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Raman spectroscopy of Co2+ doped K2MnF4
Solid State Communications.
Vol. 20, Pp. 1049—1051,
1976.
Pergamon Press.
Printed in Great Britain.
2~ DOPED K
RAMAN SPECTROSCOPY OF C
0
2MnF4
W. Lehmann, F. Macco and R. Weber Fachbereich Physik, Universität Konstanz 7750 Konstanz, GFR. (Received 27 September 1976 by R. Loudon) 2+ has been measured. By means a mean theory impurity—host exchange integral The Raman ofpair modefield spectrum of the 2D K2MnF4: Co and anisotropy constant were derived. The results are applied to predict the magnetic exciton energies in the 2D Ising antiferro— magnet K 2CoF4.
I. Introduction
consists of six lines. Five lines with the same
The 2D antiferromagnet K2MnF4 has been recent It isby perhaps the methods simplest studiedpast1’2. extensively different in the member of a variety of compounds usually known as the K 6S ground state of 2NiF4—family. the Mn2+_ion the magnetic properties Because of the are well described by a Heisenberg model. On the contrary, the isomorphic crystals A 2CoF4 (A 3. = Whereas spin wave like spectrum of K systems alkaline the ion) behave 2D Ising 1’2 there is only sparse information 2MnF4 isabout well the magnetic excitation spectrum in the Co—con— known pounds. Neither neutron4 nor far infrared tech— niques have been successful so far. Very recent— ly, Gesland et al.5 have reported results ob— tamed by Raman scattering in the planar anti— ferromagnets A 2CoF4. They assign a weak feature at 335 cm~ in K2CoF4 tentatively as the q = o magnon. We have investigated the Raman spectrum of K2CoF4 too. The measured phonon spectrum is in agreement with that of Gesland et al. However, we did not observe the line at 335 cm’, possibly due to bad optical quality of the crystals. In order to elucidate the magnetic exci— 2+ doped tation spectrum in A2CoF4—compounds we K2MnF have applied Raman scattering to Co 4. Combining our results 6 we are with able optical to estimate data on the width magnon band in K K2CoF4 of by the Maisch 2CoF4. Our results can then be compared with the experimental data of Gesland et al.
frequencies 2’7. had already Four of been themobserved are due in to the the predicted even parity phonons 2A1g + 2Eg, and pure crystal one to the two—magnon excitation. The extra line at (256+1) cm1 is shown in fig.1. With increa— sing temperature the peak frequency shifts to lower values and the line broadens considerably. A pairmode similar (s behaviour was found 2~ for 2~the We magnon therefore 0+d) in K2MnF4: Ni of the Co2’ doped course, term assign the 256 cmHcrystal. line as Ofthe magnon the pairmode “magnon” is only used loosely since the orbital angular momentum of the magnetic ions are un— quenched by the crystal field, and the lowest Co2~ transition is not purely spin—like. The high frequency exciton lines of the Co2+_ion are expected to be much weaker in intensity than the two magnon mode and are therefore not observed. The measured line shape at T = 2 K can be compared with the theoretical shape of a pair— mode in a 2D system, using the frequency of the localized s0—mode as parameter 8,2~ As is seen from fig. I the agreement is satisfactory, the deviation remaining within the limits of those found. The localized s0—mode is predicted to occur at w50=2l5cm~ but could not be oh— served experimentally. This fact is compatible INTENSITY (ARE UNITS) 10
20
30
40
50
60
70
N~) ~
2. Experimental The K2MnF4 crystals, grown by a Bridgeman The sample technique, were of good optical2~. quality. They was mounted in an optical which contained nominally 2 mol cryostat, % Co allowed to set the temperature at 2 K by imaer— sing the sample in LHe. Higher temperatures could be achieved by admitting exchange gas into the sample region. The 4880 excitation of a 3 W—Argon laser was employed as the light source. Whereas for the investigations of K 2C0F4 a back scattering geometry had to be used due to the opacity of the crystal, the 2~. 900 arrangement could be applied for K2MnF4: Co 3. Results and Discucsion The Reman spectrum of K
~j
Ph
o ~ Z
~
Fig. I:
polarisation at from 2 K K2MnF4: (7). The CoinstrumenRaman pairmode in xx tal width is 3 cm’. The full drawn curve has been calculated as described in the text.
