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Magnetic properties in amorphous Co93−XTbXZr7 thin films
Physica B 253 (1998) 142—147
Magnetic properties in amorphous Co Tb Zr thin films 93~X X 7 H. Ouahmane!,", H. Lassri#,*, A. Itri$, A. Khmou", G. Suran% ! De& partement de physique, Universite& Moulay Ismaı( l, Faculte& des sciences et techniques, d+Errachidia, Boutalamine B.P. 509 Errachidia, Morocco " LPS, Universite& Moulay Ismaı( l, Faculte& des sciences de Meknes, B.P. 4010, Morocco # LPMME, Universite& Hassan II, Faculte& des sciences Ain chok, MaaL rif, B.P. 5366, Route d’E1 Jadida, km 8, Casablanca, Morocco $ LPM, Universite& Mohammed V, Faculte& des sciences, avenue Ibn Batouta, B.P. 1014, Rabat, Morocco % Laboratoire de Magnetisme de Louis. Ne& el, CNRS, Av. des Marthyrs B.P. 38042 38 Grenoble 9 Cedex, France Received 22 January 1997; received in revised form 17 February 1998
Abstract Amorphous Co Tb Zr thin films with a well-defined in-plane uniaxial anisotropy were prepared by RF 93~X X 7 sputtering. The saturation magnetization 4pM , the uniaxial anisotropy constant K and the coercive field H were 4 6 # studied as a function of temperature and for the composition range 0(X(7. The Tb moment at 4.2 K is found to be 9k in agreement with the theoretical value. This would indicate a collinear spin structure for Tb. The mean-field theory B has been used to explain the temperature dependence of the magnetization. The exchange interactions between Co—Co and Co—Tb atom pairs have been evaluated. K and H are related by the equation H "aKn /k M with the fitting 6 # # 6 0 4 parameters a and n. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Co Tb Zr ; Thin films; Magnetic properties 93~X X 7
1. Introduction Amorphous ferromagnetically soft thin films containing rare earth metals are of interest due to their industrial applications. The films are also interesting from a scientific point of view as they offer the possibility to study various aspects of 3d and 4f magnetism. Contrary to crystalline materials these aspects can be investigated in a continuous concentration of the rare earth metal as well as in relation
* Corresponding author.
with the low local symmetry that is characteristic for the amorphous state. Rare earth metal atoms with spin—orbit interaction are known to give rise to large random anisotropy in amorphous films [1]. Amorphous films can exhibit fairly low values of the coercive field H , much smaller than 1 Oe # [2,3]. The magnitude of H is generally related to # the overall composition of the films and the deposition parameters used. The main intrinsic parameters which affect the value of the H are the # uniaxial anisotropy, the saturation magnetization and the microstructure which may lower or increase the coercive field. In this work we describe
0921-4526/98/$ — see front matter ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 3 6 5 - 2
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143
the results of our magnetic studies of amorphous Co Tb Zr films as a function of temperature 93~X X 7 in the range 4.2—300 K.
2. Experimental The amorphous films were deposited by the RF diode sputtering techniques using Argon as a sputtering gas. We used the same deposition parameters, i.e. a pressure of the sputter gas of p "2 mTorr and RF input power of 300 W. For A3 the value of P used the amorphous structure A3 appears to be most homogeneous and for a given composition the magnitude of K was minimal. 6 During the deposition a DC field of 700 Oe was applied parallel to the film plane giving rise to an in plane uniaxial anisotropy field H "2K /M . , 6 4 H was determined by M—H loop and FMR , measurements. The amorphous structure was confirmed by Xray diffraction using CuKa radiation. The exact composition was determined by electron probe microanalysis. The magnetization was measured by a vibrating sample magnetometer from 4.2 to 300 K in magnetic fields up to 1 kOe.
