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Effect of the vanadium content on the rare earth anisotropy behaviour in DyFe12−xVx compounds
Journal
of
AND CDM~UHDS ELSEVIER
Journal of Alloys and Compounds 219 (1995) 199-202
Effect of the vanadium content on the rare earth anisotropy behaviour in DyFe12_xVx compounds P. Stefafiski a, V. Ivanov b a Institute of Molecular Physics of the Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Pozna~, Poland b General Physics Institute of the Russian Academy of Sciences, Vavilov St. 38, 117942 Moscow, Russia
Abstract The spin reorientation transitions (SRTs) were investigated in DyFe12-xVx (x=l.5, 2.0, 2.75, 4.0) compounds by a.c. susceptibility vs. temperature measurements. The SRT temperature is shifted towards lower values with increasing vanadium content from TSR=170 K for x=l.5 to TSR=125 K for x=2.75. The crystal field parameter A° was calculated taking into account the preference of the 8(i) crystal site and considering the nearest neighbourhood of the rare earth ion. Charges of surrounding Fe and V atoms were established by applying the chemical bond model proposed by Pauling. The absolute value of the A ° parameter decreases when the content of vanadium increases in the 8(i) position which explains the TSR shift. Keywords: Rare earth compounds; Spin reorientation, Magnetocrystalline anisotropy; Chemical bond
1. Introduction Recent band structure calculations [1--4] showed that in the rare earth-transition metal intermetallic compounds the sphericity of the valence electron charge density of the rare earth atoms itself forms the dominant contribution to the lowest-order crystal field parameter A2°, although the lattice contribution also has its influence. The above results are in contradiction with the frequently used point charge calculations (PCCs), where the charges outside the central atom produce the dominant electric field gradient at the rare earth site. Sometimes, however, a satisfactory description of crystal field effects can be obtained using point charges [5-7]. PCCs can be applied when the difference in the electronegativities of the surrounding ions and rare earth ion is large (large charge transfer) and the distance between them is small (large area of contact). The above conditions are fulfilled in RFel~Ti nitrites [8,9] when rare earth atoms and surrounding nitrogen atoms are taken into account. The aim of this paper is to establish the influence of the change in the local environment of the rare earth ion in the ThMn12-type compounds [10] on its anisotropy. This class of compounds has been recently intensively investigated (see, for example, the review by Buschow [11]). As an example the DyFe12_xVx compounds were chosen; on substituting iron with va-
0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)05068-6
nadium, the Dy sublattice anisotropy changes which is reflected by a shift in the spin reorientation temperature.
2. Experimental The method of sample preparation and X-ray analysis can be found elsewhere [12,13]. The temperature dependence of the initial susceptibility was measured in the temperature range from 4.2 K to room temperature using an a.c. bridge of mutual inductance of the Hartshorn type. The intensity of the alternating field was 240 A m -1 and the frequency was 250 Hz. Results of measurements are displayed in Fig. 1 for various vanadium contents x. For x = 4 no anomaly was detected.
3. Pauling's chemical bond model Taking into account the coordination of the R ion at the 2(a) site [10] the crystal electric field parameters A ° were calculated regarding the site preference of Fe and V atoms. The summations were carded out considering only the nearest neighbourhood of the rare earth atom. According to the band structure calculations o f A ° parameters in various rare earth-transition metal compounds [1,2,4], the nearest neighbourhood in the vicinity of the R atoms has the most important role
200
P. Stefarlski, I~ lvanov / Journal of Alloys and Compounds 219 (1995) 199-202 Table 1 The values of single bond metallic radii D(1) and electronegativities X taken from ReL [14] 0.6
--
x=2.75
~-~
0.5
f
""_
:
[~J
x=1"5
-
",°....,...,..
0
.; -1
..)t
4
X
D(1) (~)
Dy Fe V
1.2 1.8 1.6
1.600 1.165 1.224
Table 2 The lattice parameters a and c of DyFez2_~Tx compounds and corresponding distances D(n) between the R ion and atoms in the nearest 8(i), 8(j) and 8(£) positions Vanadium content x
U
~
Compound
/~x= 2 ~,
1.5 2.0 2.75 4.0
I
a (A)
8.471 8.488 8.495 8.507
c (A)
4.770 4.773 4.774 4.775
D(n) (A) R-i
R-j
R-f
3.059 3.065 3.068 3.072
3,044 3,051 3,053 3,057
3.224 3.230 3.232 3.265
I I
-
I /
Table 3 Calculated transferred charges from Dy ion to atoms in 8(i), 8(j) and 8(f) positions for DyFe1:-xVx compounds
I
I
0.3 -I
I
Dy Fe12- ×Vx 8(i)
8(j)
8(f)
x = 1.5 Fe v
0.028 0.016
0.030 -
0.015 -
x = 2.0 Fe V
0.028 0.015
0.029
0.014
x = 2.75 Fc V
0.027 0.015
0.029
0.014
x=4.0 Fe V
0.027 0.015
0.028 -
0.014 -
I
I
100
I
I
150 200 f [K]
I
250
Fig. 1. The measured temperature dependence of the a.c. susceptibility of DyFei2_~Vx compounds.
