MÖSSBAUER STUDIES OF THE ONE-DIMENSIONAL ANTIFERROMAGNETIC SYSTEMS : A2FeF5

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MÖSSBAUER STUDIES OF THE

ONE-DIMENSIONAL ANTIFERROMAGNETIC SYSTEMS : A2FeF5

G. Gupta, D. Dickson, C. Johnson

To cite this version:

G. Gupta, D. Dickson, C. Johnson. MÖSSBAUER STUDIES OF THE ONE-DIMENSIONAL AN-

TIFERROMAGNETIC SYSTEMS : A2FeF5. Journal de Physique Colloques, 1979, 40 (C2), pp.C2-

304-C2-306. �10.1051/jphyscol:19792107�. �jpa-00218476�

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JOURNAL DE PHYSIQUE Colloque C2, supplkment au n o 3 , Tome 40, mars 1979, page C2-304

NOSSBAUER STUDIES OF THE ONE-DIMENSIONAL ANTIFERROMAGNETIC

SYSTEMS

: ^A2FeF5

G.P. Gupta, D.P.E. Dickson and C.E. Johnson

Department of Physics, University of LiverpooZ, LiverpooL L69 3BX, U.K.

REsm6.- Les 6tudes Mgssbauer de AzFeFs (A2 = K2, Rb2, N2H6) montrent que ces systsmes out une temp&

rature de Nbel basse, une faible valeur du champ hyperfin 2 saturation et une variation signigicative du champ hyperfin avec le champ appliqub. Tout cela est bien caracteristique d'un systsme anti-ferro- magn6tiquc uni-dimensionnel, et est compatible avec les prEdictions dlun modsle dlonde de spin.

Abstract.- ~gssbauer measurements on the compounds A2FeFs (A2 = K2, Rbz or N2H6) show that they exhi- bit a low NEel temperature, a low saturation value of the hyperfine field and a variation of the hyperfine field with an applied field. These are all typical characteristics of one-dimensional antiferromagnetic systems, and are consistent with the predictions of spin wave theory.

The mixed fluorides with the general formula A2FeF5 have a structure consisting of chains of

(FeF6)" octahedra separated by the A anions, which suggests that their magnetic behaviour may be one- dimensional in character. In such systems the ratio J1/J of the interchain to intrachain exchange cons- tants gives a measure of the one-dimensionality. We have made Mzssbauer Effect measurements on KzFeFs, Rb2FeFs and NzH6FeFs.

All the three compounds order antiferromagneti- cally at low temperatures TN (Table I).

Table I : Magnetic data for A2FeF5

h he

slightly higher value quoted previously /l/

was found to be in error as a result of inadequate thermal contact with the sample.

The critical exponent B was approximately 0.3 which is close to the theoretical value of 0.33 for three- dimensional' magnetic ordering. Although a purely one- dimensional system cannot sustain long range order at finite temperatures, weak interactions between the chains (J1) will lead to spontaneous magnetization at low temperatures which explains the experimental value of

B.

Oguchi / 2 / has developed a relation between TN/O and J1/J where O is the Curie-Weiss constant. The values of J/kg (where kB is Boltzmannls constant) in various one-, two- and three-dimensional magnetic systems containing adjacent (FeF6)

'-

octahedra are all around 10K which leads to a value

of 116 K for 0. Thus T /0 2 0.1 in these compounds N

and hence from Oguchils relation Jf/J

2

^5x10-~.

The saturation values B (0) of the hyperfine n

field are all around 42T (Table I). This is anoma- lously low for a high-spin ferric ion (S = 5/21 which usually has a saturated hyperfine field of about 60T. This 30% spin reduction cannot be accoun- ted for by crystal field or covalency effects and may be attributed to zero-point spin reduction which has been predicted to be large in one-dimensional anti-ferromagnets.

