170Yb Mössbauer study of the crystalline electric field and exchange interaction in YbFe2 : addendum

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170Yb Mössbauer study of the crystalline electric field and exchange interaction in YbFe2 : addendum

F. Hartmann-Boutron, C. Meyer

To cite this version:

F. Hartmann-Boutron, C. Meyer. 170Yb Mössbauer study of the crystalline electric field and exchange interaction in YbFe2 : addendum. Journal de Physique, 1980, 41 (9), pp.1075-1076.

�10.1051/jphys:019800041090107500�. �jpa-00208922�

1075

170Yb Mössbauer study ^{of the} crystalline electric field and exchange interaction in YbFe2 : ^addendum

F. Hartmann-Boutron and C. Meyer

Laboratoire de Spectrométrie Physique (*), Université Scientifique ^et Médicale de Grenoble, B.P. 53X, 38041 Grenoble Cedex, France

(Reçu ^{le 26 mars} 1980, accepté ^{le 22 mai} 1980)

Résumé. 2014 Dans la référence [1] ^{nous avons} calculé le potentiel cristallin V2 induit par la magnétostriction ^dans

la série RFe2, ^en supposant | 03BB100 | ~ | 03BB111 |, ^comme cela était admis à l’époque par ^un certain nombre d’auteurs.

Cette hypothèse s’étant révélée non fondée, ^nous établissons pour V2 ^des expressions ^nouvelles qui ^{sont valables} quels que soient 03BB100 ^et 03BB111.

Abstract.

In reference [1] ^{we derived an} expression ^{for the} crystalline potential V2 ^induced by magnetostriction

in the RFe2 series, using ^the assumption, generally accepted ^{at the} time, that | 03BB100 | ~ | 03BB111 |. ^This assumption

has now been shown to be unfounded. We therefore derive new expressions ^for V2, ^{which are} valid whatever

03BB100 ^and 03BB111.

J. Physique ⁴¹ (1980) ^{1075-1076 SEPTEMBRE 1980,}

Classification

Physics ^Abstracts

76.80

75.30

In reference [1], using ^a simple ^{model, we tried to}

estimate the contribution of magnetostriction ^to crystalline field effects and magnetocrystalline ^aniso- tropy ^{in the} RFe2 ^series (except ^{for GdFe2, since Gd3+}

is an S state ion). ^{At that} time, ^it was more or less admitted in the literature [2] ^{that in this series}

For this reason, while _eqs. (12) ^to (24) of [1] ^{are valid}

whatever Âloo and Âlll, ^we dropped ^{the terms in} Âloo

in eqs. (29) ^to (34).

The assumption that ! 10 0 1 « 1 )"111 I ^{was based}

on a comparison ^{between the} magnetostriction ^coeffi-

cients of DyFe2 (Àl00 (0 K) = - ^{70 x} 10- 6) ^and of TbFe2 (111 ^{(0 K)}

^{4 400 x} 10-6) [2]. ^Since then, magnetostriction ^{studies have also been} performed

on HoFe2 [3]. ;,100 ^was determined between 300 K and 0 K while à, ¹¹¹ (hard axis) ^could only ^{be measured}

between 300 K and 270 K. At 270 K, )" 111 ^{1 is about}

2.5 times larger than 1 ;,10, but, because of différent thermal variations, ^its extrapolated ^{value at 0} K,

776 ^x 10-6 is almost nearly equal ^{to the value}

measured for Hioo! (745 x 10-6). Consequently 1 ;, 10 0 1 - 111 ! and ^the assumption of reference [2]

is not verified. In addition 1 )"100(0 K) 1 ^{for HoFe2}

is ten times larger than that for DyFe2 (while ^still

remaining six times smaller than 2111 (0 K) ^for TbFe2).

In view of these results, ^{it seems useful to} give

corrected expressions ^{for the} crystalline potential V2,

eqs. (30) ^and (31) ^of [1], ^{when the term in} ,1100 is

retained :

or alternatively :

Eqs. (32), (33) ^and (34) ^of [1] ^{are no} longer ^valid.

However comparison ^of (31’) ^with eq. (23) ^{for the} magnetostrictive anisotropy energy KME :

shows that V2 ^and KME still have comparable ^orders

of magnitude. Since both quantities ^contain /oo

(*) ^{Associé au C.N.R.S.}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019800041090107500

1076

and à,f i i , they ^are negligible ^{(less than} 1 cm-1) ^when

calculated with the small values of à,ioo ^and ;,.111 ¹ corresponding ^{to HoFe2.} Appreciable contributions to V2 ^and KME ^will only ^{be obtained with} high ^{Â values} comparable ^{to the} Î..lll’S ^of TbFe2 ^or TmFe2. ^The

conclusions of reference [1] then remain unaltered, except ^{for the fact that now} V2 ^is always ^{non zero} (but ^{it still} depends ^{on the} magnetization ^direction

and it is still too small for explaining ^the crystal

field variations in the series).

