- Email: [email protected]
Two-magnon Raman scattering in the two-dimensional antiferromagnet K2FeF4
Solid State Communications, Vol. 24, pp. 829—831, 1977.
Pergamon Press
Printed in Great Britain
TWO-MAGNON RAMAN SCATTERING IN THE TWO-DIMENSIONAL ANTIFERROMAGNET K2FeF4 M.P.H. Thurlings, A. van der Pol and H.W. de Wijn Fysisch Laboratorium, Rijksuniversiteit, Utrecht, The Netherlands (Received 2 July 1977 by A.R. Miedema) Two-magnon Raman scattering in the planar quadratic antiferromagnet K2FeF4 is investigated. The temperature dependence of the energy shift is in good agreement with second-order Green-function theory, as is the linewidth at low temperature. Numerical results, including renormalization, are the Heisenberg exchange J/kB = —14.5 ±0.7 K and the anisotropy ~.(T=O)=gpBHA/4jJ~s=o,I8±o.o5,butwithJ[1+~(r=o)]/k~=r — 17.06 ±0.10 K, THE COMPOUND K2FeF4 is a new example of twodimensional (2D) quadratic layer antiferromagnetism. The magnetic properties have not been studied previously, but, as expected, appear to be similar to those of the isomorph Rb2FeF4, which has been investigated by MOssbauer [1] and neutron-scattering [2] techniques. the magnetic moments in K2FeF4 order below TN 60K with the axis of magnetization in the (x, y) plane [3]. K2FeF4 therefore presents an interesting contrast to K2MnF4 and K2NiF4, which are 2D antiferromagnets with uniaxial rather than basal-plane anisotropy. In this communication we report two-magnon Raman scattering as a function of temperature with the objective to obtain quantitative information on the magnetic interactions, the anisotropy, and the magnon damping. The specimen used was by a single crystal with 3 grown a horizontal zonedimenmelting sions 3 x 3 The x 6mm technique. crystallographic structure is tetragonal, identical to K 2MnF4 and K2NiF4, with lattice parameters a = 4.14 A and c = 12.98 A at 300 K [4]. In the Ramanscattering experiments the primary light, provided by ~ argon laser operating at 4880 A, was incident along the z axis and polarized along the x axis. The x-polarized component of the light scattered at 90°was analyzed by use of a double monochromator and detected by photoncounting techniques. The two-magnon Raman spectrum is observed to consist of a broad asymmetrical line, which with increasing temperature broadens and shifts towards lower energies. The peak position of the two-magnon line is presented in Fig. 1, and is seen to drop by 10% over a range of 40K. In calculating the peak position, we notice2 that a precise analysis of the crystal-field effects + in,K on Fe 2FeF4 cannot yet be developed because of lack of spectroscopic data. However, appears 2” ionitatgenerally a tetragonal site that the ground statebyofanthe Fe is closely described effective spin S = 2 with significant orbital contributions to the moment. One
therefore expects a fairly strong single-ion arusotropy, at least stronger than in the case of K2NiF4, of the general spin Hamiltonian form D[S~ ~S(S + 1)]. As said before, the spins order in the (x, y) plane so that D >0. The direction of the ordered spins within the plane will then be determined by the much weaker fourth-order anisotropy term. The Hamiltonian can thus be written as —
,j
~ s~ Sm —gpBH~(S~’ —S~) o, m)
(1)
where in the semi-classical approach HA = D(2S — l)/gp~ is an anisotropy field along the x axis, and the indices 1 and m run over the “up” and “down” sublattices, respectively. Anisotropy of the exchange parameter J, which will existinbecause of orbital contributions, been is ignored the Hamiltonian, since its precisehas strength unknown and its effects are largely incorporated in an effective anisotropy HA. At low temperatures (T< 4.2 K) the experimental peak position is 184.2 ±0.5 cm~”.Applying first-order Green-function theory with an Oguchi-renormalized [5] spin-wave Hamiltonian derived from equation (1) and a Ft-symmetry scatteringoperator, in a way analogous to that used for the 2D uniaxial antiferromagnets [6], we find from the T = OK position J[ 1 + ~(0)] /k~= — 17.06 ± 0.10K. This particular combination of J and ~(0) may readily be inferred from the J and ~(0) dependence of the dispersion relation near the zone boundary, and expresses a strong correlation of these quantities as derived from the low temperature data. To arrive at separate values for J and ~(0) it is however mandatory to include the temperature dependence of the peak position. In calculating the temperature dependence of the peak position (Fig. 1), we have taken the temperature ation of the anisotropy ~(T)/~(0), which has not beenvanmeasured in K 2FeF4, from the isomorph Rb2FeF4 (TN = 563 ±0.2 K [2]) by scaling such as to have vanishing
829
830
RAMAN SCATTERING IN THE ANTIFERROMAGNET K2FeF4 I
Vol. 24, No. 12 I
I
185—
I
40-
-
-
0 0
0o
30-
-
-
E
~0~0
165 0
I
I
I
I
10
20
30
40
TEMPERATURE
50
(K)
0
I
I
I
I
10
20
30
40
50
TEMPERATURE (K)
Fig. 1. Peak position of the two-magnon Ramanscatteringline vs temperature. The full curve represents the adjusted result of Green-function theory.