in describing the electric field gradient that "sees" the rare earth ion. In the chemical bond model proposed by Pauling [14] the number n of electrons in a chemical bond in metals is given by n = 10 lD(1)-D(n)]/0"6
(1)
where D(1) is the single bonding distance and D ( n ) is the actual distance between the two atoms considered. The amount of ionic character of the bond between atoms A and B with electronegativities XA and XB is given by Nio.~c= 1 - exp[ - (XA --XB)Z/4]
(2)
Thus the number of electrons transferred from atom A to atom B (assuming XA
(3)
In Table 1 are collected (after Pauling) quantities needed in calculations; the values of single-bond metallic radii and appropriate electronegativities.
In Table 2 the lattice parameters a and c are collected and corresponding distances between the rare earth ion and atoms in the nearest 8(i), 8(j) and 8(0 positions. Fe atoms are located in 8(i), 80) and 8(f) positions, while vanadium has 8(i) site preference [15]. Applying Eqs. (1)-(3) the charge transfers were calculated from Dy ion to V (Fe) ions in 8(i), 80) and 8(f) positions. Results are listed in Table 3. The charge transfers from Dy ion to V (Fe) atoms, as expected in metals, are quite small (see Table 3). The spinpolarized calculations (linear muffin tin orbital method) of the electronic structure of YFel0Vz and YFeloCr2 [16] also gave small values of the transferred charges: for YFeloV2 these were 0.37, 0.0175, 0.1, -0.24, and -0.04 for Y, Fe in 8(0, Fe in 8(i), V in 8(i), and Fe in 80) respectively. A large positive value ofA2o calculated
P. Stefatiski, V. lvanov /Journal of Alloys and Compounds 219 (1995) 199-202
by Jaswall et al. [16] (using the PCC method), which is in complete disagreement with the experimental value, is probably caused by incorrect signs of charges in positions 8(f) and 8(i). Gadolinium is less electronegative than vanadium or iron, and from this point of view charges in 8(0 and 8(i) should have a negative sign. For the calculation of the A ° parameter the charge of the R ion is also needed. From band structure calculations follows that the charge of the Wigner-Seitz cell of the Gd ion is approximately 0e when performed for ThCr2Si2-type compounds [2]. For GdCo5 [4] the Gd charge changes from -0.32e to + 0.21e depending on the Wigner-Seitz radii. We assumed a value of -0.3e for the Dy charge. The distance from the reference R ion to its nearest R neighbours in DyFe12_xVx is in the range 4.5/k-12/~. It appears that the screening of the charge results in the small Dy charge instead of + 3 which has frequently been used. For calculating A ° a well-known formula was used [171: 1 k q A °= ~ (-e2) j=~1 ~ (3 cos20 - 1) (4) e denotes the electron charge, and Rj and 0 are the polar coordinates of the charge qj. For the location of vanadium in the 8(i) site, the charge of this position has been varied according to the formula qj8(i)
_____O~qvS(i).4~(1 - o~)qFe 8(i)
(5)
A simple relation was found between occupation parameter a and content x of vanadium in DyFei2_xVx to be a=(1/12)x (for a = 0 we have x=0; for a = l , x = 12). The changes in lattice constants when iron is substituted by vanadium and transferred charges were considered during calculation of the A2° parameter. The experimental values of A ° obtained from 155Gd Mrssbauer spectroscopy [18] are - 140 K/ao2 for GdFe~oV2. The calculated values of A°2 have to be regarded with caution (inaccuracy of PCC calculations); however, agreement with experimental values is satisfactory. The dependence of the A ° crystal field parameter on V content in the nearest neighbourhood of the R ion is displayed in Fig. 2. The changes in terms coming from atoms in i, j and f positions are also included. The change in A°(i) is due to changes in the charge in the 8(i) position and lattice constants;A2°(j) andA2°(f) change as a result of the lattice changes. As seen in Fig. 1 the spin reorientation transition (SRT) temperature shifts toward lower values when iron is substituted by vanadium. The planar anisotropy of Dy weakens (it is reflected by a change in the A°2 parameter in Fig. 2): The rare earth anisotropy can be estimated by [18] K R~ ~ - a,J(J-
1)(rZ>A°
(6)
The second-order Stevens factor a j < 0 for Dy ion [17]; thus, when A ° having a negative sign increases,
201
0 -2O
°o o2Cf) A °
A2(j) O
~A2(i) O
-6O
-lOO
-
I
-l&~ 1
I I I 2 3 V concentration
I
I 6
x
Fig. 2. Calculated crystal field parameter A ° dependence on V atom content x in 8(i) position in DyFeI2_xV,; terms coming from 8(i), 80) and 8(t") are also displayed; a0 is the Bohr radius.
