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Magnetic susceptibility of face-centered cubic cobalt just above the ferromagnetic Curie temperature
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J. Phys. Chem. Solids Pergamon Press 1965. Vol. 26, pp. 435-437.
MAGNETIC
SUSCEPTIBILITY
OF FACE-CENTERED
CUBIC COBALT JUST ABOVE THE FERROMAGNETIC CURIE TEMPERATURE R. V. COLVIN* and S. ARqlS Edgar C. Bain Laboratory for Fundamental Research, United States Steel Corporation Research Center, Monroeville, Pennsylvania (Received 13 July 1964) Abstract-Magnetic susceptibility of face-centered polycrystalline cubic cobalt, using a spherical sample, has been measured between TFC and TF C+ 13OK, Tp’c being the ferromagnetic Curie temperature. The susceptibility is proportional to (T- TF~)s with n = - 1.21+0*04. This result is different from that found in iron (n = 1.33) which behaves as predicted theoretically on the basis of a three-dimensional Heisenberg ferromagnet. The ferromagnetic Curie temperature of face-centered cubic cobalt has been found to be 1388 + 2°K. RECENTLY the magnetic susceptibility of iron has been studied(lp 2) just above the ferromagnetic Curie temperature TIC. It has been found that the susceptibility can be represented by the equation x = A(T-TF@,
(1)
where A and n are constants. According to NOAKES and ARROTT~) n = - 1.37 5 0.04 for temperatures between TJZC and T~c+lo’K. Our studies(a) of the magnetic susceptibility of iron in the temperature interval from TFC to Tpc+30°K gave, within experimental error, n = -413. Thus the results of both investigations are consistent with the theoretical expectations for a three-dimensional Heisenberg ferromagnet.(st 4,s) This is an interesting result since it might be questioned whether iron should be considered as a Heisenberg ferromagnet. Since the nature of ferromagnetism in iron could be different from that in cobalt and nickel, it is of interest also to explore the temperature dependence of the magnetic susceptibility of these two metals above their ferromagnetic Curie temperatures. In this paper we present experimental results on cobalt. To our best knowledge information of this type has not been obtained before. * Deceased 26, March 1964.
A sphere of diameter 0.3167 cm was made from Johnson and Matthey cobalt (Cat. No. 873). The electrical resistivity of this material in ‘as received’ condition was found to be 6.06 @-cm at 298”K, and O-17 &-cm at 4~2°K. The results of a spectroscopic analysis, provided by the supplier, are presented in Table 1. The magnetic moment of this Table 1. Partial
analysis of cobalt
Impurities Si Ni cu Fe Ag Mg Al, As, Au, B, Ba, Be, Bi, Ca, Cd, Cr, Cs, Ga, Ge, Hf, Hg, In, Ir, K, Li, Mn, MO, Na, Nb, OS, P, Pb, Pd, Pt, Rb, Re, Rh, Ru, Sb, Se, Sn, Sr,Ta, Te, Ti, Tl, V, W, Zn, Zr
Amount [ppm] 2 2 1 1
Not detected
cobalt sphere at different temperatures was determined in a manner that has been described before.@)
435
436
R.
V. COLVIN
The mass magnetization c of a cobalt sphere as a function of temperature in the neighborhood of the ferromagnetic Curie point in presence of various applied magnetic fields Ha is shown in Fig. 1. It can be seen that the temperature Tbc, defined as a temperature at which the B vs. T curve becomes temperature dependent, depends upon
1380
1385
1390 1395 T [OKI
1400
and
S.
