Journal of Alloys and Compounds 458 (2008) 37–40
N. Sheloudkoa, C. Safaridisb, M. Gjokac, M. Mikhova and O. Kalogiroub,
aFaculty of Physics, “St. Kl. Ohridski” University of Sofia, 1164 Sofia, Bulgaria
bDepartment of Physics, Aristotle University of Thessaloniki, 54 124 Thessaloniki, Greece
cNCSR Demokritos, Institute for Materials Science, 153 10 Ag. Paraskevi, Athens, Greece
Abstract
The effect of Co substitution for Fe in Nd3(Fe1−xCox)27.7Ti1.3Ny (0 ≤ x ≤ 0.4) compounds on the magnetocrystalline anisotropy has been investigated. The anisotropy constants K's and the anisotropy field HA have been deduced from the magnetization curves measured on magnetically aligned powder (4–7 μm) samples. The obtained results show that at RT the anisotropy is uniaxial and HA (about 10 T) does not change substantially upon the substitution. At 5 K the results for K's give evidence for the presence of easy-cone-type anisotropy. The cone angle as well as the anisotropy field decrease upon the substitution from 21.6° to 11.8° and from 22.8 to 18.6 T, respectively.
1. Introduction
A considerable amount of research is going on R3(Fe,T)29 compounds and their nitrides, carbides and hydrides not only due to their potential for permanent magnet application but also for their intrinsic magnetic properties. The Nd3(Fe,Ti)29-type compounds (3:29) crystallize in the A2/m space group [1]. A promising substitution in the 3:29 compounds, with regard to a further enhancement of their intrinsic magnetic properties, is that of Co. Recently the synthesis and the structural and magnetic properties of Nd3(Fe1−xCox)27.7Ti1.3Ny (x = 0.1, 0.2, 0.3, 0.4) compounds have been presented [2]. For x = 0.1, 0.2 a complex magnetic anisotropy has been observed, whereas for x = 0.3, 0.4 the compounds presented uniaxial anisotropy at room temperature (RT). From X-ray diffraction on magnetically aligned powders the easy magnetization direction (EMD) determination on Nd3(Fe1−xCox)27.7Ti1.3Ny compounds indicated [2] that in the case of x = 0.3 and 0.4, at RT, the nitrides show typical uniaxial anisotropy with the EMD along the [2,0,−1] direction and hard magnetic directions along the [0 1 0] and [1 0 2] directions of the 3:29 structure. For the x = 0.1 and 0.2 nitrides the uniaxial character of the samples is weakened, and the X-ray diffraction reveals the presence of a more complex magnetic structure which should be further studied. Additionally, 57Fe Mössbauer spectra of magnetically aligned powder samples at 85 and 293 K have shown the absence of spin reorientation phenomena in that temperature interval. In this work the magnetic anisotropy of Nd3(Fe1−xCox)27.7Ti1.3Ny in a broader temperature interval down to 5 K is analyzed by means of anisotropy constants in a phenomenological approach.
2. Experimental
The preparation and the characterization of the Nd3(Fe1−xCox)27.7Ti1.3Ny series have been reported in detail in Ref. [2], where the values of some basic magnetic parameters, like saturation magnetization and Curie temperature have been also reported. As described in Ref. [2] the calculated relative lattice expansion upon nitrogenation indicates 3.5–3.7 N-atoms per formula unit, i.e. y ≈ 3.5–3.7. The maximum value for nitrogen insertion in the Nd3(Fe,Ti)29-type compounds is four nitrogen atoms per unit formula [1]. The magnetization curves used to apply the Sucksmith–Thompson method were obtained on powder samples magnetically oriented in epoxy resin, at room temperature and at 2 T, with the magnetic field applied parallel and perpendicular to the alignment direction. The size of the particles of the powder in the aligned samples was determined by SEM to be 4–7 μm (Fig. 1). Thus, it was assumed that the particles should show single domain behaviour.
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| Full-size image (59K) |
Fig. 1. SEM photograph for Nd3(Fe0.8Co0.2)27.7Ti1.3Ny.
3. Results and discussion
The [2,0,−1] direction lies in the a-c plane of the 3:29 monoclinic structures and coincides with the c-axis of the constituent 1:12 tetragonal block. The [1 0 2] direction lies in the a–c plane and coincides with the c-axis of the constituent 2:17 hexagonal block. The [0 1 0] direction corresponds to the unique b-axis of the 3:29 structure and coincides with the a-axis of the 1:12 block [3]. Since these directions are mutually orthogonal, and the EMD is along the [2,0,−1] direction, the oriented in one directed magnetic field powders should have uniaxial symmetry with the [2,0,−1] direction along the orientation direction, and the [0 1 0] and [1 0 2] directions of the different grains—uniformly distributed in the plane, normal to the orientation direction.
Assuming the z-axis corresponding to the EMD [2,0,−1], the anisotropy energy of the system, up to the fourth order terms, is given by: EA =K1 sin2 θ + K2 sin4 θ, where θ is the angle between the magnetization vector and the z-axis and K's are the phenomenological anisotropy constants.
