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Magnetocrystalline anisotropy in Y6Fe23
101
Journal of the Less-Common Metals, 167( 1990) 101-106
MAGNETOCRYSTALLINE A. V. ANDREEV,
ANISOTROPY
M. I. BARTASHEVICH
IN Y,Fe,,
and V. A. VASILKOVSKY
Permanent Magnets Laboratory, Urals State University, 620083, Sverdlovsk (U.S.S.R.) (Received May 18,199O)
Summary A study has been made of the magnetic properties and thermal expansion of Y,Fe,, single crystals. Analysis of the NMR spectra shows that the easy direction of magnetization lies along the [ 1001 axis, which is confirmed by magnetization curves and torque measurements.
1. Introduction
It is known that the iron sublattice in intermetallic compounds of rare earth actinide metals (R) with iron can possess a high magnetocrystalline anisotropy, several times greater than in the metallic iron. This may be attributed to the fact that the 3d orbital moment is not completely quenched by the crystal field effects [ 1,2]. The accurate determination of the position of the easy direction of magnetization (EDM) with respect to crystallographic axes and of the values of the anisotropy constants in such compounds is possible only on single-crystal samples, but owing to the complex peritectic reactions of the formation of the R-Fe compounds the preparation of single crystals is quite difficult. Hence, the exact values of the anisotropy constants in many compounds were not determined and the positions of the EDM were found by means of indirect methods such as Miissbauer spectroscopy measurements on powder specimens. In addition, many results were contradictory, e.g. the different positions of the EDM as inferred from Mossbauer spectra calculations obtained by different authors for Y6FeZ3[3]. In this paper the EDM position of the iron sublattice in Y,Fe,, was identified by means of NMR. Magnetic measurements, made on single-crystal specimens, verified the EDM position and made it possible to determine the values of the anisotropy constants. In addition, the thermal expansion for Y,Fe,, single crystal was studied over a wide temperature range, including magnetically ordered and disordered regions. 2. Experimental
details
The Y,Fe,, alloys were prepared from 99.9% (or better) purity starting materials by means of induction melting in an argon atmosphere. The ingots were remelted in a resistance electric furnace to,increase the grain size. According to Elsevier Sequoia/Printed in The Netherlands
102
X-ray and metallographic analysis the alloys contained less than 3% of extraneous phases. Single-crystal specimens were cut out of large grams of the ingot in the shape of a sphere of diameter approximately 2 mm. The disorientation of subgrains in the specimens used for investigation was less than 3”. The thermal expansion was studied in the temperature range 5-900 K, using an X-ray diffractometer with Fe K radiation. The crystal lattice parameter a was determined from the a- 12.00 reflection (angle of diffraction 2 8 = 146”- 150”). The NMR spectra were recorded on powder samples in a paraffin matrix by the spin echo method at 4.2 K. Measurements of magnetic characteristics were carried out using a vibrating sample magnetometer with a d.c. magnetic field in the electromagnet of up to 0.2 T in the temperature range 4.2-700 K. The position of the EDM was determined from magnetization curves along various crystallographic axes and by a torque ma~etometer.
3. Crystal structure and thermal expansion The f.c.c. compound Y6Fe,, has a crystal structure of the Th,Mn,, structure type (Fm3m space group) [4], in which the yttrium atoms have one c~sta~ograp~c position and the iron atoms have four positions. The temperature dependence of the lattice parameter a is shown in Fig. 1. The broken line shows the phonon contribution to the thermal expansion, determined by extrapolating the temperature curve from the paramagnetic to the magnetically ordered region. The extrapolation was obtained from the experimental curve in the range 500-900 K, using a Debye temperature Tr, = 390 K. This value was taken from a linear interpolation between Tn of YFe, and Y,Fe,,, determined from sound velocity measurements [5]. As can be seen from Fig. 1, in the magnetically ordered region the experimental curves differ from the predictions of the Debye theory. The relative difference Aa/a is equal to the spontaneous linear magnetostriction aB. The value of A,, as well as the value of volume ma~etost~ction defo~ation w, (in cubic crystals u, = 31,) at 5 K are shown in Table 1. As will be shown below, the EDM in the magnetically ordered region lies along the [ 1001 axis. This can lead to tetragonal distortions of a magnitude proportional to the magnetostriction constant I,,,. However, the corresponding splitting of the X-ray lines was not observed. Hence, the anisotropic ma~etostriction constant I,“, in this compound is less than 5 X 10 -s. This result is in good agreement with the value of magnetostriction in Y,Fe,, 3 x lop5 obtained in ref. 6 by strain gauge techniques at room temperature.