ARAJS
&tROTT(12)and KOUVEL(~~)technique for the determination of the spontaneous magnetjzation as a function of temperature. The internal fields were calculated from the external fields using the density p = 8.22 g cm-s for the temperature region between 1388 and 1402°K for face-centered cubic cobalt and the demagnetizing factor 1.51 as given by Myers and Sucksmith. The density value was estimated from the lattice parameters determined by NEWKIRK and GEISSLER.(~~)Generally, the spontaneous magnetizations DOT are determined by extrapolating the high field region of the o2 vs. Hijo curves to Ht = 0. By plotting &, as a
1405
FxQ 1. Mass magnetization of face-centered cubic cobalt sphere in various magnetic fields in the neighborhood of the ferromagnetic Curie temperature.
0
1387
1388
1389
T;c [“Kl FIG. 2. T& of face-centered cubic cobalt on a function of applied magnetic field.
the applied
magnetic
fields. Figure 2 presents the temperature The as a function of the fields Ha. By function of T we obtained the ferromagnetic Curie extrapolating the curve to Ha = 0; we obtain the temperature to be 1397 & 1°K. This value is slightly ferromagnetic Curie point of face-centered cobalt higher than the temperature (1394 5 3°K) given by as TFC = 1388~2°K. In an absolute sense, how- Myers and Sucksmith which is based on the WeissForrer method for evaluating the spontaneous platinum-platinum ever, since the calibrated magnetizations at different temperatures. If, howwith 10 wt. % rhodium thermocouple was not attached directly to the sample, it is believed that ever, we use the low field regions of the 02 vs. the temperature TFC should be reported as 1388 + Hi/o curves and extrapolate these to Hg = 0, then 2°K. This quantity is lower than 1394 + 3”K, the the resu1ting &ZJ vs* T plot gives 1392°K as the commonly accepted value@) of TFC for the face- ‘Curie point’ of cobalt. Figure 3 shows the mass magnetic susceptibility centered cubic cobalt. However, a careful review of face-centered cubic cobalt just above the fkrroof the previous determinations@-10) of TFC magnetic Curie temperature in the presence of an reveals a considerable scattering among the suggested values, indicating difficulties in the deter- applied magnetic field of 181 Oe. The susceptibilimination of this transition temperature. We also ties were calculated from the equation have reexamined the magnetization data of ,=” (2) MYERS and SUCKSMITH@) using the BELOW, HE
JUST
ABOVE
THE
FERROMAGNETIC
CURIE
TEMPERATURE
437
(T-TFC) plots for Ha = 45, 91, 272, 362 and 453 Oe since these are essentially identical to that 4?T given in Fig. 3. (3) It definitely appears that the magnetic behavior Hr = Ha-3p”S of cobalt above the ferromagnetic Curie temperature is not identical to that of iron. It would be of The quantity o represents the mass magnetic interest to determine the quantity 11also for nickel moment at the temperature T and in the internal and gadolinium since the nature of ferromagnetism magnetic field Hi which for a spherical sample is in these two elements is of quite different origin. related to the directly measurable Ha by equation theoretical studies of the magnetic (3). The susceptibilities fit equation (1) with Furthermore, tl = - 1*21+ 0.04. The lines associated with n = susceptibility should also be extended to the non- 1.33 and n = - 1.00 are also presented in Fig. 3. Heisenberg type ferromagnets. The value - 1.33 is approximately predicted for a
where
Acknowledgements-The authors are thankful to G. P. WRAY for his skillful assistance with the magnetic susceptibility measurements, to H. E. KNECHTEL and W. F. KINDLE for a metallographic examination of the cobalt specimen, and to A. D. DAMICKfor this assistance in the preparation of the cobalt sphere. Finally, the authors are grateful to D. S. MILLER for his interest in this study and critical reading of this paper.
c-co31
2
34 T-T,,
6 I”Kl
0
IO
20
FIG. 3. Temperature dependence of the magnetic susceptibility of face-centered cubic cobalt above the ferromagnetic Curie temperature in presence of H. = 181 Oe.
