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Effect of hydrostatic pressure on the magnetocrystalline anisotropy of iron and nickel
J. Phys. Chem. Solids
Pergamon Press 1968. Vol. 29, pp. 575-580.
Primed in Great Britain.
EFFECT OF HYDROSTATIC PRESSURE ON THE MAGNETOCRYSTALLINE ANISOTROPY OF IRON AND NICKEL NAOTO
KAWAI
and AKIRA
SAWAOKA
Department of Physics, Faculty of Engineering Science, Osaka University, Osaka, Japan (Received 5 Sepfe~ber
1967; in reuisedform
27 October 1967)
Abstract-By
the use of a new technique we have measured the pressure dependence of the first order anisotropy constant K, of both iron and nickel single crystals. The pressure dependence of i(,, (( I/#,) (dK,/dp)) in iron is -4.6 X lo-” bar-’ at room temperature and -8.0 X 10m6bar-’ at 77°K. and in nickel is -7.5 X 10-6bar-1 at room temperature and-4.8 X IO-” bar-l at 77°K. INTRODUCTION
IN ORDER
to measure the magnetic anisotropy of ferromagnetic single crystals under hydrostatic pressure, the present authors have made a very simple equipment with which the measurement is possible over a wide range of temperature, from liquid helium temperature up to 200°C. By the use of this apparatus we have determined the change of the anisotropy constant of various ferromagnetic substances under hydrostatic pressure. In this paper we describe the results on the anisotropy constants K, of both iron and nickel. So far, the change of the constants with hydrostatic pressure has been estimated indirectly from other magnetic information obtained by several authors such as Kouvel and Wilson [ I]. it was indeed a surprise for us to find that no direct measurement of such important metals have ever been undertaken, despite the lapse of time of more than 30 years since Honda and Kaya’s[2] pioneer work on the anisotropy constant. This seems to be mainly due to technical difficulties, but partly due to a lack of encouragement of the experimental scientists whose results could not be well explained on the modern theoretical bases. Nevertheless, it has been our aim to continue high pressure experiments on as many
physical properties as possible with as many substances as available. The present experiment is, therefore, the first of a series of planned high-pressure measurements. The method of measurement together with the results on the pressure dependence of the anisotropy constant are described in the following section. EXPERIMENTAL
APPARATUS
AND PROCEDURE
Samples: For measuring the magnetocrystalline anisotropy of iron and nickel, single crystals of 99.9 per cent purity were prepared. The iron single crystal was made by the strainanneal method, while the nickel crystal was made by the Bridgman method under high vacuum. The two crystals thus made were cut into discs parallel to the (I 00) plane. The size and the shape of the discs are shown in Fig. 3 and Fig. 4, together with the experimental data. Before each measurement both crystals were well annealed under high vacuum and then were inserted and fixed in a nonmagnetic high pressure bomb designed by us for this particular experiment. High Pressure Bomb: The high pressure bomb in which the single crystal was pressurized was made of hardened Cu-I -82 per cent Be alloy. Construction details are shown in Fig. 1. Oil compressed by a Bridgman type intensifier was sent through stainless steel tube
NAOTO
376
KAWAI
and AKJRA SAWAOKA
0 L
Fig. 1. High pressure bomb. A: flexible stainless steel tube; B: connector; C: bomb; D: cone type check valve: E: cone type leak valve; F: sample; G: plug; H: electric lead wires or thermocouple.
0
80
A to the bomb. When the desired pressure for each experimental run was attained within the bomb, connector B was unscrewed and the flexible tube disconnected. By the action of the cone shaped check valve D the oil was kept under pressure during the measurement. The pressure was monitored by a manganin gage also mounted in the bomb. The bomb containing the sample is then connected to an air-bearing torque magnetometer which will be described in the next section. Torque ~ffgnef~~efe~: This magnetometer consists of a very low-torsion nylon filament A to which is hung the rotating shaft E, air-jet bearing system C, unbonded strain gauge detector B and the non-magnetic high pressure vessel F. The entire assemblage is shown in Fig. 2. The magnetic torque on the specimen was detected by the unbonded strain gauge detector. The smallest force which the strain gauge could detect was t2 dyn cm. The pressure fluid was kerosene and electric transformer oil in a 1 : 1 mixture. This mixture froze at low temperature and under high pressure. The manganin gage monitor indicated
40
80 Angle,degree
80
Fig 3. Torque curves of a single crystal of iron in the (100) plane taken at room temperature with an applied magnetic field of 8600 Oe. The open and closed circles show curves observed under pressure of 1700 and 8SOObar, respectively.