4. NMR In Y,Fe,,, five NMR signals with frequency values of 34.1, 37.6, 39.3, 42.2 and 49.3 MHz (see Fig. 2) were obtained. Measurements of the NMR signals using
103 atnm), 1.216
I
1.200' 0
400
800
T(K) Fig. 1. Temperature phonon contribution
dependence of the lattice parameter a for Y,Fe,,. The broken line shows the to the thermal expansion. The arrow shows the Curie temperature.
TABLE 1 Magnetic and crystallographic
characteristics
T= 300 K
T=5K
Pnm,
(“G10-j)
1.2082
3.4
of Y,Fe,, T=4.2
K
US %) 39.3
10.2
1
34
38
40
42
F (MHz) Fig. 2. NMR spectra for Y,Fe,,. (1) 57Fe, (2) &‘Y.
50
483
104
an external magnetic field show that the most intensive 39.3 MHz signal originated from 89Y nuclei and the other signals from 57Fe nuclei. In the external magnetic field the NMR signals are displaced to the lower frequencies, indicating the presence of negative local fields on the nuclei. As seen from Fig. 2, the NMR signal on 89Y undergoes dissimilar broadening towards the lower frequencies. Such broadening can be explained, according to ref. 7, if account is taken of the anisotropic distribution of the dipole fields of iron atoms. In the general case the expression for the local magnetic field on yttrium nuclei in the multidomain specimen is as follows. 4~cM + Hdip Hoc = Hhf + ~ 3 where the first term is the hyperfine part of the field from the iron atoms, the second term is the Lorentz field and the third term is the dipole field of iron atoms
where ui is the magnetic moment of iron atom located at the sites with the radius vector ri (the centre of coordinates at the 89Y site). The summation was made extending over all iron sites in the volume of a sphere with radius R.Obviously, at the yttrium site having local magnetic symmetry lower than cubic, the dipole sum eqn. (2) will depend on the EDM of the crystal. Figure 3 shows the results of calculations of the dependence of Hdip on the angle 8 between the [loo] axis and the EDM (while rotating in the (110) plane we can pass through three main directions [ 1001, [ 11 l] and [ 1 lo]). The Hdip(e) was calculated using the values a = 1.2 112 nm, pre = 2,uu,, R = 3~. It can be seen from Fig. 3 that at 8 = 54” (EDM along [ 1111) Hdip = 0, but at 0 # 54” HdiP can adopt positive as well as negative values. In the case of 8 # 54” the crystallographic equivalent set of yttrium atoms forms two groups with HdiP of opposite signs occurring in a ratio 2 : 1. As a result, the NMR spectrum consists of two lines with different frequencies and intensities, addition of which leads to an asymmetric broadening of the resulting 89Y signal. Moreover, as is seen from Fig. 3, the broadening is different for the directions with 8 > 54” and 8 < 54”. As the local magnetic field on the yttrium nuclei is opposite to the direction of the magnetic moment pre, the experimentally observed broadening towards the low frequency can take place at 8 < 54”. The best agreement between the experimental and calculated splitting is observed for f3= O”, which corresponds to the EDM [loo]. In this case the s9Y line is the sum of two lines separated by 0.9 MHz (AH,i,=O.43 T). 5. Magnetic properties Figure 4 shows the magnetization curves of the Y,Fe,, single crystal along the main crystallographic axes at 4.2 K. The value of the iron magnetic moment, as
105
I
-0.2’
Fig. 3. Magnetic dipole fields experienced by the yttrium nuclei VS.the angle between the [loo] axis and the EDM in the (110) plane. The indexes 1 and 2 indicate the intensity ratio of the yttrium nuclei for the given field.
