Magnetic excitations in the two dimensional planar antiferromagnets K2FeF4 and Rb2FeF4

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<ul><li><p>Solid State Communications, Voi.26, pp.429-434. OO38-1098/78/0515-0429 $02.00/0 ~Pergamon Press Ltd. 1978. Printed in Great Britain </p><p>MAGNETIC EXCITATIONS IN THE TWO DIMENSIONAL PLANAR ANTIFERROMAGNETS K2FeF 4 and Rb2FeF 4 </p><p>F. Macco, W. Lehmann, W. Breitling, A.E. Slawska- Waniewska and R. Weber </p><p>Fachbereich Physik, Universit~t Konstanz, 775 Konstanz, FRG </p><p>and </p><p>U. DHrr </p><p>Physikalisches Institut (Teilinstitut 2), Universit~t Stuttgart 7000 Stuttgart, FRG </p><p>(Received 13 February 1978 by E. Burstein) </p><p>The magnetic excitation spectrum of K2FeF 4 and Rb2FeF 4, two K2NiF4-structure planar antiferromagnets with rather large anisotropy and spins perpendicular to the c-axis, has been measured by Raman and FIR-spectroscopy. One of the two pre- dicted one-magnon transitions and the two-magnon mode have been observed in K2FeF 4 (~b2FeF 4) at 48.5 cm -] (37.6 cm -]) and 182.O cm -] (160.5 cm -]) respectively. The magnetic field and temperature dependence of the spectra are reported too. The data are discussed on the basis of an easy plane spin model Hamiltonian. In K2FeF4: Mn 2+ a low lying magnetic im- purity mode is observed at 40.5 cm -I. </p><p>I. Introduction </p><p>The compounds K~FeF a and Rb2FeF 4 belong to the quadratic-layer a~ti-- ferromagnets typiefied by K2NiF 4. Very little is known about the magnetic pro- perties of the former two systems. M6B- bauer-measurements have been reported by Wertheim et al 1). Neutron quasi elastic scattering has been carried out </p><p>F " on Rb2Fe 4 only . From these investi- gations a transition temperature to a 3D ordered state of ~ 65K and of 56.3K is found for K2FeF 4 and Rb2FeF 4 respec- tively. </p><p>An interesting feature of the two magnets is the fact, that the spins point perpendicular to the tetragonal c-axis. This is in contrast to all other known members of the K2NiF 4 family which have their spins directed parallel to the c-axis. This feature has led us to Raman- and far infrared (FIR) investi- gations of the magnetic excitation spec- tra of the two systems. </p><p>The crystals were grown by Bridge- man techniques by the Stuttgarter Kristallabor. The samples were of good optical quality. Conventional Raman and FIR equipment was employed in the spectroscopic investigations. </p><p>2. Experimental results </p><p>2.1. K2FeF 4 and K2FeF 4: Mn 2+. </p><p>The Raman spectrum of K2FeF 4 at room temperature consists of four lines. Their positions are quoted for 2K in table I. With the sample immersed in LHe at 2K two extra lines occur at 48.5 + 0.5 cm -I and 182.O + 0.5 cm-lin (zx +-zy) and (xx + xy) po~arisation respectively. The latter line has re- </p><p>3) cently been studied by Thurlings et al FIR absorption measurements at LHe tem- perature reveal a line at 48.5+O.3cm -I and broad phonon absorption at--higher frequencies. The low frequency line be- longs to a magnetic dipole transition with the magnetic field vector H of the incoming radiation perpendicular to the c-axis. Its halfwidth is 1.8 cm -I. The line at 181.6 cm -I is asymmetric with a steep high frequency cut off and has a halfwidth of 12 cm -I. The aDp+lication of an external