Magnetic excitations in the two dimensional planar antiferromagnets K2FeF4 and Rb2FeF4

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  • Solid State Communications, Voi.26, pp.429-434. OO38-1098/78/0515-0429 $02.00/0 ~Pergamon Press Ltd. 1978. Printed in Great Britain

    MAGNETIC EXCITATIONS IN THE TWO DIMENSIONAL PLANAR ANTIFERROMAGNETS K2FeF 4 and Rb2FeF 4

    F. Macco, W. Lehmann, W. Breitling, A.E. Slawska- Waniewska and R. Weber

    Fachbereich Physik, Universit~t Konstanz, 775 Konstanz, FRG

    and

    U. DHrr

    Physikalisches Institut (Teilinstitut 2), Universit~t Stuttgart 7000 Stuttgart, FRG

    (Received 13 February 1978 by E. Burstein)

    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.

    I. Introduction

    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

    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.

    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.

    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.

    2. Experimental results

    2.1. K2FeF 4 and K2FeF 4: Mn 2+.

    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-

    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

    Permanent address: Institute of Physics, ON - 32 Polish Academy of Sciences 02-668 Warsaw, Poland

    429

  • 430 TWO DII~NSIONAL PLANAR ANTIFERROMAGNETS K2FeF4 and Rb2FeF 4 Voi.26, No.7

    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

    Table I

    Phonon Raman-Spectrum of K2FeF 4 and Rb2FeF 4 at 2K.

    K2FeF 4

    ~(cm -I )

    100.5+0.5

    1 3 1 . 0 + 0 . 5

    183.0+O.5

    373 .O + O. 5

    Rb2FeF 4

    co (cm-I )

    75.0+0.5

    150.0+O.5

    122.O+0.5

    356.0+0.5

    Pig

    E1g

    A1g

    A1g

    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%).

    2.2. Rb2FeF 4

    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-

    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.

    In order to obtain more information of the excitations at 48.5 cm -I and 182.O cm -I the temperature dependence

    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.

    50

    'E L)

    = 40 .9

    i n

    v

    o 30 ID D_

    li K

    K z Fe Ft.

    | = . ,

    I I I I I I

    0 20 ~0 60 Temperature ( K )

    Fig. I Peak position of the one-magnon line as function of temperature in K2FeF 4. ( ) Raman data, ( x ) FIR data.

    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

    A

    20

    ( J

    J c

    "1-

    K 2 Fe Ft.

    ! J I I I I

    0 20 40 60 Temperature (K) ~. ~.~

    Fig. 2 Temperature dependence of the halfwidth of the one-magnon line in K2FeF 4. ( ) Raman data, ( x ) FIR data.

    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

    K2FeF 4. The same holds for the higher frequency line (fig.7 and 8).

    3. Discussion

    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

  • Vol. 26, No.7 TWO DIMENSIONAL PLANAR ANTIFERROMAGNETS K2FeF 4 and Rb2FeF %

    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+-

    'E o

    C 0

    0

    180

    160

    140

    120

    ego ( o

    e o

    100 , , , i ~ L 0 20 40 60

    Temperature (K)

    Fig, 3

    K 2 Fe F~

    Two-Magnon Line

    I. e

    , iI 80

    Peak position of the two-magnon line aS function of temperature in K2FeF 4.

    100

    50

    K 2 Fe F 4 " I Two-Magnon Line

    e ee

    o

    o O ~ o e

    0 I i I I I I I I

    0 20 40 60 80 Temperature (K)

    Fig. 4 Temperature d~pendence of the halfwidth of the two-magnon line in K2FeF 4.

    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-

    E

    w-

    o I

    u

    C o_ .m

    O

    O_

    40

    35

    30

    Rb 2 Fe F 4

    I

    N

    q~ '~'~,,.. ~!~" ~'-

    I , I 'o In- o.% 0 20 40

    T e m p e r a t u r e

    { x

    (K)

    I

    6O

    Fig. 5

    431

    A

    6 L)

    ~4 XJ

    ~-2 -r

    0 0

    Fig. 6

    Rb 2 Fe . {

    . t ! , I n ,, I 20 40 6 0

    Temperature ( K )

    Temperature dependence of the halfwidth of the one-magnon line in Rb2FeF 4 as measured by FIR techniques.

    sidered in the model. The xy-model has been studied theo-

    retically by Loveluck and Lovesey 4)and by Villain 5).

