RESONANT INTERACTION OF STANDING ACOUSTIC WAVES WITH A SPIN SYSTEM I. K. Vagapov and N. K. Solovarov UDC 5372635 A theory is developed of the reaction of a spin system to a resonant action of an acoustic field and an electromagnetic field. It is shown that it is important to allow for the co- herent properties of the acoustic field that excites the spin system both for the calcula- tion of the line profile of direct acoustic absorption and for the line profile of saturation of paramagnetic resonance by sound. By studying the influence of the acoustic field on the profile of the absorption line of rf power it becomes possible to determine the mag- nitude and sign of the spin--ph0non interaction constant. At the present time, two experimental methods are used to observe magnetic acoustic resonance: direct observation of resonance absorption of sound and saturation of magnetic resonance by sound [1]. In a number of recent papers [2-4] it has been shown theoretically that because of the re-emission of the sys- tem excited by an external coherent field a number of subtle effects arise in the observation of direct mag- netic acoustic resonance and also when one observes saturation of paramagnetic resonance by sound. In [2-4] traveling acoustic waves were treated. However, standing acoustic waves are excited in the experi- ments for the direct observation of magnetic acoustic resonance and for those that use saturation of para- magnetic resonance by sound. We shall show below that allowance for this circumstance is important for the correct interpretation of the experimental results. We consider a sample with paramagnetic centers whose symmetry axis is parallel to the x axis and is bounded in the x direction by two planes perpendicular to x with coordinates x = 0 and x = I. The sample is placed in a constant magnetic field It01]z. L e t ~ico 0 be the splitting of the level of a particle with effective spin s = 1/2. Suppose that through the end x = 0 a plane longitudinal acoustic wave is introduced into the sample: q (x, t) = Re if(x, t) + ig (x, t)] exp (io~t -- itcx), (1) where K is the modulus of the wave vector of the sound; f and g are reaI functions that vary slowly in space and time compared with the exponential factor; q(x, t) is the displacement of the medium due to the pro- pagation of the acoustic wave. The acoustic wave reflected from the free surface x = l can be written in the form q' (x, t) = Re if(2/-- x, t) %- ig (2/-- x, t)] exp [io~t - - itc (2/-- x)]. (2) Here l is the length of the sample, and we have ignored losses that arise on reflection. In the case of mechanical resonance, antinodes of the standing wave are situated at the ends of the sample, and the condition l = nZ/2 is satisfied, where Z is the wavelength of the sound and n is an integer. Then q + q' = 2f' cos o~tcos Kx -- 2g' sin tot cos trx + (f-- f') cos (~ut -- nx) -- (g -- g') sin (~,~t- - ~cx), (3) where f' --- f(2l -x, t) and g, = g(2l-x, t). The equations that describe the motion of the spin system and propagation of the acoustic wave with allowance for the interaction between the two were obtained in [2, 3]. For s = 1/2 and a direction of propagation of the longitudinal acoustic wave (3) in a cubic crystal such that the acoustic wave interacts only with the mx-component of the effective spin, we have Kazan State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 77-81, October, 1973. Original article submitted July 10, 1972. 9 19 75 Plenum Publish#Ig Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any mea~ s, electronic, mechanical, photocopying, mierofilm#~g, recording or otherwise, without written perrni~sion of the publisher. A cop) of this artiele is available front the publisher for $15.00. 1402