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Critical fluctuation of staggered magnetization in antiferromagnet by AC susceptibility measurement
CRITICAL F L U C T U A T I O N O F STAGGERED M A G N E T I Z A T I O N IN A N T I F E R R O M A G N E T BY AC SUSCEPTIBILITY M E A S U R E M E N T M. MATSUURA, M. I S H I Z U K A and H. N I S H I K A W A Faculty of Engineering Science, Osaka University, Toyonaka 560, Japan
The divergence of staggered susceptibility in antiferromagnet is investigated on some crystallographic two sublattice quasi two dimensional systems by usual susceptibility measurement and analysis of the result. The frequency dependence of AC susceptibility is also examined.
In some magnetic compounds, the g tensors of magnetic ions are different from site to site reflecting the symmetry of local crystalline environments. In such a system, the staggered magnetizations as well as the uniform one are induced by an external magnetic field [1]. In the system with two inequivalent sites, which we name as crystallographic two sublattice (C2) system, the initial magnetic susceptibility is generally expressed by a linear combination of the uniform and the staggered susceptibilities of the corresponding single lattice (Ca) system as [1, 2]: X (2) = A'X~O-~. + B - X ~ I ) . B .
(1)
Based on the fact, the fluctuation of staggered magnetization can be investigated directly by usual susceptibility measurement. In the following, an application to quasi-two-dimensional antiferromagnets near TN is discussed. The magnetic characteristics of the investigated systems, which are known to be C 2 system, are summarized in table 1. Cu(HCOO)2.2H20.2CO(NH2)2: fig. la shows the temperature dependence of X (2) of this salt (hereafter called C u F U H ) [3]. The divergent nature comes from X~ °, which is plotted in logarithmic scale in fig. lb after a reasonable subtraction of X~ n term. The divergence with critical index ~, 1.7 at temperature e(= ( T - TN)/TN) > 0.1 may indicate that the phase transition is brought by a weak but non-zero anisotropy of Ising type. The remarkable rounding at c < 0.1, is firstly due to interplaner antiferromagnetic interaction, though it is very weak, and secondly due to the above anisotropy. The present X~ I) is indeed shown to be that along the hard direction [4]. The dependence of X (2) on measuring frequency was examined to study the dynamical feature but no measurable difference could be detected up to 200 MHz, which may be partly connected to the remarkable rounding of X~") n e a r T N.
XS (arbi unit) ,
Cb)
15~ (XI
o-
."
'..... •
hO
•
= h75
..
IG-
\
×
,~o .
-'~ ad
5F ,
S (= (T-];)/TN}
POWDER °° ~o. 0.1 o°O ,;~Q. oo ,i'~,~~°~° L2 .~,
0
IO
20
\.:.
~ ~ , ],~ .... ol
50
40
rx,
']-iK )J
Fig. 1. Temperature dependence of magnetic susceptibility of CuFUH. (a) X M corresponds to X (2) in eq. (1), (b) X~ to As(0 in eq. (1), respectively.
Co(HCOO)2.2H20: In this salt (CoF2H), the interplaner interaction is ferromagnetic and X~(0 is known to be that along the easy direction. The temperature dependence of X(2) near TN is shown in fig. 2a, which indicate that the divergence is suppressed by demagnetization effect. Correcting this effect and subtracting X (1) term properly, X~(n) is plotted in fig. 2b. The divergence is now fitted very well to the exponential law with critical index y - - 1 . 5 , which is different from 1.75 for Ising model. This difference is not explained at present. The following should be noteworthy. Each Co 2+ ion has an Ising type local g tensor but the principal axis is inclined to each other. As a result, the exchange interaction is no more of Ising type in the present case [5]. Mn(HCOO)2- 2H20: In this salt (MnF2H), the interplaner interaction is ferromagnetic, too. The demagnetization effect is, however, negligibly small in this case. Subtracting the X (1) term, X,(I) is shown in fig. 3. The divergent characteristic is now very sensitive to the external static field H, different from the above two salts. In the case H ~ 0, the divergence is characterized by - / ~ 2.0. While
Journal of Magnetism and Magnetic Materials 15-18 (1980) 411-412 ©North Holland
411
M. Matsuura et al./ Staggered susceptibility in antiferromagnet
412
TABLE 1 The magnetic characteristics of the salts investigated here CuFUH k TN/ J J'/J Main symmetry
CoF2H
MnF2H
0.46
1.0
10.5
+ 10-(4-5)
- 5 x 10-3
- 1 0 -3
Heisenberg
non-Ising
Heisenberg
\\
r:z.o
Mn,.C00/22.20
o .