3. Results and discussion All films exhibit in plane hysteresis loops which are characteristic of high-quality amorphous soft ferromagnetic thin films. Along the easy axis a rectangular hysteresis loop is detected, with H @H . # , Along the hard axis a loop with a shape characteristic of a thin film exhibiting a very well-defined in-plane uniaxial anisotropy is detected. Now, the magnetization process occurs by coherent rotation, so the applied field for saturation is equal to H at , all temperatures. The concentration dependence of the magnetization (4pM ) at 300 K is shown in Fig. 1. There is 4 a linear decrease in 4pM for 0(x(7. The above 4 results are characteristic of the antiferromagnetic interaction between Tb and Co atoms which is well known. The alloys moment (k ) can be written as ! k (¹)"D(93!X)k (¹)!Xk (¹)D/100. (1) ! C0 T"
Fig. 1. The Tb concentration dependence of 4pM at 4 ¹"300 K. The solid line was obtained by linear regression.
For small concentrations (X(7) of Tb, the moment of Co at 4.2 K is not perturbed. So taking the value of k "1.55k obtained from the alloy with C0 B X"0 and substituting it in (Eq. (1)); it is possible to determine k . The calculated moment is found T" to be 9k in agreement with the theoretical value. B This would indicate a collinear spin structure for Tb. The temperature dependence of the magnetization has been studied. Fig. 2 shows the results for Co Tb Zr and Co Tb Zr thin films. It is 87.3 5.7 7 88.3 4.7 7 seen that with increasing Tb content as the temperature is lowered magnetization first shows a broad peak and then starts decreasing. This decrease in magnetization is due to an increase in the magnetization of the sublattice of Tb. For the concentration studied here the compensation of moments do not occur. The mean-field theory has been used in the past by several authors to calculate the temperature dependence of the magnetization in many amorphous rare earth (R), transition metal (T) alloys [4—6]. We have performed such an analysis of the temperature dependence of the magnetization in amorphous Co Tb Zr films. (Eq. (1)) can be 93~X X 7 rewritten as k (¹)"D(93!X)g S (¹)!Xg J (¹)Dk /100, ! C0 C0 T" T" B (2)
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S (¹) and J (¹) were assumed to be expressed C0 T" by the Brillouin function as
Fig. 2. The temperature dependence of the magnetization for the amorphous Co Tb Zr alloys (X"4.7 and 5.7). The 93~X X 7 solid and dashed lines were calculated from the mean-field theory.
where S , J and k , are respectively the Co spin C0 T" B momentum, the total angular momentum of Tb and the Bhor magneton. g is the Lande´ factor i (i"Co,Tb); we take g "2 and g "1.5. C0 T"
J (¹)"J (0)B (g J k H /k ¹), (3) T" T" J(T") T" T" B T" B S (¹)"S (0)B (g S k H /k ¹), (4) C0 C0 S(C0) C0 C0 B C0 B k is the Boltzmann constant. The molecular fields B H and H are given by C0 T" H "2J z (g !1)2J /g k T" T"T" T"T" T" T" T" B #2J z (g !1)S g k , (5) C0T" T"C0 T" C0 T" B H "2J z S /g k C0 C0C0 C0C0 C0 C0 B #2J z (g !1)J /g k , (6) C0T" C0T" T" T" C0 B where z is the coordination number taken to be ij z "z "12(93!X)/100, (7) C0C0 T"C0 z "z "12X/100, (8) C0T" T"T" J ,J and J are the exchange constants C0C0 C0T" T"T" for Co—Co, Co—Tb and Tb—Tb interactions, respectively. Using the spin values given in Table 1 and adjusting the exchange interactions J ,J and C0C0 C0T" J , the sublattice magnetizations M , M and T"T" T" C0 the total magnetization M"DM !M D can be C0 T" calculated. From these fits the exchange interactions were extracted as a function of the Tb content (Table 1). It is seen that J increases and C0T" J decreases, when the Co concentration inC0C0 creases. A similar increase in J has been reported RT in intermetallic compounds and amorphous alloys also [7—10]. The 3d—5d interactions depend critically on 3d—5d hybridization according to Brooks et al. [11]. Therefore the increase in J would C0T" indicate an increase in 3d—5d hybridization when the Co concentration relative to Tb is decreased.
