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Critical line broadening of the EPR in the two-dimensional antiferromagnet crystals Rb2MnCl4 and Rb2Mn0,8Cd0,2Cl4
Solid State Communications, Printed in Great Britain.
Vo1.48,No.8,
pp.647-651,
1983.
0038-1098/83 $3.00 + .OO Pergamon Press Ltd.
CRITICAL LINE BROADENING OF THE EPR IN THE TWO-DIMERSIONAL AETIFERROMAGNEIC CRYSTALS Rb2MnC14 AN-DRb2Mn0,8Cd0,2C14 G.A.Petrakovskii, L.S.Yemelyanova, V.V.Velichko L.V.Kirensky Institute of Physics, USSR Academy of Sciences Siberian Branch, Krasnoyarsk, 660036, U.S.S.R. (Received
13
July 1983 by E.A.Kaner)
The EPR spectrum of quasi-two-dimensionalantiferromagnets has been studied in a critical Rb2tixCdl-xCl4 (x=1,0; 0,8) temperature range. Two theoretical approaches - the scaling theory and the soliton's theory - are used to explain experimental data on temperature of the EPR linewidth. In the first interpretation critical exponents are determined. For both crystal two temperature regions with different critical exponents are found. It is shown that the soliton's theory with an anomaleous great excitement energy describes the exoerimental data satistactory.
The magnetic properties of the low-dimensional magnets have been the subject of extensive studies in the last decade. In particular, antiferromagnets with plane square structure as K2BiF4 are an example of these magnets. Because the interplane exchange interaction of magnetic ions J, are much less then the intraplane exchange interaction J(J,/J 6 lO-4) fi],we can consider these compounds as the two-dimensional (2d) ones. Vermin and Wagner [2] have shown that for 2d isotropic Heisenberg antiferromagnets there is no possibility of the existence of long-range magnetic ordering at finite temperatures. The long-range order in our compounds is caused by a small dipoledipole interactions and single-ion anisotropy p]. Our crystals Rb+C14 and Rb2Mno 8Cd0 2C14 have the tetragonal 'Dig. The unit cell has the struct&e
parameters a=5,05G, c=16,18;ifor Rb2MnC14 and a=5,080;, c=16,1& for Rb2Mno 8Cd0 2C14. The static susceptibiliiy dais for powders give the Neel points: 57K for the concentrated magnet and 26~ for the diamagnetically diluted one. The exchange coupling parameters are evaluated in accordance with a maximum of the static susceptibility to be J/k=5,9K and J/k=4,6K for concentrated and diluted crystals. The antiferromagnetic resonance data for Rb2MnC1 de4 termines energy gapY0=153Gc/S,that coincides with the data by Schroder et al 141 Knowing the exchange field HE one can evaluate the anisotropy field HA= 1,7kOe. As result we oblain HA/HE=2,1* 10'3. According to Line'scalculation [5]such small anisotropy give the Neel points is to egual 46K for Rb2kMX4. The high temperature spin dynamics of diamagnetically diluted crystals Rb2MnxCd,_xC14 is given in our l
647
648
CRITICAL LINE BROADENING OF ThE EPR
work c-j).We have found a broadening of the EPR line for T 7 TR, that is related with anomalous behavior of spin-spin relaxation. Critical behavior of the spin system depends on the magnetical dimension of the lattice. In the two-dimensional magnets a temperature behavior of the EPR linewidth is given by three contributions
Vol. 48, No. 8
l/T, angle averaged over the plane perpenticular to an external magnetic field.
IL71 l
Here d involves the exchange narrowing term with qfO,p is the spin diffussion contribution with q=O ,,Co is a static susceptibility. Usualy these two contributions are enough to explain the high temperature dependence of the EPR linewidth [6,7]. But near the phase transition the main contribution to the linewidth is the j' (TP).Huber [8] and Kawasaki [P] investigated x(T) for d=3 antiferromagnets. The time of spin-spin relaxation is follows
polar anisotropy tensor has the axial symmetry with D =D =DI, Dsa=D,, for our crystals. I?is?upposed that the dipolar anisotropy lightly changes in the vicinity of q=q,, where q, is the wave number at the end of Brillouin band. Approximating the four spin correlation function as a multiplication of the two spin ones Huber has obtained following expression for the time of relaxation.