"°.--\\
• Ho:3moo ° Ho: t S O m O e
.~.~o L
J
L
i
i
-10-8-6-4-2 •
i
i
i
i
,
L
0
2
4
6
8
I0
=3mOe, (F C)
(T- T.)/T. X 103
°Oo%
b
Ids
1(54
Id 3
10-2
101
Fig. 3. Temperature dependence of magnetic susceptibility of MnF2H. (FC) means field cooling at H 0 = 150 mOe (see text). AX' corresponds to X~1) in eq. (1).
. . . . . . . .
Id'4
i
163
,
,
,
,L,,,I
,
IOa ( T - T,~)/TN
Fig. 2. Temperature dependence of magnetic susceptibility of CoF2H. (a) X corresponds to X (2) in eq. (1), (b) X, to X~O) in eq. (1), respectively. in the field of the order of earth field, " / ~ 1.75 as c a n be seen in fig. 3. T h e similar result to the latter is o b t a i n e d when the s p e c i m e n is cooled d o w n across T N in the external field a n d then X (2) is measured, heating again across T N w i t h o u t external field. It m a y be n o t e w o r t h y that the external field affects on the critical p h e n o m e n a like as Ising type anisotropy. The f r e q u e n c y d e p e n d e n c e of X (2) was also e x a m i n e d in this salt. A r e m a r k a b l e dispersion
was observed in very low frequency region. N e a r T N, the dispersion frequency goes d o w n to 3 Hz or less in the case H ~ 0. T h e origin of this dispersion is n o t clear at present, a l t h o u g h it should be concerned with some feature of critical fluctuation in this salt.
References [I] M. Matsuura and Y. Ajiro, J. Phys. Soc. Japan 41 (1976) 44. [2] M. Matsuura, J. Phys. Soc. Japan 43 (1977) 1805. [3] Y. Yamamoto, M. Matsuura and T. Haseda, J. Phys. Soc. Japan 40 (1976) 1300. [4] M. Matsuura et al., to be published. [5] H. Yamakawa, Thesis, Faculty of Engineering Science, Osaka University, Japan (1977).
The divergence of staggered susceptibility in antiferromagnet is investigated on some crystallographic two sublattice quasi two dimensional systems by usual susceptibility measurement and analysis of the result. The frequency dependence of AC susceptibility is also examined.
In some magnetic compounds, the g tensors of magnetic ions are different from site to site reflecting the symmetry of local crystalline environments. In such a system, the staggered magnetizations as well as the uniform one are induced by an external magnetic field [1]. In the system with two inequivalent sites, which we name as crystallographic two sublattice (C2) system, the initial magnetic susceptibility is generally expressed by a linear combination of the uniform and the staggered susceptibilities of the corresponding single lattice (Ca) system as [1, 2]: X (2) = A'X~O-~. + B - X ~ I ) . B .
(1)
Based on the fact, the fluctuation of staggered magnetization can be investigated directly by usual susceptibility measurement. In the following, an application to quasi-two-dimensional antiferromagnets near TN is discussed. The magnetic characteristics of the investigated systems, which are known to be C 2 system, are summarized in table 1. Cu(HCOO)2.2H20.2CO(NH2)2: fig. la shows the temperature dependence of X (2) of this salt (hereafter called C u F U H ) [3]. The divergent nature comes from X~ °, which is plotted in logarithmic scale in fig. lb after a reasonable subtraction of X~ n term. The divergence with critical index ~, 1.7 at temperature e(= ( T - TN)/TN) > 0.1 may indicate that the phase transition is brought by a weak but non-zero anisotropy of Ising type. The remarkable rounding at c < 0.1, is firstly due to interplaner antiferromagnetic interaction, though it is very weak, and secondly due to the above anisotropy. The present X~ I) is indeed shown to be that along the hard direction [4]. The dependence of X (2) on measuring frequency was examined to study the dynamical feature but no measurable difference could be detected up to 200 MHz, which may be partly connected to the remarkable rounding of X~") n e a r T N.