Fig. 2. Full width at half height of the two-magnon Raman-scattering line vs temperature. The full curve is the result of Green-function theory with the parameters deduced from Fig. 1.
anisotropy at TN. In Rb2FeF4 ,in turn, ~T) is taken to vary with the square [7] of the sublattice magnetization, which has been measured by Mössbauer techniques [1] Then, adjusting of the results of Green-function theory including renormalization leads to the solid curve in Fig. 1, corresponding to I/k8 = — 14.5 ±0.7 K and ~(0) = 0.18 ±0.05. Here, as already noticed, the errors in land ~(O) are strongly correlated, i.e. land i~(0)are restricted to those combinations that satisfy the prescription J[l + ~(O)]/k8 = — 17.06 ±0.10 K. More detailed inspection of the calculations shows that the shift of the peak position is in about equal parts due to the temperature-dependent renormalization and the drop of z~(T).It is finally noted that the effect of renormalization was to reduce J by 3.7%. As Fig. 2 shows, there is a remarkable increase of the linewidth with temperature. The full curve in Fig. 2 represents the results of the Green-function calculation to second order, with the values for land ~(T) obtained above inserted. It is quite gratifying that the linewidth at low temperatures is correctly predicted, the more so since there are no adjustable parameters involved. However, the increase of the linewidth with temperature, which Green-function theory was able to predict successfully in uniaxial 2D systems [6] ,is not satisfactorily accounted for. An explanation could be inadequate
treatment of the relevant summations over the Brilouin zone in the expression for the one-magnon damping. These are treated by use of a 2D version of a zoneboundary approximation [9], which is not likely to be effective when, because of the relatively large amsotropy, the magnon-energy distribution is rather flat. Consequently, the calculated line must be considered to be a lower limit only. In conclusion, Raman scatteringhas provided information on the magnetic interaction as well as the onemagnon damping in K2FeF4. The latter quantity is not correctly described by an approximative second-order Green-function theory. The exchange parameter is about 10% larger than the value of 13K deduced for Rb2FeF4 [2] , a factor that is commonly found between correspondi.ng Rb and K compounds. A point of interest is that K2FeF4 is a planar 2D antiferromagnet, in contrast to the more studied K2MnF4, which is uniaxial 2D. From ~(0) and! obtained here for K2FeF4 and ~(0) = 0.0039 and! = —8.40 Kin K2MnF4 [9], one may estimate the concentration x at which the spins in the mixed cornpound K2Mn1_~Fe~F4 will flop from along the c axis to the plane. At this point the Mn and Fe anisotropy energies supposedly cancel, yielding spin flop at x = 1.8 ±0.5%, in excellent accordance with the findings. of Bevaart et a!. [10].
-
Vol. 24, No. 12
RAMAN SCATTERING IN THE ANTIFERROMAGNET K2FeF4
831
REFERENCES 1.
WERTHEIM G.K., GUGGENHEIM H.J., LEVINSTEIN H.J., BUCHANAN D.N.E. & SHERWOOD R,C., Phys. Rev. 173,614 (1968).
2. 3.
BIRGENEAU R,J., GUGGENHEIM H.J. & SHIRANE G.,Phys. Rev. BI, 2211 (1970). VAN DIEPEN A.M. (private communication).
4.
DE PAPE R., Bull. Soc. Chimie France, pp. 3489—3491 (1965).
5.
OGUCHI T., Phys. Rev. 117, 117 (1960).
6.
VAN flER POL A., DE KORTE G., BOSMAN G., VAN DER WAL A,J. & DE WIJN H.W., Solid State Commun. 19, 177 (1976).
7. 8.
OGUCHI T.,Phys. Rev. 111, 1063 (1958); PINCUS P.,Phys. Rev. 113, 769 (1959). BALUCANI U. & TOGNETFI V., Phys. Rev. B8, 4247 (1973).
9.
DE WIJN H. W., WALKER L.R. & WALSTEDT R.E., Phys. Rev. 88,285(1973).
10.
