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Submitted on 1 Jan 1971
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SELECTION RULES FOR ACOUSTIC NUCLEAR MAGNETIC RESONANCE IN
ANTIFERROMAGNETICS
K. Stevens
To cite this version:
K. Stevens. SELECTION RULES FOR ACOUSTIC NUCLEAR MAGNETIC RESONANCE IN ANTIFERROMAGNETICS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-609-C1-610.
�10.1051/jphyscol:19711206�. �jpa-00214031�
AN TIFERRO MA GNE TIQUES CUBIQ UES A BX3
SELECTION RULES FOR ACOUSTIC NUCLEAR MAGNETIC RESONANCE IN ANTIFERROMAGNETIC S
K. W. H. STEVENS
Department of Physics, University of Nottingham, England
Rbume. - Une onde acoustique de basse frequence dans un solide magnbtique deforme le rkseau et peut produire une rkorientation des sous-rkseaux magnetiques qui varie avec le temps. Le champ hype* au niveau du noyau suivra la reorientation et on peut provoquer une forte resonance nuclbaire. Les frequences de resonance nuclbaire sont depla&s par suite du couplage aux modes de magnon et des dkompositions sont observees.
Abstract. - A low frequency acoustic wave in a magnetic material distorts the lattice and may result in a time dependent reorientation of the magnetic sublattices. The hyperfine field at a nucleus will follow the reorientation and strong nuclear resonance can be induced. The nuclear resonance frequencies are displaced by coupling to the magnon modes, so splittings are observed.
It has recently been shown [l, 2,3] that strong acous- tic absorption is found in the spin-flopped phase of antiferromagnetic RbMnF,, when the acoustic fre- quency is approximately that for the Mn nuclear reso- nance. The effect does not take place through electric quadrupole coupling to the lattice, but occurs through modulation of the magnetic hyperfine interaction, even though this is not directly coupled to an acoustic wave.
There have been a number of papers discussing acoustically induced nuclear resonance, a recent one being by Fedders [4], which deals specifically with cubic antiferromagnetics. An earlier paper by Silverstein [5]
is more concerned with uniaxial antiferromagn z t' ICS.
In general the theoretical discussions are involved, and as this can be a disadvantage in the early stages of the development of a new technique we shall here attempt to give a more physical account of the phe- nomenon.
An antiferromagnetic is usually regarded as a superlattice of fixed magnetic moments, together with magnon excitations. A low frequency acoustic wave will distort the crystal lattice and we suppose that the magnetic system readjusts itself to a slightly different superlattice, with magnons. The order of magnitude of the acoustic absorption in RbMnF, suggests that the moments rotate through angles of the order of the acoustic strain 161. The field at a manganese nucleus will have a steady component of 654 kOe, and a transverse oscillating component of
E x 654 kOe, where E is the acoustic strain. The orders of magnitude are such that remarkably high transverse fields can be obtained with modest acoustic strains.
The antiferromagnetic resonance modes of RbMnF, are well understood, particularly in the spin-flopped phase [7]. o,, is field independent and can be excited with an r. f. magnetic field which is parallel to the steady external field. w, is field dependent and is excited by a transverse field. They correspond to two points on the magnon dispersion surfaces. The Mn nuclei add further surfaces [8], and the coupling between the magnons and the nuclear spin waves results in pulling of both types of modes [9]. Thus when nuclear resonance is induced by an r. f. field, different resonances are seen according to whether the field is parallel or perpendicular to the applied steady field.
T o understand this it is useful to examine the sym- metries of the wll and w, modes. o,, is invariant to a displacement through one lattice constant followed by a rotation through .n about the steady field. o, is reversed by this operation. To excite all directly the r. f. field must have the wll symmetry, and this is achieved with the r. f. field parallel to the external field. With the excitation perpendicular to H the sym- metry is that of o,, which can therefore be excited.
Of course no excitations occur unless the frequency is correct. It is not however necessary to excite at wll and a,, for they are each coupled to nuclear modes at on. Excitation can therefore occur near w,, of two kinds of nuclear modes.