Table 1 Some magnetic parameters of amorphous Co Tb Zr thin films 93~X X 7 X
S C0 (k ) B
J C0C0 (10~16 erg)
J C0T" (10~16 erg)
J T"T" (10~16 erg)
¹ # (K)
A (10~8 erg/cm)
0 4.7 5.7 6.5
0.69 0.69 0.69 0.69
184 170 160 155
— 15 15.5 16.5
— 1.6 1.6 1.7
1160 1018 929 906
61 53 49 47
H. Ouahmane et al. / Physica B 253 (1998) 142—147
145
The temperature dependence of M is shown in Fig. 2 for two different compositions. It is seen that experimental points align well with the calculated curve. We also calculated the temperature dependences of M and M which are also shown in C0 T" Fig. 2. The Curie temperature ¹ is expressed as [12] C 3k ¹ "a #a #[(a #a )2 B C C0C0 T"T" C0C0 T"T" !4(a
a !a a )]1@2, C0C0 T"T" C0T" T"C0
(9)
a "z J S (S #1), C0C0 C0C0 C0C0 C0 C0
(10)
a "z J J (J #1)(g !1)2, T"T" T"T" T"T" T" T" T"
(11)
a a "z z (J )2(g !1)2 C0T" T"C0 C0T" T"C0 C0T" T" ]S (S #1)J (J #1). C0 C0 T" T"
(12)
Thus knowing all the parameters, ¹ could be C calculated. It is seen that ¹ is decreased by the C addition of Tb and arised mainly from the weakening of the Co—Co interaction. The exchange stiffness constant A can be calculated after Hasegawa [13] from the relation N A(¹)"Mn J (g !1)2J2 (¹)[X/100]2/r T" T"T" T"T" T"T" T" #M[n #n ]J [g !1]J (¹)S (¹) C0T" T"C0 C0T" T" T" C0 ]X(93!X)/1002/r
N T"C0
N, #Mn J S2 (¹)[(93!X)/100]2/r C0C0 C0C0 C0C0 C0 (13) where n is the maximum permissible atom pairs ij per unit volume extended to first neighbors. In our case, we take n to be 2; r are the interatomic ij ij distances, which are taken to be r "2.5 A_ , C0C0 r "3.0 A_ and r "3.5 A_ , in accordance with C0T" T"T" the structural data of Harris et al. [14]. Thus obtained A is listed in Table 1 as a function of composition at 4.2 K. This behaviour of A is in conformity with the variation of the Curie temperature in Table 1. The uniaxial anisotropy constant K of 6 Co Tb Zr films can be described in terms of 93~X X 7 the dipolar coupling coefficients C for all combiij nations of the two elements and single-ion coeffic-
Fig. 3. Experimental data of the K for the composition 6 Co Tb Zr at room temperature. The solid line was ob93~X X 7 tained by linear regression.
ient D for Tb [15] 1 (14) K " + C M M #DX(m )2, ij i j T" 6 2 ij where M represent the Co and Tb sublattice magi,j netizations, X the Tb content and m " T" M (¹)/M (0). The C are the dipolar coupling T" T" ij constants and D is the single-ion anisotropy constant. The room-temperature variation of K versus Tb 6 concentration is shown in Fig. 3. K increases with 6 increasing Tb content. The solid line was obtained from linear regression. This behavior demonstrated the leading contribution of the single-ion term of Tb in (Eq. (14)). Fig. 4 shows K versus temperature for two 6 compositions Co Tb Zr and Co Tb Zr . 87.3 5.7 7 88.3 4.7 7 Using the sublattice magnetizations inferred from the mean-field analysis, the dependence of K on 6 temperature can be calculated. The coercivity is essentially controlled by the microstructure, the uniaxial anisotropy and the saturation magnetization [16]. Hansen correlated H and K for Tb-based alloys in a simple relation # 6 [17] H "aKn /k M , (15) # 6 0 4 where a represents a microstructural parameter.
