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Torque measurements and magnetic domain structure of UFe9AlSi2 intermetallic compound
Journal of Magnetism and Magnetic Materials 140-144 (1995) 1915-1916
~
Journalof renalnetlsm magnetic ~ i materials
ELSEVIER
Torque measurements and magnetic domain structure of UFegA1Si 2 intermetallic compound J.J. Wystocki a,* W. Suski b, p. Pawlik a, K. Wochowski b a Institute of Physics, Technical University ofCzqstochowa, AI. Armii Krajowej 19, 42-200 Cz(stochowa, Poland b W. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 937, 50-950 Wroctaw 2, Poland
Abstract The magnetic torque T, rotational hysteresis energy Wr and its integral R of the UFe9AISi a compound were determined. Moreover, magnetic domain structures were studied using the powder pattern method.
UFe9AlSi 2 is an actinide representative of the RFe12_xM x class of magnetic materials with tetragonal ThMn12-type of structure [1,2]. We have chosen this compound for present examination, because it is one of few materials which does not contain an admixture of ot-Fe [1]. Now we report on the magnetic domain structure and its characteristic parameters. Moreover, in order to obtain information concerning the magnetization reversal process in the UFe9AiSie, we have extended our investigations on magnetic torque measurements and rotational hysteresis energy. This research is a continuation of our earlier examination of domain structure of UFeloSi 2 and UCol0Si 2 [3]. The UFe9AlSi 2 aligned material was obtained by melting the components in stoichiometric quantities in arc furnace under an Ar protective atmosphere, and annealing them at 900°C for two weeks. The torque intensity T as a function of the angle (9 between the applied magnetic field direction and easy magnetization axis laying in the plane perpendicular to the cooling surface of the sample was measured at room temperature using a torque magnetometer in a magnetic field up to 2000 k A / m . The rotational hysteresis energy Wr, i.e. energy necessary for a 360 ° turn of the magnetic material in constant magnetic field was calculated from the torque curves according to Ref. [4]. The anisotropy constants K1 = 4.8 X 105 J / m 3 and K 2 = 0.7 X 105 J / m 3 were determined from the Fourier analysis of the torque curves. Moreover, the anisotropy constant K~ and saturation magnetization M= were calculated from the following dependence: (d~9/dT)e=lo =
1 / 2 K 1 + 1 / H M s. This dependence gives the same value for K 1 = 4.8 × 105 J / m 3, as from Fourier analysis and M= = 59.4 mT. Typical torque curves T for UFe9AISi 2 compound are shown in Fig. 1. The torque curves measured for two different directions of magnetic field rotation (clockwise CW and anticlockwise - ACW) are identical when the rotational hysteresis energy Wr is equal to zero. It is observed when the value of the magnetic field is too low (Fig. la, H = 34 k A / m ) or when the value of the field is sufficiently high and Wr is no longer present. The curves in Fig. lb correspond to the field H = 334 k A / m , when the rotational hysteresis energy reaches its maximum value (an area enclosed by CW and A C W curves is a measure of the value of Wr). All torque curves are described by the function sin 2@ type. In Fig. 2 the relationship between
3.0 / ~
H = 34 k N m
'
2.0
1o
CW
~oo iO-1.0
[i
, a)
" ~ E A n g l e , e [ d e g ] "~,~
-2.0
.=°i
0
~--2o * Corresponding author. Fax: +48-34-612385. 0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 4 ) 0 1 2 5 7 - 1
)
le
Fig. 1. Torque curves for the UFe9AlSi2 compound.
