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Submitted on 1 Jan 1988
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A TWO RATE DESCRIPTION OF ELECTRON SPIN
RESONANCE. APPLICATION TO
ONE-DIMENSIONAL MAGNETIC SYSTEMS
S. Clément, E. Bize, J. Renard
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, Suppl6ment au no 12, Tome 49, d6cembre 1988
A TWO RATE DESCRIPTION OF ELECTRON SPIN RESONANCE. APPLICATION TO ONE-DIMENSIONAL MAGNETIC SYSTEMS
S. ClBment, E. Bize and J. P. Renard
Institut d'Electronique Fondamentale, CNRS UA 022, BCt. 220, Unzversite' Paris-Sud, F-91405 Orsay Cedex, France
Abstract. - A comparison is made between electronic resonance lines measured at 25 MHz in the quasi onedimensional systems TMMC and CMC. The analysis with generalized Bloch equations shows strongly anisotropic relaxation rates in TMMC but almost isotropic ones in CMC. The doping enhances the anisotropy of the rates.
Magnetic resonance lines in exchange-coupled sys- tems are often Lorentzian in shape and they can be described by means of a relaxation rate 1
/
T2 : it cor- responds to an exponential relaxation of the total spin component perpendicular to the static field.Such a description is not valid at "low" frequen- cies f l ] (at frequency of the order or lower than the linewidth). An illustration is given in the following. In figure 1 are shown two electron spin resonance derivative lines obtained a t room temperature in quasi one-dimensional (ID) paramagnetic compounds. In both cases the static field Bo is perpendicular to the chain axis, and the frequency of oscillation is 25 MHz (the maximum absorption occurs at sero field). The spectra are very similar, the lineshape appearing t o be Lorentzian with a damping rate 1
/
T2 E 2.5 x10' rad.s-l.
In fact these looking like spectra correspond to very different situations. One line has been obtained in a sample of (CH3), NMnC13 (TMMC), which is one of the best quasi 1D systems [2], characterized by well separated chains; the other line has been obtained in a sample of CsMnC13. 2H20 (CMC) [3], in which the
/
\
j
chain axis U B,Fig. 1. - The derivative ESR absorption signal in two quasi ID systems at 25 MHz. The ordinate is in arbitrary units. The oscillating field is directed along the chain axis in both cases.
chains of spins are closed from each other. In fact, &om a geometric point of view the structure is almost tridi- mensional in this latter case: the ratio of intrachain to interchain nearest-neighbour separation of ~ n ions ~ + is 1:1.26 in CMC and 1:2.8 in TMMC.
We showed previously [l] that at very low frequency it is necessary t o take into account the polarization of the oscillating field. If a phenomenologic description is allowable, the Bloch equations must be generalized in order to include relaxation times in the oscillating field direction (Tz,) and in the direction perpendicular to both fields (T2,,). The absorption line becomes thus:
w, being the static field (directed along 0 , ) expressed into angular frequency unit.
In this way a relaxation rate can be defined for each spatial orientation. In TMMC we have found quite different rates in the chain direction (1
/
Tzch) = 5 x 10' rad.sW1) and in the perpendicular direction (1/
T2t = 10" rad.s-I).These values can be measured by varying the angle between the chain axis and the oscillating field B1, in the plane perpendicular to the static field: the maxi- mum ratio of line amplitudes is approximately in the inverse ratio of these rates, while the lineshape remains unchanged, in agreement with relation (1). In fact a lot of couples (1
/
Tzx, 1/
Tzy) can explain the lineshape (each corresponding t o a common value of the product of rates), but only one gives the correct amplitude.In
CMC
we recorded the lines for all configura- tions of the static and the oscillating fields, being ap- plied along the crystallographic axes a, b, c (here ais the chain axis). The line amplitude is found to be nearly the same for all configurations, contrarily to the TMMC case, showing the quasi isotropy of the relax- ation rates. An analysis based on equation (1) gives the following rates:
1
/
T2b 1! 1/
Tzc N 2.3 x 10' rad/s-'1
/
T2, 1/
T2ch r! 2.7 X 10' r i d s - l .JOURNAL DE PHYSIQUE
Fig. 2. - ESR lines in Cu-doped TMMC a t 25 MHz. The chain axis is rotated in the plane containing the fields. 6 is the angle between the static field and the chain axis.
This latter value gives evidence of the main role played by interchain dipolar interactions in CMC (the contribution of intrachain ones to 1
/
Tzch is zero).It is known that impurities placed into the chains slow down the spin diffusion and enhance the spin re- laxation rates [4]. In figure 2 we present spectra ob-
tained in TMMC doped with paramagnetic cu2' ions, the impurity concentration being x = 0.08. The chain axis is rotated in the plane
(Bo,
B1).
The linewidth is as expected broadened. We have compared the arnpli- tudes of the derivative lines in pure and doped TMMC when the chain axis is perpendicular toBo
(for a simi- lar weight of compound). The pure TMMC signal was greater by a factor 1.4. The analysis: with equation (1) gives the parameters.The damping in the chain direction appears to be weakly affected by the doping. As the angle between the chain axis and
Bo
is reduced the signal weakens considerably. However this case cannot be described by a phenomenologic theory because the relaxation then is no more exponential [5]. It does again whenBo
is parallel to the chain axis.[I] Clement, S., Bize, E., Renard, J. P., Phys. Rev.
Lett. 53 (1984) 2508.
[2] Steiner, M., Villain, J., Wind!sor, C. G., Adv. Phys. 25 (1976) 87.
[3] Nagata, K., Hirosawa, T., J. Phys. Soc. J p n 40
(1976) 1584.
[4] Richards, P. M., Phys. Rev. B 10 (1974) 805. [5] Bize, E., Clement, S., Fknard, J. P., Phys. Rev.