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Fig. 4. Temperature dependence of K for Co Tb Zr and 6 87.3 5.7 7 Co Tb Zr thin films. 88.3 4.7 7
Fig. 6. Coercive energy versus uniaxial anisotropy measured between 80 and 300 K on samples with different Tb contents for amorphous Co Tb Zr . The solid line was fitted to the data 93~X X 7 yielding n and a. (m, X"5.7), (j, X"4.7) and (v, for different Tb contents at 300 K).
Fig. 5. Coercive field (H ) versus composition for # Co Tb Zr films at ¹"300 K. The solid line was obtained 93~X X 7 by linear regression.
The room temperature variations of the coercive field H versus Tb content is presented in Fig. 5. # H increases continuously with the increasing Tb C content. According to (Eq. (15)), the coercivity is expected to increase with Kn , where n is determined by the 6 mechanism controlling H . The linear increase of # K with Tb content in amorphous Co Tb Zr 6 93~X X 7 thin films was well established and a plot
Fig. 7. Temperature dependence of H for Co Tb Zr (j) # 87.3 5.7 7 and Co Tb Zr (m) films. The solid lines were calculated 88.3 4.7 7 using (Eq. (15)).
1/2(k H M ) versus K presented in Fig. 6 for dif0 # 4 6 ferent Tb contents and at temperature between 80 and 300 K yield n"1.27 and log a"!2.9. Friedberg and Paul showed that H is propor# tional to K3@2 at a given microstructure if the 6 magnetization reversal process takes place by the
H. Ouahmane et al. / Physica B 253 (1998) 142—147
domain wall motion [18]. Kronmu¨ller obtained a value of n"5 from theoretical calculations under 4 the assumption that the domain wall motion is dominated by exchange fluctuations [19,20]. Polak et al. concluded that the coercivity due to the surface roughness appears to be directly proportional to the domain wall energy and H increases in # proportion with K1@2 [21]. 6 Fig. 7 shows the coercive field measurements (H ) on Co Tb Zr and Co Tb Zr in # 87.3 5.7 7 88.3 4.7 7 comparison to calculations using (Eq. (15)) with the above mentioned n and a. A reasonable agreement of calculation and experiment for ¹'80 K indicated that the domain wall motion is dominated by exchange fluctuations. 4. Conclusion The magnetic properties of Co Tb Zr films 93~X X 7 were investigated with respect to their compositional and temperature dependence. The saturation magnetization was analyzed in terms of the meanfield theory. The Co moment, the Curie temperature and the exchange interactions J and C0C0 J were evaluated. Therefore the increase of C0T" J with an increase of Tb content is attributable C0T" to the 3d—5d hybridization effect. The uniaxial anisotropy and the coercive field augment with the increasing Tb content. References [1] R. Harris, M. Plischke, M.J. Zuckermann, Phys. Rev. Lett. 31 (1973) 160.
147
[2] A.P. Valanju, I.S. Leong, D.Y. Kim, R.M. Walser, J. Appl. Phys. 64 (1988) 5443. [3] G. Suran, H. Ouahmane, J. Sztern, J. Magn. Magn. Mater. 140—144 (1995) 691. [4] R. Hasegawa, B.E. Argyle, L.J. Tao, AIP Conf. Proc. 24 (1975) 110. [5] A. Gangulee, R.J. Kobliska, J. Appl. Phys. 49 (1978) 4169. [6] R. Krishnan, O. El Marrakchi, H. Lassri, P. Rougier, J. Appl. Phys. 73 (1993) 7599. [7] N.H. Duc, Phys. Stat. Sol. 164 (1991) 545. [8] N.H. Duc, T.D. Hien, D. Givord, J. Magn. Magn. Mater. 104—107 (1991) 1344. [9] S. Ishio, N. Obara, S. Negami, T. Miyazaki, T. Kamimori, H. Tange, M. Goto, J. Magn. Magn. Mater. 119 (1993) 271. [10] R. Krishnan, H. Lassri, L. Driouch, F.E. Kayzel, J.J.M. Franse, J. Magn. Magn. Mater. 131 (1994) 297. [11] M.S.S. Brooks, L. Nordstom, B. Johanson, J. Phys. Condens. Mater. 