MAGNETIC EXCITATIONS IN Ni-DOPED KMnF3

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MAGNETIC EXCITATIONS IN Ni-DOPED KMnF3

T. Holden, R. Cowley, W. Buyers, E. Svensson, R. Stevenson

To cite this version:

T. Holden, R. Cowley, W. Buyers, E. Svensson, R. Stevenson. MAGNETIC EXCITATIONS IN Ni-DOPED KMnF3. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-1184-C1-1185.

�10.1051/jphyscol:19711424�. �jpa-00214467�

JOURNAL DE PHYSIQUE

Colloque C I , szrpplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 1184

MAGNETIC EXCITATIONS IN Ni-DOPED KMnF,

T. M. HOLDEN, R. A. COWLEY, W. J. L. BUYERS AND E. C . SVENSSON Chalk River Nuclear Laboratories

Atomic Energy of Canada Limited Chalk River, Ontario, Canada

and

R. H. W. STEVENSON Aberdeen University, Scotland

R&um6.

Les excitations magnetiques dans un cristal de KMno.97Nio.03F3 ont kt6 CtudiQs & 15 OK par diffusion inelastique de neutrons. Les frequences des ondes de spin acoustiques ne sont que peu deplackes des valeurs correspon- dantes pour KMnF3 pur. Prks des frontikres de zones, les modes acoustiques se confondent avec une bande de modes magnetiques ayant des frequences dans la bande 2,05-2,30 THz. Ces derniers sont observes dans des zones de Brillouin contenant les points du rkseau rkciproque magnetique et nucleaire et sont associes avec des excitations localisks sur les voisins Mn d'une impurete Ni. Un mode magnetique est aussi observe a 7,7 .f 0,3 THz correspondant a une excitation localisQ sur une impurete Ni. Des calculs de perturbation des modes acousti.ques et les energies des modes d'impurete, calcules selon des techniques de fonctions de Green, donnent un agkment quahtattf avec les observations.

Abstract. - The magnetic excitations in a crystal of KMn0.97Nio. 03F

have been studied at 15 OK

means of neutron inelastic scattering. The frequencies of the acoustic spin waves are only slightly shifted from the corresponding values for pure KMnF3. Near the zone boundaries the acoustic modes merge with a band of magnetic modes having fre- quencies in the range 2.05-2.30 THz. The latter are observed in Brillouin zones containing nuclear and magnetic reciprocal lattice points and are associated with excitations localized on the Mn neighbours of a Ni impurity. A magnetic mode is also observed at 7.7

0.3 THz which corresponds to an excitation localized on a Ni impurity. Calculations of the pertur- bation of the acoustic modes and the energies of the impurity modes carried out with Green-function techniques, give qualitative agreement with the observations.

Experiment. - Neutron inelastic scattering measu- rements have been made of the magnetic excitations in antiferromagnetic nickel-doped KMnF,. Since NiZf has spin 1 compared with 512 for Mn2+, and since the exchange between nickel and manganese differs from that between host ions, the magnetic excitations will be perturbed by the nickel impurities and local [ l ] and/ or resonant [2] impurity modes may occur.

The measurements were carried out with a triple- axis crystal spectrometer at the NRU reactor. The constant-momentum transfer (constant-Q) technique

(PICKART et a \ , l1

0.50 - ^0.0 -

⁵

REDUCED WAVEVECTOR

5

FIG.

- The (110) plane of the reciprocal lattice of KMnF3.

Nuclear (magnetic) reciprocal lattice points are indicated

open (closed) circles. Also shown are several typical neutron groups observed at

at the positions indicated.

B show band and shell modes in the ^[0051 and [cc<] directions.

C

D show shell and local

modes and their absence at high temperatures.

was used to measure the scattering for momentum transfers in zones containing magnetic and nuclear reci- procal-lattice points. Magnetic modes were observed at several frequencies (Fig. 1) and could be divided into local, shell, and band modes. The local mode was observed at a frequency of 7.7 f 0.3 THz (Fig. Id) which was independent of Q. This mode (so) corres- ponds to a spin deviation that is essentially localized on the nickel impurity.

The shell modes (s,, p, d modes) were observed in the frequency range 2.05-2.3 THz and are associated with spin deviations on the shell of manganese ions that are nearest neighbours to a nickel impurity ion.