three dimensional Heisenberg ferromagnet as mentioned above, The value 7t = - 1.00 has been used by LANDAU and LIFSHITZo5) in their discussion of ferromagnetics near the Curie point. This behavior results from theories based on the mean molecular field.(ls) It should be noted that, within the experimental error, the quantity 71for cobah is independent of the applied magnetic fields. For simplicity we are not presenting In x vs. In
REFERENCES 1. NOAKESJ. E. and ARROTT A., J. Appl. Phys. 35,931 (1964). 2. ARAJS S. and COLVIN R. V., J. Appl. Phys. 35, 2424 (1964). 3. DOMB C. and SYKES M. F., Proc. Roy Sot., Lond. 240, 214 (1957). 4. DOMB C. and SYKES M. F., Phys. Reo. 128, 168 (1962). 5. GAMMEL J., MARSHALL W. and MORGAN L., Proc. Roy. Sot., Lond. A275, 257 (1963). 6. Gmelins Handbuch der anorganischen Chemie, Vol. 58,Pt.A, p. 128,Verlag, Berlinl932,Vol. 59, Pt. D, p. 188, Verlag, Weinheim 1959. 7. MEYER A. J. P. and TACLANC P., Compt. Rend. 231, 612 (1950). 8. MYERS H. P. and SUCK~MITHW., Proc. Roy. Sot., A207, 427 (1951). 9. PATRICK L., Phys. Rev. 93, 384 (1954). 10. CRANCLE J., Phil. Mug. 46, 499 (1955). 11. BELOX K. P., Magnetic Transitions p. 34, Consultants Bureau, New York (1961). 12. ARROTT A., Phyr. Rev. 108, 1394 (1957). 13. KOUVEL J. S., Methods for Determining the Curie Temperature of a Ferromagnet, General Electric Research Laboratory Rept. No. 57-RL-1799 (September 1957). 14. NEWKIRK J. B. and GEISSLERA. M., Acta Met. 1,456 (1953). 15. LANDAUL. D. and LIF~HITZ E. M., Electrodynamics of Continuous Media, p. 146, Pergamon Press, New York (1960). 16. DOME C., Adwanc. Phys. 9, 149 (1960).
J. Phys. Chem. Solids Pergamon Press 1965. Vol. 26, pp. 435-437.
MAGNETIC
SUSCEPTIBILITY
OF FACE-CENTERED
CUBIC COBALT JUST ABOVE THE FERROMAGNETIC CURIE TEMPERATURE R. V. COLVIN* and S. ARqlS Edgar C. Bain Laboratory for Fundamental Research, United States Steel Corporation Research Center, Monroeville, Pennsylvania (Received 13 July 1964) Abstract-Magnetic susceptibility of face-centered polycrystalline cubic cobalt, using a spherical sample, has been measured between TFC and TF C+ 13OK, Tp’c being the ferromagnetic Curie temperature. The susceptibility is proportional to (T- TF~)s with n = - 1.21+0*04. This result is different from that found in iron (n = 1.33) which behaves as predicted theoretically on the basis of a three-dimensional Heisenberg ferromagnet. The ferromagnetic Curie temperature of face-centered cubic cobalt has been found to be 1388 + 2°K. RECENTLY the magnetic susceptibility of iron has been studied(lp 2) just above the ferromagnetic Curie temperature TIC. It has been found that the susceptibility can be represented by the equation x = A(T-TF@,
(1)
where A and n are constants. According to NOAKES and ARROTT~) n = - 1.37 5 0.04 for temperatures between TJZC and T~c+lo’K. Our studies(a) of the magnetic susceptibility of iron in the temperature interval from TFC to Tpc+30°K gave, within experimental error, n = -413. Thus the results of both investigations are consistent with the theoretical expectations for a three-dimensional Heisenberg ferromagnet.(st 4,s) This is an interesting result since it might be questioned whether iron should be considered as a Heisenberg ferromagnet. Since the nature of ferromagnetism in iron could be different from that in cobalt and nickel, it is of interest also to explore the temperature dependence of the magnetic susceptibility of these two metals above their ferromagnetic Curie temperatures. In this paper we present experimental results on cobalt. To our best knowledge information of this type has not been obtained before. * Deceased 26, March 1964.