The EPR linewidth is proportional to
This formula is correct provided that wocc rs/, where ufOis the EPR resonance frequency, is the decay rate of 'e the fluctuations at q. Usually the Fischer-Burford approximation PO] is used for the correlation function in the vicinity of T,:
is the critical index where q =q-q,, '7,
is correlation length. dimensional magnets (5) and (6) give
where n=(3-22)Y for d=2. Bxperemental data show IL nl3 PI* Recently Xikeska fl3] suggested to take into account soliton's with the excitement energy E to describe the spin correlation function. In this case (SS)-exp(E/kT). The soliton theory explains the Mossbauer broadening in onedimensional magnets ['4] and the critical behavior of the neutron cross-section in TETVICf15J. Waldner u6] used the Mikeska theory to interpretate data on the EPR linewidth in the 2d magnets. Because the EPR linewidth is proportional to the square of the spinspin correlation we have
.
Our measurements of the linewidth were carried out in the short circuited wavwguide to avoid additional broadening EPR linewidth. Gane's diod was employes as h-f.- generator with y = 35Gc/S. The sample with 232x0,8 mm3size was glued on the wall of the waveguide. An errors are 5% for measurement of the linewidth and 0,05K for temperature. For temperature lower than the liguid nitrogen one a dependence of the EPR linewidth on angle between magnetic field and tetragonal axis of the crystal changes from the form aH=A + B(3cos20-112 for room temperature to AR4 + B(l+cos2) under decreasis a temperature. The temperature behavior of the linewidth is shown in Fig.1. Continuous curve shows the value (;X,T);'. Eote that in Rb2Mno,8Cd0,2C14 a slight absorptionis observed for HLc4 even in
400
8
G
649
CRITICAL LINE BROADENING OF THE EPR
Vol. 48, No. 8
.i
600 8
8 :; _'9
-
. . .
% I
-. ..;
a
0
h 'p P
‘44
20
3
40
60
80
100
T(K)
Fig.1. Temperature dependence of line@,A> widths bHHpp for Rb2WX4 and Rbpo,8Cd0,2C14 (0,. >.
-
c I50 -
75 -
0 A
HIIC
0'
HlC
Fig.2. Dependence of critical part of EPR linewidth on 2= (T-TBJ)/TB for Rb2NnC14 (a,A > and Rb21irZno,8Cd0,2C14 (0,. 1. the magnetically ordered region. In Fig.2 a critical part of the linewidth is shown to compare scaling theory predictions. It is seen that for both crystals there are two critical regions characterizeed by different values of
the critical index n. In Rb2RnC14 I) for HIIc n=1,83 %0,07 when z 7 0,l and n=O,6T 0,05 when rcO,l. 2) for Hlc n=2,17T 0,O'j' whenr>0,135 and n=1,04 whenZc 0,135. Cl for HIIc n=l,'j'i 0,4 In Rb2En0,8Cd0,2 4
Vol. 48, No. 8
CRITICAL LINE BROADENING OF THE EPR
650
when 13c:O,2. As for Hlc there are three critical regions: 27 0,5, when 0,14~~$0,5 n= l,O, when C< 0,14 n= 0,5. Anders and Volotskii observed such a crossover in BaMnF4 and CsMnC132H20 c173* The crossover is possibility related with breaking of the condition ~,CC %-
It is suprising that the formula (8) unlike the scaling theory describes the critical broadening very well in all critical region excepting that just near TN(Fig.3). In Rb2MnC14 E/kTN=8,5 7 0,5 for HIIc and E/kl!N=9,670,5for HI c. In Rb2Mn0,8Cd0,2C14 E/kT,=4,8&0,5 for Hllc and E/kTN=5,4T0,5 for Hlc. The soliton exciting energy E in our crystal is lower than in the other two-dimensional crystals 031, but much more than Mikeska's prediction. We can not maintain for sure the critical EPR linewidth is caused namely by solitons. But our experements shown that it is necessary to improve the dynamical responce theory near the Neel point for the two-dimensional magnets. We suppose that additional data on the neutron scatering or the time of nuclear spin-lallice relaxation make the
.’
HIC
TN /T
Fig.3. Dependence of critical part of EPR linewidth on TN/T for Rb2MnC14 (A,A > and Rb2Mno &do 2C14 (o,* 1. ,
,
dynamic picture near TN more transparent. ACKNOWLEDGEMENT - We are thankful to Fedoseeva N.V. and Korolev V.K. for data on static susceptibility in Rb2MnCl, 8Cd0 ,C14 and to Kokov-1-T. ’ and Rbp, for help t: groi the single crystals.