3 (1991) 2357. [12] N. Heimann, K. Lee, R. Potter, S. Kirkpatrick, J. Appl. Phys. 47 (1976) 2634. [13] R. Hasegawa, J. Appl. Phys. 45 (1974) 3109. [14] V.G. Harris, K.D. Aylesworth, B.N. Das, W.T. Elam, N.C. Koon, Phys. Rev. Lett. 69 (1992) 1939. [15] P. Hansen, S. Klahn, C. Clausen, G. Munch, K. Witter, J. Appl. Phys. 69 (1991) 3194. [16] D. Givord, Q. Lu, M.F. Rossignol, P. Tenaud, T. Viadieu, J. Magn. Magn. Mater. 83 (1990) 183. [17] P. Hansen, In: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, Magnetic Amorphous Alloys, Vol. 6, Ch. 4, Elsevier, Amsterdam, 1991, p. 390. [18] R. Friedberg, D.I. Paul, Phys. Rev. Lett. 34 (1975) 1234. [19] H. Kronmu¨ller, J. Magn. Magn. Mater. 24 (1981) 159. [20] H. Kronmu¨ller, J. Appl. Phys. 52 (1981) 1859. [21] Ch. Polak, M. Knobel, R. Gro¨ssinger, R. SatoTurtelli, J. Magn. Magn. Mater. 134 (1994) 1.
Magnetic properties in amorphous Co Tb Zr thin films 93~X X 7 H. Ouahmane!,", H. Lassri#,*, A. Itri$, A. Khmou", G. Suran% ! De& partement de physique, Universite& Moulay Ismaı( l, Faculte& des sciences et techniques, d+Errachidia, Boutalamine B.P. 509 Errachidia, Morocco " LPS, Universite& Moulay Ismaı( l, Faculte& des sciences de Meknes, B.P. 4010, Morocco # LPMME, Universite& Hassan II, Faculte& des sciences Ain chok, MaaL rif, B.P. 5366, Route d’E1 Jadida, km 8, Casablanca, Morocco $ LPM, Universite& Mohammed V, Faculte& des sciences, avenue Ibn Batouta, B.P. 1014, Rabat, Morocco % Laboratoire de Magnetisme de Louis. Ne& el, CNRS, Av. des Marthyrs B.P. 38042 38 Grenoble 9 Cedex, France Received 22 January 1997; received in revised form 17 February 1998
Abstract Amorphous Co Tb Zr thin films with a well-defined in-plane uniaxial anisotropy were prepared by RF 93~X X 7 sputtering. The saturation magnetization 4pM , the uniaxial anisotropy constant K and the coercive field H were 4 6 # studied as a function of temperature and for the composition range 0(X(7. The Tb moment at 4.2 K is found to be 9k in agreement with the theoretical value. This would indicate a collinear spin structure for Tb. The mean-field theory B has been used to explain the temperature dependence of the magnetization. The exchange interactions between Co—Co and Co—Tb atom pairs have been evaluated. K and H are related by the equation H "aKn /k M with the fitting 6 # # 6 0 4 parameters a and n. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Co Tb Zr ; Thin films; Magnetic properties 93~X X 7
1. Introduction Amorphous ferromagnetically soft thin films containing rare earth metals are of interest due to their industrial applications. The films are also interesting from a scientific point of view as they offer the possibility to study various aspects of 3d and 4f magnetism. Contrary to crystalline materials these aspects can be investigated in a continuous concentration of the rare earth metal as well as in relation
* Corresponding author.
with the low local symmetry that is characteristic for the amorphous state. Rare earth metal atoms with spin—orbit interaction are known to give rise to large random anisotropy in amorphous films [1]. Amorphous films can exhibit fairly low values of the coercive field H , much smaller than 1 Oe # [2,3]. The magnitude of H is generally related to # the overall composition of the films and the deposition parameters used. The main intrinsic parameters which affect the value of the H are the # uniaxial anisotropy, the saturation magnetization and the microstructure which may lower or increase the coercive field. In this work we describe
0921-4526/98/$ — see front matter ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 3 6 5 - 2
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143
the results of our magnetic studies of amorphous Co Tb Zr films as a function of temperature 93~X X 7 in the range 4.2—300 K.