    In order to explain our experimen- tal data quantitatively, we have compu- ted the dispersion curves starting from the effective spin Hamiltonian

    2 2 H = Z JS.S. + ~ DS~ + Z Dsz + ^ i>j ^z^3 i j 3

    + gpBHA(Z S x - Z S 3) + i i j

    + g~BHoA (Z. S xi + .E S;) (1) l l

    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,

    2 4

  • 432 TWO DIMENSIONAL PLANAR ANTIFERROMAGNETS K2FeF ~ and Rb2FeF 4 Voi.26, No.7

    160

    E -- 140 w-

    o =_

    P 120

    o a_

    100

    t s = e

    Rb 2 Fe Fz.

    Two-Magnon Line

    I I I I I I l l

    0 20 40 60 80 Temperature (K}

    +4,2y2Ho2+ (2JSz)22.D2S2 2 H 2 Y+t -Y o ) k 7+ = _I Z eik.6 k z

    w' = JSz + DS + yH A

    Y = g~B (2)

    Two magnon branches result which are degenerate at the zone boundary. With the approximation JSz>>DS>~ yH A the fre- quency at k = z /2a becomes

    = ~' + (3) ~max -- YHo

    Fig. 7 Peak position of the two-magnon line as function of temperature in Rb2FeF 4.

    A

    , 80 E U

    "u

    o I

    Rb 2 Fe Fz. Two-Magnon Line

    t p

    0 i , i I i i i I

    0 20 40 60 80 Temperature (K)

    Fig. 8 Temperature dependence of the halfwidth of the two-magnon line in Rb2FeF 4.

    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-

    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 ( > ~ , ) the dispersion re- lation is obtained as a function of the three parameters J, D and yH A.

    2 2 22 22 2 2 ~ = {~' -D S - (~Sz) ~+~ H o } +_

    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

    2 2 ~I = ~i(O) + 3y2H~ (4a)

    p

    2 2 y2H2 ~2 = ~2 (O) - o (4b)

    where

    w~(O) = 4 JSz DS;

    w~(O) = 2 JSz yH A-

    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

    ~2Mag = 2~max - J"

    No predictions for the value of the in plane anisotropy field are possible from our data. The values for the other para- meters are

    K2FeF 4 : J = 11.4 cm-1; D = 3.2 cm -I

    -I -I Rb2FeF4: J = 10.1 cm ; D = 2.2 cm

    We do not compare these values with those derived bv Thurlinqs et al 3).

  • Voi.26, No.7 TWO DIMENSIONAL PLANAR ANTIFERROMAGNETS K2FeF 4 and Rb2FeF 4

    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.

    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

    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

    433

    In this case equ. (4a)7has) to be re- placed by the formula

    2 2 2 2 = ~I (O) +y H o. (5)

    Compared with the magnetic field depen- dence for Hol ~" the shift is expected

    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.

    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).

    Table 2

    Magnetic field behaviour of the k = 0 one-magnon mode in K2FeF 4 and Rb2FeF 4 as measured by FIR techniques at 2K.

    H o

    (T)

    3.36

    5.6

    7.84

    HOl c

    A~ exp

    (cm -I )

    ~0.2

    0.6+0.2

    0.6+0.2

    K2FeF 4

    A~cal c

    (cm -1 )

    0 . 3

    0.84

    1.6

    H O

    A~ex p

    (cm - 1 )

    0.5+0.2

    0.8+0.2

    c

    A~calc

    (em -I )

    0.44

    0.85

    Rb2FeF 4

    ~oll c

    A~ex p A~calc

    (cm -I ) (cm -I )

    0.6+0.2

    1.0+0.2

    0.56

    1.1

    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.

    The magnetic field behaviour for ~oI| ~ is easier to discuss since the experimental situation is well defined.

    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 found to agree rather good with M(T).

    This result may be compared with the T-dependence of the AFMR in the Ising like systems CoF 2 9) and CsCoCI~ O).

    The frequency shift of the two- magnon mode as function of temperature in the two systems under investigation is very similar. In comparison to other 2D systems it is striking that the varia- tion is considerably larger. For in- Stance the renormalisation at the Ne~l temperature is 18% for both systems whereas for K2NiF 4 11) and K2MnF 4 12)a frequency shift of the two-magnon line of only 5% and 10% respectively is ob- served. Since the exchange constants

  • 434 TWO DIMENSIONAL PLANAR ANTIFERROMAGNETS K2FeF 4 and Rb2FeF 4 Voi.26, No.7

    and spins are of the same order of mag- nitude as in those magnets, the larger renormalisation may be due to a stronger temperature dependence of the (out of plane) anisotropy energy which is con- siderably larger than in the two other systemS. We have not tried to compute the shift of the lines with temperature, since the calculation becomes very complicated for a planar antiferromag- net. The available theories are appli- cable for uniaxial spin systems only.

