- Email: [email protected]
Internal field in orthoferrites and the one third power law
Solid State Communications Vol. 4, pp. 141-145, 1966. Pergamon Press Ltd. Printed in Great BrItatn~
D~TERNALFIELD IN ORTHOFERRITES AND TEE ONE THIRD POWER L&W* M. EibschUtz, S. ShtrlkmanandD. Trevea~ Department of Electronics, The Weizxnann Institute of Science, Rehovoth, Israel (ReceIved 7 February 1966 by E. Burstein) The temperature dependence of the internal field in orthoferrites at the iron nucleus was measured using the Mössbauer effect. It was found that, in the range 0.6 TN < T < 0.99 TN, the internal field varies approximately as the 1/3 power of (1-T/TN). THE RELATIVE SUBLATTICE magnetization as a function of temperature, T, ne~.rthe point 5andNéel experihas been~opnd theoretically~ mentally ~ to both follow the equation aCT)
TB =
_____
/
D(1
-
f—)
(1)
can operate at any temperature between liquid air temperature and 8700K. Thesample cryciurnace keeps the temperature over the uniform within one degree. Typical Mössbsuer spectra are shown in Fig. 1. In Fig. 2, are plotted, on a double logarithmic scale, the internal field Hfi(T)/H~(O)versus (1-T/TN). These plots are sbaighflines
N
where a 5(T) is the sublattice magnetization at a given temperature and T~is the Néel temperature. Different values of B have been reported in the literature. A summary of the present situation is given In Table 1.
in the range 0.60 < T/TN <0.99. Here the upper bound is determine~bythe resolution of the spectra in the experiment (see Fig. 1).
We report here measurements of B In the orthoferrites. These materials with chemical formu1a RFeO3, where R is Yttrium or a rare earth Ion, are to a good approximation, Heisenberg. antiferromagnets with the iron ions forming essentially a simple-cubic structure. 10, 11 The magnetism of the rare earth ions may be neglected in the present study. To measure the temperature dependence of the sublattice magnetization we assumed, as customary, that the sublattice m~.gpetizationiS proportional to the internal field°°and have used the Mössbauer effect to determine the latter. 12-14 The Mössbauer spectra were taken 5 with The sample an automatic was inrecording a vacuumspectrometer.’ cryofurnace~6that
The exponent B and the coefficient I) obtained from the logarithmic plots are given in Table 2. The error in B is * 0.005 and in D is * 0.02. We find that on ~e average B z 0.348, i.e. quite close to 1/3.1k The error in the determination of B comes from the experimental uncertainties in the measurements of the ternperature, * 1°K,and internal field, e 2KOe. We have also tried to determine B following the method of Heller and Benedek, 7 namely by plotting AT
(Tw_T)
1 H~(T)~1/$ H ~ (2) N N n’ ‘) versus T/TN for various B. The curves for LaFeO3 are shown in Fig. 3. Equation (1) holds =
______
-
~ L.
*Thè research reported in this document has been sponsored in part by the AIr Force Materials Laboratory, Research and Technology Division, AFSC through the European Office of Aerospace Research, U. S. Air Force. §Temporary address: Ampex Corporation, California, U.S. A. 141
142
INTERNAL FIELD IN ORTHOFEERITES
Vol. 4, No. 3
TABLE 1
Theoretical and Experimental Values of Theory
B
Accuracy of 8
Range T/TC
Molecular Field
1/2
Exact theory
T ~Tc
Landau’s theory of second order phase tranáistor
1/2
Exact theory
T
-.
1/8
Exact theory
T
—
e 0.007
T~
B
and D
D
Accuracy of D
1.441
References
1, 5
T~
1
T~
2
Two dimensional Ising models
Three dimensional Islng model 5/16 Green Function R.P.A.
3,4
1/3
1.11
5
Green Function Callen Decoupling 1/3
1.09
5
1.124
5
Two spin cluster theory
1/3
0.73
1/2
T~Tc
Two spin cluster theory
5
Experiment
EnS
0.333 0.33
*0.003 *0.015
9?
Fe57 In Ni
0.33
0.03
84
8
Fe57 In Ni
0. 51.
0.04
996
8
MnF2
Fe57 In Fe metal 0.33
.
0.348
1.145
6 ±0.02
*0.005
.80
1.32
0.02
99
1.14
0.02
*0.005
.60
Fe57 In RFeO 3
1.2
7
9 In the
present work
INTERNAL FIELD IN CRTHOFER.RITES
Vol. 4, No. 3
.,.~
143
~,.
T=709°K
T~7O4°K
~
.~
~.!
T:702.5°K
~
(
_________
IIIIII~::::;;:;;1.