magnetic field H o perpendi- cular or parallel to the c-axis influ- ences the spectrum only weakly. In the Raman scattering experiments fields up to 5 T were employed. FIR-absorption measurements could be carried out up to fields of 7.84 T. The line at 48.5 cm -I </p><p>Permanent address: Institute of Physics, ON - 32 Polish Academy of Sciences 02-668 Warsaw, Poland </p><p>429 </p></li><li><p>430 TWO DII~NSIONAL PLANAR ANTIFERROMAGNETS K2FeF4 and Rb2FeF 4 Voi.26, No.7 </p><p>increases gradually in frequency. At 7.84 T a shift of 0.6 + 0.2 cm -I was found for H o in some arbitrary direction in the xy-plane, whereas with the field </p><p>Table I </p><p>Phonon Raman-Spectrum of K2FeF 4 and Rb2FeF 4 at 2K. </p><p>K2FeF 4 </p><p>~(cm -I ) </p><p>100.5+0.5 </p><p>1 3 1 . 0 + 0 . 5 </p><p>183.0+O.5 </p><p>373 .O + O. 5 </p><p>Rb2FeF 4 </p><p>co (cm-I ) </p><p>75.0+0.5 </p><p>150.0+O.5 </p><p>122.O+0.5 </p><p>356.0+0.5 </p><p>Pig </p><p>E1g </p><p>A1g </p><p>A1g </p><p>shoulder of the 48.5 cm -I line with the same polarisation properties. By simu- lation of the spectra the peak frequen- cy of the new line is found to be 40.5 + I cm -I with a halfwidth of 4 cm -I at T-- 2K. For a Mn 2+ doping of 2 mol% the strength of this line becomes compa- rable with that of the 48.5 cm -I line. The temperature dependence of the peak position is the same as that of the 48.5 cm -I line within experimental error ( IO%). </p><p>2.2. Rb2FeF 4 </p><p>The spectra of Rb2FeF 4 are similar to those of K2FeF 4. Besides the four Raman active phonons (see table I) two addi- tional lines occur at 2Kwith frequencies of 37.6 + 0.5 cm -I and 160.5 + 0.5 cm -I The first line is again observed in FIR- </p><p>directed parallel to the c-axis the shift was 0.8 + 0.2 cm -I. Further data are collected in table 2. No change of the line at 181.6 cm -I could be detected. </p><p>In order to obtain more information of the excitations at 48.5 cm -I and 182.O cm -I the temperature dependence </p><p>of the two lines have been studied. Care was taken to avoid heating of the samples by the laser. The results are shown in Fig.l-4. The line center fre- quencies decrease with increasing tem- perature and broaden considerably. </p><p>50 </p><p>'E L) </p><p>= 40 .9 </p><p>i n </p><p>v </p><p>o 30 ID D_ </p><p>li K </p><p>K z Fe Ft. </p><p>| = . , </p><p>I I I I I I </p><p>0 20 ~0 60 Temperature ( K ) </p><p>Fig. I Peak position of the one-magnon line as function of temperature in K2FeF 4. ( ) Raman data, ( x ) FIR data. </p><p>The high frequency line could be followed up to 8OK which is clear above the Ne~l temperature of about 65K. Good agreement is obtained between Raman- and FIR-in- vestigations regarding the data for the 48.5 cm -I line. Measurements have also been carried out on Mn 2+ doped K2FeF 4- samples with different impurity concen- trations. An extra line is observed as a </p><p>A </p><p>20 </p><p>( J </p><p>J c </p><p>"1- </p><p>K 2 Fe Ft. </p><p>! J I I I I </p><p>0 20 40 60 Temperature (K) ~. ~.