A sphere of diameter 0.3167 cm was made from Johnson and Matthey cobalt (Cat. No. 873). The electrical resistivity of this material in ‘as received’ condition was found to be 6.06 @-cm at 298”K, and O-17 &-cm at 4~2°K. The results of a spectroscopic analysis, provided by the supplier, are presented in Table 1. The magnetic moment of this Table 1. Partial
analysis of cobalt
Impurities Si Ni cu Fe Ag Mg Al, As, Au, B, Ba, Be, Bi, Ca, Cd, Cr, Cs, Ga, Ge, Hf, Hg, In, Ir, K, Li, Mn, MO, Na, Nb, OS, P, Pb, Pd, Pt, Rb, Re, Rh, Ru, Sb, Se, Sn, Sr,Ta, Te, Ti, Tl, V, W, Zn, Zr
Amount [ppm] 2 2 1 1
Not detected
cobalt sphere at different temperatures was determined in a manner that has been described before.@)
435
436
R.
V. COLVIN
The mass magnetization c of a cobalt sphere as a function of temperature in the neighborhood of the ferromagnetic Curie point in presence of various applied magnetic fields Ha is shown in Fig. 1. It can be seen that the temperature Tbc, defined as a temperature at which the B vs. T curve becomes temperature dependent, depends upon
1380
1385
1390 1395 T [OKI
1400
and
S.
ARAJS
&tROTT(12)and KOUVEL(~~)technique for the determination of the spontaneous magnetjzation as a function of temperature. The internal fields were calculated from the external fields using the density p = 8.22 g cm-s for the temperature region between 1388 and 1402°K for face-centered cubic cobalt and the demagnetizing factor 1.51 as given by Myers and Sucksmith. The density value was estimated from the lattice parameters determined by NEWKIRK and GEISSLER.(~~)Generally, the spontaneous magnetizations DOT are determined by extrapolating the high field region of the o2 vs. Hijo curves to Ht = 0. By plotting &, as a
1405
FxQ 1. Mass magnetization of face-centered cubic cobalt sphere in various magnetic fields in the neighborhood of the ferromagnetic Curie temperature.
0
1387
1388
1389
T;c [“Kl FIG. 2. T& of face-centered cubic cobalt on a function of applied magnetic field.
the applied
magnetic
fields. Figure 2 presents the temperature The as a function of the fields Ha. By function of T we obtained the ferromagnetic Curie extrapolating the curve to Ha = 0; we obtain the temperature to be 1397 & 1°K. This value is slightly ferromagnetic Curie point of face-centered cobalt higher than the temperature (1394 5 3°K) given by as TFC = 1388~2°K. In an absolute sense, how- Myers and Sucksmith which is based on the WeissForrer method for evaluating the spontaneous platinum-platinum ever, since the calibrated magnetizations at different temperatures. If, howwith 10 wt. % rhodium thermocouple was not attached directly to the sample, it is believed that ever, we use the low field regions of the 02 vs. the temperature TFC should be reported as 1388 + Hi/o curves and extrapolate these to Hg = 0, then 2°K. This quantity is lower than 1394 + 3”K, the the resu1ting &ZJ vs* T plot gives 1392°K as the commonly accepted value@) of TFC for the face- ‘Curie point’ of cobalt. Figure 3 shows the mass magnetic susceptibility centered cubic cobalt. However, a careful review of face-centered cubic cobalt just above the fkrroof the previous determinations@-10) of TFC magnetic Curie temperature in the presence of an reveals a considerable scattering among the suggested values, indicating difficulties in the deter- applied magnetic field of 181 Oe. The susceptibilimination of this transition temperature. We also ties were calculated from the equation have reexamined the magnetization data of ,=” (2) MYERS and SUCKSMITH@) using the BELOW, HE