.
‘
Fig. 2. General assembly of the torque magnetometer connected to high pressure bomb. A. nylon filament; B. unbonded strain gauge detector; C. air bearing; D. air jet inlet; E. quartz rod; F. high pressure bomb.
[Facing page 5761
HYDROSTATIC
PRESSURE
0
ON
THE
klAGNETOCRYSTALLiNE
20
40
60
Angle.
ANISOTROPY
577
80
degree
Fig. 4. Torque curves of a single crystal of nickel in the (100) plane taken at room temperature with an applied magnetic field of 86000e. The open and closed circles show curves observed under pressure of 1700 and 6800 bar, respectively.
that the pressure loss at the time of freezing was 3500 bar. A complete description of the entire equipment will be published in the Review of Scientific Instruments [3]. Torque was recorded from the reading of the unbonded strain gage at 5” intervals of rotation of a uniform magnetic field around the high pressure bomb. Measurements at 77°K were carried out putting the bomb directly into liquid nitrogen contained in a cryostat. EXPERIMENTAL
RESULTS
In Fig. 3 and Fig. 4 are shown some typical torque curves of both Fe and Ni single crystals at room temperature under high pressure. In general, in a crystal having cubic symmetry the anisotropy energy & can be expressed in the following equation
where (Q~, (Ye,c+) are the direction cosines of the magnetization vector relative to the crystallographic axis. The torque L is given by the
derivative rotation:
E, with respect
to the angle B of
(2) The torque in the (100) plane is exactly L ( 100) = -$
sin 48.
(3)
In our experiment, however, errors of about +l” took place in crystals. This misorientation of the (100) plane during the measurements caused slight deviations of the curve from that expected from the above equation. The vafue of I(, was, therefore, determined by averaging the difference of the maximum and minimum of deflection of the measured torque curve. In Figs. 5 and 6 are shown the values of AK,/K, of both iron and nickel at the room temperature and at 77°K. The pressure dependences, K,-‘( dK,/dp) are also tabulated in Table 1. DISCUSSION Kouvel and Wilsonfl] have estimated ~~-‘(d~*~d~) of an iron single crystal con-
NAOTO KAWAI and AKIRA SAWAOKA
578
0
“0
-1
r: -2
q-3 ST =! -4 -5 -6 -7
0123458739
Pressure,
kb
Fig. 5. Pressure dependence of magnetic first order anisotropy constant K1 of iron. The open and closed circles show pressure dependence at room temperature and 77”K, respectively.
taining 3.5 per cent silicon at room temperam-e from their results of magnetization measurements under hydrostatic pressure. The value, -64 x lo-’ atm-I, is consistent with our results of torque measurement for iron. The measured pressure dependence of the anisotropy, K,-l(dK,/dp’) was transformed into the volume dependence ( V/K,) (dK,ldP’)
by using the compressibility -(l/V) (dI/ldp) of these metals[4] at room temperature. The values are tabulated in the Table 2. Becker and Diring[3] have estimated ( V/Kz > (dK,/dV) for iron to be 9.4 from volumemagnetostriction measurements. In contrast, the present experiment is a direct observation of the value when the volume is reduced under
0 -1
“0
Z-2
tz h-3 w s-4 -5 -6 -7 0123456789
Pressure,
kb
Fig. 6. Pressure dependence of magnetic first order anisotropy constant K, of nickel. The open and closed circles show pressure dependence at room temperature and 77”K, respectively.
