209

RAMAN SCATTERING BY MAGNETIC EXCITATIONS IN SUBSTITUTIONALLY DISORDERED ANTIFERROMAGNETS

J.P. GOSSO and P. MOCH Laboratoire P.M.T.M., Universit~ Paris XIII, A~. J.B. Clement, 93430 Villetaneuse, France

One and two-magnon Raman scattering was observed in the mixed antiferromagnets Mn, ,Co.F2, RbMn, ,Co,.F~ and KMn~ ,Co, F3: the experimental results agree with a previously proposed CPA model and, for some lines, with a concentration dependent self-consistent molecular field model. Preliminary measurements concerning Ni, ,Coc F2 are given: they show a transition from a weakly ferromagnetic to an antiferromagnetic phase when c increases, as expected. Finally, Raman scattering involving inter and intra electronic Kramers doublets transitions under an applied magnetic field was studied in diluted Zn, ,.Co,F.., allowing g tensor evaluations.

1. Introduction

The properties of disordered mixed crystals have given rise to a considerable amount of studies in the past few years [1]. Because of the short range of magnetic interactions, a relatively simple example is provided by the substitution- ally disordered insulating antiferromagnets where two different magnetic ions are randomly distributed in a fixed lattice, or by materials where only one of the two ions is magnetic (diluted antiferromagnets): it is possible to pre- pare such crystals in the case of rutile type fluorides (McM'I-~Fz) or fluoperovskites (AM, M'~_,F3, where A is an alkali metal) on a wide range of c concentrations for a number of M-M' combinations. Most of the experimental work concerning these materials has been per- formed using inelastic neutron scattering [2] while there are still few optical studies like Raman scattering measurements [3-5]. This paper summarizes the present state of our Raman studies in Co-Mn, Co-Zn and Co-Ni mixed crystals. The choice of Co 2+ as one of the members of the M-M' couple was dictated by a number of reasons: the main one is that the one magnon Raman scattering, which is related to the spin-orbit coupling and then generally ab- sent or weak for ions with a quenched orbital momentum in the ground state, is intense in Co 2+ compounds, due to the orbital degeneracy of the 4F~ ground state. Another consequence of the orbital degeneracy of 4F~ is the occurrence in the spectra, besides the lowest exciton line (magnon), of a complex manifold of various excitonic lines arising from the sublevels of 4Fj. Notice that some of the mixed crystals in- vestigated in this paper have given rise to theoretical studies and other experimental measurements such as antiferromagnetic

resonance [6] and inelastic neutron scattering [7].

2. Experiments

Polarized 90 ° Raman spectra were measured on crystals immersed in superfluid helium ( - 2 K ) or at higher temperature using a Coderg triple monochromator . Eventually a magnetic field, up to 50 kG, was applied along the scattered direction. A relatively complete study concerning the Mn-Co compounds (Mnl_,Co, F2, RbMnl_,CocF3, KMnl_cCocF3) has been made. For the Zn-Co case we only analyse Znl cCocFz in the low concentrat ion range (c 0.05) where it remains diamagnetic at T = 0. Finally, we give some preliminary results concerning Nil ,Co,:F2 and KNi~ , .CocF3.

3. Results and discussion

3. I. Mn-Co

Buyers et al. [2] have proposed a coherent potential approximation (CPA) model for the low energy magnetic excitations, which fits reasonably well their inelastic neutron scat- tering results: it gives rise to two spin-waves bands, the higher one (A) looking essentially like a Co excitation, while the lower one (B) can be viewed as being principally a Mn excitation. With this model, one expects two one-magnon Raman lines, respectively, connected with the A and B CPA k = 0 spin-waves and we have ob- served them in both rutile and perovskite struc- tures. When c moves off from 0 to 1, the CPA model leads to a large broadening of the A band whence the B one remains sharp, as confirmed by our measurements.