J
0’ 0
0.2
0.4
Hi(T) Fig.4. MagnetizationcurvesforY,Fe,,at T=4.2K.(1)H~~[100],(2)H~J[111],(3)H~~[110].Theinset shows the torque curve in the plane (110) at T= 290 K.
well as the Curie temperature, given in Table 1, are in a good agreement with those obtained in ref. 8. It can be seen that the EDM lies along the [ 1001 axis, as has been shown from the NMR spectra analysis. The hard magnetization direction is [l lo] and the intermediate axis is [ 1111. The anisotropy constant K, can be obtained from the subtraction of the areas under the magnetization curves along the axes [l lo] and [loo], i.e. according to ref. 9, K, =4 (A,,,-A,,,)= 3.6X lo5 J mm3 at T= 4.2K. However, the anisotropy field H, = 2K,/M, = 8.5 mT along the [ 1 lo] axis is much greater than the experimental value H, = 0.5 T. Such behaviour may be attributed to (1) the effect of higher order anisotropy constants or (2) a possible deformation of the magnetic structure under the magnetization of the multisublattice ferromagnet along the hard magnetization axis. With increasing temperature the distinction in the magnetization curves along various axes sharply decreases and at T= 290 K these curves become practically indistinguishable.
106
It is to be noted that torque magnetometer measurements on a Y,Fe,, single crystal in the ( 110) plane at T= 77 and 290 K (see Fig. 4) completely confirm the distribution of the magnetization directions obtained from the magnetization curves.
6. Conclusions Magnetic and crystallographic measurements on a Y,Fe,, single crystal were made. Results of NMR measurements showed that the EDM lies along the [loo] axis, which was confirmed from the magnetization curves and torque magnetometer measurements.
References 1 2 3 4 5 6 7 8 9
J. J. M. Franse, N. P. Thuy and N. M. Hong, J. Magn. Map Mater., 72 (1988) 36 1. B. Szpunar, J. Less-Common Met., 127( 1987) 55. H. R. Kirchmayr and C. A. Poldy, J. Map Magn. Muter., 8 (1978) 1. C. E. Crowder and W. J. James, J. Less-Common Met., 95 (1983) 1. G. M. Quashnin, personal communication, 1985. J. J. Croat, J. Mugn. Magn. Mater., 15-18( 1980) 597. M. P. Dariel, U. Atzmony and D. Lebenbaum, Phys. Status Solidi B, 59 ( 1973) 6 15. K. H. J. Buschow, Solid State Commun., 19 ( 1976) 42 1. G. S. Krinchik, Magnetic Phenomena Physics, Moscow University, 1985, p. 157.
Journal of the Less-Common Metals, 167( 1990) 101-106
MAGNETOCRYSTALLINE A. V. ANDREEV,
ANISOTROPY
M. I. BARTASHEVICH
IN Y,Fe,,
and V. A. VASILKOVSKY
Permanent Magnets Laboratory, Urals State University, 620083, Sverdlovsk (U.S.S.R.) (Received May 18,199O)
Summary A study has been made of the magnetic properties and thermal expansion of Y,Fe,, single crystals. Analysis of the NMR spectra shows that the easy direction of magnetization lies along the [ 1001 axis, which is confirmed by magnetization curves and torque measurements.
1. Introduction
It is known that the iron sublattice in intermetallic compounds of rare earth actinide metals (R) with iron can possess a high magnetocrystalline anisotropy, several times greater than in the metallic iron. This may be attributed to the fact that the 3d orbital moment is not completely quenched by the crystal field effects [ 1,2]. The accurate determination of the position of the easy direction of magnetization (EDM) with respect to crystallographic axes and of the values of the anisotropy constants in such compounds is possible only on single-crystal samples, but owing to the complex peritectic reactions of the formation of the R-Fe compounds the preparation of single crystals is quite difficult. Hence, the exact values of the anisotropy constants in many compounds were not determined and the positions of the EDM were found by means of indirect methods such as Miissbauer spectroscopy measurements on powder specimens. In addition, many results were contradictory, e.g. the different positions of the EDM as inferred from Mossbauer spectra calculations obtained by different authors for Y6FeZ3[3]. In this paper the EDM position of the iron sublattice in Y,Fe,, was identified by means of NMR. Magnetic measurements, made on single-crystal specimens, verified the EDM position and made it possible to determine the values of the anisotropy constants. In addition, the thermal expansion for Y,Fe,, single crystal was studied over a wide temperature range, including magnetically ordered and disordered regions. 2. Experimental
details
The Y,Fe,, alloys were prepared from 99.9% (or better) purity starting materials by means of induction melting in an argon atmosphere. The ingots were remelted in a resistance electric furnace to,increase the grain size. According to Elsevier Sequoia/Printed in The Netherlands
102
X-ray and metallographic analysis the alloys contained less than 3% of extraneous phases. Single-crystal specimens were cut out of large grams of the ingot in the shape of a sphere of diameter approximately 2 mm. The disorientation of subgrains in the specimens used for investigation was less than 3”. The thermal expansion was studied in the temperature range 5-900 K, using an X-ray diffractometer with Fe K radiation. The crystal lattice parameter a was determined from the a- 12.00 reflection (angle of diffraction 2 8 = 146”- 150”). The NMR spectra were recorded on powder samples in a paraffin matrix by the spin echo method at 4.2 K. Measurements of magnetic characteristics were carried out using a vibrating sample magnetometer with a d.c. magnetic field in the electromagnet of up to 0.2 T in the temperature range 4.2-700 K. The position of the EDM was determined from magnetization curves along various crystallographic axes and by a torque ma~etometer.