REFERENCES 1.
2. 3*
4.
5. 6.
de Wijn, L.R.Walker, R.E.Walstedt. Phys.Rev. E, 285, (1973). N.D.Mermin, H.Vagner, Phys. Rev. Lett., a, 1133, (1966). C.A.LI.Mulder,H.L.Spipdok, P.H.Kes, A.I. van Dnyneveldt, L.I. de Jongh, Physica, m, 380, (1982). B.Schroder, V.Wagner, N.Lenker, K. Keskarwani, R.Geick. Phys.stat.801. (b), 97, 501, (1980). M.E.Llnes. J.Phys.Chem.Sol. ,3l, 101, (1970). G.B.Pctrakovskii,L.S.Yemelyanova, J.T.Kokov, G.V.Bondarenko, A.V.Baranov. Zh.Eksp.Teor.Fiz.,8J, 2176,
H.W.
(1982).
7.
8.
W.M.Walsh, Jr.R.I.Birgeneau, L.W. RuPP, ir.H.1.Gugenhei.m.Phys.Rev. z, 4645, (1979). D.L.Huber. Phys.Rev. I&, 3180,
(19724. K.Kavasaki. Progr.theor. Phys. 2, 9. 285, (1968). 10. M.E.Ficher, R.I.Burford. Phys.Rev. u, 583, (1976). 11. P.M.Richards, Sol.State Comm. 2, 253, (1973). 12. C.M.I. van Uijn, H.W. de Wijn. Phys. Rev. =4,5368, (1981). 13* H.I.Mikeska. J.Phys.C. 12, 2913, (1980).
. Vol. 48, No. 8
CRITICAL LINE BROADENING OF
14. R.C.Thice, H. de Graff, L.I. de Jongh. Phys. Rev. Lett., a, 1415, (1981).
15. I.P.Boucher, L.P.Regnault, I.RossatMignod, I.P.Renard, J.Bouillot, W.G. Stirling. Sol.State Comm., 22, 171, (1980).
THE EPR
16. F.Waldner. JMMM, a-2,
651
1203,
(1983) 17. A.G.Anders, S.V.Volotskii. Fiz. Nizk. Temp., 8, 963, (1982). l
Vo1.48,No.8,
pp.647-651,
1983.
0038-1098/83 $3.00 + .OO Pergamon Press Ltd.
CRITICAL LINE BROADENING OF THE EPR IN THE TWO-DIMERSIONAL AETIFERROMAGNEIC CRYSTALS Rb2MnC14 AN-DRb2Mn0,8Cd0,2C14 G.A.Petrakovskii, L.S.Yemelyanova, V.V.Velichko L.V.Kirensky Institute of Physics, USSR Academy of Sciences Siberian Branch, Krasnoyarsk, 660036, U.S.S.R. (Received
13
July 1983 by E.A.Kaner)
The EPR spectrum of quasi-two-dimensionalantiferromagnets has been studied in a critical Rb2tixCdl-xCl4 (x=1,0; 0,8) temperature range. Two theoretical approaches - the scaling theory and the soliton's theory - are used to explain experimental data on temperature of the EPR linewidth. In the first interpretation critical exponents are determined. For both crystal two temperature regions with different critical exponents are found. It is shown that the soliton's theory with an anomaleous great excitement energy describes the exoerimental data satistactory.