HYDROSTATIC
PRESSURE
ON THE MAGNETOCRYSTALLINE
hydrostatic pressure. The two values obtained independently by different methods agree reasonably well. The temperature dependence of K, in general is expressed by K,(T)= K,(O) where
ANISOTROPY
579
a hydrostatic pressure to compensate the thermal expansion of the crystal, and to estimate the anisotropy in this state. The effect of this compensation 6K, is shown by the following equation:
(4)
K,(O) and zrs(0)
are the first order
Table 1. Pressure dependence of magnetocrystalhe anisotropy constant K, of iron and nickel Metal
(K,-‘dK,/dP) * at room temp.
Iron Nickel
-4.6 x IO-"bar-* -7.5 X IO-"bar-’
where a, T, and V are the thermal expansion coefficient, temperature and volume of the specimen. Therefore, the hypothetical anisotropy constant 1y, (hyp) is
(K,-‘dK,ldP)t at 77°K -8.0X IO-"bar-’ -4.8 X 1O-sbar-*
*Obtained with applied magnetic field of 8600 Oe. Obtained with applied magnetic field of 6800 Oe.
anisotropy constant and the saturation magnetization at O”K, and K, ( T) and cs( T) are the values at PK. In the case of iron it was first reported by Zener[G] that n is equal to IO and secondly by Carr[7] that n was reduced to 5 at low temperature. Equation (4) is a theoretical formula derived for constant volume. Carr mentioned that the effect of the thermal expansion to occur at low temperature was not taken mto consideration in Zener’s work, and that the deviations
(6)
K1(hyp) =1Yt---~I(n-
The thermal expansion coefficient reported by Nix and MacNair[S] was used. The volume dependence (~/~i) (dK,ldV) at at 77°K and room temperature. The temperature dependence of K1 of Fe at constant volume, obtained in this way, is shown in Fig. 7. The values coincide reasonably with the theoretical curve obtained by Zener co~esponding to the case n = 10.
7
Table 2. V&me dependence of magnetocrystalline anisotropy constant K, of iron and nickel 3
Metal Il-OIl
Nickel
Linear compressibility 5.9 X 10w7bar-’ 5.3 x lo-‘bar-’
at room temp.
at 77°K
7.8 14.2
13.5 IO.2
of various experimental data from the theory are the result of this volume change. We, therefore, have considered an ideal fictitious state in which no thermal expansion takes place at low temperature. It is possible in principle to acheive this state when we apply
Temperature
,*K
Fig. 7. Temperature dependence of K, of iron at constant pressure and constant volume. Open symbols are values measured at constant pressure; closed symbols are values corrected to constant volume: A- Values observed by Graham[9]; O-Measurements of Bozorth as given by Graham [9]; 0 - Older values of Bozorth [ IO]as calculated from magnetization curves of Honda, Masumoto, and Kaya[3]. The dotted and solid lines show the 5th and 10th power law, respectively.
In the case of nickel, however, the observed vaiues coincide with the curve with n equal to
580
NAOTO
KAWAI
50. At present there is no satisfactory expiaining the redts.
and AKIRA
theory
Acknowledgements-The authors express their thanks to Professor E. Fujita and Mr. M. lnokuchi of Osaka University, who kindly provided the iron single crystal in this experiment and also Professor H. Takaki and Dr. M. Mekata of Kyoto University for providing the nickel single crystal. REFERENCES 1. KOUVEL J. S. and WILSON R. H., Progress in Very High Pressure Research (Edited by F. P. Bundy et al.), p. 27 I. Wiley, New York f 1961).
SAWAOKA
2. HONDA K., MASUMOTO H. and KAYA S., S&en?. Rep. Tohoku Imp. Univ. 17,111 (1928). 3. KAWAI N. and SAWAOKA A., Rev. sci. Instrum. (Dec. 1967). 4. LANDOLT-BijRNSTERN TABELLEN, Eg. 1, 522. 5. BECKER R. and DGRING W., Ferromagnetismus, p. 298. Springer, Berlin (1939). 6. ZENERC., Pkys. Reu.96, 1335 (1954). 7. CARR W. J. Jr.,J.uppl.Phys. 31,69 (1960). 8. NIX F. C. and MACNAIR D., Phys. Rev. 60,597 (1941). 9. GRAHAM C. D. Jr., Phys. Reu. 1X2,11 17 (1958). 10. BOZORTH R. M.,.!. appl. Phys. 8,575 (1937).