Jd. Wystocki et aL /Journal of Magnetism and Magnetic Materials 140-144 (1995) 1915-1916
1916
the rotational hysteresis energy Wr and magnetic field H for the UFe9AISi 2 compound is presented. This curve shows that rotational hysteresis energy begins for fields as low as H = 82 k A / m , reaching its maximum (Wr)max = 9.55 k J / m 3 in a field h = H / H A = 0.2 (where anisotropy field H A = 2(K 1 + 2 K 2 ) / M s = 1630 k A / m ) and then decreases. The results obtained in this work, concerning the rotational hysteresis energy, can be explained on the basis of Shtrikman-Treves theory [5]. The theoretical curves given by this theory show that maximum rotational hysteresis occurs at a field h < 0.5, which depends on the parameter S. When S < 1 a reversal mechanism occurs by coherent rotation of the magnetization vector and when S > 1.47, magnetization reversal occurs by incoherent mechanism. According to the Shtrikman-Treves theory values of h obtained in this work correspond to S = 2.0 and hence to magnetization reversal by the incoherent mechanism. We have also calculated the rotational hysteresis integral R. From theoretical calculations it is known that when R = 0.415 to 4.0 (depending on the value of S) the magnetization reversal process occurs by incoherent mechanism. For UFe9A1Si 2 compound this integral amounts to R = 2.25. This value of R corresponds to the value of S = 2.1 and therefore adds further support to the conclusion that changes in the magnetization occur principally by the incoherent mechanism. The domain structures observed in the UFe9AISi 2 compound are characteristic of crystals with high uniaxial magnetocrystalline anisotropy. In Fig. 3 typical magnetic domains for this compound are shown using the powder pattern method. Fig. 3a presents the grain surface parallel to the easy axis (perpendicular to the cooling direction). In this plane domains with 180 ° Bloch walls dominate. At the ends of such domains, i.e. at the grain boundaries, closure domains occur in the form of spikes. From the theory of domain structures it is known that for such domains the dependence of 180 ° domain width D on crystal thickness L satisfies the equation D = k T 1 / 3 L 2/3, where k is a parameter characteristic of the material [6]. From this 10
!1~ Fig. 3. Magnetic domain structure of the UFe9AISi 2 compound on the surface of the grains parallel (a) and perpendicular (b) to the easy axis (the powder pattern method). dependence we have determined the domain wall energy y = 11.4 e r g / c m 2. The domain structure presented in Fig. 3a indicates that the UFe9AISi 2 compound is not perfectly aligned, because besides the 180 ° domain walls there are more complex domains (e.g. in the form of daggers) on grain surfaces slightly inclined to the plane in which the magnetic easy direction lies. Fig. 3b shows domain structure on the grain surfaces perpendicular to the magnetic easy direction. The domains form a characteristic star-like structure with spike-like closure domains. For the domain structure revealed on the basal plane, the method of Bodenberger and Hubert [7] has been applied to calculate the domain wall energy y = 10.8 e r g / c m 2. Compared with the value of 11.4 e r g / c m 2 calculated from D(L) dependence, this value gives good agreement, if one takes into account the considerable simplifications of both methods. From the domain wall energy y and anisotropy constant K 1 we have also calculated the exchange constant A = y 2 / 1 6 K 1 = 1.5 × 10 -6 ergo/cm, the domain wall thickness 6 B = 7 r y / 4 K 1 = 180 A, and the critical diameter for single-domain particle D c = 1.4T/M s = 0.43 ~m. References
8
~6
2 0
1
0
500
1000 1500 Applied field, H [kA/rn]
2000
Fig. 2. The dependence of the rotational hysteresis energy Wr on the applied field H for the UFegAISi2 compound.
[1] W. Suski, A. Baran, K. Wochowski and T. Mydlarz, J. Magn. Magn. Mater. 95 (1991) L 133. [2] A.V. Andreev and W. Suski, J. Alloys for Compounds 187 (1992) 381. [3] J.J. Wys~ocki, W. Suski and A. Baran, J. Less-Common Met. 163 (1990) 115. [4] R.M. Bozorth, Ferromagnetism (Van Nostrand, New York, 1951) ch. 11. [5] S. Shtrikman and D. Treves, J. Phys. Radium 20 (1959) 286. [6] R. Szymczak, Acta Phys. Pol. A 43 (1973) 571. [7] R. Bodenberger and A. Hubert, Phys. Stat. Sol. (a) 44 (1979) K7.