BEVAART L., FRIKKEE E. & DE JONG L.J. [to be presented at the Conf. Stat. Phys. 13, Haifa (1977)1.
Pergamon Press
Printed in Great Britain
TWO-MAGNON RAMAN SCATTERING IN THE TWO-DIMENSIONAL ANTIFERROMAGNET K2FeF4 M.P.H. Thurlings, A. van der Pol and H.W. de Wijn Fysisch Laboratorium, Rijksuniversiteit, Utrecht, The Netherlands (Received 2 July 1977 by A.R. Miedema) Two-magnon Raman scattering in the planar quadratic antiferromagnet K2FeF4 is investigated. The temperature dependence of the energy shift is in good agreement with second-order Green-function theory, as is the linewidth at low temperature. Numerical results, including renormalization, are the Heisenberg exchange J/kB = —14.5 ±0.7 K and the anisotropy ~.(T=O)=gpBHA/4jJ~s=o,I8±o.o5,butwithJ[1+~(r=o)]/k~=r — 17.06 ±0.10 K, THE COMPOUND K2FeF4 is a new example of twodimensional (2D) quadratic layer antiferromagnetism. The magnetic properties have not been studied previously, but, as expected, appear to be similar to those of the isomorph Rb2FeF4, which has been investigated by MOssbauer [1] and neutron-scattering [2] techniques. the magnetic moments in K2FeF4 order below TN 60K with the axis of magnetization in the (x, y) plane [3]. K2FeF4 therefore presents an interesting contrast to K2MnF4 and K2NiF4, which are 2D antiferromagnets with uniaxial rather than basal-plane anisotropy. In this communication we report two-magnon Raman scattering as a function of temperature with the objective to obtain quantitative information on the magnetic interactions, the anisotropy, and the magnon damping. The specimen used was by a single crystal with 3 grown a horizontal zonedimenmelting sions 3 x 3 The x 6mm technique. crystallographic structure is tetragonal, identical to K 2MnF4 and K2NiF4, with lattice parameters a = 4.14 A and c = 12.98 A at 300 K [4]. In the Ramanscattering experiments the primary light, provided by ~ argon laser operating at 4880 A, was incident along the z axis and polarized along the x axis. The x-polarized component of the light scattered at 90°was analyzed by use of a double monochromator and detected by photoncounting techniques. The two-magnon Raman spectrum is observed to consist of a broad asymmetrical line, which with increasing temperature broadens and shifts towards lower energies. The peak position of the two-magnon line is presented in Fig. 1, and is seen to drop by 10% over a range of 40K. In calculating the peak position, we notice2 that a precise analysis of the crystal-field effects + in,K on Fe 2FeF4 cannot yet be developed because of lack of spectroscopic data. However, appears 2” ionitatgenerally a tetragonal site that the ground statebyofanthe Fe is closely described effective spin S = 2 with significant orbital contributions to the moment. One
therefore expects a fairly strong single-ion arusotropy, at least stronger than in the case of K2NiF4, of the general spin Hamiltonian form D[S~ ~S(S + 1)]. As said before, the spins order in the (x, y) plane so that D >0. The direction of the ordered spins within the plane will then be determined by the much weaker fourth-order anisotropy term. The Hamiltonian can thus be written as —
,j
~ s~ Sm —gpBH~(S~’ —S~) o, m)
(1)
where in the semi-classical approach HA = D(2S — l)/gp~ is an anisotropy field along the x axis, and the indices 1 and m run over the “up” and “down” sublattices, respectively. Anisotropy of the exchange parameter J, which will existinbecause of orbital contributions, been is ignored the Hamiltonian, since its precisehas strength unknown and its effects are largely incorporated in an effective anisotropy HA. At low temperatures (T< 4.2 K) the experimental peak position is 184.2 ±0.5 cm~”.Applying first-order Green-function theory with an Oguchi-renormalized [5] spin-wave Hamiltonian derived from equation (1) and a Ft-symmetry scatteringoperator, in a way analogous to that used for the 2D uniaxial antiferromagnets [6], we find from the T = OK position J[ 1 + ~(0)] /k~= — 17.06 ± 0.10K. This particular combination of J and ~(0) may readily be inferred from the J and ~(0) dependence of the dispersion relation near the zone boundary, and expresses a strong correlation of these quantities as derived from the low temperature data. To arrive at separate values for J and ~(0) it is however mandatory to include the temperature dependence of the peak position. In calculating the temperature dependence of the peak position (Fig. 1), we have taken the temperature ation of the anisotropy ~(T)/~(0), which has not beenvanmeasured in K 2FeF4, from the isomorph Rb2FeF4 (TN = 563 ±0.2 K [2]) by scaling such as to have vanishing
829
830
RAMAN SCATTERING IN THE ANTIFERROMAGNET K2FeF4 I
Vol. 24, No. 12 I
I
185—
I
40-
-
-
0 0
0o
30-
-
-
E
~0~0
165 0
I
I
I
I
10
20
30
40
TEMPERATURE
50
(K)
0
I
I
I
I
10
20
30
40
50
TEMPERATURE (K)
Fig. 1. Peak position of the two-magnon Ramanscatteringline vs temperature. The full curve represents the adjusted result of Green-function theory.
