linewidth A b,hom 1//(qTT2) --=-80 kHz. To clarify the origin of the larger MASEPR linewidth, the influence of experimental parameters on the MAS-EPR spectrum was investigated. The magnetic field inhomogeneity in the sample region was found to be less than an equivalent of 200 kHz and can thus be neglected as a major source of broadening. Since a deviation of the rotor axis orientation from the magic angle leads to an imperfect averaging of the anisotropy, MAS-EPR signals have been measured at various rotor axis orientations. From this we can exclude that this broadening effect is dominant. Furthermore, the MAS averaging is perfect only if the storing time intervals correspond exactly to ~b = 120 °, see Fig. 2 and Eq. 3. Therefore, the rotor has to spin reliably. As mentioned above, at fast sample rotation the spinning frequency varies only of the order of + 10 Hz. This corresponds to a jitter of less than _ 0.02 °. Hence, we can neglect this effect. Since the investigated experimental parameters are apparently not responsible for the broadening of the MAS-EPR line, we suppose that the MAS-EPR line shows a distribution of isotropic g-factor values of the E'~ centers, which might be caused by heterogeneities in the y-irradiated glassy silica. This is also consistent with the anisotropic spectrum, Fig. 4b. The powder spectrum cannot be simulated by a single tensor and the transversal relaxation alone. Rather an additional intrinsic broadening of the order of 1 MHz has to be assumed. With the MAS-EPR experiment we are now able to show whether this broadening results from a distribution of isotropic electron g-factors in the amorphous sample. To clarify this point, further experiments are in progress on a powdered single crystal, for which a single g-factor is expected. =




tl [p.s]








vl [MHz]

Fig. 4. (a) Time d o m a i n electron spin e c h o signal of E'~ centers. Experimental parameters are: Vrot = 0, t~/2 = 32 ns, ~" = 1 Ixs. (b) P o w d e r E P R s p e c t r u m of El centers. Fourier t r a n s f o r m o f the time d o m a i n signal in Fig. 5a. (c) Evolution o f the refocused M A S - E P R signal in the t t t i m e - d o m a i n . Experimental parameters are: ~'rot = 16.79 kHz, t~/2 = 32 ns, ~- = 1 Ixs, Ti20o = 19848 ns. (d) M A S - E P R s p e c t r u m of E' I . Fourier t r a n s f o r m o f (b) The anisotropic contributions of the electron Z e e m a n interaction are a v e r a g e d out, leading to the single line at the isotropic signal frequency vi~o = 3.5 M H z with a w i d t h o f A v t = 1 M H z , m u c h smaller than the anisotropic spectral width.

early example of Fourier transform EPR[25]. The second half of the ESE signal for a static sample (Urot = 0) is shown in Fig. 4a, measured with pulse lengths t~/2 = 32 ns, a pulse spacing of 1 its, a total time window of 4 p.s and a dwell time of 5 ns. The signal is governed by the anisotropic electron Zeeman interaction leading to a fast time-domain decay. The spectral shape of the Fourier transform spectrum (Fig. 4b) corresponds to the anisotropic electron Zeeman interaction. With the refocused MAS-EPR sequence the time evolution of the maximum of the final rotational echo has been measured during the sample rotation with Urot = 16.79 kHz. Clearly, the envelope of the refocused MAS-EPR signal (Fig. 4c) decays on a much longer time than that of the static sample, Fig. 4a, and oscillations are observed. A Fourier transform of the refocused MAS-EPR signal leads to the single line in Fig. 4d, which has a


M. Hubrich et al. / Chemical Physics Letters 273 (1997) 259-264

5. Conclusions and outlook Pulsed E P R experiments under m a g i c - a n g l e spinn i n g have been performed at the E' 1 center of disordered fused silica to average an anisotropic electron Z e e m a n coupling. For this, electron coherence evolves at three rotor orientations during the M A S E P R e x p e r i m e n t at a rotation frequency o f more than 15 kHz. The obtained i s o t r o p i c spectrum is a narrow single resonance line, with a spectral width of 1 MHz. The resolution e n h a n c e m e n t achieved is about a factor of 7 and demonstrates the capability of the M A S - E P R experiment. It has a high potential in the study of paramagnetic c o m p o u n d s in disordered systems. Indeed, it seems that the residual linewidth contains information about a heterogeneous distribution of isotropic g-factors in the glassy sample. W i t h the first M A S - E P R e x p e r i m e n t a n e w class of experimental techniques is n o w applicable for studies of paramagnetic centers in disordered crystalline materials or glassy materials. Currently, more a d v a n c e d M A S - E P R methods, such as 2D experiments[18,19], are being developed in order to separate isotropic couplings and anisotropic couplings with high spectral resolution and full tensorial information. Furthermore, the c o m b i n a t i o n of E S E E M or pulsed E N D O R techniques with M A S experiments will allow high-resolution studies of electron spin density distributions in disordered solid-state materials with a spectral resolution k n o w n from liquid E N D O R experiments. With high-resolution E P R M A S experiments it is n o w feasible to investigate the molecular structure and d y n a m i c s of paramagnetic defects, reaction centers or spin probes in disordered materials in m u c h more detail.

Acknowledgements The authors thank Dr. S. Hafner for helpful discussions on the principles of M A S experiments and W. L~immler ( E T H Zurich) for irradiation of the sample. Special thanks b e l o n g to Prof. Dr. A. Schweiger ( E T H Zurich) and Dr. G. Jeschke (Rheinische Friedrich-Wilhelms-Universit~it B o n n ) for very helpful discussions and suggestions, which

have been important to the success of the M A S - E P R experiment.

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