2. Experimental The amorphous films were deposited by the RF diode sputtering techniques using Argon as a sputtering gas. We used the same deposition parameters, i.e. a pressure of the sputter gas of p "2 mTorr and RF input power of 300 W. For A3 the value of P used the amorphous structure A3 appears to be most homogeneous and for a given composition the magnitude of K was minimal. 6 During the deposition a DC field of 700 Oe was applied parallel to the film plane giving rise to an in plane uniaxial anisotropy field H "2K /M . , 6 4 H was determined by M—H loop and FMR , measurements. The amorphous structure was confirmed by Xray diffraction using CuKa radiation. The exact composition was determined by electron probe microanalysis. The magnetization was measured by a vibrating sample magnetometer from 4.2 to 300 K in magnetic fields up to 1 kOe.
3. Results and discussion All films exhibit in plane hysteresis loops which are characteristic of high-quality amorphous soft ferromagnetic thin films. Along the easy axis a rectangular hysteresis loop is detected, with H @H . # , Along the hard axis a loop with a shape characteristic of a thin film exhibiting a very well-defined in-plane uniaxial anisotropy is detected. Now, the magnetization process occurs by coherent rotation, so the applied field for saturation is equal to H at , all temperatures. The concentration dependence of the magnetization (4pM ) at 300 K is shown in Fig. 1. There is 4 a linear decrease in 4pM for 0(x(7. The above 4 results are characteristic of the antiferromagnetic interaction between Tb and Co atoms which is well known. The alloys moment (k ) can be written as ! k (¹)"D(93!X)k (¹)!Xk (¹)D/100. (1) ! C0 T"
Fig. 1. The Tb concentration dependence of 4pM at 4 ¹"300 K. The solid line was obtained by linear regression.
For small concentrations (X(7) of Tb, the moment of Co at 4.2 K is not perturbed. So taking the value of k "1.55k obtained from the alloy with C0 B X"0 and substituting it in (Eq. (1)); it is possible to determine k . The calculated moment is found T" to be 9k in agreement with the theoretical value. B This would indicate a collinear spin structure for Tb. The temperature dependence of the magnetization has been studied. Fig. 2 shows the results for Co Tb Zr and Co Tb Zr thin films. It is 87.3 5.7 7 88.3 4.7 7 seen that with increasing Tb content as the temperature is lowered magnetization first shows a broad peak and then starts decreasing. This decrease in magnetization is due to an increase in the magnetization of the sublattice of Tb. For the concentration studied here the compensation of moments do not occur. The mean-field theory has been used in the past by several authors to calculate the temperature dependence of the magnetization in many amorphous rare earth (R), transition metal (T) alloys [4—6]. We have performed such an analysis of the temperature dependence of the magnetization in amorphous Co Tb Zr films. (Eq. (1)) can be 93~X X 7 rewritten as k (¹)"D(93!X)g S (¹)!Xg J (¹)Dk /100, ! C0 C0 T" T" B (2)
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H. Ouahmane / Physica B 253 (1998) 142—147
S (¹) and J (¹) were assumed to be expressed C0 T" by the Brillouin function as
Fig. 2. The temperature dependence of the magnetization for the amorphous Co Tb Zr alloys (X"4.7 and 5.7). The 93~X X 7 solid and dashed lines were calculated from the mean-field theory.