Pergamon Press 1968. Vol. 29, pp. 575-580.
Primed in Great Britain.
EFFECT OF HYDROSTATIC PRESSURE ON THE MAGNETOCRYSTALLINE ANISOTROPY OF IRON AND NICKEL NAOTO
KAWAI
and AKIRA
SAWAOKA
Department of Physics, Faculty of Engineering Science, Osaka University, Osaka, Japan (Received 5 Sepfe~ber
1967; in reuisedform
27 October 1967)
Abstract-By
the use of a new technique we have measured the pressure dependence of the first order anisotropy constant K, of both iron and nickel single crystals. The pressure dependence of i(,, (( I/#,) (dK,/dp)) in iron is -4.6 X lo-” bar-’ at room temperature and -8.0 X 10m6bar-’ at 77°K. and in nickel is -7.5 X 10-6bar-1 at room temperature and-4.8 X IO-” bar-l at 77°K. INTRODUCTION
IN ORDER
to measure the magnetic anisotropy of ferromagnetic single crystals under hydrostatic pressure, the present authors have made a very simple equipment with which the measurement is possible over a wide range of temperature, from liquid helium temperature up to 200°C. By the use of this apparatus we have determined the change of the anisotropy constant of various ferromagnetic substances under hydrostatic pressure. In this paper we describe the results on the anisotropy constants K, of both iron and nickel. So far, the change of the constants with hydrostatic pressure has been estimated indirectly from other magnetic information obtained by several authors such as Kouvel and Wilson [ I]. it was indeed a surprise for us to find that no direct measurement of such important metals have ever been undertaken, despite the lapse of time of more than 30 years since Honda and Kaya’s[2] pioneer work on the anisotropy constant. This seems to be mainly due to technical difficulties, but partly due to a lack of encouragement of the experimental scientists whose results could not be well explained on the modern theoretical bases. Nevertheless, it has been our aim to continue high pressure experiments on as many
physical properties as possible with as many substances as available. The present experiment is, therefore, the first of a series of planned high-pressure measurements. The method of measurement together with the results on the pressure dependence of the anisotropy constant are described in the following section. EXPERIMENTAL
APPARATUS
AND PROCEDURE
Samples: For measuring the magnetocrystalline anisotropy of iron and nickel, single crystals of 99.9 per cent purity were prepared. The iron single crystal was made by the strainanneal method, while the nickel crystal was made by the Bridgman method under high vacuum. The two crystals thus made were cut into discs parallel to the (I 00) plane. The size and the shape of the discs are shown in Fig. 3 and Fig. 4, together with the experimental data. Before each measurement both crystals were well annealed under high vacuum and then were inserted and fixed in a nonmagnetic high pressure bomb designed by us for this particular experiment. High Pressure Bomb: The high pressure bomb in which the single crystal was pressurized was made of hardened Cu-I -82 per cent Be alloy. Construction details are shown in Fig. 1. Oil compressed by a Bridgman type intensifier was sent through stainless steel tube
NAOTO
376
KAWAI
and AKJRA SAWAOKA
0 L
Fig. 1. High pressure bomb. A: flexible stainless steel tube; B: connector; C: bomb; D: cone type check valve: E: cone type leak valve; F: sample; G: plug; H: electric lead wires or thermocouple.
0
80
A to the bomb. When the desired pressure for each experimental run was attained within the bomb, connector B was unscrewed and the flexible tube disconnected. By the action of the cone shaped check valve D the oil was kept under pressure during the measurement. The pressure was monitored by a manganin gage also mounted in the bomb. The bomb containing the sample is then connected to an air-bearing torque magnetometer which will be described in the next section. Torque ~ffgnef~~efe~: This magnetometer consists of a very low-torsion nylon filament A to which is hung the rotating shaft E, air-jet bearing system C, unbonded strain gauge detector B and the non-magnetic high pressure vessel F. The entire assemblage is shown in Fig. 2. The magnetic torque on the specimen was detected by the unbonded strain gauge detector. The smallest force which the strain gauge could detect was t2 dyn cm. The pressure fluid was kerosene and electric transformer oil in a 1 : 1 mixture. This mixture froze at low temperature and under high pressure. The manganin gage monitor indicated
40
80 Angle,degree
80
Fig 3. Torque curves of a single crystal of iron in the (100) plane taken at room temperature with an applied magnetic field of 8600 Oe. The open and closed circles show curves observed under pressure of 1700 and 8SOObar, respectively.
