D. SXRZYPEK: Critical Behaviour of the Magnetic Resonance in KNi,Mnl -%Fa 695

phys. stat. sol. (b) 167, 695 (1990)

Subject classification: 75.30 and 76.30; S9

Institute of Physics, Silesian University, Katowicel)

Critical Behaviour of the Magnetic Resonance in KNi,Mnl,,Fs

BY D. SKRZYPEK

A series of KNi,Mnl-,F3 (0.3 < z < 0.8) with cubic structure is examined by electron paramag- netic resonance in the region of the magnetic phase transition. The broadening of the linewidth AB and the shift of the resonance field B, at a fixed frequency are caused by the onset of magnetic ordering. The work proves Huber’s theory that the effects observed near magnetic phase transitions in antiferromagnets depend on the symmetry of the system examined.

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1. Introduction

A series of KNi,Mnl-.F, crystals (0.3 < x < 0.8) was examined with electron para- magnetic resonance in the temperature range close to the magnetic phase transition. The method for preparing these compounds was discussed in detail in [l].

Single crystals were prepared by the Bridgman method from the starting compounds KHF,, NiF,, MnF, ground at adequate stoichiometric ratios. Magnetostatic measure- ments of the series are presented in [2]. The examined samples are antiferromagnets. The structure of these crystals was found to be cubic both in the paramagnetic and the antiferromagnetic phases. A crystallographic phase transition that ‘occurs in KMnF, a t 186 K is suppressed by adding Ni2+ ions. No transition was observed for x > 0.3 when examined by X-ray diffraction methods. Similar results were obtained by Cowley and Carneiro [3] in optical studies of these fluorides.

EPR examinations of KNi,Mnl -%Fa in the paramagnetic phase were performed by Skrzypek and Bialas-Borgiel [l]. It was found there that strong changes in the reson- ance linewidth AE with a change of nickel concentration and sample temperature can be explained by contributions to A B originating from spin-phonon coupling.

The main purpose of the present work is to show that the abrupt increase of the linewidth AB and the change in magnetic field B, observed below a certain temper- ature (characteristic of a given specimen), are caused by the occurrence of an ordered magnetic phase. The temperatures from which on the beginning of these changes is observed are denoted as temperatures TN (see Fig. 1) of the particular specimens. These temperatures correlate satisfactorily with T, determined for this series of optical and magnetic measurements [2, 41.

l) Uniwersytecka 4, PL-40-007 Katowice, Poland.

696 D. SKRZYPEK

Fig. 1. The temperature of magnetic phase transi- tion TN vs. nickel content in KNi,Mnl-,F,. The value determined by EPR measurements (+) was compared with those obtained in optical determina- tions [4] (0) and static susceptibility measurements 121 (0 )

2. Experimental Procedure

The samples containing nickel in concentrations x = 0.36, 0.45, 0.71, 0.81 were examined. For the single crystal KNi,,Mn,,,F3, the measurements were conducted depending on orientation. The EPR spectra were observed with a standard spectro- meter operating at X-band. For all specimens the EPR spectrum consisted of the single resonance line, the shape of which differed considerably from the classical Lorentzian shape, was found. As the observed linewidths were of the same order of magnitude as the resonance fields, the experimental line was fitted to the following function [5 ] :

where B is the external magnetic field, B, the resonance field, and AB the half linewidth. The linewidth AB and the resonance field. B, for different concentrations and temperatures are shown in Fig. 2 to 4. The parameters A B and B, were obtained by fitting the experimental line to the function (1).

3. Discussion

The theory of the critical-point anomalies in the EPR linewidth in antiferromagnets was presented by Huber [6] who demonstrated that the growth of the linewidth as T -+ T N from the high-temperature side reflects the increase in the lifetime and the correlation length of the critical fluctuations. According to the prediction of this theory, anisotropy plays a fundamental role in the nature of the anomaly observed near the NBel temperature T,.

The EPR linewidth near T N can be written as follows:

AB - ABnctitt T) + ABcrit(T) , (2) where the factors ABncrit and A Bcrit represent the non-critical and critical contribu- tions to the linewidth, respectively. ABncrlt is also a function of temperature as results from [l].

To describe these quantities in detail, let us remind the main results given in [I] and [6]. In [I], the model of relaxation processes in the system KNi,Mnl-,F3 in the paramagnetic phase was performed. The contributions to the linewidth in such systems

Critical Behaviour of the Magnetic Resonance in KNi,Mnl-,FJ 697

were written as

ABncrit = ABsu + ABu-ph + ABss-ph 7 (3) where AB,, concerns the spin-spin interaction, relates to the spin-phonon contribution due to the vibrational modulation of the crystalline field, ABss-ph is the spin-phonon contribution due to the vibrational modulation of the exchange inter- action.

As proved, the most essential contribution to the linewidth is A Bss-ph. This quantity is expressed by

where C$ is the high-temperature approximation of the magnetic specific heat, J the exchange integral, p the mass density, v the velocity of sound, and z the number of the nearest neighbours.