where S , J and k , are respectively the Co spin C0 T" B momentum, the total angular momentum of Tb and the Bhor magneton. g is the Lande´ factor i (i"Co,Tb); we take g "2 and g "1.5. C0 T"
J (¹)"J (0)B (g J k H /k ¹), (3) T" T" J(T") T" T" B T" B S (¹)"S (0)B (g S k H /k ¹), (4) C0 C0 S(C0) C0 C0 B C0 B k is the Boltzmann constant. The molecular fields B H and H are given by C0 T" H "2J z (g !1)2J /g k T" T"T" T"T" T" T" T" B #2J z (g !1)S g k , (5) C0T" T"C0 T" C0 T" B H "2J z S /g k C0 C0C0 C0C0 C0 C0 B #2J z (g !1)J /g k , (6) C0T" C0T" T" T" C0 B where z is the coordination number taken to be ij z "z "12(93!X)/100, (7) C0C0 T"C0 z "z "12X/100, (8) C0T" T"T" J ,J and J are the exchange constants C0C0 C0T" T"T" for Co—Co, Co—Tb and Tb—Tb interactions, respectively. Using the spin values given in Table 1 and adjusting the exchange interactions J ,J and C0C0 C0T" J , the sublattice magnetizations M , M and T"T" T" C0 the total magnetization M"DM !M D can be C0 T" calculated. From these fits the exchange interactions were extracted as a function of the Tb content (Table 1). It is seen that J increases and C0T" J decreases, when the Co concentration inC0C0 creases. A similar increase in J has been reported RT in intermetallic compounds and amorphous alloys also [7—10]. The 3d—5d interactions depend critically on 3d—5d hybridization according to Brooks et al. [11]. Therefore the increase in J would C0T" indicate an increase in 3d—5d hybridization when the Co concentration relative to Tb is decreased.
Table 1 Some magnetic parameters of amorphous Co Tb Zr thin films 93~X X 7 X
S C0 (k ) B
J C0C0 (10~16 erg)
J C0T" (10~16 erg)
J T"T" (10~16 erg)
¹ # (K)
A (10~8 erg/cm)
0 4.7 5.7 6.5
0.69 0.69 0.69 0.69
184 170 160 155
— 15 15.5 16.5
— 1.6 1.6 1.7
1160 1018 929 906
61 53 49 47
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145
The temperature dependence of M is shown in Fig. 2 for two different compositions. It is seen that experimental points align well with the calculated curve. We also calculated the temperature dependences of M and M which are also shown in C0 T" Fig. 2. The Curie temperature ¹ is expressed as [12] C 3k ¹ "a #a #[(a #a )2 B C C0C0 T"T" C0C0 T"T" !4(a
a !a a )]1@2, C0C0 T"T" C0T" T"C0
(9)
a "z J S (S #1), C0C0 C0C0 C0C0 C0 C0
(10)
a "z J J (J #1)(g !1)2, T"T" T"T" T"T" T" T" T"
(11)
a a "z z (J )2(g !1)2 C0T" T"C0 C0T" T"C0 C0T" T" ]S (S #1)J (J #1). C0 C0 T" T"
(12)
Thus knowing all the parameters, ¹ could be C calculated. It is seen that ¹ is decreased by the C addition of Tb and arised mainly from the weakening of the Co—Co interaction. The exchange stiffness constant A can be calculated after Hasegawa [13] from the relation N A(¹)"Mn J (g !1)2J2 (¹)[X/100]2/r T" T"T" T"T" T"T" T" #M[n #n ]J [g !1]J (¹)S (¹) C0T" T"C0 C0T" T" T" C0 ]X(93!X)/1002/r
N T"C0
N, #Mn J S2 (¹)[(93!X)/100]2/r C0C0 C0C0 C0C0 C0 (13) where n is the maximum permissible atom pairs ij per unit volume extended to first neighbors. In our case, we take n to be 2; r are the interatomic ij ij distances, which are taken to be r "2.5 A_ , C0C0 r "3.0 A_ and r "3.5 A_ , in accordance with C0T" T"T" the structural data of Harris et al. [14]. Thus obtained A is listed in Table 1 as a function of composition at 4.2 K. This behaviour of A is in conformity with the variation of the Curie temperature in Table 1. The uniaxial anisotropy constant K of 6 Co Tb Zr films can be described in terms of 93~X X 7 the dipolar coupling coefficients C for all combiij nations of the two elements and single-ion coeffic-
Fig. 3. Experimental data of the K for the composition 6 Co Tb Zr at room temperature. The solid line was ob93~X X 7 tained by linear regression.