2~ at 2 K 2MnF4: Co 1049
2~DOPED K
1050
RAMAN SPECTROSCOPY OF Co
2~ doped pervoskites9. with the non observation of a localized mode in in CoNext we calculate the impurity—host ex— change constant ~Co—Mn within the Ising appro— ximation supposing an exchange consisting of one Co—Mn exchange constant between nearest neigh— bours within the Mn(Co)F 2—planes. The derived energy levels are found by diagonalizing the Hamiltonian (1) 2+ ion. The Racah parameter B and ofthe crystal field within the 4F and 4P manifold the free Co and spin orbit coupling parameters to be used FlA
=
HACUbic + ~LS + ~tetragonal
~exchange
10’6. parameters in the calculation are Applying available these for K2CoF4 to Co2~ in K work from optical 2’ ion the as in K tetragonal 2MnF4 implies same field felt by the Co 2CoF4. As can 11 of this be seen from the positions the condition different is fuilfilled a good approximation. The 4F ions in the totwo compounds ground state is split under the action of the first three terms in the Hamiltonian into six Kramers doublets. The remaining degeneracy is lifted by the exchange field operator: H ~exchange
z
>0~c
oMn AGO
0 the expectation value of the z—com— ponent in the ground state. The localized s0—mode corresponds to a transition within the lowest lying Kramersdoublet in the Ising picture. It should be mentioned that this represents a good approximation here since >>~°~K MnF4). The impurity host eX— fit the constant max pairmode 2 isand the ins the computation to change used 0—mode respectively, resulting in 1. ~Co—Mn= 9 cm Writing the s 0—mode energy formally as a sur’. of an exchange and anisotropy term, =
thW~x +
a value for the latter is determined as
wI
=
Vol. 20, No. 11
= 13.4 cm’. When this ~co_9o is compared with that oh— tamed by de Breed’ from susceptibility mea— surements it turns out that perfect agreement exists between the two values. Although this
good coincidence is only accidental it gives us confidence to go one step beyond and calcu— late the energies of the exchange split Kramers doublets. Using the above derived value for ~Tc0~c0 the predicted energies of the six lowest excitonare states in the mean field Ising approximation calculated inserting Rh
=
115 cm~.
Finally, employing the relation ~~o—Mn COCO
which has been shown to hold true approximately 9 a value for with the exchange even for systems unpaired constant orbital in momen— K turn 2CoF4 can be estimated giving
Z
< Sc
in the Hainiltonian, eq.1.
0 > ~Co—Co ~Co The results are
listed in table 1. The energy of the lowest lying exciton has been set at zero wavenumber. magnon energy which has deduced the Included are values for been the AFMR and from the two energy of the split ground state taking into account magnon—magnon interaction. The emer— gies are in good agreement with those obtained by a similar calculation by Folen et al.13. Table 1
sZ
~Go—Mn is the exchange constant between a Co2+ in— 2~ ~ purity spin and its z nearest neighbour Mn and
thOso
2MnF4
Energies (cm1) of the lowest electronic energy states in K signated by their Mj value. 2CoF4. The Kramers doublets are de—
EAFMA
E112
_________________
151
167
E2Hag E112 E312 _________________________________ 321 352 370 481 570
Returning to the Raman spectrum of K2CoF4 1 as the q = 0 to magnon (EAFMA) it does not seen appropriate correlate t~e line at 335 cm which is estimated to occur at a much lower agrees fairly well with the energy of the two— frequency. On the other hand, the line position magnon mode and wIth the first excited Kramers doublet (exciton). An additional very weak line reported by Gesland et al. at 453 cm~ corres— satisfactory with the lowest level of the third (E312) Kramers doublet. The discrepancy in our assignment of the lines with that of Gesland et al. is caused by the neglect of the exchange interaction by the latter.
