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NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY OF LOW-TEMPERATURE
TUNNELLING IN MOLECULAR SOLIDS
P. van Hecke, G. Janssens
To cite this version:
P. van Hecke, G. Janssens. NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY OF LOW-
TEMPERATURE TUNNELLING IN MOLECULAR SOLIDS. Journal de Physique Colloques, 1978,
39 (C6), pp.C6-1178-C6-1179. �10.1051/jphyscol:19786521�. �jpa-00218007�
JOURNAL DE PHYSIQUE Colloque C6, supplgment au no
8, Tome 39, aoat 1978, page C6-1178
NUCLEAR MAGNETIC RESONANCE S P E C T R O S C O P Y O F LOW-TEMPERATURE TUNNELLING I N MOLECULAR S O L I D S
P. Van Hecke and G. Janssens i%
Laboratoriwn voor Vaste Stof-Fysika en Magnetisme, Katholieke Universiteit Leuven, Leuven, Belgiwn
RQsum6.- Une mbthode RMN est dbcrite qui permet une mesure directe d'dnergies tunnel infbrieu- res P 1 VeV. Le principe de base est dlaccorder l'bnergie nuclbaire Zeeman 1 l'bnergie tunnel de lamolbcule. L'bchange rbsonant d'dnergie qui en rssulte est observb par le truchement de la vir tesse de relaxation de l'aimantation nuclbaire. La mdthode est appliqube au silane 1 basse tempd- rature.
Abstract.- A NMR field cycling method is described for the direct measurement of tunnel energies smaller than 1 UeV. The basic principle is to match the nuclear Zeeman splitting to the tunnel splitting of the molecule. The subsequent resonant exchange of energy is observed through the relaxation rate of the nuclear magnetization. The method is applied to solid SiH4
.
The spectroscopy of molecular energies below 1 peV is at present not accessible to neutron scat- tering spectrometers. Quite a lot of molecules or ionic groups (-CH3, -NH4,
...
) though, show at low temperatures strong indications of librational tun- nelling in the sub-peV range for which no direct spectroscopi-c evidence has been given up to now. We describe here a new method, based on a nuclear ma- gnetic resonance technique, which allows for a direct measurement of tunnel splittings in the radiofre- quency range, say 1-
100 MHz, or, 0.004-
0.4 peV.In order to clarify some features of the experiment, let us briefly recall without entering into any details, that the spin-lattice relaxation rate of a spin system for which the dipole-dipole interaction is modulated by random molecular motions (e.g. reorientations), is proportional to the den- sity functions J(wo) and J(2wo). These are assumed to have a Lorentzian shape
J(u) = 2T/(f + m2T2)
spin-lattice relaxation rate will show as a func- tion of frequency a sharp maximum at those frequen- cies (fields) where nuo= Wt (n = 1, 2). In other words, the tunnel splitting wt will give rise to a pair of peaks in l/T1, at wt and wt/2. Actually, this matching of Zeeman- and tunnel levels is noth- ing else than fulfilling the level crossing condi- tion for these nuclear Zeeman levels separated by the tunnel energy splitting wt. A condition for the experiment is to be on the low temperature side of the classical T minimum, so that W ~ > T1 and ~
1
J(w) a 1/w2r
.
This condition however is fulfilled in most solids at low temperatures.Our experiment, then goes as follows. The nuclear magnetization is saturated by means of a pulse train, in a given external magnetic field Ho.
This field is then quickly (much faster than T ) 1 decreased to a value H, where the nuclear magneti- zation is allowed to partly relax for a given time t (t < TI ; typically 30 sec). The magnetic field is then adiabatically switched back to its original w is the nuclear Zeeman splitting in the external ma-
o value Ho, where the amplitude of the partly relaxed
gnetic field and T is the thermally activated corre-
magnetization (in field H) is measured by means of lation time of the random motion. In the presence of
a 90' pulse. The whole cycle is now repeated for a tunnel splitting wt, the spin-lattice relaxation
another value of the field H (lower or higher than rate will now also be function of the spectral den-
reference field Ho). The amplitude of the partly sities J(w
+
w) and J(wt f 2w). We refer to thet relaxed magnetization is then plotted as a function
litterature for exact calculations as well on 3- as
of the magnetic field. If the field reaches the on 4-spin groups or molecules 11, 21. Hence, the
-
condition for which the Zeeman splitting~~matches w- (or wL/2), the spin-lattice relaxation rate is
I: E - -
*
"Bevoegdverklaardnavorser" of the Belgian "Natio-enhanced and the partly relaxed magnetization (at naal Fonds voor Wetenschappelijk Onderzoek".
time t) will have a much larger value than outside
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786521
this resonance, resulting in a peak in the plot of the magnetization vs. magnetic field. The position of this peak yields the tunnel energy splitting, the width of this peak is related to the lifetime of the tunnel~level and to various broadening mecha- nisms inherent to the sample.