For the rutile structure the B line position perfectly fits with the CPA model and with

Physica 89B (1977) 209-212 © North-Holland

210

previous ant i ferromagnet ic resonance measurements [6]. At low c, the A line f requency decrease is slightly smaller than pre- dicted by CPA and is probably better described by our self-consistent molecular field ap- proximation (MFA). in this approximation, which is reasonably well justified by the good localization of the A mode, we expressed the f requency by solving self-consistently the } spin- hamiltonian:

# . y c ) - T(S~-+S~)+,SN: - ~ , ( c ) S , 1)

with

~ ( c ) = ( 2Z],I, - 2Z>I:)(S: t ('))

+(2,IIZ'j 2Z~J~)(1 --c)(S~),

where (S.(c)) is the mean value of the Co spin S. in the ground state, (S~)= ~ is the spin of a Mn first neighbour of a Co ion, Z, = 2, Z , = 8 mumber s of first and second magnetic neigh- bours). The exchange and single ion coefficients can be found in the literature: however , different sets of such parameters are available and lead to different f requency values (1 [8]. 2 [9] and 3 [10] in fig. 1) which makes the fitting with exper iment difficult. However , MFA leads to a slope of the A f requency concentrat ion dependence in better agreement than the CPA model. The magnetic field splitting was measured for the B line: it leads to an effective ~: value which decreases from 2 to 1 when c increases from 0 to I: the MFA model would lead to a nearly constant ~: = 2 value, but this approximat ion fails for the B line: the predic- tions of the CPA model would be useful here. The A line splitting was measured only for low c in Mn~ ,Co, F:, due to the broadening of the line. The CPA model views the disordered crystal as having the same symmet ry as the pure one: in the ruffle case we found polarization selection rules roughly in agreement with this hypothesis which predicts scattering in XZ, YZ , Z X and Z Y polarizations. The Z X component of the Raman tensor is considerably more intense than the X Z one in the strongly mixed crystals. Notice that the B line is, as expected, absent of the pure MnF~ spectrum since it draws its intensity from the spin-orbit coupling which is negligible in the Mn compounds . However , due to the admixture of orbital momentum caused by the Mn-Co interaction, its intensity rapidly increases with ~' and the line can be detected for

.... 0.01. A quantitative interpretation of the absolute and relative intensities of the polarized spectra is not yet available.

In an averaged crystal model like CPA, a two- magnon state, to be observed by Raman scat- tering, has to show a k = 0 wave vector and is then obtained from a pair of two magnons with opposite wave-vectors : one predicts three txao- magnon bands ( A - A , A - B , B - B ) . Neglecting the magnon-magnon interaction (about 5 cm ~), from density of states considerations, the maxima of the two-magnon Raman lines will occur at the sum of the zone boundar} frequencies of the involved one-magnon bran- ches. Very roughly speaking, since the A-A. A - B and B - B bands are related to C o - ( ' o , Co -Mn and Mn-Mn pairs, the Raman intensities should be proportional to c:, 2 c ( 1 - c ) and ( 1 - <7) 2. Due to this concentrat ion dependence and to the large increase of the optical density with c, we do not observe simultaneously more than two two-magnon lines. For the rutile

" ' - 2 +o r

.++ {+..

r 4 , - .

• " ~ j r

+

]

- 2

" F

L ~

+ . .

. .I]1( ~ ]. ". • . . . . , . r

+ .

.5 - , ' I

T.,

' %

t

Fig, I. O n e - a n d lV+,o+magnon s p e c t r a m M n ( '~ . t . . ,X: " C o " line, B: " M n " line, MFA: molecular tield ap- proximation, ( 'PA : coherent potential approximation {see t ex t ) .

211

structure the observed two-magnon lines frequencies roughly agree with the CPA predic- tions. Alternatively we also developed a self- consistent MFA model: it seems to provide a slightly better agreement with experiments (fig. 1). Depending upon the polarized spectra (XY or XZ), the two-magnon bands occur at slightly different frequencies, as could be predicted from a band model or even from an improved cluster model taking into account the non trans- verse part of the hamiltonian.

The experiments concerning the perovskite structure are more fragmentary and complete numerical results of the CPA model have not been available to us: our measurements fit with the CPA model semi-quantitatively. Alter- natively, they agree with a MFA model analogous to the above one described for the rutile structure. However , in contrast with the rutile case, the experimental polarization selection rules do not agree with a group theoretical analysis.

For both structures, in addition to the low energy magnon lines, other higher energy lines have been observed. They are related to the various sublevels arising from 4F~ when taking into account the spin-orbit coupling, the low symmetry crystalline field and the exchange. In pure CoF2 and weakly doped MnF2, the spectrum, previously reported [ l l ] , is well interpreted. A detailed analysis for other concentrat ions will be reported later. In the perovskite case, mul- t iphonon Raman scattering is superimposed to the excitonic lines and obscures the interpretation; however, some of the observed lines are unam- biguously of excitonic origin.