_~—~---~~
---------~
~
T=701°K
~
°‘
T~697°K
3,IO~
3~IO~~
3Z10’
3.iO~
3iiQ~
T=692°K FIG.2
Internal field of Fe57 in RFeO3 as
~ -6
-4
-2
0
2
4
mm / sec FIG. 1 Mössbauer spectra In the vicinity of the Ned points 57 In Chromium, of PrFeO3. 10 The source sec counting is Co time and 16000 counts per channel. About 60 channels per mm/sec. The Iron in the sample was enriched in Fe57, thus some saturatIon resulted.
6
a function of 1
-
t, where t
-
T/TN.
~io•’
INTERNAL FIELD IN ORTHOFERBITES
144
Vol. 4, No. 3
TABLE 2
Values of B and D in Orthoferrites Range T/TN R
max.
TN[OKJ
B
D
mm.
La Pr Nd
0.347 0.345 0.353
1.11 1.12 1.14
0.60 0.55 0.70
0.993 0.996 0.993
740
Sm Eu
0.342 0.350
1.13 1.17
0.60
0.990
674
0.65
0.985
682
Gd Tb
0.354 0.349
1.15 1.12
0.70 0.55
0.980 0.990
657 647
Dy
0.348
1.14
0.65
0.990
645
Y Ho Er Tm
0.354 0.342 0.357 0.349
1.16 1.15 1.15 1.15
0.70
0.975 0.980 0.980
640
Yb Lu
0.339 0.342
1.13 1.17
0.60
0.60 0.70 0.65 0.65
707 687
0.990
639 636 632
0.993 0.997
627 623
50 40 30 20
to. Q
.:
0
FIG.3
I~Q33 o -5
. .
-
.
.
‘
Deviations from Equation (1) for three choices of 8. The most approprIate choice is the one for which the plot AT/TN vs. T/TN
has no curvature as T -20
P.0.30
•
-30
-400.6
0.7
0.8 t. T/TN
09
1.0
-.
TN.
Vol. 4, No. 3
INTERNAL FIELD IN ~THOFERRITES
in the region where the curve from Fig. 3 has no curvature. Figure 3 shows that the data are in good agreement with the equation (1) for
145
iron metal from Preston etal. 9, we also find that the one third power law holds in the range 0. 80
LaFeO3 in the range of temperature 0.60 T~ T
<
0.993 TN for B ~ 0.33
It is Interesting to note that If we take the internal field as a function of temperature for
We thus conclude that the dependence of the internal field in orthoferrites in the range 0.60 TN < T < 0.99 TN follows relation (1) with B close to 1/3.
References 1.
LANDAU L. D. and LIFSRITZ E. M., Statistical Physics, Pergamon Press, New York (1958).
2.
YANGC.N., Phys. Rev., 85, 808 (1952).
3.
BAKER G.A., Jr., Phys. Rev. 124, 768 (1961).
4.
ESSAM J.W. and FISHER M. F., J. Chem. Phys. 38, 802 (1963).
5.
CALLEN E. and CALLEN H. B., J. Appi. Phys. 36, 1140 (1965).
6.
HELLER P. and BENEDEK G., Phys. Rev. Letters 8, 428 (1962).
7.
HELLER P. and BENEDEK G., Phys. Rev. Letters 14, 71 (1965).
8.
HONWARD D. G., DUNLAP B. D. and DASH J. G., Phys. Rev. Letters 15, 628 (1965).
9.
PRESTON R. S., HANNA S.S. and HEBERLE J., Phys. Rev. 128, 2207 (1962).
10.
GELLER S., J. Chem. Phys. 24, 1236 (1956).
11.
COPPENS P. and EIBSCHUTZ M., Acta Cryst. 19, 524 (1965).
12.
EIBSCRUTZ M., GORODETSKY. G., SHTRIKMAN S. and TREVES D., J. Appi. Pl~ys. 35, 1071
13.
(1964). EIBSCHIJTZ M., Ph.D. Thesis, In Hebrew (1965).
14.
EIBSCHt~TZM., SHTRIKMAN S. and TREVES D., to be published.
15.
LIPKIN J., SCHECHTER B., SHTRIKMAN S. and TREVES D., Rev. Sd. Insir. 35, 1336 (1964).
16.
SHARON B. and TREVES D., to be published.
17.
GORODETSKY G., SHTRIKMAN S. and TREVES D., Solid Slate Communications91s 4, 147 it was (1966). found The the that same canting results angle holdisalso independent for the ferromagnetic of T for T/TNmoment < 0.99. for TREVES 0.60 < T/TN D., J.< Appl. 0. 9 Phys. Suppi.
=
36, 1033 (1965). La dépendance du champ interne de In temperature dane le noyau du fer dana les orthoferrites est mesuré par l’effet M~ssbauer. Nous avons trouvê que le champ interne vane avec (1 - T/TN) Ia puissance 1/3 dane Ia region de temperature 0.8 TN< T< 0.99 TN. ~.