The magnetic properties of the low-dimensional magnets have been the subject of extensive studies in the last decade. In particular, antiferromagnets with plane square structure as K2BiF4 are an example of these magnets. Because the interplane exchange interaction of magnetic ions J, are much less then the intraplane exchange interaction J(J,/J 6 lO-4) fi],we can consider these compounds as the two-dimensional (2d) ones. Vermin and Wagner [2] have shown that for 2d isotropic Heisenberg antiferromagnets there is no possibility of the existence of long-range magnetic ordering at finite temperatures. The long-range order in our compounds is caused by a small dipoledipole interactions and single-ion anisotropy p]. Our crystals Rb+C14 and Rb2Mno 8Cd0 2C14 have the tetragonal 'Dig. The unit cell has the struct&e
parameters a=5,05G, c=16,18;ifor Rb2MnC14 and a=5,080;, c=16,1& for Rb2Mno 8Cd0 2C14. The static susceptibiliiy dais for powders give the Neel points: 57K for the concentrated magnet and 26~ for the diamagnetically diluted one. The exchange coupling parameters are evaluated in accordance with a maximum of the static susceptibility to be J/k=5,9K and J/k=4,6K for concentrated and diluted crystals. The antiferromagnetic resonance data for Rb2MnC1 de4 termines energy gapY0=153Gc/S,that coincides with the data by Schroder et al 141 Knowing the exchange field HE one can evaluate the anisotropy field HA= 1,7kOe. As result we oblain HA/HE=2,1* 10'3. According to Line'scalculation [5]such small anisotropy give the Neel points is to egual 46K for Rb2kMX4. The high temperature spin dynamics of diamagnetically diluted crystals Rb2MnxCd,_xC14 is given in our l
647
648
CRITICAL LINE BROADENING OF ThE EPR
work c-j).We have found a broadening of the EPR line for T 7 TR, that is related with anomalous behavior of spin-spin relaxation. Critical behavior of the spin system depends on the magnetical dimension of the lattice. In the two-dimensional magnets a temperature behavior of the EPR linewidth is given by three contributions
Vol. 48, No. 8
l/T, angle averaged over the plane perpenticular to an external magnetic field.
IL71 l
Here d involves the exchange narrowing term with qfO,p is the spin diffussion contribution with q=O ,,Co is a static susceptibility. Usualy these two contributions are enough to explain the high temperature dependence of the EPR linewidth [6,7]. But near the phase transition the main contribution to the linewidth is the j' (TP).Huber [8] and Kawasaki [P] investigated x(T) for d=3 antiferromagnets. The time of spin-spin relaxation is follows
polar anisotropy tensor has the axial symmetry with D =D =DI, Dsa=D,, for our crystals. I?is?upposed that the dipolar anisotropy lightly changes in the vicinity of q=q,, where q, is the wave number at the end of Brillouin band. Approximating the four spin correlation function as a multiplication of the two spin ones Huber has obtained following expression for the time of relaxation.
The EPR linewidth is proportional to
This formula is correct provided that wocc rs/, where ufOis the EPR resonance frequency, is the decay rate of 'e the fluctuations at q. Usually the Fischer-Burford approximation PO] is used for the correlation function in the vicinity of T,:
is the critical index where q =q-q,, '7,
is correlation length. dimensional magnets (5) and (6) give
where n=(3-22)Y for d=2. Bxperemental data show IL nl3 PI* Recently Xikeska fl3] suggested to take into account soliton's with the excitement energy E to describe the spin correlation function. In this case (SS)-exp(E/kT). The soliton theory explains the Mossbauer broadening in onedimensional magnets ['4] and the critical behavior of the neutron cross-section in TETVICf15J. Waldner u6] used the Mikeska theory to interpretate data on the EPR linewidth in the 2d magnets. Because the EPR linewidth is proportional to the square of the spinspin correlation we have
.
Our measurements of the linewidth were carried out in the short circuited wavwguide to avoid additional broadening EPR linewidth. Gane's diod was employes as h-f.- generator with y = 35Gc/S. The sample with 232x0,8 mm3size was glued on the wall of the waveguide. An errors are 5% for measurement of the linewidth and 0,05K for temperature. For temperature lower than the liguid nitrogen one a dependence of the EPR linewidth on angle between magnetic field and tetragonal axis of the crystal changes from the form aH=A + B(3cos20-112 for room temperature to AR4 + B(l+cos2) under decreasis a temperature. The temperature behavior of the linewidth is shown in Fig.1. Continuous curve shows the value (;X,T);'. Eote that in Rb2Mno,8Cd0,2C14 a slight absorptionis observed for HLc4 even in
400
8
G
649
CRITICAL LINE BROADENING OF THE EPR
Vol. 48, No. 8
.i
600 8
8 :; _'9
-
. . .
% I
-. ..;
a
0
h 'p P
‘44
20
3
40
60
80
100
T(K)
Fig.1. Temperature dependence of line@,A> widths bHHpp for Rb2WX4 and Rbpo,8Cd0,2C14 (0,. >.