3.2. Zn-Co

In the studied concentrat ion range one can neglect any Co-Co interaction and the results are interpreted in terms of Co single ion levels. The Dzh site symmetry occurring here leads to six

4 + Kramers doublets arising from the F4(Oh) ground state. A basis for the two wave functions of the nth Kramers doublet is written as [8, 12]:

In + ) = a.]0, + l ) + b . ] _ + 1, -~½) + C.I-T- 1, -+3)

+d, lO, w-3)+e,l-v-l, wl)+.f.l+l,+-), (2)

where the two numbers appearing in each ket, respectively, stand for a pseudo L = 1 orbital momentum and a S = ~- spin component along the z axis. In an applied magnetic field the

Kramers degeneracy is lifted and the splitting of each doublet is described by a g. tensor which is diagonal along the three symmetry axes of the Co site. The components of g, are easily cal- culated from the coefficients in expression (2). We have observed the electronic Raman spec- trum within the above energy structure. However , we only discuss here the two lowest Kramers doublets where the occurrence of rather sharp lines easily allows measurements in a magnetic field. For H = 0, the Raman line corresponding to the n = 1 to n = 2 Kramers level transition occurs at 155.5 cm t (T = 2 K), which is very close to previously reported values for Co 2* in similar hosts (MgF2, MnF2, CoF2). For HIIz, we observed a low frequency line related to the splitting of the n = 1 Kramers doublet and 2 lines around 160cm ~ connected with the splitting of the n = 2 Kramers doublet. The g~. and g~ measured values agree with previous experimental measurements and theoretical predictions [12]. The polarization selection rules are the expected ones from a group theoretical analysis. For H±z, due to the existence of two kinds of sites for the Co 2* ions, the experimental situation is more complex and leads to six lines instead of three, but here again the measure- ments are in agreement with other experiments and theoretical predictions [12] (table I).

3.3. Ni-Co

We have previously reported one-magnon Raman scattering measurements in KNiF3 and KCocNi~_,,F3 (c ~ 1%) [13]: in this concentrat ion range, the low f requency line shows a fast increase with c, which is interpreted in terms of an effective c-dependent anisotropy coefficient, while a CPA model would not lead to satis- factory predictions.

We have recently observed one- and two- magnon scattering in mixed Ni,_cCOcF2 samples: since NiF2 is a weak ferromagnet with spins

T a b l e I

E x p e r i m e n t a l a n d c a l c u l a t e d g v a l u e s in Zn , , Co, F2

Kramer~ g x x g ' y gzz doublet ~ 1 2 1 2- 1 2

calculated 5.84 0.78 2.14 5.38 4.12 0.78

exp. Raman 6.2 0.6 2.5 5.0 4.2 0.7

exp. R.~EO. 2) 6.027 J 2.296 J 4.240 J

~1 ~

203

/

',, / / / k \ J

- - " 2 0 2 "" C°a~ N/o.s ,Fz

Co Ni F 20.5 oJ o-9 2

H=0

212

Co Ni F ~g 0.5 2 c m .i

10 30 40 t~ 150 200 250

Fig. 2. Some Raman features in Ni, , ('o. P

lying perpendicular to the z axis, while CoF, is an antiferromagnet with spins parallel to z, the behaviour of the one-magnon spectrum with respect to the concentration is predicted to be complex, while the two-magnon scattering should not qualitatively differ from the Mn-Co case. In preliminary measurements we have observed two-magnon scattering (corresponding to Ni -Ni pairs) in the c = 0 to c = 0.5 concen- tration range: the line is qot strongly concen- tration dependent and shews a frequency shift

of a b o u l 10 cm t. At u :: O, b e c a u s e o f the can-- ted magnetic structure, lhere are two k - 0 spin- waves which have been observed previousl3, 13 and 31cm '). We followed the higher line for low concentration (of aboul 0.1): this line shifts io low frequencies. For high c (0 .5) , w e obsc|-~c a one-magnon line which is split by a magnetic field, indicating the two-fold degeneracy predic- ted in an antiferromagne! with spins parallel Io : ~fig. 2).

We thank l)rs. H.J. (hlggenheim, W..I,I

B u y e r s , J. Nouet and ,I.P. C h a m i n a d e for

providing us with differen! crystals.

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