XS (arbi unit) ,
Cb)
15~ (XI
o-
."
'..... •
hO
•
= h75
..
IG-
\
×
,~o .
-'~ ad
5F ,
S (= (T-];)/TN}
POWDER °° ~o. 0.1 o°O ,;~Q. oo ,i'~,~~°~° L2 .~,
0
IO
20
\.:.
~ ~ , ],~ .... ol
50
40
rx,
']-iK )J
Fig. 1. Temperature dependence of magnetic susceptibility of CuFUH. (a) X M corresponds to X (2) in eq. (1), (b) X~ to As(0 in eq. (1), respectively.
Co(HCOO)2.2H20: In this salt (CoF2H), the interplaner interaction is ferromagnetic and X~(0 is known to be that along the easy direction. The temperature dependence of X(2) near TN is shown in fig. 2a, which indicate that the divergence is suppressed by demagnetization effect. Correcting this effect and subtracting X (1) term properly, X~(n) is plotted in fig. 2b. The divergence is now fitted very well to the exponential law with critical index y - - 1 . 5 , which is different from 1.75 for Ising model. This difference is not explained at present. The following should be noteworthy. Each Co 2+ ion has an Ising type local g tensor but the principal axis is inclined to each other. As a result, the exchange interaction is no more of Ising type in the present case [5]. Mn(HCOO)2- 2H20: In this salt (MnF2H), the interplaner interaction is ferromagnetic, too. The demagnetization effect is, however, negligibly small in this case. Subtracting the X (1) term, X,(I) is shown in fig. 3. The divergent characteristic is now very sensitive to the external static field H, different from the above two salts. In the case H ~ 0, the divergence is characterized by - / ~ 2.0. While
Journal of Magnetism and Magnetic Materials 15-18 (1980) 411-412 ©North Holland
411
M. Matsuura et al./ Staggered susceptibility in antiferromagnet
412
TABLE 1 The magnetic characteristics of the salts investigated here CuFUH k TN/ J J'/J Main symmetry
CoF2H
MnF2H
0.46
1.0
10.5
+ 10-(4-5)
- 5 x 10-3
- 1 0 -3
Heisenberg
non-Ising
Heisenberg
\\
r:z.o
Mn,.C00/22.20
o .
"°.--\\
• Ho:3moo ° Ho: t S O m O e
.~.~o L
J
L
i
i
-10-8-6-4-2 •
i
i
i
i
,
L
0
2
4
6
8
I0
=3mOe, (F C)
(T- T.)/T. X 103
°Oo%
b
Ids
1(54
Id 3
10-2
101
Fig. 3. Temperature dependence of magnetic susceptibility of MnF2H. (FC) means field cooling at H 0 = 150 mOe (see text). AX' corresponds to X~1) in eq. (1).
. . . . . . . .
Id'4
i
163
,
,
,
,L,,,I
,
IOa ( T - T,~)/TN
Fig. 2. Temperature dependence of magnetic susceptibility of CoF2H. (a) X corresponds to X (2) in eq. (1), (b) X, to X~O) in eq. (1), respectively. in the field of the order of earth field, " / ~ 1.75 as c a n be seen in fig. 3. T h e similar result to the latter is o b t a i n e d when the s p e c i m e n is cooled d o w n across T N in the external field a n d then X (2) is measured, heating again across T N w i t h o u t external field. It m a y be n o t e w o r t h y that the external field affects on the critical p h e n o m e n a like as Ising type anisotropy. The f r e q u e n c y d e p e n d e n c e of X (2) was also e x a m i n e d in this salt. A r e m a r k a b l e dispersion
was observed in very low frequency region. N e a r T N, the dispersion frequency goes d o w n to 3 Hz or less in the case H ~ 0. T h e origin of this dispersion is n o t clear at present, a l t h o u g h it should be concerned with some feature of critical fluctuation in this salt.
References [I] M. Matsuura and Y. Ajiro, J. Phys. Soc. Japan 41 (1976) 44. [2] M. Matsuura, J. Phys. Soc. Japan 43 (1977) 1805. [3] Y. Yamamoto, M. Matsuura and T. Haseda, J. Phys. Soc. Japan 40 (1976) 1300. [4] M. Matsuura et al., to be published. [5] H. Yamakawa, Thesis, Faculty of Engineering Science, Osaka University, Japan (1977).