In the calculations given in [6] and [7] it is assumed that the dominant spin-spin interaction is the isotropic exchange coupling of Heisenberg type and that the dipole- dipole interaction being the source of anisotropy play a particular role in relaxation processes in the area immediately above the critical point. According to this suggestion, the Hamiltonian Xss of the system was written in the form

where N is number of spins, the sum over q is taken on the Brillouin zone associated with the magnetic lattice, Sr(q) is the Fourier transform of the spin operator, J(q ) and U(q) are the Fourier transforms of the exchange interaction and anisotropy tensor, respectively.

The relaxation time Tz for the fluctuations of the spins S is given by m

- 1 - - gs dt (&), 3 ) , T2 XT

0

where - 2 s= - [ S , Z ] , h

(...) denotes the relaxation function, xT is the static susceptibility. Using the random phase approximation, Huber wrote this expression as follows:

The Uup(q) are related to the Fourier transform of the spatial part of the dipolar interaction,

698 D. SKRZYPEK

The main contribution to T, near T N comes from the wave vectors near q - KO for antiferromagnets. Therefore, the critical contribution to l /Tz can be written as

where

The quantity 1/T, is a measure of the previously critical contribution to a linewidth AB,,it. From (9) it is seen that AB,,it can be written as the product of two factors: an angular part which reflects the symmetry of the magnetic lattice and an isotropic part given by A ( T ) . The dipolar sums U,p(q) were computed for different cases by Cohen and Keffer [S]. For the cubic system such as KNi,Mnl-,F, (z> 0.3)) the angular part is zero a t all temperatures, hence AB,,it is zero and no anomaly in the EPR linewidth near TN can be expected in these compounds.

The temperature dependence of the linewidth and the resonance field are shown in Fig. 2 and 3. When the temperature is reduced, starting from , T N , the shift of reson- ance field B, and the increase of resonance linewidth A B are observed. These effects occur continuously up to temperatures lower than those shown in figures. We believe that they relate to the phase of magnetic ordering. The linewidth as T -+ T , from the high-temperature side will be described only by ABncrit whose value affects basic- ally t,he magnitude of ABsl-*h as described by (4). Assuming after [l] the values of

I T N I 1 I I I $ O 740 d o %O Id ZOO 270 220 230 240

T ( K 7- Fig. 2. The dependence of resonance linewidth AB near the magnetic phase transition on temper- ature for different nickel concentrations in o KN&,36Mn,,aF3, + KN$.,,Mn,,,,F,, 0 KN&.,lMq,z9F3, and x KNio.slMrb.,9F3

Critical Behaviour of the Magnetic Resonance in KNi,Mnl -zF3 699

Fig. 3. The dependence of resonance field B, near the magnetic phase transition for different nickel concentrations in KNi,Mnl-,F, (symbols as in Fig. 2)

parameters a In J -- - 9.4, w = 5 x lo6 cmls , C h * N C h * a ~ n r

IJ/kl (KNiF,) = 47 K ,

the estimated value AB - zx (20 to 50) mT agrees with those given in the experiment. The dependence of AB and B, on temperature for BJI (110) and BII (001) is

illustrated in Fig. 4. It can be seen that no anisotropy of the system occurred. The behaviour of the g-factor in EPR near TN was discussed in [9]. The effective g-factor

+79---- I I I

F L

50

t I I I

I

Fig.4. The dependence of linewidth and resonance field on temperature for KNi,,3,,Mno.6,F3. + B I I (110) and o L) 1 1 <001)

P

700

was defined by

D. SKRZYPEK: Critical Behaviour of the Magnetic Resonance in KNi,Mn, -%F3

SeffpBBr = hv * (10) The predictions of the theory are compared with experimental data in Fig. 2 and 3. It is seen that the g,H-factor near T, in the considered system is equal to the g-factor characteristic of the paramagnetic phase.

4. Conclusions

The EPR linewidth and also the resonance field exhibit no anomalies, when approach- ing T N from the high-temperature side. The values of A B and B, in this region are dependent on those characteristic of the paramagnetic phase. Due to the symmetry of the examined system, the critical contribution to the linewidth is zero proving in this way the Huber theory.

The description of antiferromagnetic resonance for KNi,Mnl -,FS will be presented separately.

Acknowledgements

The author expresses sincere thanks to Dr. A. Ratuszna for her valuable information on X-ray diffraction examinations in KNi,Mnl -,Fa.

This work was supported in part by the Project C.P.B.P. 01.12 of Polish Academy of Sciences.

Reference8

,1] D. SKRZYPEK and K. BIALAS-BORG~EL, J. Phys. C 21, 1807 (1988). ,2] 2. CELI~~SKI and D. SKRZYPEK, Acta phys. Pol. A66, 149 (1984). '31 R. A. COWLEY and K. CARNEIRO, J. Phys. C 13,3281 (1980). :4] D. J. LOCKWOOD, G. J. COOMBS, and R. A. COWLEY, J. Phys. C 13, 4611 (1979). :5] A. ABRAGAM, The Principles of Nuclear Magnetism, Oxford University Press London (1961). :6] D. L. HUBER, Phys. Rev. B 6,3180 (1972). -71 D. L. HUBER, J. Phys. Chem. Solids 33, 2145 (1971). -81 M. H. COHEN and F. KEFFER, Phys. Rev. 99, 1128 (1955). -91 D. L. HUBER and M. S. SEEERA, phys. stat. sol. (b) i4, 145 (1976).

(Received May 16, 1989; in revised form September 22, 1989)