~ </p><p>Fig. 2 Temperature dependence of the halfwidth of the one-magnon line in K2FeF 4. ( ) Raman data, ( x ) FIR data. </p><p>absorption~as a magnetic dipole transi- tlon wlth Hc. The magnetlc fleld depen- dence for ~oll~can be seen from table 2. The temperature dependence of the 37.6 cm -I line (see fig.5 and 6) is si- milar to that of the 48.5 cm -I line in </p><p>K2FeF 4. The same holds for the higher frequency line (fig.7 and 8). </p><p>3. Discussion </p><p>The asymmetrical shape an d the large width of the line at 182.0 cm-l and at 160.5 cm -I in K2FeF 4 and Rb2FeF 4 re- spectively, together with their tempera- ture dependence indicates that they are both due to a two-magnon transition. Be- cause of its polarisation properties and temperature dependence the low fre- quency line in both systems is assigned to a one magnon transition at zero wave- vector. Since the magnetic unit cell con- sists of two spins, two magnon branches </p></li><li><p>Vol. 26, No.7 TWO DIMENSIONAL PLANAR ANTIFERROMAGNETS K2FeF 4 and Rb2FeF % </p><p>are expected. As a shift in frequency of the line rather than a splitting is observed, the two branches should have different energies at zero wavevector. Only the higher energy line could be observed. These findings are in accor- dance with the assumption that the Fe 2+- </p><p>'E o </p><p>C 0 </p><p> 0 </p><p>180 </p><p>160 </p><p>140 </p><p>120 </p><p>ego ( o </p><p>e o </p><p>100 , , , i ~ L 0 20 40 60 </p><p>Temperature (K) </p><p>Fig, 3 </p><p>K 2 Fe F~ </p><p>Two-Magnon Line </p><p>I. e </p><p>, iI 80 </p><p>Peak position of the two-magnon line aS function of temperature in K2FeF 4. </p><p>100 </p><p>50 </p><p>K 2 Fe F 4 " I Two-Magnon Line </p><p>e ee </p><p>o </p><p>o O ~ o e </p><p>0 I i I I I I I I </p><p>0 20 40 60 80 Temperature (K) </p><p>Fig. 4 Temperature d~pendence of the halfwidth of the two-magnon line in K2FeF 4. </p><p>compounds should be described by a planar xy-model rather than by an anisotropic Heisenberg model. As pointed out above the direction of the spins is perpendi- cular to the tetragonal c-axis,and there are domains with different directions of spins. A large single ion (out of plane) anisotropy term and an additional (weaker) in plane anisotropy term have to be con- </p><p>E </p><p>w- </p><p>o I </p><p>u </p><p>C o_ .m </p><p>O </p><p>O_ </p><p>40 </p><p>35 </p><p>30 </p><p>Rb 2 Fe F 4 </p><p>I </p><p>N </p><p>q~ '~'~,,.. ~!~" ~'- </p><p>I , I 'o In- o.% 0 20 40 </p><p>T e m p e r a t u r e </p><p>{ x </p><p>(K) </p><p>I </p><p>6O </p><p>Fig. 5 </p><p>431 </p><p>A </p><p>6 L) </p><p>~4 XJ </p><p>~-2 -r </p><p>0 0 </p><p>Fig. 6 </p><p>Rb 2 Fe . { </p><p>. t ! , I n ,, I 20 40 6 0 </p><p>Temperature ( K ) </p><p>Temperature dependence of the halfwidth of the one-magnon line in Rb2FeF 4 as measured by FIR techniques. </p><p>sidered in the model. The xy-model has been studied theo- </p><p>retically by Loveluck and Lovesey 4)and by Villain 5). </p><p>In order to explain our experimen- tal data quantitatively, we have compu- ted the dispersion curves starting from the effective spin Hamiltonian </p><p>2 2 H = Z JS.S. + ~ DS~ + Z Dsz + ^ i&gt;j ^z^3 i j 3 </p><p>+ gpBHA(Z S x - Z S 3) + i i j </p><p>+ g~BHoA (Z. S xi + .E S;) (1) l l </p><p>Peak position of the one-magnon line as function of temperature in Rb2FeF 4 as measured by FIR techniques. Insert: Normalized sublattice magneti- zation (, ), and peak position of the one-magnon line in K2FeF. (---) and Rb FeF (---) as functio~ of T/TN, </p><p>2 4 </p></li><li><p>432 TWO DIMENSIONAL PLANAR ANTIFERROMAGNETS K2FeF ~ and Rb2FeF 4 Voi.26, No.7 </p><p>160 </p><p>E -- 140 