.
‘
Fig. 2. General assembly of the torque magnetometer connected to high pressure bomb. A. nylon filament; B. unbonded strain gauge detector; C. air bearing; D. air jet inlet; E. quartz rod; F. high pressure bomb.
[Facing page 5761
HYDROSTATIC
PRESSURE
0
ON
THE
klAGNETOCRYSTALLiNE
20
40
60
Angle.
ANISOTROPY
577
80
degree
Fig. 4. Torque curves of a single crystal of nickel in the (100) plane taken at room temperature with an applied magnetic field of 86000e. The open and closed circles show curves observed under pressure of 1700 and 6800 bar, respectively.
that the pressure loss at the time of freezing was 3500 bar. A complete description of the entire equipment will be published in the Review of Scientific Instruments [3]. Torque was recorded from the reading of the unbonded strain gage at 5” intervals of rotation of a uniform magnetic field around the high pressure bomb. Measurements at 77°K were carried out putting the bomb directly into liquid nitrogen contained in a cryostat. EXPERIMENTAL
RESULTS
In Fig. 3 and Fig. 4 are shown some typical torque curves of both Fe and Ni single crystals at room temperature under high pressure. In general, in a crystal having cubic symmetry the anisotropy energy & can be expressed in the following equation
where (Q~, (Ye,c+) are the direction cosines of the magnetization vector relative to the crystallographic axis. The torque L is given by the
derivative rotation:
E, with respect
to the angle B of
(2) The torque in the (100) plane is exactly L ( 100) = -$
sin 48.
(3)
In our experiment, however, errors of about +l” took place in crystals. This misorientation of the (100) plane during the measurements caused slight deviations of the curve from that expected from the above equation. The vafue of I(, was, therefore, determined by averaging the difference of the maximum and minimum of deflection of the measured torque curve. In Figs. 5 and 6 are shown the values of AK,/K, of both iron and nickel at the room temperature and at 77°K. The pressure dependences, K,-‘( dK,/dp) are also tabulated in Table 1. DISCUSSION Kouvel and Wilsonfl] have estimated ~~-‘(d~*~d~) of an iron single crystal con-
NAOTO KAWAI and AKIRA SAWAOKA
578
0
“0
-1
r: -2
q-3 ST =! -4 -5 -6 -7
0123458739
Pressure,
kb
Fig. 5. Pressure dependence of magnetic first order anisotropy constant K1 of iron. The open and closed circles show pressure dependence at room temperature and 77”K, respectively.
taining 3.5 per cent silicon at room temperam-e from their results of magnetization measurements under hydrostatic pressure. The value, -64 x lo-’ atm-I, is consistent with our results of torque measurement for iron. The measured pressure dependence of the anisotropy, K,-l(dK,/dp’) was transformed into the volume dependence ( V/K,) (dK,ldP’)
by using the compressibility -(l/V) (dI/ldp) of these metals[4] at room temperature. The values are tabulated in the Table 2. Becker and Diring[3] have estimated ( V/Kz > (dK,/dV) for iron to be 9.4 from volumemagnetostriction measurements. In contrast, the present experiment is a direct observation of the value when the volume is reduced under
0 -1
“0
Z-2
tz h-3 w s-4 -5 -6 -7 0123456789
Pressure,
kb
Fig. 6. Pressure dependence of magnetic first order anisotropy constant K, of nickel. The open and closed circles show pressure dependence at room temperature and 77”K, respectively.