the rare earth anisotropy decreases. J is the total angular momentum of the rare earth ion and (r 2) is the radial integral for the 4f electrons [19]. Weakening of the rare earth anisotropy when the content of vanadium increases is also confirmed in TbFe12_xVx [20]. Moreover, the axial iron anisotropy becomes planar for x = 4 in YFeaV4 [20]. In DyFesV4 no SRT anomaly was detected; for anisotropies both Dy and Fe are planar for this vanadium content and there is no competition between them. On the contrary, in ErFe~2_xVx the values of TSR increase with increasing vanadium content [20]. There are two causes of this; it seems that higher-order crystal field terms which mainly determine Er anisotropy in this class of compounds [21] are not as sensitive to vanadium content and simultaneously the Fe anisotropy weakens when x increases.
References [1] R. Coehoorn, J. Magn. Magn. Mater., 99 (1991) 55. [2] R. Coehoorn, K.H.J. Buschow, M.W. Dirken and R.C. Thiel, Phys. Rev. B, 42 (1990) 4645. [3] K.H.J. Buschow, R. Coehoorn, F.M. Mulder and R.C. Thiel, J. Magn. Magn. Mater., 118 (1993) 347. [4] R. Coehoorn and G.H.O. Daalderop, Z Magn. Magn. Mater., 104-107 (1992) 1081. [5] J.G. Sankar, V.U.S. Rao, E. Segal, W.E. Wallace, W.G.D. Frederick and H.J. Garrett, Phys. Rev. B, 11 (1975) 435. [6] J.M. Cadogan and J.M.D. Coey, Phys. Rev. B, 30 (1984) 4326. [71 H.H.A. Smit, R.C. Thiel and K.H.J. Buschow, J. Phys. F, 18 (1988) 295. [8] H.-S. Li and J.M. Cadogan, Solid State Commun., 80 (1991) 905.
202
P. Stefatiski, V lvanov / Journal of Alloys and Compounds 219 (1995) 199-202
[9] H.-S. Li and J.M. Cadogan, J. Magn. Magn. Mater., 109 (1992) L153. [10] D.B. de Mooij and K.H.J. Buschow, J. Less-Common Met., 136 (1998) 207. [11] K.H.J. Buschow, J. Magn. Magn. Mater., 100 (1991) 79. [12] P. Stefafiski, A. Kowalczyk and A. Wrzeciono, Z Magn. Magn. Mater., 81 (1989) 155. [13] P. Stefafiski and A. Wrzeciono, J. Magn. Magn. Mater., 82 (1989) 125. [14] L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, NY, 3rd edn., 1960, p. 255.
[15] Th. Sinnemann. K. Erdmann, M. Rosenberg and K.H.J. Buschow, Hyperfine Interact., 50 (1989) 675. [16] S.S. Jaswall, Y.G. Ren and D.J. Sellmeyr, J. Appl. Phys., 67 (1990) 4564. [17] M.T. Hutchings, Solid State Phys., 16 (1964) 227. [18] K.H.J. Buschow, D.B. de Mooij, M. Brouha, H.H.A. Smit and R.C. Thiel, IEEE Trans. Magn., 24 (1988) 1611. [19] A.J. Freeman and J.P. Desclaux, J. Magn. Magn. Mater., 12 (1979) 11. [20] L. Pareti, M. Solzi, G. Marusi, M.R. Ibarra and P.A. Algarabel, J. Appl. Phys., 70 (1991) 3753. [21] P. Stefafiski and A. Kowalczyk, Solid State Commun., 77 (1991) 397.