Some additional remarks must be made. In refe-

rence [1], p. 409, ^note (5), ^{we said that} K2 « K1. ^In reality ^{this is not true at low} temperature. ^{On the} other hand, ^{one should not} forget ^{that the} physical

effects of the anisotropy ^{are not} characterized by Kl ^and K2, ^but by ^{the maximum} angular variations, 1 K1 /3 1 and K2/27 1, ^{of the two} contributions to the

anisotropy energy (Eq. (A.9) ^of [1]), ^{as one rotates}

the magnetization. ^{The order of} magnitude ^{of these} quantities ^{at 0 K} in the whole series can be estimated with the help of eqs. (A. 10) ^and (A. 11) of [ 1], together

with tentative values of A4 r4 > ^and A6 r6 > (1) : 1 ^{K2 (0} K)/27 is ^{found to be} smaller than or compa- rable to K1 (0 K)/3 ( but certainly ^{not much smaller.}

Therefore, in connection with note (5) ^{of reference} [1],

p. 409, ^{the fact of} neglecting ^{terms of order} higher

A6 a8/kB

^{1 K and we used} the r4 >4f, r 6 )4f ^{values of}

Freeman and Watson (Phys. ^{Rev. 127} (1962) 2058); ^{the numerical}

results of this calculation are given ^{in C.} Meyer’s Doctoral Thesis (Grenoble, 1980). ^{Note that in} reality, ^{as shown in} [1], A4, A6

are not constant.

than two in the computation ^of the additional crystal-

line potential ^{due to} magnetostriction, ^must only ^be

considered as a (widely used) simplifying assump- tion [4], justified by the lack of information concern-

ing ^{the exact} mechanisms involved in this change.

Finally ^one should also recall the limited validity ^of

the description ^of anisotropy ^{effects in terms of an} anisotropy energy (Eq. (A. 9) of [1]). Strictly speaking,

it can only ^{be valid if the} modulations (of ^{the order} 1 Kl (0 K)/6 , K2 (0 K)/54) 1) ^{of the} Zeeman energy levels of the Rare Earth ion by crystal field effects when the magnetization rotates, ^are appreciably

smaller than the Zeeman interval 2(gj - ^{1) IÀB} Hex 1

associated with the RE-Fe exchange field. With /’B H,,,,IkB - ^{150 K and} the above mentioned tentative values of the crystalline ^{field, it is found that} (except

for Pr3 +) K1 ⁽⁰ K)/6 and K2 ⁽⁰ K)/54 are ^indeed

smaller than the Zeeman interval, ^but only by ^{a factor}

of the order two to five so that the validity ^condition

is practically ^never satisfied. Therefore, ^for precise

calculations it is necessary ^{to use} the exact free energy,

as was done in the investigations ^of ternary phase diagrams [5] ^{and in our own work} [6] ; ^{however in}

view of the uncertainty ^on A4 ^and A6 ^the simpler description ^{in terms of an} anisotropy energy is still of great interest when only ^{orders of} magnitude ^esti-

mates are needed, ^{as in reference} [1]. ^{The same remark} applies ^to the standard treatment of magnetostric-

tion given ⁱⁿ [1] ^{and also to the Callen and Callen}

law [7], [3] :

for the thermal variation of magnetostriction.

References

[1] MEYER, C., GROS, Y., HARTMANN-BOUTRON, F., CAPPONI, ^J. J., J. Physique ⁴⁰ (1979) ^403.

[2] CULLEN, ^J. R., CLARK, A. E., Phys. ^{Rev. B 15} (1977) ^4510.

HATHAWAY, ^K. B., CULLEN, ^J. R., ^J. Appl. Phys. ⁴⁹ (1978) ^1975.

[3] ABBUNDI, R., CLARK, A. E., KOON, ^N. C., ^J. Appl. Phys. ⁵⁰ (1979) ^1671.

[4] ^{For a recent} discussion on this subject ^see CAMPBELL, I. A., CREUZET, G., SANCHEZ, J., Phys. ^{Rev. Lett. 43} (1979) ^234.

[5] ATZMONY, U., DARIEL, ^M. P., DUBLON, G., Phys. ^{Rev. B 15} (1977) 3565.

[6] MEYER, C., SROUR, B., GROS, Y., HARTMANN-BOUTRON, F., CAPPONI, ^J. J., ^J. Physique ³⁸ (1977) ^1449.

[7] CALLEN, E., CALLEN, ^H. B., Phys. ^{Rev. 139A} (1965) ^455.

CALLEN, ^H. B., CALLEN, E., ^J. Phys. Chem. Solids 27 (1966)

1271.