ponds
Acknowledgements — The authors are indebted to Prof. Pick and the Stuttgarter Kristallabor for furnishing the crystals, and to Dr. R. Leonhardt, Konstanz, for confirming the struc— the grate— turalDeutsche data of Forschungsgemeinschaft the samples. Financial ishelp of fully acknowledged.
Vol. 20, No. 11
2~DOPED K
RAMAN SPECTROSCOPY OF Co
2MnF4
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. ID. 11. 12. 13.
BIRGENAU R.J., GUGGENHEIM H.J., and SHIRANE G., Phys. Rev. B8, 304 (1973). LEHMANN W., and WEBER R., J. Phys.C, to be published. DE JONGH L.J., and MIEDEMA A.R., Adv. Phys. 23, I (1974). HIRAKAWA K., STEINER M., and Hutchings M.T., Priv. Communication. GESLAND J.Y., QUILICHINI M., and SCOTT J.F., Sol. State Commun. 18, 1243 (1976). MAISCH W.G., J. Appl. Phys. 40, 1330 (1969). LEHMANN W., and WEBER R., Phys. Letters 45A, 33 (1973) THORPE M.F., Phys. Rev. 82, 2690 (1969). COWLEY R.A., and BUYERS W.J.L., Rev. Mod. Phys. 44, 406 (1972). KbNIG E., Z. Naturforschung 27b, 1 (1972). WYKOFF R.W.G., Crystal Structures, John Wiley and Sons, New York (1965) Vol.3. DE BREED J.J., GILIJANSE K., and MIEDEMA A.R., Physics 45, 205 (1969). FOLEN V.J., KREBS J.J. and RUBENSTEIN M., Sol. State Coinmun. 6, 865 (1968).
1051
Vol. 20, Pp. 1049—1051,
1976.
Pergamon Press.
Printed in Great Britain.
2~ DOPED K
RAMAN SPECTROSCOPY OF C
0
2MnF4
W. Lehmann, F. Macco and R. Weber Fachbereich Physik, Universität Konstanz 7750 Konstanz, GFR. (Received 27 September 1976 by R. Loudon) 2+ has been measured. By means a mean theory impurity—host exchange integral The Raman ofpair modefield spectrum of the 2D K2MnF4: Co and anisotropy constant were derived. The results are applied to predict the magnetic exciton energies in the 2D Ising antiferro— magnet K 2CoF4.
I. Introduction
consists of six lines. Five lines with the same
The 2D antiferromagnet K2MnF4 has been recent It isby perhaps the methods simplest studiedpast1’2. extensively different in the member of a variety of compounds usually known as the K 6S ground state of 2NiF4—family. the Mn2+_ion the magnetic properties Because of the are well described by a Heisenberg model. On the contrary, the isomorphic crystals A 2CoF4 (A 3. = Whereas spin wave like spectrum of K systems alkaline the ion) behave 2D Ising 1’2 there is only sparse information 2MnF4 isabout well the magnetic excitation spectrum in the Co—con— known pounds. Neither neutron4 nor far infrared tech— niques have been successful so far. Very recent— ly, Gesland et al.5 have reported results ob— tamed by Raman scattering in the planar anti— ferromagnets A 2CoF4. They assign a weak feature at 335 cm~ in K2CoF4 tentatively as the q = o magnon. We have investigated the Raman spectrum of K2CoF4 too. The measured phonon spectrum is in agreement with that of Gesland et al. However, we did not observe the line at 335 cm’, possibly due to bad optical quality of the crystals. In order to elucidate the magnetic exci— 2+ doped tation spectrum in A2CoF4—compounds we K2MnF have applied Raman scattering to Co 4. Combining our results 6 we are with able optical to estimate data on the width magnon band in K K2CoF4 of by the Maisch 2CoF4. Our results can then be compared with the experimental data of Gesland et al.
