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Submitted on 1 Jan 1979
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Effect of magnetostriction on the anisotropy energy of cubic rare earth laves phase compounds
N. Koon, C. Williams
To cite this version:
N. Koon, C. Williams. Effect of magnetostriction on the anisotropy energy of cubic rare earth laves phase compounds. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-194-C5-195.
�10.1051/jphyscol:1979571�. �jpa-00218988�
Effect of magnetostriction on the anisotropy energy of cubic rare earth laves phase compounds
N C Koon and C. M. Williams Naval Research Laboratory, Washington, D C. 20375. USA
Abstract. — In high magnetostriction compounds such as DyJCTb1_xFe2 the magnetostrictive contribution to anisotropy produces a significant shift of the spin reorientation compositions away from those predicted using only the standard cubic crystal field terms. We present anisotropy calculations which take into account the magne- tostrictive contribution to the anisotropy as well as the cubic crystal field. The results are in excellent agreement with the complex spin rotations observed in both Ho^Tb! _xFe2 and Dy;cTb1_;(.Fe2.
1. Introduction. — Ternary rare earth-iron Laves phase compounds of the form R ^ ' R ^ i J F e j are of considerable technical interest because for certain compositions the total anisotropy energy can be made relatively low, while the compounds still exhibit large magnetostrictive strains at room tempe- rature. A model which accurately describes the magnetic anisotropy of these compounds is therefore of practical as well as scientific interest.
It was first pointed out by Atzmony, Dariel, and Dublon [1] in the case of D y ^ T b j ^ F e j that spin reorientation compositions calculated using standard cubic crystal field terms were considerably different from the observed ones. Furthermore, there were no values of the crystal field and exchange parameters which could reconcile theory and experiment. We pointed out [2] that the variation in magnetoelastic energy with spin orientation could account for most of the difference between the two. In the present work we have improved the model by using neutron inelastic scattering to determine the exchange and the magnitude of the crystal field, taking into account the renormalization of the mean field exchange constants due to the temperature dependence of the iron sublattice magnetization, and adding a small contribution to the anisotropy from the iron sublattice.
2. Theory. — The model is a straightforward extension of the usual single ion theory [3] to include the effects of magnetostriction. The Hamiltonian is
where Hexch and Hc{ are the usual exchange and crystal field terms [3]. Hme is the magnetoelastic part of the Hamiltonian which we evaluate in perturbation
Fig. 1. — Spin reorientation diagram of DyxTb1_:cFe2. The dashed line and the circle represent the approximate experimental boundary as determined from Mossbauer measurements [3] and from a single crystal torque measurement. The solid curves on the right represent the full theory with 2 nB He%ch = 28.0 meV,
and
The A^j (magnetostriction) parameters are the same as [2] The left hand curves are the crystal field only calculation. The dotted regions represent easy axis directions which are not along principal crystallographic axes. AK1 (Fe) shifts the curves less than 1 at. %.
Most of the difference between the curves is due to magnetostriction.
JOURNAL DE PHYSIQUE Colloque C5, supplément au n° 5, Tome 40, Mai 1979, page C5-194
Résumé. — Dans les composés à haute magnétostriction tels que D y ^ T b ^ ^ F e j la contribution magnétostrictive à l'anisotropie produit un décalage significatif des compositions de réorientation de spin par rapport à celles qui sont prédites, en utilisant les seuls termes ordinaires de champ cristallin cubique. On présente des calculs d'anisotropie qui mettent en ligne de compte la contribution magnétostrictive à l'anisotropie aussi bien que le champ cristallin cubique. Les résultats s'accordent bien avec les rotations de spin complexes observées pour Ho;cTb1_;(Fe2 aussi bien que pour DyxTbL _^.Fe2.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979571
EFFECT OF MAGNETOSTRICTION O N THE ANISOTROPY ENERGY C5- 195
theory to get the usual AK, effect on the magnetic anisotropy [2]. H,, is the iron contribution to the Hamiltonian, which we assume to give a small nega- tive K , consistent with the [ I l l ] easy axis observed in YFe,.
The exchange field at low temperatures is fixed within narrow limits by neutron diffraction measure- ments on ErFe, [4], and we assume that its tempe- rature dependence is the same as that of the iron sublattice magnetization determined by Bowden et al. [5]. The spin wave gap parameter fixes the magnitude of the crystal field, so that only the ratio of crystal field parameters A , / A , and the negative K ,
from the iron sublattice remain as free parameters.
These are both determined by comparison of the calculation to the spin orientation diagram of HoxTb, -,Fez [6], which is very sensitive to A,/A,.
With all parameters fixed, we compare theory and experiment for the DyxTb, -,Fez system in figure 1 . The complete theory agrees within 1-2 at.
%
of the experiment, while the crystal field only calculation is almost 15 at.%
off at 300 K. The results are similar for HoxTbl -,Fez, except that in the spin reorienta- tion region the magnetostrictive contribution is less, so that the crystal field only theory is not so far off.References
[I] ATZMONY, U., DARIEL, M. P., DUBLQN, G., Phys. Rev. B 15 (1977) 3565.
[2] KOON, N . C., WILLIAMS, C. M., J. Appl. Phys. 49 (1978) 1948.
[3] ATZMONY, U. and DARIEL, M. P., Phys. Rev. B 13 (1976) 4006.
[4] KOON, N . C. and RHYNE, J. J., Solid State Commun. 26 (1978) 537.
[5] BOWDEN, G. J., BUNBURY, D. ST. P., GUIMARAES, A. P. and SNYDER, R. E., J. Phys. C 1 (1968) 1376.
[6] WILLIAMS, C. M., KOON, N. C., Solid State Commun. 27 (1978) 81.
