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Magnetocrystalline anisotropy in Nd2Fe14B intermetallic compound
Journal
of Magnetism
and Magnetic
Materials
MAGNETOCRYSTALLINE 0. YAMADA,
54-57
(1986) 585-586
ANISOTROPY
H. TOKUHARA,
5x5
IN Nd,Fe,,B
F. ONO. M. SAGAWA
INTERMETALLIC
COMPOUND
* and Y. MATSUURA
*
Deprtrtmrnt of Phystrs, Okqrrma University, 3 I I, Tsushlmu - naku. Okqzmu 700, Japan *Sumitomo Specral Metals Co. Ltd., Egawa, Shimumotorh.vo. M~.shrmugun. O.wkcr 618, Jupon
Magnetic torque measurements have been made in Nd?Fe,,B intermetallic compound at various temperatures between 4.2 K and room temperature, and the magnetocrystalline anisotropy constants were determined for the first time. The temperature dependence of the anisotropy constant K, changes its sign at 133 K. below which the easy magnetization axis tilts from [OOl]-direction towards (OOl)-plane.
Recently, high energy permanent magnets have been developed on the basis of Nd,Fe,,B intermetallic compound [1.2]. Though these magnets have very high energy products, the coercive forces decrease rapidly with increasing temperature in the range of ordinary use. It was pointed out that this characteristic is due to the rapid decrease of the magnetocrystalline anisotropy energy of this intermetallic compound [3-51. To obtain a more stable magnet it is desirable to study further the magnetocrystalline anisotropy of this material. From the work of Givord et al. [3] and our detailed measurements of the temperature dependence of the magnetization along the easy direction of a single crystal specimen [6], a sharp kink was observed at 135 K, below which the magnetic moment began to tilt from the [OOl]-direction towards the [IlO]-direction. However, from the magnetization measurements it is not easy to determine the magnetocrystalline anisotropy constants up to sufficiently higher orders, and therefore only an approximate value of the tilt angle can be determined. A more precise determination is possible only by torque measurements. In the present paper we describe magnetic torque measurements of single crystal specimens of Nd 2 Fe,, B intermetallic compound. The torque magnetometer used in the present experiments is an automatic recording type with two light nonmagnetic ballbearings with which the distortion of the specimen-holding shaft by the magnetic attractive force between the specimen and the pole pieces of the electro-magnet was able to be avoided. The specimen used in the present experiments was a disc which was cut and formed from a single crystal of Nd,Fe,,B. The disc plane was parallel to the (110) crystallographic plane. The diameter and the thickness of the specimen were 1.00 and 0.16 mm, respectively. The crystallographic plane of the specimen was determined within an error of about f 1” by using the X-ray diffraction technique. Torque curves were measured in a constant magnetic field of 16.9 kOe at various temperatures between 4.2 K and room temperature. The temperature of the specimen was kept constant during a measurement of a
0304-8853/86/$03.50
0 Elsevier Science Publishers
torque curve by controlling the evaporation rate of the liquid nitrogen or helium. The temperature variation of the observed torque curves are shown in fig. 1. From this figure it is seen that the shape of the torque curves at low temperatures are quite different from those at high temperatures. At high temperatures the shape of the torque curve was a typical uniaxial type, while that at low temperatures was more complicated. The small peaks around the [OOl] direction vanished at temperatures above 133 K. From the observed torque curves it is very
easy
to determine
the easy
magnetization
axis.
while from the magnetization measurements, which have been made for convenience, an elaborate study is needed. The easy axis was determined as the intercept of the 0 axis of the torque intensity from positive to negative with increasing 0. Thus, the temperature variation of the easy magnetization axis is immediately seen from fig. 1.
c I
2
I
1
0
I
I
Nd,Fet,B (110) Plane Hex=16.9kOe r\
so
I
I
180 0 (degree)
270
I
J
I
360
Fig. 1. Observed torque curves for Nd z Fe,, B (1lO)-disc specimen at various temperatures at the magnetic field of 16.9 kOe.
B.V.
:
‘.
‘.
‘.
‘.\’
K2-K3
: \ :
7
! \
!-.- ._._.. ~_ I
I
100 200 TEMPERATURE
u
f;lg. 2. Temperature
aniwtrop?.co”hla”ts present
_ ..
I
I
300 T(K)
dependrnces of the mannetocr\istalline K, -and (K, - K,) determined fkm the
experiments.