of
AND CDM~UHDS ELSEVIER
Journal of Alloys and Compounds 219 (1995) 199-202
Effect of the vanadium content on the rare earth anisotropy behaviour in DyFe12_xVx compounds P. Stefafiski a, V. Ivanov b a Institute of Molecular Physics of the Polish Academy of Sciences, Smoluchowskiego 17, 60-179 Pozna~, Poland b General Physics Institute of the Russian Academy of Sciences, Vavilov St. 38, 117942 Moscow, Russia
Abstract The spin reorientation transitions (SRTs) were investigated in DyFe12-xVx (x=l.5, 2.0, 2.75, 4.0) compounds by a.c. susceptibility vs. temperature measurements. The SRT temperature is shifted towards lower values with increasing vanadium content from TSR=170 K for x=l.5 to TSR=125 K for x=2.75. The crystal field parameter A° was calculated taking into account the preference of the 8(i) crystal site and considering the nearest neighbourhood of the rare earth ion. Charges of surrounding Fe and V atoms were established by applying the chemical bond model proposed by Pauling. The absolute value of the A ° parameter decreases when the content of vanadium increases in the 8(i) position which explains the TSR shift. Keywords: Rare earth compounds; Spin reorientation, Magnetocrystalline anisotropy; Chemical bond
1. Introduction Recent band structure calculations [1--4] showed that in the rare earth-transition metal intermetallic compounds the sphericity of the valence electron charge density of the rare earth atoms itself forms the dominant contribution to the lowest-order crystal field parameter A2°, although the lattice contribution also has its influence. The above results are in contradiction with the frequently used point charge calculations (PCCs), where the charges outside the central atom produce the dominant electric field gradient at the rare earth site. Sometimes, however, a satisfactory description of crystal field effects can be obtained using point charges [5-7]. PCCs can be applied when the difference in the electronegativities of the surrounding ions and rare earth ion is large (large charge transfer) and the distance between them is small (large area of contact). The above conditions are fulfilled in RFel~Ti nitrites [8,9] when rare earth atoms and surrounding nitrogen atoms are taken into account. The aim of this paper is to establish the influence of the change in the local environment of the rare earth ion in the ThMn12-type compounds [10] on its anisotropy. This class of compounds has been recently intensively investigated (see, for example, the review by Buschow [11]). As an example the DyFe12_xVx compounds were chosen; on substituting iron with va-
0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)05068-6
nadium, the Dy sublattice anisotropy changes which is reflected by a shift in the spin reorientation temperature.
2. Experimental The method of sample preparation and X-ray analysis can be found elsewhere [12,13]. The temperature dependence of the initial susceptibility was measured in the temperature range from 4.2 K to room temperature using an a.c. bridge of mutual inductance of the Hartshorn type. The intensity of the alternating field was 240 A m -1 and the frequency was 250 Hz. Results of measurements are displayed in Fig. 1 for various vanadium contents x. For x = 4 no anomaly was detected.
3. Pauling's chemical bond model Taking into account the coordination of the R ion at the 2(a) site [10] the crystal electric field parameters A ° were calculated regarding the site preference of Fe and V atoms. The summations were carded out considering only the nearest neighbourhood of the rare earth atom. According to the band structure calculations o f A ° parameters in various rare earth-transition metal compounds [1,2,4], the nearest neighbourhood in the vicinity of the R atoms has the most important role
200
P. Stefarlski, I~ lvanov / Journal of Alloys and Compounds 219 (1995) 199-202 Table 1 The values of single bond metallic radii D(1) and electronegativities X taken from ReL [14] 0.6
--
x=2.75
~-~
0.5
f
""_
:
[~J
x=1"5
-
",°....,...,..
0
.; -1
..)t
4
X
D(1) (~)
Dy Fe V
1.2 1.8 1.6
1.600 1.165 1.224
Table 2 The lattice parameters a and c of DyFez2_~Tx compounds and corresponding distances D(n) between the R ion and atoms in the nearest 8(i), 8(j) and 8(£) positions Vanadium content x
U
~
Compound
/~x= 2 ~,
1.5 2.0 2.75 4.0
I
a (A)
8.471 8.488 8.495 8.507
c (A)
4.770 4.773 4.774 4.775
D(n) (A) R-i
R-j
R-f
3.059 3.065 3.068 3.072
3,044 3,051 3,053 3,057
3.224 3.230 3.232 3.265
I I
-
I /
Table 3 Calculated transferred charges from Dy ion to atoms in 8(i), 8(j) and 8(f) positions for DyFe1:-xVx compounds
I
I
0.3 -I
I
Dy Fe12- ×Vx 8(i)
8(j)
8(f)
x = 1.5 Fe v
0.028 0.016
0.030 -
0.015 -
x = 2.0 Fe V
0.028 0.015
0.029
0.014
x = 2.75 Fc V
0.027 0.015
0.029
0.014
x=4.0 Fe V
0.027 0.015
0.028 -
0.014 -
I
I
100
I
I
150 200 f [K]
I
250
Fig. 1. The measured temperature dependence of the a.c. susceptibility of DyFei2_~Vx compounds.