The shell modes are we11 separated (Fig. l a and Ib) from the band modes except near zone boundaries where the two excitations merge and appear as a single neutron group. The band modes, which corres- pond to modes of the host crystal perturbed by the impurities, are strong in magnetic zones but weak in nuclear zones. By contrast, the shell modes have comparable intensity in both zones. We have confirmed that all three types of excitation are of magnetic character by observing that they are absent above the NCel temperature (Fig. Ic and Id).

The dispersion curves for the shell and band modes for the [00(] and [[([I directions are shown in figure 2.

In general, the band modes differ little from those for pure KMnF, as determined by Pickart et al. [3]

by neutron scattering which are shown as the solid line in figure 2. There is a significant difference near the zone center (5

⁰⁾ ; however, the ( = 0 frequency of Pickart et al. is much higher than is indicated by AFMR measurements [4]. The shell modes do not exhibit any marked dispersion, but there is some

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711424

MAGNETIC EXCITATIONS IN Ni-DOPED KMnF3 C

-

FREQUENCY (THz)

FIG.

- Dispersion relation for shell and band modes in K M I I O . ~ ~ N ~ ~ . O ~ F ~ determined

neutron scattering. 5 has

units

indication that their frequency is higher at the nuclear zone centre than at the magnetic zone centre. This behaviour could arise if several modes having no dispersion but with different frequencies and structure factors were contributing to the scattering as suggested by the Green-function calculation discussed below. It is quite possible, however, that the apparent dispersion of the shell modes may occur because of the proximity of the band modes or because of the possibility of competing scattering processes.

These results are in good agreement with fluores- cence measurements for the

local mode [5] and with the shell mode frequency obtained by subtracting the so frequency from the Raman scattering frequency [6] for the so + d pair excitation corrected for the interaction as calculated by Thorpe [7].

Ising model.

Because the magnon density of states for an antiferronlagnet is strongly peaked near the zone boundary frequency the Ising model gives a good description of many of its properties, in particular the frequencies of impurity modes. The frequency of the so mode localized on a Ni2+ impurity surrounded by six Mn2+ ions is 30

which gives

As was found for cobalt-doped KMnF, [8] the geome- tric mean relationship

reasonably accurately predicts the magnitude of the impurity-host exchange. The values of JMn-,, and JNi-Ni were taken from the results of Pickart et al. [3]

and Lines 191.

In the Ising model the s,, p and d modes are dege- nerate with a frequency of

which is z 0.13 THz above the band. Since the experimental frequencies lie in the range 2.05-2.30 THz, the Ising model is again seen to give a reasonable description of the results. Although the maximum frequency of the band modes is only approximately known, the occurrence of the shell modes over a large region of reciprocal space with about equal intensity suggests that they are indeed local, in agreement with the Ising model.

Green-function theory. - The properties of the magnetic excitations in KMn,,g7Nioo,F, have been calculated using Green-function techniques following the method of Elliott and Taylor [lo]. Three shell modes with different structure factors are found at 0.05 THz (s,), 0.07 THz(p) and 0.08 THz (4 above the top of the band, in better agreement with experiment than the Ising model. A calculation by Parkinson [ l l ]

gave very similar shell mode frequencies (0.10 THz and 0.1 1 THz above the top of the band for p and d modes). From our theory we have also obtained widths and shifts (< 0.02 THz) for the band modes which are consistent with experiment where compari- son is possible.

Summary. - The local, shell and band modes in KMno~g7Nio,o,F3 have been studied by neutron inelastic scattering techniaues. The shell modes are localized in this crystal bicause JS for the impurity- host interaction is - ^{40 %} greater than JS for the host. The results are in good agreement with optical measurements which, unlike neutron scattering, do not determine the shell mode frequency directly. Our experimental results are described qualitatively by an Ising model, and somewhat more fully by a Green- function theory.

J,, - , , ⁼ 0.256 THz

Acknowledgements.

We wish to thank E. A. Gla- for the nearest neighbour Ni-Mn exchange constant. ser and R. Campbell for expert experimental assistance.

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& STEVENSON (R. W. H.), J . Appl. Phys., 1968,

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