~
Journalof renalnetlsm magnetic ~ i materials
ELSEVIER
Torque measurements and magnetic domain structure of UFegA1Si 2 intermetallic compound J.J. Wystocki a,* W. Suski b, p. Pawlik a, K. Wochowski b a Institute of Physics, Technical University ofCzqstochowa, AI. Armii Krajowej 19, 42-200 Cz(stochowa, Poland b W. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P.O. Box 937, 50-950 Wroctaw 2, Poland
Abstract The magnetic torque T, rotational hysteresis energy Wr and its integral R of the UFe9AISi a compound were determined. Moreover, magnetic domain structures were studied using the powder pattern method.
UFe9AlSi 2 is an actinide representative of the RFe12_xM x class of magnetic materials with tetragonal ThMn12-type of structure [1,2]. We have chosen this compound for present examination, because it is one of few materials which does not contain an admixture of ot-Fe [1]. Now we report on the magnetic domain structure and its characteristic parameters. Moreover, in order to obtain information concerning the magnetization reversal process in the UFe9AiSie, we have extended our investigations on magnetic torque measurements and rotational hysteresis energy. This research is a continuation of our earlier examination of domain structure of UFeloSi 2 and UCol0Si 2 [3]. The UFe9AlSi 2 aligned material was obtained by melting the components in stoichiometric quantities in arc furnace under an Ar protective atmosphere, and annealing them at 900°C for two weeks. The torque intensity T as a function of the angle (9 between the applied magnetic field direction and easy magnetization axis laying in the plane perpendicular to the cooling surface of the sample was measured at room temperature using a torque magnetometer in a magnetic field up to 2000 k A / m . The rotational hysteresis energy Wr, i.e. energy necessary for a 360 ° turn of the magnetic material in constant magnetic field was calculated from the torque curves according to Ref. [4]. The anisotropy constants K1 = 4.8 X 105 J / m 3 and K 2 = 0.7 X 105 J / m 3 were determined from the Fourier analysis of the torque curves. Moreover, the anisotropy constant K~ and saturation magnetization M= were calculated from the following dependence: (d~9/dT)e=lo =
1 / 2 K 1 + 1 / H M s. This dependence gives the same value for K 1 = 4.8 × 105 J / m 3, as from Fourier analysis and M= = 59.4 mT. Typical torque curves T for UFe9AISi 2 compound are shown in Fig. 1. The torque curves measured for two different directions of magnetic field rotation (clockwise CW and anticlockwise - ACW) are identical when the rotational hysteresis energy Wr is equal to zero. It is observed when the value of the magnetic field is too low (Fig. la, H = 34 k A / m ) or when the value of the field is sufficiently high and Wr is no longer present. The curves in Fig. lb correspond to the field H = 334 k A / m , when the rotational hysteresis energy reaches its maximum value (an area enclosed by CW and A C W curves is a measure of the value of Wr). All torque curves are described by the function sin 2@ type. In Fig. 2 the relationship between
3.0 / ~
H = 34 k N m
'
2.0
1o
CW
~oo iO-1.0
[i
, a)
" ~ E A n g l e , e [ d e g ] "~,~
-2.0
.=°i
0
~--2o * Corresponding author. Fax: +48-34-612385. 0304-8853/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 8 8 5 3 ( 9 4 ) 0 1 2 5 7 - 1
)
le
Fig. 1. Torque curves for the UFe9AlSi2 compound.