in describing the electric field gradient that "sees" the rare earth ion. In the chemical bond model proposed by Pauling [14] the number n of electrons in a chemical bond in metals is given by n = 10 lD(1)-D(n)]/0"6
(1)
where D(1) is the single bonding distance and D ( n ) is the actual distance between the two atoms considered. The amount of ionic character of the bond between atoms A and B with electronegativities XA and XB is given by Nio.~c= 1 - exp[ - (XA --XB)Z/4]
(2)
Thus the number of electrons transferred from atom A to atom B (assuming XA
(3)
In Table 1 are collected (after Pauling) quantities needed in calculations; the values of single-bond metallic radii and appropriate electronegativities.
In Table 2 the lattice parameters a and c are collected and corresponding distances between the rare earth ion and atoms in the nearest 8(i), 8(j) and 8(0 positions. Fe atoms are located in 8(i), 80) and 8(f) positions, while vanadium has 8(i) site preference [15]. Applying Eqs. (1)-(3) the charge transfers were calculated from Dy ion to V (Fe) ions in 8(i), 80) and 8(f) positions. Results are listed in Table 3. The charge transfers from Dy ion to V (Fe) atoms, as expected in metals, are quite small (see Table 3). The spinpolarized calculations (linear muffin tin orbital method) of the electronic structure of YFel0Vz and YFeloCr2 [16] also gave small values of the transferred charges: for YFeloV2 these were 0.37, 0.0175, 0.1, -0.24, and -0.04 for Y, Fe in 8(0, Fe in 8(i), V in 8(i), and Fe in 80) respectively. A large positive value ofA2o calculated
P. Stefatiski, V. lvanov /Journal of Alloys and Compounds 219 (1995) 199-202
by Jaswall et al. [16] (using the PCC method), which is in complete disagreement with the experimental value, is probably caused by incorrect signs of charges in positions 8(f) and 8(i). Gadolinium is less electronegative than vanadium or iron, and from this point of view charges in 8(0 and 8(i) should have a negative sign. For the calculation of the A ° parameter the charge of the R ion is also needed. From band structure calculations follows that the charge of the Wigner-Seitz cell of the Gd ion is approximately 0e when performed for ThCr2Si2-type compounds [2]. For GdCo5 [4] the Gd charge changes from -0.32e to + 0.21e depending on the Wigner-Seitz radii. We assumed a value of -0.3e for the Dy charge. The distance from the reference R ion to its nearest R neighbours in DyFe12_xVx is in the range 4.5/k-12/~. It appears that the screening of the charge results in the small Dy charge instead of + 3 which has frequently been used. For calculating A ° a well-known formula was used [171: 1 k q A °= ~ (-e2) j=~1 ~ (3 cos20 - 1) (4) e denotes the electron charge, and Rj and 0 are the polar coordinates of the charge qj. For the location of vanadium in the 8(i) site, the charge of this position has been varied according to the formula qj8(i)
_____O~qvS(i).4~(1 - o~)qFe 8(i)
(5)
A simple relation was found between occupation parameter a and content x of vanadium in DyFei2_xVx to be a=(1/12)x (for a = 0 we have x=0; for a = l , x = 12). The changes in lattice constants when iron is substituted by vanadium and transferred charges were considered during calculation of the A2° parameter. The experimental values of A ° obtained from 155Gd Mrssbauer spectroscopy [18] are - 140 K/ao2 for GdFe~oV2. The calculated values of A°2 have to be regarded with caution (inaccuracy of PCC calculations); however, agreement with experimental values is satisfactory. The dependence of the A ° crystal field parameter on V content in the nearest neighbourhood of the R ion is displayed in Fig. 2. The changes in terms coming from atoms in i, j and f positions are also included. The change in A°(i) is due to changes in the charge in the 8(i) position and lattice constants;A2°(j) andA2°(f) change as a result of the lattice changes. As seen in Fig. 1 the spin reorientation transition (SRT) temperature shifts toward lower values when iron is substituted by vanadium. The planar anisotropy of Dy weakens (it is reflected by a change in the A°2 parameter in Fig. 2): The rare earth anisotropy can be estimated by [18] K R~ ~ - a,J(J-
1)(rZ>A°
(6)
The second-order Stevens factor a j < 0 for Dy ion [17]; thus, when A ° having a negative sign increases,
201
0 -2O
°o o2Cf) A °
A2(j) O
~A2(i) O
-6O
-lOO
-
I
-l&~ 1
I I I 2 3 V concentration
I
I 6
x
Fig. 2. Calculated crystal field parameter A ° dependence on V atom content x in 8(i) position in DyFeI2_xV,; terms coming from 8(i), 80) and 8(t") are also displayed; a0 is the Bohr radius.