-
c I50 -
75 -
0 A
HIIC
0'
HlC
Fig.2. Dependence of critical part of EPR linewidth on 2= (T-TBJ)/TB for Rb2NnC14 (a,A > and Rb21irZno,8Cd0,2C14 (0,. 1. the magnetically ordered region. In Fig.2 a critical part of the linewidth is shown to compare scaling theory predictions. It is seen that for both crystals there are two critical regions characterizeed by different values of
the critical index n. In Rb2RnC14 I) for HIIc n=1,83 %0,07 when z 7 0,l and n=O,6T 0,05 when rcO,l. 2) for Hlc n=2,17T 0,O'j' whenr>0,135 and n=1,04 whenZc 0,135. Cl for HIIc n=l,'j'i 0,4 In Rb2En0,8Cd0,2 4
Vol. 48, No. 8
CRITICAL LINE BROADENING OF THE EPR
650
when 13c:O,2. As for Hlc there are three critical regions: 27 0,5, when 0,14~~$0,5 n= l,O, when C< 0,14 n= 0,5. Anders and Volotskii observed such a crossover in BaMnF4 and CsMnC132H20 c173* The crossover is possibility related with breaking of the condition ~,CC %-
It is suprising that the formula (8) unlike the scaling theory describes the critical broadening very well in all critical region excepting that just near TN(Fig.3). In Rb2MnC14 E/kTN=8,5 7 0,5 for HIIc and E/kl!N=9,670,5for HI c. In Rb2Mn0,8Cd0,2C14 E/kT,=4,8&0,5 for Hllc and E/kTN=5,4T0,5 for Hlc. The soliton exciting energy E in our crystal is lower than in the other two-dimensional crystals 031, but much more than Mikeska's prediction. We can not maintain for sure the critical EPR linewidth is caused namely by solitons. But our experements shown that it is necessary to improve the dynamical responce theory near the Neel point for the two-dimensional magnets. We suppose that additional data on the neutron scatering or the time of nuclear spin-lallice relaxation make the
.’
HIC
TN /T
Fig.3. Dependence of critical part of EPR linewidth on TN/T for Rb2MnC14 (A,A > and Rb2Mno &do 2C14 (o,* 1. ,
,
dynamic picture near TN more transparent. ACKNOWLEDGEMENT - We are thankful to Fedoseeva N.V. and Korolev V.K. for data on static susceptibility in Rb2MnCl, 8Cd0 ,C14 and to Kokov-1-T. ’ and Rbp, for help t: groi the single crystals.
REFERENCES 1.
2. 3*
4.
5. 6.
de Wijn, L.R.Walker, R.E.Walstedt. Phys.Rev. E, 285, (1973). N.D.Mermin, H.Vagner, Phys. Rev. Lett., a, 1133, (1966). C.A.LI.Mulder,H.L.Spipdok, P.H.Kes, A.I. van Dnyneveldt, L.I. de Jongh, Physica, m, 380, (1982). B.Schroder, V.Wagner, N.Lenker, K. Keskarwani, R.Geick. Phys.stat.801. (b), 97, 501, (1980). M.E.Llnes. J.Phys.Chem.Sol. ,3l, 101, (1970). G.B.Pctrakovskii,L.S.Yemelyanova, J.T.Kokov, G.V.Bondarenko, A.V.Baranov. Zh.Eksp.Teor.Fiz.,8J, 2176,
H.W.
(1982).
7.
8.
W.M.Walsh, Jr.R.I.Birgeneau, L.W. RuPP, ir.H.1.Gugenhei.m.Phys.Rev. z, 4645, (1979). D.L.Huber. Phys.Rev. I&, 3180,
(19724. K.Kavasaki. Progr.theor. Phys. 2, 9. 285, (1968). 10. M.E.Ficher, R.I.Burford. Phys.Rev. u, 583, (1976). 11. P.M.Richards, Sol.State Comm. 2, 253, (1973). 12. C.M.I. van Uijn, H.W. de Wijn. Phys. Rev. =4,5368, (1981). 13* H.I.Mikeska. J.Phys.C. 12, 2913, (1980).
. Vol. 48, No. 8
CRITICAL LINE BROADENING OF
14. R.C.Thice, H. de Graff, L.I. de Jongh. Phys. Rev. Lett., a, 1415, (1981).
15. I.P.Boucher, L.P.Regnault, I.RossatMignod, I.P.Renard, J.Bouillot, W.G. Stirling. Sol.State Comm., 22, 171, (1980).
THE EPR
16. F.Waldner. JMMM, a-2,
651
1203,
(1983) 17. A.G.Anders, S.V.Volotskii. Fiz. Nizk. Temp., 8, 963, (1982). l