HAL Id: jpa-00228961
https://hal.archives-ouvertes.fr/jpa-00228961
Submitted on 1 Jan 1988
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
DYNAMICS OF NONEQUILIBRIUM
LARGE-WAVE-VECTOR MAGNONS IN MnF2
G. Jongerden, A. Arts, J. Dijkhuis, H. de Wijn
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, Suppl6ment au no 12, Tome 49, dhcembre 1988
DYNAMICS OF NONEQUILIBRIUM LARGE-WAVE-VECTOR MAGNONS IN MnF2
G . J. Jongerden, A.I?.
M. Arts, J. I. Dijkhuis and H. W. de WijnFysisch Laboratorium, Rijksuniversiteit Utrecht, P.O. Box 80.000, 3508 TA Utrecht, The Netherlands
Abstract.
-
A new method relying on optical generation, inductive detection, and separation of the magnon branches in an external magnetic field allows to determine the time constants of both intersublattice and intrasublattic processes relaxing large-wave-vector magnons in antiferromagnetic MnF2.We present a new method, utilizing a combination of optical generation, inductive detection, and the lift- ing of the magnon degeneracy by an external mag- netic field, to examine the dynamics of nonequilibrium magnons of very large wave vector. The method, here applied to the archetypal antiferrornagnet MnF2, en- ables to distinguish between intrasublattice and inter- sublattice relaxation.
The principle of the method is as follows. (i) Cre- ation of the magnons is accomplished in the nonra- diative processes following resonant pulsed laser ex- citation of the a1 exciton-magnon side band associ-
ated with
R ,
the lowest exciton state arising from the6 ~g - 4 ~ 1 1 transition of the MR" ions. Excitation
of a1 gives rise to an interacting exciton-magnon pair with total k
=
0, whose energy is 57.4 cm-' aboveE l . The pair virtually instantaneously decays t o Ez under the emission of a free magnon taking up the energy deficit of 40.5 cm-' [I]. The free magnons pro- duced thus have k's of about 60 % out towards the zone boundary. They further propagate on a single sublat- tice [2], at least in the event the exciting laser light is suitably polarized. (ii) In the course of their history, the magnons experience fast intrasublattice processes as well as slower intenublattice relaxation to magnons on the other sublattice, carrying the opposite mag- netization. Contrary to the intrasublattice processes, therefore, the intersublattice relaxation, occurring on a time scale of a few nanoseconds, gives rise to a tran- sient magnetization, which is detectable in the f o ~ m of an induction voltage in a coil wound around the sam- ple. (The El exciton emerging from the nonradiative decay has, likewise with coil detection [3], been found to decay on a microsecond time scale, much too long to be of interest here.) (iii) The method is completed by a gradual lifting of the degeneracy of the upper and lower magnon branches with a field along the [001] preferential axis, breaking the energy conservation re- quired by the intersublattice processes. The field at which the intersublattice relaxation rate has dropped by, say, a factor of two thus is a direct gauge of the homogeneous width of the magnon branches, i.e., the
conversion of the magnons into one another by intra- sublattice processes.