JUST
ABOVE
THE
FERROMAGNETIC
CURIE
TEMPERATURE
437
(T-TFC) plots for Ha = 45, 91, 272, 362 and 453 Oe since these are essentially identical to that 4?T given in Fig. 3. (3) It definitely appears that the magnetic behavior Hr = Ha-3p”S of cobalt above the ferromagnetic Curie temperature is not identical to that of iron. It would be of The quantity o represents the mass magnetic interest to determine the quantity 11also for nickel moment at the temperature T and in the internal and gadolinium since the nature of ferromagnetism magnetic field Hi which for a spherical sample is in these two elements is of quite different origin. related to the directly measurable Ha by equation theoretical studies of the magnetic (3). The susceptibilities fit equation (1) with Furthermore, tl = - 1*21+ 0.04. The lines associated with n = susceptibility should also be extended to the non- 1.33 and n = - 1.00 are also presented in Fig. 3. Heisenberg type ferromagnets. The value - 1.33 is approximately predicted for a
where
Acknowledgements-The authors are thankful to G. P. WRAY for his skillful assistance with the magnetic susceptibility measurements, to H. E. KNECHTEL and W. F. KINDLE for a metallographic examination of the cobalt specimen, and to A. D. DAMICKfor this assistance in the preparation of the cobalt sphere. Finally, the authors are grateful to D. S. MILLER for his interest in this study and critical reading of this paper.
c-co31
2
34 T-T,,
6 I”Kl
0
IO
20
FIG. 3. Temperature dependence of the magnetic susceptibility of face-centered cubic cobalt above the ferromagnetic Curie temperature in presence of H. = 181 Oe.
three dimensional Heisenberg ferromagnet as mentioned above, The value 7t = - 1.00 has been used by LANDAU and LIFSHITZo5) in their discussion of ferromagnetics near the Curie point. This behavior results from theories based on the mean molecular field.(ls) It should be noted that, within the experimental error, the quantity 71for cobah is independent of the applied magnetic fields. For simplicity we are not presenting In x vs. In
REFERENCES 1. NOAKESJ. E. and ARROTT A., J. Appl. Phys. 35,931 (1964). 2. ARAJS S. and COLVIN R. V., J. Appl. Phys. 35, 2424 (1964). 3. DOMB C. and SYKES M. F., Proc. Roy Sot., Lond. 240, 214 (1957). 4. DOMB C. and SYKES M. F., Phys. Reo. 128, 168 (1962). 5. GAMMEL J., MARSHALL W. and MORGAN L., Proc. Roy. Sot., Lond. A275, 257 (1963). 6. Gmelins Handbuch der anorganischen Chemie, Vol. 58,Pt.A, p. 128,Verlag, Berlinl932,Vol. 59, Pt. D, p. 188, Verlag, Weinheim 1959. 7. MEYER A. J. P. and TACLANC P., Compt. Rend. 231, 612 (1950). 8. MYERS H. P. and SUCK~MITHW., Proc. Roy. Sot., A207, 427 (1951). 9. PATRICK L., Phys. Rev. 93, 384 (1954). 10. CRANCLE J., Phil. Mug. 46, 499 (1955). 11. BELOX K. P., Magnetic Transitions p. 34, Consultants Bureau, New York (1961). 12. ARROTT A., Phyr. Rev. 108, 1394 (1957). 13. KOUVEL J. S., Methods for Determining the Curie Temperature of a Ferromagnet, General Electric Research Laboratory Rept. No. 57-RL-1799 (September 1957). 14. NEWKIRK J. B. and GEISSLERA. M., Acta Met. 1,456 (1953). 15. LANDAUL. D. and LIF~HITZ E. M., Electrodynamics of Continuous Media, p. 146, Pergamon Press, New York (1960). 16. DOME C., Adwanc. Phys. 9, 149 (1960).