HYDROSTATIC
PRESSURE
ON THE MAGNETOCRYSTALLINE
hydrostatic pressure. The two values obtained independently by different methods agree reasonably well. The temperature dependence of K, in general is expressed by K,(T)= K,(O) where
ANISOTROPY
579
a hydrostatic pressure to compensate the thermal expansion of the crystal, and to estimate the anisotropy in this state. The effect of this compensation 6K, is shown by the following equation:
(4)
K,(O) and zrs(0)
are the first order
Table 1. Pressure dependence of magnetocrystalhe anisotropy constant K, of iron and nickel Metal
(K,-‘dK,/dP) * at room temp.
Iron Nickel
-4.6 x IO-"bar-* -7.5 X IO-"bar-’
where a, T, and V are the thermal expansion coefficient, temperature and volume of the specimen. Therefore, the hypothetical anisotropy constant 1y, (hyp) is
(K,-‘dK,ldP)t at 77°K -8.0X IO-"bar-’ -4.8 X 1O-sbar-*
*Obtained with applied magnetic field of 8600 Oe. Obtained with applied magnetic field of 6800 Oe.
anisotropy constant and the saturation magnetization at O”K, and K, ( T) and cs( T) are the values at PK. In the case of iron it was first reported by Zener[G] that n is equal to IO and secondly by Carr[7] that n was reduced to 5 at low temperature. Equation (4) is a theoretical formula derived for constant volume. Carr mentioned that the effect of the thermal expansion to occur at low temperature was not taken mto consideration in Zener’s work, and that the deviations
(6)
K1(hyp) =1Yt---~I(n-
The thermal expansion coefficient reported by Nix and MacNair[S] was used. The volume dependence (~/~i) (dK,ldV) at at 77°K and room temperature. The temperature dependence of K1 of Fe at constant volume, obtained in this way, is shown in Fig. 7. The values coincide reasonably with the theoretical curve obtained by Zener co~esponding to the case n = 10.
7
Table 2. V&me dependence of magnetocrystalline anisotropy constant K, of iron and nickel 3
Metal Il-OIl
Nickel
Linear compressibility 5.9 X 10w7bar-’ 5.3 x lo-‘bar-’
at room temp.
at 77°K
7.8 14.2
13.5 IO.2
of various experimental data from the theory are the result of this volume change. We, therefore, have considered an ideal fictitious state in which no thermal expansion takes place at low temperature. It is possible in principle to acheive this state when we apply
Temperature
,*K
Fig. 7. Temperature dependence of K, of iron at constant pressure and constant volume. Open symbols are values measured at constant pressure; closed symbols are values corrected to constant volume: A- Values observed by Graham[9]; O-Measurements of Bozorth as given by Graham [9]; 0 - Older values of Bozorth [ IO]as calculated from magnetization curves of Honda, Masumoto, and Kaya[3]. The dotted and solid lines show the 5th and 10th power law, respectively.
In the case of nickel, however, the observed vaiues coincide with the curve with n equal to
580
NAOTO
KAWAI
50. At present there is no satisfactory expiaining the redts.
and AKIRA
theory
Acknowledgements-The authors express their thanks to Professor E. Fujita and Mr. M. lnokuchi of Osaka University, who kindly provided the iron single crystal in this experiment and also Professor H. Takaki and Dr. M. Mekata of Kyoto University for providing the nickel single crystal. REFERENCES 1. KOUVEL J. S. and WILSON R. H., Progress in Very High Pressure Research (Edited by F. P. Bundy et al.), p. 27 I. Wiley, New York f 1961).
SAWAOKA
2. HONDA K., MASUMOTO H. and KAYA S., S&en?. Rep. Tohoku Imp. Univ. 17,111 (1928). 3. KAWAI N. and SAWAOKA A., Rev. sci. Instrum. (Dec. 1967). 4. LANDOLT-BijRNSTERN TABELLEN, Eg. 1, 522. 5. BECKER R. and DGRING W., Ferromagnetismus, p. 298. Springer, Berlin (1939). 6. ZENERC., Pkys. Reu.96, 1335 (1954). 7. CARR W. J. Jr.,J.uppl.Phys. 31,69 (1960). 8. NIX F. C. and MACNAIR D., Phys. Rev. 60,597 (1941). 9. GRAHAM C. D. Jr., Phys. Reu. 1X2,11 17 (1958). 10. BOZORTH R. M.,.!. appl. Phys. 8,575 (1937).