Fig. 2. Full width at half height of the two-magnon Raman-scattering line vs temperature. The full curve is the result of Green-function theory with the parameters deduced from Fig. 1.
anisotropy at TN. In Rb2FeF4 ,in turn, ~T) is taken to vary with the square [7] of the sublattice magnetization, which has been measured by Mössbauer techniques [1] Then, adjusting of the results of Green-function theory including renormalization leads to the solid curve in Fig. 1, corresponding to I/k8 = — 14.5 ±0.7 K and ~(0) = 0.18 ±0.05. Here, as already noticed, the errors in land ~(O) are strongly correlated, i.e. land i~(0)are restricted to those combinations that satisfy the prescription J[l + ~(O)]/k8 = — 17.06 ±0.10 K. More detailed inspection of the calculations shows that the shift of the peak position is in about equal parts due to the temperature-dependent renormalization and the drop of z~(T).It is finally noted that the effect of renormalization was to reduce J by 3.7%. As Fig. 2 shows, there is a remarkable increase of the linewidth with temperature. The full curve in Fig. 2 represents the results of the Green-function calculation to second order, with the values for land ~(T) obtained above inserted. It is quite gratifying that the linewidth at low temperatures is correctly predicted, the more so since there are no adjustable parameters involved. However, the increase of the linewidth with temperature, which Green-function theory was able to predict successfully in uniaxial 2D systems [6] ,is not satisfactorily accounted for. An explanation could be inadequate
treatment of the relevant summations over the Brilouin zone in the expression for the one-magnon damping. These are treated by use of a 2D version of a zoneboundary approximation [9], which is not likely to be effective when, because of the relatively large amsotropy, the magnon-energy distribution is rather flat. Consequently, the calculated line must be considered to be a lower limit only. In conclusion, Raman scatteringhas provided information on the magnetic interaction as well as the onemagnon damping in K2FeF4. The latter quantity is not correctly described by an approximative second-order Green-function theory. The exchange parameter is about 10% larger than the value of 13K deduced for Rb2FeF4 [2] , a factor that is commonly found between correspondi.ng Rb and K compounds. A point of interest is that K2FeF4 is a planar 2D antiferromagnet, in contrast to the more studied K2MnF4, which is uniaxial 2D. From ~(0) and! obtained here for K2FeF4 and ~(0) = 0.0039 and! = —8.40 Kin K2MnF4 [9], one may estimate the concentration x at which the spins in the mixed cornpound K2Mn1_~Fe~F4 will flop from along the c axis to the plane. At this point the Mn and Fe anisotropy energies supposedly cancel, yielding spin flop at x = 1.8 ±0.5%, in excellent accordance with the findings. of Bevaart et a!. [10].
-
Vol. 24, No. 12
RAMAN SCATTERING IN THE ANTIFERROMAGNET K2FeF4
831
REFERENCES 1.
WERTHEIM G.K., GUGGENHEIM H.J., LEVINSTEIN H.J., BUCHANAN D.N.E. & SHERWOOD R,C., Phys. Rev. 173,614 (1968).
2. 3.
BIRGENEAU R,J., GUGGENHEIM H.J. & SHIRANE G.,Phys. Rev. BI, 2211 (1970). VAN DIEPEN A.M. (private communication).
4.
DE PAPE R., Bull. Soc. Chimie France, pp. 3489—3491 (1965).
5.
OGUCHI T., Phys. Rev. 117, 117 (1960).
6.
VAN flER POL A., DE KORTE G., BOSMAN G., VAN DER WAL A,J. & DE WIJN H.W., Solid State Commun. 19, 177 (1976).
7. 8.
OGUCHI T.,Phys. Rev. 111, 1063 (1958); PINCUS P.,Phys. Rev. 113, 769 (1959). BALUCANI U. & TOGNETFI V., Phys. Rev. B8, 4247 (1973).
9.
DE WIJN H. W., WALKER L.R. & WALSTEDT R.E., Phys. Rev. 88,285(1973).
10.
BEVAART L., FRIKKEE E. & DE JONG L.J. [to be presented at the Conf. Stat. Phys. 13, Haifa (1977)1.