frequencies 2’7. had already Four of been themobserved are due in to the the predicted even parity phonons 2A1g + 2Eg, and pure crystal one to the two—magnon excitation. The extra line at (256+1) cm1 is shown in fig.1. With increa— sing temperature the peak frequency shifts to lower values and the line broadens considerably. A pairmode similar (s behaviour was found 2~ for 2~the We magnon therefore 0+d) in K2MnF4: Ni of the Co2’ doped course, term assign the 256 cmHcrystal. line as Ofthe magnon the pairmode “magnon” is only used loosely since the orbital angular momentum of the magnetic ions are un— quenched by the crystal field, and the lowest Co2~ transition is not purely spin—like. The high frequency exciton lines of the Co2+_ion are expected to be much weaker in intensity than the two magnon mode and are therefore not observed. The measured line shape at T = 2 K can be compared with the theoretical shape of a pair— mode in a 2D system, using the frequency of the localized s0—mode as parameter 8,2~ As is seen from fig. I the agreement is satisfactory, the deviation remaining within the limits of those found. The localized s0—mode is predicted to occur at w50=2l5cm~ but could not be oh— served experimentally. This fact is compatible INTENSITY (ARE UNITS) 10
20
30
40
50
60
70
N~) ~
2. Experimental The K2MnF4 crystals, grown by a Bridgeman The sample technique, were of good optical2~. quality. They was mounted in an optical which contained nominally 2 mol cryostat, % Co allowed to set the temperature at 2 K by imaer— sing the sample in LHe. Higher temperatures could be achieved by admitting exchange gas into the sample region. The 4880 excitation of a 3 W—Argon laser was employed as the light source. Whereas for the investigations of K 2C0F4 a back scattering geometry had to be used due to the opacity of the crystal, the 2~. 900 arrangement could be applied for K2MnF4: Co 3. Results and Discucsion The Reman spectrum of K
~j
Ph
o ~ Z
~
Fig. I:
polarisation at from 2 K K2MnF4: (7). The CoinstrumenRaman pairmode in xx tal width is 3 cm’. The full drawn curve has been calculated as described in the text.
2~ at 2 K 2MnF4: Co 1049
2~DOPED K
1050
RAMAN SPECTROSCOPY OF Co
2~ doped pervoskites9. with the non observation of a localized mode in in CoNext we calculate the impurity—host ex— change constant ~Co—Mn within the Ising appro— ximation supposing an exchange consisting of one Co—Mn exchange constant between nearest neigh— bours within the Mn(Co)F 2—planes. The derived energy levels are found by diagonalizing the Hamiltonian (1) 2+ ion. The Racah parameter B and ofthe crystal field within the 4F and 4P manifold the free Co and spin orbit coupling parameters to be used FlA
=
HACUbic + ~LS + ~tetragonal
~exchange
10’6. parameters in the calculation are Applying available these for K2CoF4 to Co2~ in K work from optical 2’ ion the as in K tetragonal 2MnF4 implies same field felt by the Co 2CoF4. As can 11 of this be seen from the positions the condition different is fuilfilled a good approximation. The 4F ions in the totwo compounds ground state is split under the action of the first three terms in the Hamiltonian into six Kramers doublets. The remaining degeneracy is lifted by the exchange field operator: H ~exchange
z
>0~c
oMn AGO
0 the expectation value of the z—com— ponent in the ground state. The localized s0—mode corresponds to a transition within the lowest lying Kramersdoublet in the Ising picture. It should be mentioned that this represents a good approximation here since >>~°~K MnF4). The impurity host eX— fit the constant max pairmode 2 isand the ins the computation to change used 0—mode respectively, resulting in 1. ~Co—Mn= 9 cm Writing the s 0—mode energy formally as a sur’. of an exchange and anisotropy term, =
thW~x +
a value for the latter is determined as
wI
=
Vol. 20, No. 11
= 13.4 cm’. When this ~co_9o is compared with that oh— tamed by de Breed’ from susceptibility mea— surements it turns out that perfect agreement exists between the two values. Although this
good coincidence is only accidental it gives us confidence to go one step beyond and calcu— late the energies of the exchange split Kramers doublets. Using the above derived value for ~Tc0~c0 the predicted energies of the six lowest excitonare states in the mean field Ising approximation calculated inserting Rh
=
115 cm~.