the rare earth anisotropy decreases. J is the total angular momentum of the rare earth ion and (r 2) is the radial integral for the 4f electrons [19]. Weakening of the rare earth anisotropy when the content of vanadium increases is also confirmed in TbFe12_xVx [20]. Moreover, the axial iron anisotropy becomes planar for x = 4 in YFeaV4 [20]. In DyFesV4 no SRT anomaly was detected; for anisotropies both Dy and Fe are planar for this vanadium content and there is no competition between them. On the contrary, in ErFe~2_xVx the values of TSR increase with increasing vanadium content [20]. There are two causes of this; it seems that higher-order crystal field terms which mainly determine Er anisotropy in this class of compounds [21] are not as sensitive to vanadium content and simultaneously the Fe anisotropy weakens when x increases.
References [1] R. Coehoorn, J. Magn. Magn. Mater., 99 (1991) 55. [2] R. Coehoorn, K.H.J. Buschow, M.W. Dirken and R.C. Thiel, Phys. Rev. B, 42 (1990) 4645. [3] K.H.J. Buschow, R. Coehoorn, F.M. Mulder and R.C. Thiel, J. Magn. Magn. Mater., 118 (1993) 347. [4] R. Coehoorn and G.H.O. Daalderop, Z Magn. Magn. Mater., 104-107 (1992) 1081. [5] J.G. Sankar, V.U.S. Rao, E. Segal, W.E. Wallace, W.G.D. Frederick and H.J. Garrett, Phys. Rev. B, 11 (1975) 435. [6] J.M. Cadogan and J.M.D. Coey, Phys. Rev. B, 30 (1984) 4326. [71 H.H.A. Smit, R.C. Thiel and K.H.J. Buschow, J. Phys. F, 18 (1988) 295. [8] H.-S. Li and J.M. Cadogan, Solid State Commun., 80 (1991) 905.
202
P. Stefatiski, V lvanov / Journal of Alloys and Compounds 219 (1995) 199-202
[9] H.-S. Li and J.M. Cadogan, J. Magn. Magn. Mater., 109 (1992) L153. [10] D.B. de Mooij and K.H.J. Buschow, J. Less-Common Met., 136 (1998) 207. [11] K.H.J. Buschow, J. Magn. Magn. Mater., 100 (1991) 79. [12] P. Stefafiski, A. Kowalczyk and A. Wrzeciono, Z Magn. Magn. Mater., 81 (1989) 155. [13] P. Stefafiski and A. Wrzeciono, J. Magn. Magn. Mater., 82 (1989) 125. [14] L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, NY, 3rd edn., 1960, p. 255.
[15] Th. Sinnemann. K. Erdmann, M. Rosenberg and K.H.J. Buschow, Hyperfine Interact., 50 (1989) 675. [16] S.S. Jaswall, Y.G. Ren and D.J. Sellmeyr, J. Appl. Phys., 67 (1990) 4564. [17] M.T. Hutchings, Solid State Phys., 16 (1964) 227. [18] K.H.J. Buschow, D.B. de Mooij, M. Brouha, H.H.A. Smit and R.C. Thiel, IEEE Trans. Magn., 24 (1988) 1611. [19] A.J. Freeman and J.P. Desclaux, J. Magn. Magn. Mater., 12 (1979) 11. [20] L. Pareti, M. Solzi, G. Marusi, M.R. Ibarra and P.A. Algarabel, J. Appl. Phys., 70 (1991) 3753. [21] P. Stefafiski and A. Kowalczyk, Solid State Commun., 77 (1991) 397.