In the present experiment, the optical excitation is performed with an excimer-pumped dye laser, gener- ating linearly polarized light pulses of 100-kW peak power and 10-ns duration. The light beam propagates along the [OOl] axis. The sample is kept at 1.5 K. The pickup coil and its associated circuitry have a single- exponential response, with a response time of about 10 ns. As a function of time the measured induction voltage accordingly takes on the form of the double convolution
V
(t) = Al
dt'l1
dt"$ (t") '7: x xexp[-
(t-
t')/
T ~ ] v-..lexP[-
(t'-
tl')/
rc],, (1) 0 0 1 2 3 MAGNETIC FIELD ( T )Fig. 1. - Dependence of the decay rate
rzl
on a magnetic field along [OOl]. Apart from a residual constant rate, the solid line represents a gradual lifting of the magnon degen- eracy according to equation (2).Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888722
C8 - 1580 JOURNAL DE PHYSIQUE
in which rm is the decay time of the magnetization, T,
is the characteristic response time of the coil, q5 (t) is the profile of the excitation pulse, and A is a factor determining the sensitivity. The maximum of V (t) typically amounts t o 3 mV. Least-squares adjustment of equation (1) to the data points with T,,,
,
rc, and A asadjustable parameters generally appeared to result in faithful fits. In zero magnetic field, the fitting yielded
T~ = 2.5
f
0.5 ns and T, = 11.8f
1.0 ns.Fits as just described have further been carried out for similar data taken in external magnetic fields of up to 6 T along [OOl]. As is seen in figure 1, showing the resultant field dependence of r l l , the rate T'; drops
to half its zero-field value at about 0.3 T and dimin- ishes by as much as an order of magnitude already in the first Tesla. In high fields, Tm levels off at a constant
value of about 50 ns, which time obviously is due to magnon-phonon processes. On the reasonable assump- tions that the energies of the magnon branches at fixed k have Lorentzian profiles and that the intersublattice transfer rate decreases in proportion with the spectral overlap of the up and down magnon branches, we have
with 2 g p ~ H the energy separation of the magnon branches in a field H, and A the half width at half maximum of the magnon branch. Adjustment of equa- tion (2) t o the data after supplementing a small con- stant rate
T F ~
(solid line in Fig. 1) provides A = 0.52 f 0.05 cm-l, corresponding to a magnon life- time T against intrasublattice processes of 10 ps, andrp = 44 f 8 ns. Recall that we found for the time to be associated with intersublattice decay the value rm = 2.5
f
0.5 ns in zero field.In order to account for the T,,, (H = 0) and T found,
we consider momentum conserving scattering of a magnon on the up sublattice to one on the down sublattice of the form a k ~ l k , and non-momentum- conserving elastic intrasublattice scattering of the form aka;:, respectively. In the former case, processes invo ving more than two magnons are ruled out by
quite general arguments [4]. The two-magnon coupling
a k ~ t k
is provided by the nonsecular parts of the dipo- lar interactions [5]. Carrying out the relevant lattice summations for k's in various directions and averaging the results, we estimate T,,, to be of order 1 ns, which, given the uncertainties, is in conformity with the ex- periment. The matrix element pertaining to akatk
may be derived from the interaction between substi- tutional magnetic impurities, like ~ i and ca2+. In ~ ' the case of magnetic vacancies, i.e., complete cutting of the isotropic exchange bonds between the impurity site and its ~ n neighbors, a detailed calculation based ~ + on spin-wave-like excitations in impure systems, much in the spirit of reference [6], yields T = 5 ps for theindependently measured impurity level of 0.9
f
0.4 %,which again is in agreement with the experiment. Acknowledgments
Invaluable technical assistance by C. R. de Kok is gratefully acknowledged. One of us (G.J.J.) was sup- ported by the Foundation Janivo. Financial support was further provided by the Netherlands Foundations FOM and ZWO.
[I] Macfarlane, R. M., Luntz, A. C., Phys. Rev. Lett.
31 (1973) 832.
[2] Keffer, F., Encyclopedia of Physics, Ed. S. Fliigge (Springer) 1966, Vol. XVIII, Part 11.
[3] Holzrichter, J. F., Macfarlane, R. M., Schawlow, A. C., Phys. Rev. Lett. 26 (1971) 652.
[4] Lax, M., Hu, P., Narayanamurti, V., Phys. Rev.
B 23 (1981) 3095.
[5] Harris, A. B., Phys. Rev. 143 (1966) 353.
[6] Walker, L. R., Chambers, B. C., Hone, D., Callen,
H., Phys. Rev. B 5 (1972) 1144;
Van Luijk, J. A., Arts, A. F. M., de Wijn, H. W.,