Suppose now that the nuclear modes are t o be exci- ted by acoustic waves. In the spin-flopped phase the sub-lattice magnetizations are antiparallel and in the plane perpendicular to H, apart from a slight canting towards H. If the wave causes the sub-lattices to rotate in the perpendicular plane, while remaining anti- parallel, the symmetry of the transverse components of the hyperfine fields at the Mn nuclei is that of all, and the corresponding nuclear resonance can be exci- ted. To excite the resonance corresponding to w, the acoustic wave must either rotate the sub-lattices in opposite directions about H, so that they are no longer antiparallel, or tilt them in opposite directions with respect to H.
The easy direction of magnetization in RbMnF, is (1, 1, I). If a field sufficient to cause spin-flopping is applied along (1, 0, 0) the moments move into the perpendicular plane and point along (0, 1, I), with small tilts towards (1, 0, 0). A longitudinal acoustic wave travelling along (1,0,O) will displace the (1,0,0) planes, without causing rotations in the plane. There will be no coupling to all and w,. On the other hand there may be a change in tilt, in which case there should be coupling to wll. The experimental position is that no resonances have been observed under these conditions. If the same wave is now directed perpen- dicularly to (1, 0, 0), it is in the plane of the moments and they are likely to rotate without change in tilt angle. This motion gives coupling to wll except when the wave is along (0,1, 1) and (0, 1, - 1). That, is paral- lel or perpendicular to the moments, when the rota- tions will be zero. all is observed to show this selec- tion rule.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711206
C 1 - 610 K. W. H. STEVENS To excite a, it would seem best to have an acoustic
excitation which keeps the moments antiparallel but tilts their plane with respect t o H. This is most rea- dily achieved by setting H at a skew angle to the crys- tal axes. Then an acoustic wave a t almost any angle is likely to increase the tilt angle for one sub-lattice and decrease it for the other. The reported results for o, are in agreement with this conclusion.
The phenomenon of acoustically induced nuclear magnetic resonance is unlikely to be confined to RbMnF,, and it is expected to be observable in a wide range of ordered magnetic materials. The nuclear spin-magnon coupling is important because it displa- ces the nuclear resonances slightly, and thereby offers the possibility of resolving modes of different symme- tries. An important factor in determining the separation in the nuclear modes is the separation between the nuclear frequency and the magnon frequency to which
it is coupled. If the separation is small then the dis- placement may be large. This suggests that interesting effects should be obtained in substances where, for magnons, o ( k ) -, 0 as k + 0. Soft magnetic modes suggest themselves, and also materials where the wavelength of a k = 0 magnon mode is incommensu- rate with the lattice constant, as for example occurs with chromium and some of the rare earth metals and alloys. Another interesting area to explore would be the use of surface acoustic modes, both to observe nuclear resonance in surfaces and t o study the moment orientations in magnetically ordered surfaces.
Throughout this discussion it has been convenient to assume that the acoustic wave has k = 0. This is not quite right, but the required changes are small and readily made.
References
[I] MERRY (J. B.) and BOLEF (D. I.), Phys. Rev. Lett., [7] FREISER (M. J.), JOENK (R. J.), SEIDEN (P. E.) and
1969, 23, 126. TEANEY (D. T.), Proceedings of the International
[2] PLATZKER (A.) and MORGENTHALER (F. R.), Phys. Conference on Magnetism, Nottingham, 1964,
Lett., 1969, 30 A, 515. 1965, 432.
[31 MERRY (J. B.) and BOLEP (D. 1.1, J . A P P ~ . P ~ Y s . , 1970, 181 DE GENNES (P. G.), PINCUS (P. A.), HARTMANN-BOU-
41, 1412. TRON (F.) and WINTER (J. M.), Phys. Rev., 1963,
[4] FEDDERS (P. A.), Phys. Rev., 1970, 1, 3756. 129, 1105.
[5] SILVERSTE~N (S. D.), P ~ J ' s . Rev., 1963, 132, 997.
[6] SHRIVASTAVA (K. N.) and Stevens (K. W. H.), J . [9] INCE (W. J.), Phys. Rev., 1969, 184, 574.
Phys. C., 1970, 3, L64.