The magnetocrystalline nal symmetry
is expressed
anisotropy
energy
in tetrago-
[7] as.
surement by using a (OOl)-specimen. with which measurements are in progress. From the observed torque curves in the (110) apecimen the magnetocrystalline anisotropy constants K, and ( K2 ~ K,) were determined. The experimental error in determining K, ~vas estimated to be about 10%. The values thus obtained were plotted in fig. 2 as functions of temperature. From this figure it is seen that the first anisotropy constant K, is negative at 4.2 K, and gradually increases with increasing the temperature up to 133 K ivhere it changes sign. The value of K, at the room temperature is 5.7 X 10’ erg/cm’. This value is slightI> larger than 4.3, 4.8 and 5 x lO’erg/cn?, obtained from magnetization measurements made by Sagawa et al. [l I. Givord et al. [3] and Koon et al. [5], respectively. The value of (K, - K3) is positive and very large at 4.2 K comparing with K,. while decreases rapidly with increasing the temperature. and becomes almost Lcro at the room temperature. In fig. 2 the tilt angle of the magnetization from the [OOl] axis determined from the present torque measurements is also ahoun. From this figure it is seen that the temperature at which the tilt angle becomes Lero corresponds well with the sharp kinks in the anisotropl constants. This is the first time the magnetocrystalline anisotropy constants are determined from magnetic torque measurements for NdzFe,,B.
f!‘, = K, sin’ 0 + K? ain4 0 +K,sin4Bcoa4++
where to the (001) torque putting
. . . .
(1)
~9 is the angle of the magnetization with respect [OOl] axis and I$ the angle projected onto the plane with respect to the [loo] direction. The in the (110) plane can then be described by 0 = ~/4 as.
I>II0 = -aE,/t)8= 4( K, ~ K,)
-2K,
sin 0cos
sin3 H cos 0.
0 (2)
It is not possible. at this stage, to obtain the constants k, and K, separately. The basal plane anisotropy constant K, can be determined from a separate mea-
The authors wish to thank Mr. Y. Ohtsu for his help in the present experiments.
[II M. Sagawa. S. Fujimura.
N. Toga-a. H. Yamamoto and Y. Matsuura. J. Appl. Phys. 55 (1984) 20X3. PI D. Givord. H.S. LI and F. Tassel. ibid. 57 (1985) 4100. PI D. Gl\ord. H.S. Li and P. de La Baltic Solid State Con“1U”. 51 (1984) x57. S. FuJmmra. H. Yamamoto. Y. Matauura dnd [41 M. Sagaua. S. Hirosawa. J. Appl. Phqs. 57 (19X5) 4094. 151 N.C. Koon. B.N. Das. M. Rubinstein and J. Tvson. ihid. 57 (1985) 4091. Y. Ohtau. F. One, 0. Yamada. M. Sagawa Lb1 K. Tokuhara, and Y. Matauura. Solid State C‘ommun. 56 (19X5) 333. [71 W.P. Mason. Phys. Rev. 96 (1954) 302.
of Magnetism
and Magnetic
Materials
MAGNETOCRYSTALLINE 0. YAMADA,
54-57
(1986) 585-586
ANISOTROPY
H. TOKUHARA,
5x5
IN Nd,Fe,,B
F. ONO. M. SAGAWA
INTERMETALLIC
COMPOUND
* and Y. MATSUURA
*
Deprtrtmrnt of Phystrs, Okqrrma University, 3 I I, Tsushlmu - naku. Okqzmu 700, Japan *Sumitomo Specral Metals Co. Ltd., Egawa, Shimumotorh.vo. M~.shrmugun. O.wkcr 618, Jupon
Magnetic torque measurements have been made in Nd?Fe,,B intermetallic compound at various temperatures between 4.2 K and room temperature, and the magnetocrystalline anisotropy constants were determined for the first time. The temperature dependence of the anisotropy constant K, changes its sign at 133 K. below which the easy magnetization axis tilts from [OOl]-direction towards (OOl)-plane.
Recently, high energy permanent magnets have been developed on the basis of Nd,Fe,,B intermetallic compound [1.2]. Though these magnets have very high energy products, the coercive forces decrease rapidly with increasing temperature in the range of ordinary use. It was pointed out that this characteristic is due to the rapid decrease of the magnetocrystalline anisotropy energy of this intermetallic compound [3-51. To obtain a more stable magnet it is desirable to study further the magnetocrystalline anisotropy of this material. From the work of Givord et al. [3] and our detailed measurements of the temperature dependence of the magnetization along the easy direction of a single crystal specimen [6], a sharp kink was observed at 135 K, below which the magnetic moment began to tilt from the [OOl]-direction towards the [IlO]-direction. However, from the magnetization measurements it is not easy to determine the magnetocrystalline anisotropy constants up to sufficiently higher orders, and therefore only an approximate value of the tilt angle can be determined. A more precise determination is possible only by torque measurements. In the present paper we describe magnetic torque measurements of single crystal specimens of Nd 2 Fe,, B intermetallic compound. The torque magnetometer used in the present experiments is an automatic recording type with two light nonmagnetic ballbearings with which the distortion of the specimen-holding shaft by the magnetic attractive force between the specimen and the pole pieces of the electro-magnet was able to be avoided. The specimen used in the present experiments was a disc which was cut and formed from a single crystal of Nd,Fe,,B. The disc plane was parallel to the (110) crystallographic plane. The diameter and the thickness of the specimen were 1.00 and 0.16 mm, respectively. The crystallographic plane of the specimen was determined within an error of about f 1” by using the X-ray diffraction technique. Torque curves were measured in a constant magnetic field of 16.9 kOe at various temperatures between 4.2 K and room temperature. The temperature of the specimen was kept constant during a measurement of a
0304-8853/86/$03.50
0 Elsevier Science Publishers
torque curve by controlling the evaporation rate of the liquid nitrogen or helium. The temperature variation of the observed torque curves are shown in fig. 1. From this figure it is seen that the shape of the torque curves at low temperatures are quite different from those at high temperatures. At high temperatures the shape of the torque curve was a typical uniaxial type, while that at low temperatures was more complicated. The small peaks around the [OOl] direction vanished at temperatures above 133 K. From the observed torque curves it is very
easy
to determine
the easy
magnetization
axis.