D~TERNALFIELD IN ORTHOFERRITES AND TEE ONE THIRD POWER L&W* M. EibschUtz, S. ShtrlkmanandD. Trevea~ Department of Electronics, The Weizxnann Institute of Science, Rehovoth, Israel (ReceIved 7 February 1966 by E. Burstein) The temperature dependence of the internal field in orthoferrites at the iron nucleus was measured using the Mössbauer effect. It was found that, in the range 0.6 TN < T < 0.99 TN, the internal field varies approximately as the 1/3 power of (1-T/TN). THE RELATIVE SUBLATTICE magnetization as a function of temperature, T, ne~.rthe point 5andNéel experihas been~opnd theoretically~ mentally ~ to both follow the equation aCT)
TB =
_____
/
D(1
-
f—)
(1)
can operate at any temperature between liquid air temperature and 8700K. Thesample cryciurnace keeps the temperature over the uniform within one degree. Typical Mössbsuer spectra are shown in Fig. 1. In Fig. 2, are plotted, on a double logarithmic scale, the internal field Hfi(T)/H~(O)versus (1-T/TN). These plots are sbaighflines
N
where a 5(T) is the sublattice magnetization at a given temperature and T~is the Néel temperature. Different values of B have been reported in the literature. A summary of the present situation is given In Table 1.
in the range 0.60 < T/TN <0.99. Here the upper bound is determine~bythe resolution of the spectra in the experiment (see Fig. 1).
We report here measurements of B In the orthoferrites. These materials with chemical formu1a RFeO3, where R is Yttrium or a rare earth Ion, are to a good approximation, Heisenberg. antiferromagnets with the iron ions forming essentially a simple-cubic structure. 10, 11 The magnetism of the rare earth ions may be neglected in the present study. To measure the temperature dependence of the sublattice magnetization we assumed, as customary, that the sublattice m~.gpetizationiS proportional to the internal field°°and have used the Mössbauer effect to determine the latter. 12-14 The Mössbauer spectra were taken 5 with The sample an automatic was inrecording a vacuumspectrometer.’ cryofurnace~6that
The exponent B and the coefficient I) obtained from the logarithmic plots are given in Table 2. The error in B is * 0.005 and in D is * 0.02. We find that on ~e average B z 0.348, i.e. quite close to 1/3.1k The error in the determination of B comes from the experimental uncertainties in the measurements of the ternperature, * 1°K,and internal field, e 2KOe. We have also tried to determine B following the method of Heller and Benedek, 7 namely by plotting AT
(Tw_T)
1 H~(T)~1/$ H ~ (2) N N n’ ‘) versus T/TN for various B. The curves for LaFeO3 are shown in Fig. 3. Equation (1) holds =
______
-
~ L.
*Thè research reported in this document has been sponsored in part by the AIr Force Materials Laboratory, Research and Technology Division, AFSC through the European Office of Aerospace Research, U. S. Air Force. §Temporary address: Ampex Corporation, California, U.S. A. 141
142
INTERNAL FIELD IN ORTHOFEERITES
Vol. 4, No. 3
TABLE 1
Theoretical and Experimental Values of Theory
B
Accuracy of 8
Range T/TC
Molecular Field
1/2
Exact theory
T ~Tc
Landau’s theory of second order phase tranáistor
1/2
Exact theory
T
-.
1/8
Exact theory
T
—
e 0.007
T~
B
and D
D
Accuracy of D
1.441
References
1, 5
T~
1
T~
2
Two dimensional Ising models
Three dimensional Islng model 5/16 Green Function R.P.A.
3,4
1/3
1.11
5
Green Function Callen Decoupling 1/3
1.09
5
1.124
5
Two spin cluster theory
1/3
0.73
1/2
T~Tc
Two spin cluster theory
5
Experiment
EnS
0.333 0.33
*0.003 *0.015
9?
Fe57 In Ni
0.33
0.03
84
8
Fe57 In Ni
0. 51.
0.04
996
8
MnF2
Fe57 In Fe metal 0.33
.
0.348
1.145
6 ±0.02
*0.005
.80
1.32
0.02
99
1.14
0.02
*0.005
.60
Fe57 In RFeO 3
1.2
7
9 In the
present work
INTERNAL FIELD IN CRTHOFER.RITES
Vol. 4, No. 3
.,.~
143
~,.
T=709°K
T~7O4°K
~
.~
~.!
T:702.5°K
~
(
_________
IIIIII~::::;;:;;1.