Jd. Wystocki et aL /Journal of Magnetism and Magnetic Materials 140-144 (1995) 1915-1916
1916
the rotational hysteresis energy Wr and magnetic field H for the UFe9AISi 2 compound is presented. This curve shows that rotational hysteresis energy begins for fields as low as H = 82 k A / m , reaching its maximum (Wr)max = 9.55 k J / m 3 in a field h = H / H A = 0.2 (where anisotropy field H A = 2(K 1 + 2 K 2 ) / M s = 1630 k A / m ) and then decreases. The results obtained in this work, concerning the rotational hysteresis energy, can be explained on the basis of Shtrikman-Treves theory [5]. The theoretical curves given by this theory show that maximum rotational hysteresis occurs at a field h < 0.5, which depends on the parameter S. When S < 1 a reversal mechanism occurs by coherent rotation of the magnetization vector and when S > 1.47, magnetization reversal occurs by incoherent mechanism. According to the Shtrikman-Treves theory values of h obtained in this work correspond to S = 2.0 and hence to magnetization reversal by the incoherent mechanism. We have also calculated the rotational hysteresis integral R. From theoretical calculations it is known that when R = 0.415 to 4.0 (depending on the value of S) the magnetization reversal process occurs by incoherent mechanism. For UFe9A1Si 2 compound this integral amounts to R = 2.25. This value of R corresponds to the value of S = 2.1 and therefore adds further support to the conclusion that changes in the magnetization occur principally by the incoherent mechanism. The domain structures observed in the UFe9AISi 2 compound are characteristic of crystals with high uniaxial magnetocrystalline anisotropy. In Fig. 3 typical magnetic domains for this compound are shown using the powder pattern method. Fig. 3a presents the grain surface parallel to the easy axis (perpendicular to the cooling direction). In this plane domains with 180 ° Bloch walls dominate. At the ends of such domains, i.e. at the grain boundaries, closure domains occur in the form of spikes. From the theory of domain structures it is known that for such domains the dependence of 180 ° domain width D on crystal thickness L satisfies the equation D = k T 1 / 3 L 2/3, where k is a parameter characteristic of the material [6]. From this 10
!1~ Fig. 3. Magnetic domain structure of the UFe9AISi 2 compound on the surface of the grains parallel (a) and perpendicular (b) to the easy axis (the powder pattern method). dependence we have determined the domain wall energy y = 11.4 e r g / c m 2. The domain structure presented in Fig. 3a indicates that the UFe9AISi 2 compound is not perfectly aligned, because besides the 180 ° domain walls there are more complex domains (e.g. in the form of daggers) on grain surfaces slightly inclined to the plane in which the magnetic easy direction lies. Fig. 3b shows domain structure on the grain surfaces perpendicular to the magnetic easy direction. The domains form a characteristic star-like structure with spike-like closure domains. For the domain structure revealed on the basal plane, the method of Bodenberger and Hubert [7] has been applied to calculate the domain wall energy y = 10.8 e r g / c m 2. Compared with the value of 11.4 e r g / c m 2 calculated from D(L) dependence, this value gives good agreement, if one takes into account the considerable simplifications of both methods. From the domain wall energy y and anisotropy constant K 1 we have also calculated the exchange constant A = y 2 / 1 6 K 1 = 1.5 × 10 -6 ergo/cm, the domain wall thickness 6 B = 7 r y / 4 K 1 = 180 A, and the critical diameter for single-domain particle D c = 1.4T/M s = 0.43 ~m. References
8
~6
2 0
1
0
500
1000 1500 Applied field, H [kA/rn]
2000
Fig. 2. The dependence of the rotational hysteresis energy Wr on the applied field H for the UFegAISi2 compound.
[1] W. Suski, A. Baran, K. Wochowski and T. Mydlarz, J. Magn. Magn. Mater. 95 (1991) L 133. [2] A.V. Andreev and W. Suski, J. Alloys for Compounds 187 (1992) 381. [3] J.J. Wys~ocki, W. Suski and A. Baran, J. Less-Common Met. 163 (1990) 115. [4] R.M. Bozorth, Ferromagnetism (Van Nostrand, New York, 1951) ch. 11. [5] S. Shtrikman and D. Treves, J. Phys. Radium 20 (1959) 286. [6] R. Szymczak, Acta Phys. Pol. A 43 (1973) 571. [7] R. Bodenberger and A. Hubert, Phys. Stat. Sol. (a) 44 (1979) K7.