3. Crystal structure and thermal expansion The f.c.c. compound Y6Fe,, has a crystal structure of the Th,Mn,, structure type (Fm3m space group) [4], in which the yttrium atoms have one c~sta~ograp~c position and the iron atoms have four positions. The temperature dependence of the lattice parameter a is shown in Fig. 1. The broken line shows the phonon contribution to the thermal expansion, determined by extrapolating the temperature curve from the paramagnetic to the magnetically ordered region. The extrapolation was obtained from the experimental curve in the range 500-900 K, using a Debye temperature Tr, = 390 K. This value was taken from a linear interpolation between Tn of YFe, and Y,Fe,,, determined from sound velocity measurements [5]. As can be seen from Fig. 1, in the magnetically ordered region the experimental curves differ from the predictions of the Debye theory. The relative difference Aa/a is equal to the spontaneous linear magnetostriction aB. The value of A,, as well as the value of volume ma~etost~ction defo~ation w, (in cubic crystals u, = 31,) at 5 K are shown in Table 1. As will be shown below, the EDM in the magnetically ordered region lies along the [ 1001 axis. This can lead to tetragonal distortions of a magnitude proportional to the magnetostriction constant I,,,. However, the corresponding splitting of the X-ray lines was not observed. Hence, the anisotropic ma~etostriction constant I,“, in this compound is less than 5 X 10 -s. This result is in good agreement with the value of magnetostriction in Y,Fe,, 3 x lop5 obtained in ref. 6 by strain gauge techniques at room temperature.
4. NMR In Y,Fe,,, five NMR signals with frequency values of 34.1, 37.6, 39.3, 42.2 and 49.3 MHz (see Fig. 2) were obtained. Measurements of the NMR signals using
103 atnm), 1.216
I
1.200' 0
400
800
T(K) Fig. 1. Temperature phonon contribution
dependence of the lattice parameter a for Y,Fe,,. The broken line shows the to the thermal expansion. The arrow shows the Curie temperature.
TABLE 1 Magnetic and crystallographic
characteristics
T= 300 K
T=5K
Pnm,
(“G10-j)
1.2082
3.4
of Y,Fe,, T=4.2
K
US %) 39.3
10.2
1
34
38
40
42
F (MHz) Fig. 2. NMR spectra for Y,Fe,,. (1) 57Fe, (2) &‘Y.
