IEEE TRANSACTIONS ON MAGNETICS, VOL. 25, NO. 5 , SEPTEMBER 1989 3443

ESTIMATION OF THE EXCHANGE AND CRYSTALLINE FIELD PARAMEERS AT R SITES IN R2Fe14B COMPOUNDS (R-Pr, Nd, Sm, Tb, Dy, Ho, Er AND "h)

Zhu Yhg, Zhao Tiesong and Jin Hanmin Department of Physics, Jilin University, Changchun, China

Yang Funing, Xie Jinqiang, Li Xinwen and Zhao Ruwen Magnetism Laboratory, Institute of Physics, Academia Sinica, Beijing, China

and E.R. de Boer

Natuurkundig Laboratorium, University of Ansterdam, 1018 XE Amsterdam, The Netherlands

Abstract

The values of Fe-R exchange field and crystalline field parameters averaged over the f and g sites in R2Fe14B (R=Pr, Nd, Sin, Tb, Dy, Ho, Er and Tm) are evalu- ated by calculations based on a series of experiments. The experiments for all R compounds are the magnetiza- tion curves and the temperature dependence of the angle made by the magnetic easy axis with the c-axis. For the heavy R compounds, the temperature dependence of the magnetic moment is also included. The spin-phase dia- grams of (R1-xR:)2Fe14B [ (R,R')=(Pr,Ho), (Nd,Ho)] sys- tems are constructed experimentally. The phase dia rams of (R,R')=(Pr,Ho), (Nd,Pr), (Nd,Y), (Nd,Ho), (Er,Yy and (Er,Gd) systems calculated by using the empirically fit- ted parameters reproduce the experiments well.

Introduction

The magnetic anisotropy of R2Fe14B (R: Rare-earth) has been analyzed through the study of R ion subjected to a crystalline electric field (CEF) combined with the Fe-R exchange field H,ex [1,2]. This paper evaluates the values of CEF parameters Alm and Hex(T=O) by fitting the calculations with a series of experiments. The experi- ments for all the R compounds are the magnetization cur- ves M(H) at 4.2 K and the temperature dependence of the angle between the magnetic easy axis and the c-axis B(T). For the heavy R compounds, the measured M(H) at a higher temperature and the temperature dependence of magnetic moment M(T) are also included.

The spin-phase diagrams of (R1-xR:)2Fe14B [ (R,R')= (Pr,Ho), (Nd,Ho)] systems are constructed experimentall

It is shown that the spin-phase dia rams of (R,R'yz (Pr,Ho), (Nd,Ho), (Nd,Y), (Nd,Pr), (Er,Yf and (Er,Gd) compound systems can be reproduced well by the calcula- tions using the empirically fitted parameters.

Evaluation of the values of A,,,, and H,,(O)

Neglecting the difference between the f and g sites, there are two magnetically ine uivalent R sites: R(1) and R(2). The Haniltonian of Rqj) ion is expressed as

R(j>=2 Alm(j)[4jf/(21+l)l*/2 +Ylm(oi ,pi> 1 ,m -2pBBs*Fjex +hS*E +rB(2S+Z).T!, (1)

where Alm and Hex are averages of the f and g sites, Alm(l)=(-l)m/2Al-m(l)=(-1)m/2Alm(2) in the <loo> coor- dinate system with z axis along <001>, and (ei,pi) are the polar angles of the ith 4f electron vector displace- ment. The free energy of R2Fe14B is given by

F=-W 3 In[ 2 exp(-En(j )/m) 1 ( 2 ) +14(KFesin n2 oFe -flFe*fl),

where En is the eigenvalue of Eq.1 and oFeis the angle

made by $e with the c-axis. The equilibriun direction of qe is determined from the minim of the free ener- gy F, and the magnetization is calculated as

R= -dF/dR. (3) It is assumed that Alm is invariant with temperature, Hex is proportional to %e, and MFe(Tflc )/MFe(0) and 14KFe(Tflc) are those of Y2Fe14B [3]. The eigenvalues of Eq.1 are calculated by using the irreducible tensor operator technique within the ground multiplet except for Sm3 where the two lowest excited multiplets are included with h=41C)K. It is also calculated for Pr3+ within the ground and the lowest excited multiplets with h=610K. For the light R compounds, the values of Alm and Hex(0) are obtained by the least square method which is programed and calculated through by a IBM-370 computer. The fit was carried out more prudently for the heavy R compounds and will appear elsewhere [4].The value of MFe(0) for each R compound is adjusted for a better fit. Fig.1 shows the M(H) curves cf the light R compounds and Fig.2 and Fig.3 illustrate the M(H) and M(T)curves for the Tm compound. The fit of e(T) for

40 I f

-0 5 0 100 150 200 H(kOe)

L i \ 20-

0 50 100 150 200 H(k0e)

0018-9464/89/o9oo-3443$01 .WO 1989 IEEE

3444

Comparison $f calculation with experiments of spin-phase diagram

The spin-phase diagrams of ~Rl,xR~)2Fe14B [ (R,R')= (Pr,Ho), (Nd,Ho), (Nd,Y), (Ndp-), are calculated by using the fitted parameters. The cal- culation reproduces the experiments well (Fig.4). Pr3 ion, the calculation is carried out within the ground multiplet. It is assuned that the value of Alm for the R ion is invariant with respect to the canposi- tion (x), and the free energy of the pseudoternary sys- tem is given by

and (Er,Gd)l

For

FmI=(l-~)FR+xFR, . (4)