w- </p><p>o =_ </p><p>P 120 </p><p>o a_ </p><p>100 </p><p>t s = e </p><p>Rb 2 Fe Fz. </p><p>Two-Magnon Line </p><p>I I I I I I l l </p><p>0 20 40 60 80 Temperature (K} </p><p>+4,2y2Ho2+ (2JSz)22.D2S2 2 H 2 Y+t -Y o ) k 7+ = _I Z eik.6 k z </p><p>w' = JSz + DS + yH A </p><p>Y = g~B (2) </p><p>Two magnon branches result which are degenerate at the zone boundary. With the approximation JSz&gt;&gt;DS&gt;~ yH A the fre- quency at k = z /2a becomes </p><p>= ~' + (3) ~max -- YHo </p><p>Fig. 7 Peak position of the two-magnon line as function of temperature in Rb2FeF 4. </p><p>A </p><p>, 80 E U </p><p>"u </p><p>o I </p><p>Rb 2 Fe Fz. Two-Magnon Line </p><p>t p </p><p>0 i , i I i i i I </p><p>0 20 40 60 80 Temperature (K) </p><p>Fig. 8 Temperature dependence of the halfwidth of the two-magnon line in Rb2FeF 4. </p><p>In this expression z is the direction of the tetragonal axis and x denotes the direction of the spin. J is the nearest neighbour exchange integral and D the single ion (out of plane) anisotropy pa- </p><p>rameter which is positive in our case. H A represents the effective in plane anisotropy field and H o a magnetic field applied parallel to the spin di- rection. Solving the equation of motion by the usual decoupling scheme ( &gt; ~ , ) the dispersion re- lation is obtained as a function of the three parameters J, D and yH A. </p><p>2 2 22 22 2 2 ~ = {~' -D S - (~Sz) ~+~ H o } +_ </p><p>At k = O two modes with different fre- quencies ~I and ~2 are obtained, an out of plane and an in plane mode 4,5). Within the above approximation their frequencies are given by the expressions </p><p>2 2 ~I = ~i(O) + 3y2H~ (4a) </p><p>p </p><p>2 2 y2H2 ~2 = ~2 (O) - o (4b) </p><p>where </p><p>w~(O) = 4 JSz DS; </p><p>w~(O) = 2 JSz yH A- </p><p>The out of plane mode is connected with an oscillating magnetic dipole moment along the y-direction within the xy-plane (H~ c). In comparison with this the in plane mode possesses a much smaller magnetic dipole moment. Naturally, the former mode depends strongly on the out of plane anisotropy energy, while the in plane anisotropy term influences the mode frequency only weakly. The opposite holds for the in plane mode. Using the above dispersion formula, neglecting the in plane anisotropy, the nearest neigh- bour exchange constant J and the single ion parameter D can be fitted to the one and two magnon line for both K2FeF 4 and Rb2FeF 4. The magnon-magnon inter- action has been taken into account by the Ising approximation </p><p>~2Mag = 2~max - J" </p><p>No predictions for the value of the in plane anisotropy field are possible from our data. The values for the other para- meters are </p><p>K2FeF 4 : J = 11.4 cm-1; D = 3.2 cm -I </p><p>-I -I Rb2FeF4: J = 10.1 cm ; D = 2.2 cm </p><p>We do not compare these values with those derived bv Thurlinqs et al 3). </p></li><li><p>Voi.26, No.7 TWO DIMENSIONAL PLANAR ANTIFERROMAGNETS K2FeF 4 and Rb2FeF 4 </p><p>since our dispersion relation deviates from the one used in their calculation. The value for J in Rb~FeF 4 agrees within 10% with that calcul~ted-by Birgenau et al 2). In this context it should be remarked that our values for J are ob- tained by a calculation that is based on the Ne~l ground state. </p><p>Next we turn to the magnetic field dependence of the out of plane one mag- non mode ~'n