ient D for Tb [15] 1 (14) K " + C M M #DX(m )2, ij i j T" 6 2 ij where M represent the Co and Tb sublattice magi,j netizations, X the Tb content and m " T" M (¹)/M (0). The C are the dipolar coupling T" T" ij constants and D is the single-ion anisotropy constant. The room-temperature variation of K versus Tb 6 concentration is shown in Fig. 3. K increases with 6 increasing Tb content. The solid line was obtained from linear regression. This behavior demonstrated the leading contribution of the single-ion term of Tb in (Eq. (14)). Fig. 4 shows K versus temperature for two 6 compositions Co Tb Zr and Co Tb Zr . 87.3 5.7 7 88.3 4.7 7 Using the sublattice magnetizations inferred from the mean-field analysis, the dependence of K on 6 temperature can be calculated. The coercivity is essentially controlled by the microstructure, the uniaxial anisotropy and the saturation magnetization [16]. Hansen correlated H and K for Tb-based alloys in a simple relation # 6 [17] H "aKn /k M , (15) # 6 0 4 where a represents a microstructural parameter.
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Fig. 4. Temperature dependence of K for Co Tb Zr and 6 87.3 5.7 7 Co Tb Zr thin films. 88.3 4.7 7
Fig. 6. Coercive energy versus uniaxial anisotropy measured between 80 and 300 K on samples with different Tb contents for amorphous Co Tb Zr . The solid line was fitted to the data 93~X X 7 yielding n and a. (m, X"5.7), (j, X"4.7) and (v, for different Tb contents at 300 K).
Fig. 5. Coercive field (H ) versus composition for # Co Tb Zr films at ¹"300 K. The solid line was obtained 93~X X 7 by linear regression.
The room temperature variations of the coercive field H versus Tb content is presented in Fig. 5. # H increases continuously with the increasing Tb C content. According to (Eq. (15)), the coercivity is expected to increase with Kn , where n is determined by the 6 mechanism controlling H . The linear increase of # K with Tb content in amorphous Co Tb Zr 6 93~X X 7 thin films was well established and a plot
Fig. 7. Temperature dependence of H for Co Tb Zr (j) # 87.3 5.7 7 and Co Tb Zr (m) films. The solid lines were calculated 88.3 4.7 7 using (Eq. (15)).
1/2(k H M ) versus K presented in Fig. 6 for dif0 # 4 6 ferent Tb contents and at temperature between 80 and 300 K yield n"1.27 and log a"!2.9. Friedberg and Paul showed that H is propor# tional to K3@2 at a given microstructure if the 6 magnetization reversal process takes place by the
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domain wall motion [18]. Kronmu¨ller obtained a value of n"5 from theoretical calculations under 4 the assumption that the domain wall motion is dominated by exchange fluctuations [19,20]. Polak et al. concluded that the coercivity due to the surface roughness appears to be directly proportional to the domain wall energy and H increases in # proportion with K1@2 [21]. 6 Fig. 7 shows the coercive field measurements (H ) on Co Tb Zr and Co Tb Zr in # 87.3 5.7 7 88.3 4.7 7 comparison to calculations using (Eq. (15)) with the above mentioned n and a. A reasonable agreement of calculation and experiment for ¹'80 K indicated that the domain wall motion is dominated by exchange fluctuations. 4. Conclusion The magnetic properties of Co Tb Zr films 93~X X 7 were investigated with respect to their compositional and temperature dependence. The saturation magnetization was analyzed in terms of the meanfield theory. The Co moment, the Curie temperature and the exchange interactions J and C0C0 J were evaluated. Therefore the increase of C0T" J with an increase of Tb content is attributable C0T" to the 3d—5d hybridization effect. The uniaxial anisotropy and the coercive field augment with the increasing Tb content. References [1] R. Harris, M. Plischke, M.J. Zuckermann, Phys. Rev. Lett. 31 (1973) 160.
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