_~—~---~~
---------~
~
T=701°K
~
°‘
T~697°K
3,IO~
3~IO~~
3Z10’
3.iO~
3iiQ~
T=692°K FIG.2
Internal field of Fe57 in RFeO3 as
~ -6
-4
-2
0
2
4
mm / sec FIG. 1 Mössbauer spectra In the vicinity of the Ned points 57 In Chromium, of PrFeO3. 10 The source sec counting is Co time and 16000 counts per channel. About 60 channels per mm/sec. The Iron in the sample was enriched in Fe57, thus some saturatIon resulted.
6
a function of 1
-
t, where t
-
T/TN.
~io•’
INTERNAL FIELD IN ORTHOFERBITES
144
Vol. 4, No. 3
TABLE 2
Values of B and D in Orthoferrites Range T/TN R
max.
TN[OKJ
B
D
mm.
La Pr Nd
0.347 0.345 0.353
1.11 1.12 1.14
0.60 0.55 0.70
0.993 0.996 0.993
740
Sm Eu
0.342 0.350
1.13 1.17
0.60
0.990
674
0.65
0.985
682
Gd Tb
0.354 0.349
1.15 1.12
0.70 0.55
0.980 0.990
657 647
Dy
0.348
1.14
0.65
0.990
645
Y Ho Er Tm
0.354 0.342 0.357 0.349
1.16 1.15 1.15 1.15
0.70
0.975 0.980 0.980
640
Yb Lu
0.339 0.342
1.13 1.17
0.60
0.60 0.70 0.65 0.65
707 687
0.990
639 636 632
0.993 0.997
627 623
50 40 30 20
to. Q
.:
0
FIG.3
I~Q33 o -5
. .
-
.
.
‘
Deviations from Equation (1) for three choices of 8. The most approprIate choice is the one for which the plot AT/TN vs. T/TN
has no curvature as T -20
P.0.30
•
-30
-400.6
0.7
0.8 t. T/TN
09
1.0
-.
TN.
Vol. 4, No. 3
INTERNAL FIELD IN ~THOFERRITES
in the region where the curve from Fig. 3 has no curvature. Figure 3 shows that the data are in good agreement with the equation (1) for
145
iron metal from Preston etal. 9, we also find that the one third power law holds in the range 0. 80
LaFeO3 in the range of temperature 0.60 T~ T
<
0.993 TN for B ~ 0.33
It is Interesting to note that If we take the internal field as a function of temperature for
We thus conclude that the dependence of the internal field in orthoferrites in the range 0.60 TN < T < 0.99 TN follows relation (1) with B close to 1/3.
References 1.
LANDAU L. D. and LIFSRITZ E. M., Statistical Physics, Pergamon Press, New York (1958).
2.
YANGC.N., Phys. Rev., 85, 808 (1952).
3.
BAKER G.A., Jr., Phys. Rev. 124, 768 (1961).
4.
ESSAM J.W. and FISHER M. F., J. Chem. Phys. 38, 802 (1963).
5.
CALLEN E. and CALLEN H. B., J. Appi. Phys. 36, 1140 (1965).
6.
HELLER P. and BENEDEK G., Phys. Rev. Letters 8, 428 (1962).
7.
HELLER P. and BENEDEK G., Phys. Rev. Letters 14, 71 (1965).
8.
HONWARD D. G., DUNLAP B. D. and DASH J. G., Phys. Rev. Letters 15, 628 (1965).
9.
PRESTON R. S., HANNA S.S. and HEBERLE J., Phys. Rev. 128, 2207 (1962).
10.
GELLER S., J. Chem. Phys. 24, 1236 (1956).
11.
COPPENS P. and EIBSCHUTZ M., Acta Cryst. 19, 524 (1965).
12.
EIBSCRUTZ M., GORODETSKY. G., SHTRIKMAN S. and TREVES D., J. Appi. Pl~ys. 35, 1071
13.
(1964). EIBSCHIJTZ M., Ph.D. Thesis, In Hebrew (1965).
14.
EIBSCHt~TZM., SHTRIKMAN S. and TREVES D., to be published.
15.
LIPKIN J., SCHECHTER B., SHTRIKMAN S. and TREVES D., Rev. Sd. Insir. 35, 1336 (1964).
16.
SHARON B. and TREVES D., to be published.
17.
GORODETSKY G., SHTRIKMAN S. and TREVES D., Solid Slate Communications91s 4, 147 it was (1966). found The the that same canting results angle holdisalso independent for the ferromagnetic of T for T/TNmoment < 0.99. for TREVES 0.60 < T/TN D., J.< Appl. 0. 9 Phys. Suppi.
=
36, 1033 (1965). La dépendance du champ interne de In temperature dane le noyau du fer dana les orthoferrites est mesuré par l’effet M~ssbauer. Nous avons trouvê que le champ interne vane avec (1 - T/TN) Ia puissance 1/3 dane Ia region de temperature 0.8 TN< T< 0.99 TN. ~.