K2~eF4. The.experimental~ data for H i c and ~ |Jc are summarlzed </p><p>o . o in table 2. F~rst we concentrate on the case where the field vector lies within the basal plane (Hol ~). Calculation shows that in this case the line posi- tion should increase with the square of the magnetic field (equ. 4a). The data are consistent with the theoretical result up to 5.6 T (see table 2). A quan- titative comparison with the experimen- tal data can not be made because of different reasons. Firstly, the magnetic field direction was only known to lie within the xy-plane but the angle bet- ween field and spin was not known. Se- condly, susceptibility measurements I) suggest a domain structure with mutually </p><p>433 </p><p>In this case equ. (4a)7has) to be re- placed by the formula </p><p>2 2 2 2 = ~I (O) +y H o. (5) </p><p>Compared with the magnetic field depen- dence for Hol ~" the shift is expected </p><p>to be smaller, which in turn makes accu- rate comparison with the experimental data still difficult. Nevertheless, good agreement is obtained between theory and experiment by fitting the gi; ~factor to g jj = 2.5 for both K2FeF 4 and Rb2FeF 4 (see table 2). Because of the lack of other spectroscopic information, no other values for g exist. Therefore no comparison is possible. </p><p>The temperature dependence of the lines deviates somewhat from the one ob- served in other 2D antiferromagnets. Whereas in K2NiF 4 the AFMR frequency de- creases with increasing temperature in proportion to the sublattice magnetiza- tion M(T) 8), in Rb2FeF 4 the out of plane one magnon mode frequency ~I (T) decreases more slowly than M(T) as mea- sured by Wertheim et al I) (see fig.5). </p><p>Table 2 </p><p>Magnetic field behaviour of the k = 0 one-magnon mode in K2FeF 4 and Rb2FeF 4 as measured by FIR techniques at 2K. </p><p>H o </p><p>(T) </p><p>3.36 </p><p>5.6 </p><p>7.84 </p><p>HOl c </p><p>A~ exp </p><p>(cm -I ) </p><p>~0.2 </p><p>0.6+0.2 </p><p>0.6+0.2 </p><p>K2FeF 4 </p><p>A~cal c </p><p>(cm -1 ) </p><p>0 . 3 </p><p>0.84 </p><p>1.6 </p><p>H O </p><p>A~ex p </p><p>(cm - 1 ) </p><p>0.5+0.2 </p><p>0.8+0.2 </p><p>c </p><p>A~calc </p><p>(em -I ) </p><p>0.44 </p><p>0.85 </p><p>Rb2FeF 4 </p><p>~oll c </p><p>A~ex p A~calc </p><p>(cm -I ) (cm -I ) </p><p>0.6+0.2 </p><p>1.0+0.2 </p><p>0.56 </p><p>1.1 </p><p>DerDendicular spins. The spins of these domains are affected differently by a magnetic field in the xy-plane. Finally, measurements of the angular dependence of the in plane susceptibility 6) suggest, that with increasing field some of the spins may rotate in a direction perpendicular to the external field di- rection. The value of this "spin flop" field will depend mainly on the in plane anisotropy field. Above this transition, equ. (4b) will no longer be valid and the field dependence will change. There is some indication that such a situation occursin K2FeF4, since no increase of frequency is observed when the field is raised from 5.6 T to 7.84 T. </p><p>The magnetic field behaviour for ~oI| ~ is easier to discuss since the experimental situation is well defined. </p><p>In K2FeF 4 the T-variation of the sub- lattice magnetization is not known. If the values for M(T) in Rb2FeF 4 are taken over, the T-dependence of e1(K2FeF4 ) is f...</p></li></ul>

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