This field cycling method is straightfopwed and rather simple as it only involves measurements of the nuclear magnetization at one frequency (field).
It is much easier than a full T measurement, as a 1
function of frequency. First of all, the latter re- quires a frequency variable spectrometer (for low temperature work). Moreover, as those resonant peaks can be rather sharp, a careful scanning of the fre- quency range is required, which becomes rather cum- bersome.
It is important to keep t smaller than T I at all fields i.e. to keep the partly relaxed magnetiza- tion below its thermal equilibrium value, in order to see any extra growth due to the enhanced relaxation rate. Thus, the obvious limitation to this method is the relaxation time TI. If it becomes too short, say below 1 min, the whole field cycle can hardly been done in a time shorter than TI. However, this again is hardly a limitation for solids at low temperatures.
Finally, the value of the reference field Ho (and the resonance frequency Wo of the spectrometer) can be taken at the convenience'of the experimenter ; the maximum field attainable (i.e. the highest ener- gy that can be determined) will be the one that can be reached by the (electro) magnet at hand. As to the lowest field, one should remember that for fields of the order of the internal (local) magnetic field
(typically 10 G) the growth of the magnetization will be determined by the relaxation of the dipolar reser- voir, which can be very fast. For these lowest fields
(10-50 G) however, one can use a method similar to the one described above, making use of a NMR rotating frame technique (the rotating frame Zeeman levels are now matched to the tunnel levels by means of the am- plitude of the external radiofrequency field). Such an experiment has been recently performed / 3 / .
As a first application, the method has been used to determine the tunnel splitting of the ground librational state of solid SiH4 below 20 K. Making use of the theoretical calculations on the molecular states of CH' and CD4 in their ordered state 141, we predicted the tunnelsplitting of the ground libra- tional level of solid SiH4 to be about 0.3 VeV. It should be emphasized here, that very little is known
about the crystal structure and field symmetry of SiH4 at low temperatures so that only rough esti- makes can at best ve put forward.
From a field cycling experiment (proton NMR) as described above, up to 1.8 T, we found a ground librational A-T tunnel splitting of 0.22 pev and another, smaller, splitting of 0.033 peV, that we described to a T
-
T fine level splitting,
ari-sing from a lower than tetrahedral site symmetry in SiH4. The width of the peak at 0.22 peV accoucts very well for this T - T splitting. It should be observed that not only the position of the peak pair (for each splitting) fulfills the 2:l ratio, but also the width, as one might expect the "in- homogeneous" mechanisms which broaden these lines buch as fine splittings and the distribution of the value of the tunnel splitting throughout the crys- tallites of the powder sample). A detailed discus- sion of the SiH4 case is given elsewhere /5/.
AS a conclusion we can say that this NMR spectroscopic technique is simple, of a wide appli- cation range and very promising as it extends the tunnel energy spectroscopy down to the neV range.
Further work along these lines is now in progress on various molecules.
We are very much indebted to Professor L.
Van Gerven for his support to this joint NMR-neu- tron diffraction work financed by the Belgian Interuniversitair Instituut voor Kernwetenschappen.
References
/ I / Clough, S., J. Phys. C : Sol. State Phys.
2
(1976) 1553
/2/ Nijman, A.J. and Trappeniers, N..J., in "Proc.
XIXth Congres Ampere, Heidelberg, 1976", ed.
H. Brunner, K.H. Hausser and D. Schweitzer (Groupement AMPERE, Heidelberg-Geneva, 1976) p. 353
/3/ Hallsworth, R.S., Nicoll, D.W., Peternelj, J.
and Pintar, M.M., Phys. Rev. Lett.
39
(1977) 1493/4/ Huller, A. and Kroll, D.M., J. Chem. Phys.
63
(1975) 4495
/5/ Van Hecke, P. and Janssens, G., Phys. Rev. B (1978), in the press