50
483
104
an external magnetic field show that the most intensive 39.3 MHz signal originated from 89Y nuclei and the other signals from 57Fe nuclei. In the external magnetic field the NMR signals are displaced to the lower frequencies, indicating the presence of negative local fields on the nuclei. As seen from Fig. 2, the NMR signal on 89Y undergoes dissimilar broadening towards the lower frequencies. Such broadening can be explained, according to ref. 7, if account is taken of the anisotropic distribution of the dipole fields of iron atoms. In the general case the expression for the local magnetic field on yttrium nuclei in the multidomain specimen is as follows. 4~cM + Hdip Hoc = Hhf + ~ 3 where the first term is the hyperfine part of the field from the iron atoms, the second term is the Lorentz field and the third term is the dipole field of iron atoms
where ui is the magnetic moment of iron atom located at the sites with the radius vector ri (the centre of coordinates at the 89Y site). The summation was made extending over all iron sites in the volume of a sphere with radius R.Obviously, at the yttrium site having local magnetic symmetry lower than cubic, the dipole sum eqn. (2) will depend on the EDM of the crystal. Figure 3 shows the results of calculations of the dependence of Hdip on the angle 8 between the [loo] axis and the EDM (while rotating in the (110) plane we can pass through three main directions [ 1001, [ 11 l] and [ 1 lo]). The Hdip(e) was calculated using the values a = 1.2 112 nm, pre = 2,uu,, R = 3~. It can be seen from Fig. 3 that at 8 = 54” (EDM along [ 1111) Hdip = 0, but at 0 # 54” HdiP can adopt positive as well as negative values. In the case of 8 # 54” the crystallographic equivalent set of yttrium atoms forms two groups with HdiP of opposite signs occurring in a ratio 2 : 1. As a result, the NMR spectrum consists of two lines with different frequencies and intensities, addition of which leads to an asymmetric broadening of the resulting 89Y signal. Moreover, as is seen from Fig. 3, the broadening is different for the directions with 8 > 54” and 8 < 54”. As the local magnetic field on the yttrium nuclei is opposite to the direction of the magnetic moment pre, the experimentally observed broadening towards the low frequency can take place at 8 < 54”. The best agreement between the experimental and calculated splitting is observed for f3= O”, which corresponds to the EDM [loo]. In this case the s9Y line is the sum of two lines separated by 0.9 MHz (AH,i,=O.43 T). 5. Magnetic properties Figure 4 shows the magnetization curves of the Y,Fe,, single crystal along the main crystallographic axes at 4.2 K. The value of the iron magnetic moment, as
105
I
-0.2’
Fig. 3. Magnetic dipole fields experienced by the yttrium nuclei VS.the angle between the [loo] axis and the EDM in the (110) plane. The indexes 1 and 2 indicate the intensity ratio of the yttrium nuclei for the given field.
J
0’ 0
0.2
0.4
Hi(T) Fig.4. MagnetizationcurvesforY,Fe,,at T=4.2K.(1)H~~[100],(2)H~J[111],(3)H~~[110].Theinset shows the torque curve in the plane (110) at T= 290 K.
well as the Curie temperature, given in Table 1, are in a good agreement with those obtained in ref. 8. It can be seen that the EDM lies along the [ 1001 axis, as has been shown from the NMR spectra analysis. The hard magnetization direction is [l lo] and the intermediate axis is [ 1111. The anisotropy constant K, can be obtained from the subtraction of the areas under the magnetization curves along the axes [l lo] and [loo], i.e. according to ref. 9, K, =4 (A,,,-A,,,)= 3.6X lo5 J mm3 at T= 4.2K. However, the anisotropy field H, = 2K,/M, = 8.5 mT along the [ 1 lo] axis is much greater than the experimental value H, = 0.5 T. Such behaviour may be attributed to (1) the effect of higher order anisotropy constants or (2) a possible deformation of the magnetic structure under the magnetization of the multisublattice ferromagnet along the hard magnetization axis. With increasing temperature the distinction in the magnetization curves along various axes sharply decreases and at T= 290 K these curves become practically indistinguishable.
106
It is to be noted that torque magnetometer measurements on a Y,Fe,, single crystal in the ( 110) plane at T= 77 and 290 K (see Fig. 4) completely confirm the distribution of the magnetization directions obtained from the magnetization curves.
6. Conclusions Magnetic and crystallographic measurements on a Y,Fe,, single crystal were made. Results of NMR measurements showed that the EDM lies along the [loo] axis, which was confirmed from the magnetization curves and torque magnetometer measurements.
References 1 2 3 4 5 6 7 8 9
J. J. M. Franse, N. P. Thuy and N. M. Hong, J. Magn. Map Mater., 72 (1988) 36 1. B. Szpunar, J. Less-Common Met., 127( 1987) 55. H. R. Kirchmayr and C. A. Poldy, J. Map Magn. Muter., 8 (1978) 1. C. E. Crowder and W. J. James, J. Less-Common Met., 95 (1983) 1. G. M. Quashnin, personal communication, 1985. J. J. Croat, J. Mugn. Magn. Mater., 15-18( 1980) 597. M. P. Dariel, U. Atzmony and D. Lebenbaum, Phys. Status Solidi B, 59 ( 1973) 6 15. K. H. J. Buschow, Solid State Commun., 19 ( 1976) 42 1. G. S. Krinchik, Magnetic Phenomena Physics, Moscow University, 1985, p. 157.