while from the magnetization measurements, which have been made for convenience, an elaborate study is needed. The easy axis was determined as the intercept of the 0 axis of the torque intensity from positive to negative with increasing 0. Thus, the temperature variation of the easy magnetization axis is immediately seen from fig. 1.
c I
2
I
1
0
I
I
Nd,Fet,B (110) Plane Hex=16.9kOe r\
so
I
I
180 0 (degree)
270
I
J
I
360
Fig. 1. Observed torque curves for Nd z Fe,, B (1lO)-disc specimen at various temperatures at the magnetic field of 16.9 kOe.
B.V.
:
‘.
‘.
‘.
‘.\’
K2-K3
: \ :
7
! \
!-.- ._._.. ~_ I
I
100 200 TEMPERATURE
u
f;lg. 2. Temperature
aniwtrop?.co”hla”ts present
_ ..
I
I
300 T(K)
dependrnces of the mannetocr\istalline K, -and (K, - K,) determined fkm the
experiments.
The magnetocrystalline nal symmetry
is expressed
anisotropy
energy
in tetrago-
[7] as.
surement by using a (OOl)-specimen. with which measurements are in progress. From the observed torque curves in the (110) apecimen the magnetocrystalline anisotropy constants K, and ( K2 ~ K,) were determined. The experimental error in determining K, ~vas estimated to be about 10%. The values thus obtained were plotted in fig. 2 as functions of temperature. From this figure it is seen that the first anisotropy constant K, is negative at 4.2 K, and gradually increases with increasing the temperature up to 133 K ivhere it changes sign. The value of K, at the room temperature is 5.7 X 10’ erg/cm’. This value is slightI> larger than 4.3, 4.8 and 5 x lO’erg/cn?, obtained from magnetization measurements made by Sagawa et al. [l I. Givord et al. [3] and Koon et al. [5], respectively. The value of (K, - K3) is positive and very large at 4.2 K comparing with K,. while decreases rapidly with increasing the temperature. and becomes almost Lcro at the room temperature. In fig. 2 the tilt angle of the magnetization from the [OOl] axis determined from the present torque measurements is also ahoun. From this figure it is seen that the temperature at which the tilt angle becomes Lero corresponds well with the sharp kinks in the anisotropl constants. This is the first time the magnetocrystalline anisotropy constants are determined from magnetic torque measurements for NdzFe,,B.
f!‘, = K, sin’ 0 + K? ain4 0 +K,sin4Bcoa4++
where to the (001) torque putting
. . . .
(1)
~9 is the angle of the magnetization with respect [OOl] axis and I$ the angle projected onto the plane with respect to the [loo] direction. The in the (110) plane can then be described by 0 = ~/4 as.
I>II0 = -aE,/t)8= 4( K, ~ K,)
-2K,
sin 0cos
sin3 H cos 0.
0 (2)
It is not possible. at this stage, to obtain the constants k, and K, separately. The basal plane anisotropy constant K, can be determined from a separate mea-
The authors wish to thank Mr. Y. Ohtsu for his help in the present experiments.
[II M. Sagawa. S. Fujimura.
N. Toga-a. H. Yamamoto and Y. Matsuura. J. Appl. Phys. 55 (1984) 20X3. PI D. Givord. H.S. LI and F. Tassel. ibid. 57 (1985) 4100. PI D. Gl\ord. H.S. Li and P. de La Baltic Solid State Con“1U”. 51 (1984) x57. S. FuJmmra. H. Yamamoto. Y. Matauura dnd [41 M. Sagaua. S. Hirosawa. J. Appl. Phqs. 57 (19X5) 4094. 151 N.C. Koon. B.N. Das. M. Rubinstein and J. Tvson. ihid. 57 (1985) 4091. Y. Ohtau. F. One, 0. Yamada. M. Sagawa Lb1 K. Tokuhara, and Y. Matauura. Solid State C‘ommun. 56 (19X5) 333. [71 W.P. Mason. Phys. Rev. 96 (1954) 302.