The values of K's were derived from the hard demagnetization curves (Fig. 2), measured on aligned samples normal to the orientation direction and applying the Sucksmith–Thompson method [4]. The Sucksmith–Thompson plots at RT (Fig. 3) have linear character in the whole field range, up to 5 T for x = 0.2, 0.3 and 0.4, and up to 4 T for x = 0.1, confirming the single domain behavior of the sample. The anisotropy constants were calculated from the coefficients a and b of the linear dependence: 
, by the appropriate for the case (magnetization measured in field normal to the EMD on uniaxial samples) expressions [4]:
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| Full-size image (12K) |
Fig. 2. Reduced magnetization curves M vs. μ0H.
|
| Full-size image (4K) |
Fig. 3. Sucksmith–Thompson plots H/M
vs. 
at RT.
The obtained values of K1 and K2 (Table 1) satisfy the relations for axial anisotropy: K1 > 0 and K1 + 2K2 > 0. The anisotropy field, HA, was calculated by the expression:
The obtained values are reported in Table 1. From the concentration dependence it is seen that K's (Fig. 4) and HA (Fig. 5) do not change substantially at RT upon the substitution of Fe by Co.
Table 1.
The anisotropy constants, K1, K2 and the anisotropy field, HA, at RT
| x | K1 (J/kg) | K2 (J/kg) | μ0HA (T) |
| 0.1 | 74.0 | 415.5 | 10.2 |
| 0.2 | 65.4 | 401.5 | 9.6 |
| 0.3 | 80.6 | 364.0 | 8.8 |
| 0.4 | 75.5 | 357.0 | 9.3 |
|
| Full-size image (5K) |
Fig. 4. Concentration dependence of the anisotropy constants, K1 and K2.
|
| Full-size image (4K) |
Fig. 5. Concentration dependence of the anisotropy field, HA, and of the cone angle, θc.
At low temperature (5 K) the Sucksmith–Thompson plots are linear above 1 T (Fig. 6). The values of K's were derived from the linear part of Sucksmith–Thompson plots in higher fields, from 1 up to 5 T, by the expressions (1). The obtained values (Table 2) of K1 are negative, of K2 are positive, satisfying the relation K1 + 2K2 > 0. For such a case the EMD lies along a cone about the z-axis of the system. The cone angle θc is determined by the expression 
. The anisotropy field at 5 K was calculated by the expression (2). The obtained values of K's, HA and θc at 5 K are reported in Table 2 and their concentration dependence presented at Fig. 4 and Fig. 5. From the concentration dependence it can be seen that at 5 K the anisotropy field decreases (from 45.2 to 35.2 T) and the cone angle decreases monotonically (from 21.6° to 11.8°) with the substitution of Fe by Co.
|
| Full-size image (4K) |
Fig. 6. Sucksmith–Thompson plots H/M vs. at 5 K.
Table 2.
The anisotropy constants, K1 and K2, the cone angle, θc, and the anisotropy field, HA, at 5 K
| x | K1 (J/kg) | K2 (J/kg) | μ0HA (T) | θc (°) |
| 0.1 | −304 | 2249 | 45.2 | 21.6 |
| 0.2 | −361 | 1788 | 34.6 | 18.5 |
| 0.3 | −212 | 1640 | 33.8 | 14.5 |
| 0.4 | −136.9 | 1526 | 35.2 | 11.8 |
From the obtained values of the phenomenological anisotropy constants for all the samples it is summarized that: (i) K1 changes sign from positive at RT to negative at low temperature; K2 is positive throughout. (ii) K1 is similar in magnitude to the values reported for the second order magnetocrystalline anisotropy constant in the 3:29 phase [5], whereas K2 takes on very large values (in comparison for example with the single crystal Y3(Fe,Ti)29, where 
is about 0.06 both at RT and 5 K [6]). In principle, two factors may be responsible for the large values of the phenomenological fourth order anisotropy constant K2: (i) An overestimating of K2 associated with extracting the constants from the limited data M/Ms versus μ0H (here—at 5 K, Fig. 2), since the precision with which the higher order individual constants can be determined is dependant on their relative magnitude and the applied field available [7]. (ii) The difference between the aligned samples and a single crystal; in the latter the magnetization changes from the EMD [2,0,−1] to the hardest [1 0 2] direction, while in the aligned samples from the EMD to different directions in the normal to the [2,0,−1] plane for the different grains. A further consideration of the question why such large values of K2 are present in these alloys is connected with their two sublattice magnetic structure. It has been shown [8] that in circumstances of competing sublattice anisotropies, higher order “effective anisotropy constants” are generated. In the case when only K1 is considered for each sublattice, they have shown that an effective K2 and K3 become apparent due to a varying canting angle between the individual sublattice magnetic moments.
4. Conclusions
The anisotropy constants, K1 and K2, and the anisotropy field, HA, were deduced from the magnetization curves measured on magnetically aligned powder (4–7 μm) samples, using the Sucksmith–Thompson method. At RT the obtained values for K1 and K2 correspond to axial anisotropy; the anisotropy field is about 10 T and does not change substantially upon the substitution. At 5 K the results for K1 and K2 give evidence that the EMD is at an angle θc from the easy [2,0,−1] direction. The angle θc as well as the anisotropy field at 5 K decrease upon the substitution from 21.6° to 11.8° and from 22.8 to 18.6 T, respectively.
Acknowledgement
This work was supported by the 089-c bilateral Greek-Bulgarian project of the General Secretary for Research and Technology, Greece.
References
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