3 o o k Ax ia I

Planar

I Conical+\ nL 1 I I 1 I \ -0 0.2 0.4 0.6 0.8 1.0 x

Fig.4. The spin-phase diagrams of (Rl,xRi)2Fe14B systems. e: Exp., -:Gal.. (R R')=(a) (Pr,Ho) (b) (Nd,Ho), (c) (Nd,Y), (d) (Nd Pr), ( ~ j (Er,Y) and (f) (Er,Gd). Exp.: (a) (b) This work, (c)(d) [9], (e) [lo] and ( f ) [Il l .

Acknowledgement

This work is supported by the National Natural Science! Fohdation of China.

References

0 0.2 0.4 0.6 0.8 1.0 X

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7.

8.

9.

10.

11.

M. Yamada, H. Kato, H. Yamamoto and Y. Nakagawa, Phys. Rev. B38 (1988) 620. D. Givord, V S . Li, J. M. Gadogan, J. M. D. Coey, J. P. Gavigan, 0. Yamada, H. Maruyama, M. Sagawa and S. Hirosawa, J. Appl. Phys. 63 (1988) 3731. S. Hirosawa, Y. Matsuura, H. Yamamoto, S. Fu'imura, M. Sagawa and H. Yamauchi, J. App. Phys. 2 11986) 873. Zhao Tiesong, Jin Hanmin and Zhu Yong, be published in J. Magn. Magn. Mater. (1989). H. Hiroyoshi, H. Kato, M. Yamada, N. Saito, Y. Nakagawa, S . Hirosawa and M. Sagawa, Solid State Comnun. 62 (1987) 475. S. SinnG, R. Verhoef, J. J. Franse and F. R. de Boer, Proc. 9th Int. Workshop Rare-Earth Magnets, Part lI,p.69 (1987). H. Hiroyoshi, H. Yamauchi, Y. Yamamoto, Y. Nakagawa and M. Sagawa, Solid State Commun. 54 (1985) 41. H. Hiroyoshi, N. Saito, G. Kido, Y.Takagawa, S. Hirosawa and M. Sagawa, J. Magn. Magn. Mater. 54-57 (1986) 583. Z. D. Zhang, Y. K. Huang, X. K. Sun, Y. C. Chuang, F. M. Yang, E. Bruck, F. R. de Boer and R. J. Radwanski, to be published. E. B. Boltich, A. T. Pedziwiatr and W. E. Wallace, Mat. Res. Soc. Proc. 98 (1987) 119. A. Vasquez and J. P. snchez, J. Less-Comnon Met. - 127 (1987) 71.

to

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A

3445

2 50 100 150 200

0 0

H(kOe) 40 I c1003 1

L I

c

Y

t d i CO 0 11

H(kOe1 Fig.1. M(H) curves of R2Fe14B (R=Pr, Nd and Sm)

at 4.2K. - --. . Exp., -' . Cal.. (a) (b) R=Pr. Exp. [5]. Calculated within the subspace of (a) the ground multiplet and (b) the ground and the first excited multi lets. (c) R=Nd. Exp. [6]. (d) R=Sm. Exp. 871.

theNd and Ho compounds is excellent.

MFe(0) are Smrized in Tab.1. The fitted values of Alm and Hex(0) along with of

Experimental

(Prl-xHox)2Fe14B and (Ndl,xHox)2Fe14B compounds of x=O, 0.2, 0.4, 0.6, 0.8 and 1.0 are melted in an arc- furnace under an pure argon atmosphere. The ingots are homogenized at 1000°C for ten days in a vacuum.'Ihesirgle

phase state is confirmed by X-ray diffraction pattern. The spin-reorientation temperature (Tsr) is determined from the temperature dependence of initial permeability.

i i 150K ' i 0 I - - - . _ J 0 50 100 150 200

H(k0e)

Fig.2. M(H) ames ofT9,B at 4.2 and 15OK. 0 : Exp. [2] for 4.2K and [8] for 150K. - Cal.

1 .- .

2 5 c

Fig.3. M(T) curve of Tm2Fe14B. 0 : Exp. [3]. .: Exp. [2]. -: Cal.

Pr Pr * Nd Sm Tb

Ho Er Tm

DY

2.23 2.23 2.23 2.34 2.23 2.24 2.23 2.20 2.20

708 780 622 500 335 3 20 310 300 2 70

479 341 565 494 440 420 400 380 350

165 -235 -108 182 -1570 563 -318 289 -38 91 673 -2569 -765 -408 280 -66 55 816 -892 -44 -968 275 -229 0 -20 -626 0 -679 270 -190 0 -70 -60 30 -115 260 -170 0 -65 -55 28 -100 250 -160 0 -60 -45 25 -90 240 -155 0 -55 -30 22 -75 240 -150 0 -40 -30 20 -50

-343 439 54 0 0 0 0 0 0

J: The first excited multiplet is taken into account in the calculation.