    Finally, a few remarks may be made regarding the extra line occuring in Mn 2+ doped K2FeF 4 at 40.5 cm -I. This line according to its FIR polarisation properties also corresponds to a magne- tic dipole transition. We therefore a@sign the line as being due to a magne- tic impurity mode of the s-type. It is interesting to note that the same mode is also observed by Raman scattering. Since no case is known to us where one magnon modes could be detected in Mn 2+ compounds by Raman techniques, we con- clude that a large part of the s-mode resides on the surrounding Fe 2+ spins . Because of the same polarisa-

    tion properties of the s-mode and the k = O out of plane mode in K2FeF4:Mn2+ the s-mode might be considered as a mag- netic gap mode, lying just below the magnon band 13). However this neglects the lower energy magnon branch. Inclu- ding this into the picture the s-mode may be regarded as a resonant band mode since it ranges within the spinwave re- gion. In both cases, a considerable part of the excitation is expected to be spread out over the neighbouring Fe 2+ ions. The frequency of a gap mode or a low lying resonant band mode is appro- ximately given by the equation 14)

    S ! ~S % zSJ' (I - ~)

    where S' denotes the impurity spin and J'the impurity host exchange constant. Putting the measured frequency into the above expression the value for J' be- comes

    J' = 7.6 cm -I

    on the other hand, J' may be estimated by the geometric mean of the two host exchange constants JMnMn and JFeFe in K2MnF 4 and K2FeF 4 respectively 13)

    j, I/2 8.3 cm -I = (JMnMn JFeFe ) =

    The two values are in good agreement with each other.

    In summary, the spectroscopic mea- surements confine that K2FeF 4 and Rb2FeF 4 are both planar 2D antiferro- magnets. The LHe data including the magnetic field behaviour of the excita- tion can be described by a simple easy plane spin model. In comparison to the other 2D magnets of the K2NiF 4 family the temperature dependence of the two magnon excitations is stronger. A theo- retical treatment applicable to the two systems is not yet available at present time.

    Acknowledgement - The authors would like to thank Dr. Reuter, Stuttgart, for supplying the crystals. One of us (U.D.) is grateful to Professor Pick, Stuttgart, for his interest and support. Financial support by the Deutsche For- schungsgemeinschaft and the SFB 67 is gratefully acknowledged.

    REFERENCES

    I. WERTHEIM, G.K., GUGGENHEIM, H.J., LEVINSTEIN, H.J., BUCHANAN, D.N.E., and SHERWOOD, R.C., Phys. Rev. 173, 614 (1968).

    2. BIRGENAU, R.J., GUGGENHEIM, H.J., and SHIRANE, G., Phys. Rev. B_!1 , 2211 (1970) 3. THURLINGS , M.P.H. , VAN DER POL, A. , and DE WIJN, H.W., Sol. State Commun.

    24, 829 (1977) . 4. L--OVELUCK, J.M., and LOVESEY, S.W., J.Phys. C, Solid State Phys. --8, 3857

    (1975) . 5. VILLAIN, J., J.Physique 35, 27 (1974).

    6. NOSSELT, J., priv. Communication 7. see TUROV, E.A., Phys.Properties of Magnetically Ordered Crystals

    (Acad. Press) p.55ff (1965).

    8. BIRGENAU, R.J., DE ROSA, F., and GUGGENHEIM, H.J., Sol. State Commun.

    8, 13 (1970). 9. ~LARTEL, P., COWLEY, R.A. and STEVENSON, R.W.H., Can. J.Phys. 46_, 1355 (1968).

    10. BREITLING, W., LEHMANN, W., SRINIVASAN, T.P. and WEBER, R. , Sol. State Commun. 24, 267 (1977).

    11. FLEURY, P.---A., and GUGGENHEIM, H.J., Phys. Rev. Letters 24, 1346 (1970), Int. J. Magn. 1, 75 (1970).

    12. LEHMANN, W., and WEBER, R., J.Phys. ~ I_~0, 97 (1977), 13. for a review see

    COWLEY, R.A., and BUYERS, W.J.L., Rev.Mod.Phys. 44, 406 (1972). 14. WEBER, R., Z.Phys. 223, 299 (1969).

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