Using a Hamiltonian incorporating the chain- like behaviour (see e.g. /I/)the zero-point spin reduction may be given as a function of J'/J and B A /B E

(the ratio of anisotropy and exchange fields) as AS(O) = l

E ^f

(cosh 2xk-l) (1) where cosh 2xk ~ - Y ~ / ( I + B ~ / B ~ ) ~ ~ 2; (2) and Yk = {cos kxa + (Jf/J) (COS k Y b + COS k C)} /

/(1+2J1/J) ( 3 )

The zero point spin reduction for different values of BA/BE and J1/J has been calculated using the above expression / l / . For the values of anisotropy (BA/BE) estimated from the spin-flopping and the field dependence of spin reduction (see later) the experimental values of B (0) for the three compounds

n

under investigation all lead to J1/J 2 1 0 ~ ~ . This is consistent with the values of J'/J obtained from TN/O.

A characteristic feature of the Gssbauer spectra of these materials, which is observed in all cases but can be seen most strikingly in the spectra of K2FeF5 (Fig. l ) , is that the hyperfine field ini- tially decreases with increasing applied field but after reaching a minimum at the spin-flop field (3.7T) it increases again.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19792107

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Fig. 1 : ~gssbauer spectra of KzFeFs at 4.2K in magnetic fields applied parallel to the direction of the gamma ray beam.

This unusual behaviour is also a result of the one-dimensionality of these systems and can be un- derstood in terms of the field dependence of the spin reduction. In zero field at temperature T the spin reduction is

AS(T) = I

1

nk cosh 2xk (4)

k

where nk = E x p {Mwk/kB~)-g

-'

⁽⁵⁾

and

\

are the normal mode frequencies.

On applying a field B parallel to the antiferromagnetic axis

cosh 2xk (6)

where nf = [rexp{ (M%fgpB~) /kg~l-q-'

k (7)

Comparing (4) and (6) it is seen that the effect of the field is to replace nk by the average of n i and

- -

nk and from (7) it is seen that nk increases much faster with field than

4

decreases. Hence the average of the two increases and the spin reduction AS(B,T) increases with the applied field. Further the variation of the spin reduction with the applied field depends strongly on the dimensionality and the anisotropy because of the coefficient cosh2xk which is also responsible for the zero-point spin reduction ( 1 ) . The field dependence of the spin reduction like zero-point spin reduction is very

pronounced for low dimensional cases. This explains why this phenomenon has not been observed in pre- vious investigations of spin reorientation.

Figure 2 shows the experimental variation of the hyperfine field with applied field with the calculated values of the spin reduction for different values of J1/J assuming BA/BE = 1.4x10-~ which cor- responds to the observed value fo spin-flopping field Bsf = 3.7T /l/.

Fig. 2 : The experimental values and calculated cur- ves for KzFeF5. The spin reduction is expressed both in (for S = 512) and in terms of the hyperfine field normalized to 60T for S = 5 1 2 .

In view of the approximationsinvolved in the theory the observed values of the hyperfine field may be considered to be in good agreement with those calculated for J1/J = 10-'.

A similar behaviour is observed in the spectra of single crystal specimens of RbzFeFs although the spins could not be flopped in the fields available in the laboratory /3/. The large increase in the value of spin reduction indicates that the spin-flopping field is close to the maximm field applied (6.OT). A comparison of the experimental and calculated behaviour suggests J 1 / J < 10- and B /B 2

A E 3 . 8 ~ 1 0 - ~ i.e. Bsf 6.5T.

Measurements on powder samples in a fixed applied field can give information on the variation of the hyperfine field over the distribution of angles between the hyperfine and applied fields. This can be fitted to the dependence of the spin reduction on the orientation of the applied field. This was done in the case of both RbpFeFs /3/ and N2H6FeFS (to be published) which also suggests J'/J < I o - ~ and B /B

A E

-

^3.8x10-=.

The authors are indebted to Mrs. B.M. Wanklyn and Dr. D. Hanzel for the preparation of samples used in this work.

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JOURNAL DE PHYSIQUE R e f e r e n c e s

/ l / G u p t a , G.P., D i c k s o n , D.P.E. a n d J o h n s o n , C.E., J . P h y s . C : S o l i d S t a t e P h y s .

fi

(1978) 215.

/ 2 / O g u c h i , T . , Phys. Rev.

2

(1964) 1098.

/ 3 / G u p t a , G.P., D i c k s o n , D.P .E., J o h n s o n , C.E. a n d Wanklyn, B.M., J . P h y s . C : S o l i d S t a t e P h y s .

1 1 (1978) 3889.