Finally, employing the relation ~~o—Mn COCO
which has been shown to hold true approximately 9 a value for with the exchange even for systems unpaired constant orbital in momen— K turn 2CoF4 can be estimated giving
Z
< Sc
in the Hainiltonian, eq.1.
0 > ~Co—Co ~Co The results are
listed in table 1. The energy of the lowest lying exciton has been set at zero wavenumber. magnon energy which has deduced the Included are values for been the AFMR and from the two energy of the split ground state taking into account magnon—magnon interaction. The emer— gies are in good agreement with those obtained by a similar calculation by Folen et al.13. Table 1
sZ
~Go—Mn is the exchange constant between a Co2+ in— 2~ ~ purity spin and its z nearest neighbour Mn and
thOso
2MnF4
Energies (cm1) of the lowest electronic energy states in K signated by their Mj value. 2CoF4. The Kramers doublets are de—
EAFMA
E112
_________________
151
167
E2Hag E112 E312 _________________________________ 321 352 370 481 570
Returning to the Raman spectrum of K2CoF4 1 as the q = 0 to magnon (EAFMA) it does not seen appropriate correlate t~e line at 335 cm which is estimated to occur at a much lower agrees fairly well with the energy of the two— frequency. On the other hand, the line position magnon mode and wIth the first excited Kramers doublet (exciton). An additional very weak line reported by Gesland et al. at 453 cm~ corres— satisfactory with the lowest level of the third (E312) Kramers doublet. The discrepancy in our assignment of the lines with that of Gesland et al. is caused by the neglect of the exchange interaction by the latter.
ponds
Acknowledgements — The authors are indebted to Prof. Pick and the Stuttgarter Kristallabor for furnishing the crystals, and to Dr. R. Leonhardt, Konstanz, for confirming the struc— the grate— turalDeutsche data of Forschungsgemeinschaft the samples. Financial ishelp of fully acknowledged.
Vol. 20, No. 11
2~DOPED K
RAMAN SPECTROSCOPY OF Co
2MnF4
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. ID. 11. 12. 13.
BIRGENAU R.J., GUGGENHEIM H.J., and SHIRANE G., Phys. Rev. B8, 304 (1973). LEHMANN W., and WEBER R., J. Phys.C, to be published. DE JONGH L.J., and MIEDEMA A.R., Adv. Phys. 23, I (1974). HIRAKAWA K., STEINER M., and Hutchings M.T., Priv. Communication. GESLAND J.Y., QUILICHINI M., and SCOTT J.F., Sol. State Commun. 18, 1243 (1976). MAISCH W.G., J. Appl. Phys. 40, 1330 (1969). LEHMANN W., and WEBER R., Phys. Letters 45A, 33 (1973) THORPE M.F., Phys. Rev. 82, 2690 (1969). COWLEY R.A., and BUYERS W.J.L., Rev. Mod. Phys. 44, 406 (1972). KbNIG E., Z. Naturforschung 27b, 1 (1972). WYKOFF R.W.G., Crystal Structures, John Wiley and Sons, New York (1965) Vol.3. DE BREED J.J., GILIJANSE K., and MIEDEMA A.R., Physics 45, 205 (1969). FOLEN V.J., KREBS J.J. and RUBENSTEIN M., Sol. State Coinmun. 6, 865 (1968).
1051