ELSEVIER Physica B 226 (1996) 391-398

Volume dependence of magnetic interactions in R2Fel 7 and RzFe14B and their interstitial compounds

with H, C and N

N g u y e n M i n h H o n g

Low Temperature Physics Laboratory, Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic and Cryogenic Laboratory, Faculty of Physics, University of HanoL Viet Nam

Received 30 October 1995; revised 22 January 1996

Abstract

The pressure effect and the influence of the interstitial H, C or N atoms on the Curie temperature of R2Fel7 and the effect of pressure and interstitial H atoms on the Curie temperature of R2Fel4B are analysed in the framework of the two sublattice molecular field model. It is pointed out that the volume effect plays a major role in the variation of the exchange interactions due to either interstitial atoms or pressure. Upon increasing the volume, the Fe-Fe interaction is found to increase in R2Fe17 and decrease in R=Fet4B, while the R-Fe interaction decrease in both these two types of compounds.

I . Introduct ion

Among the binary R~Fem compounds, R2FeI7 exhi- bit a number of magnetic peculiarities [1, 2], namely: - a highest value for the iron magnetic moment but

the lowest Curie temperature. - l a r g e and negative magnetovolume effects, i.e.

the large and negative pressure effect on the Curie temperature and the magnetic moment and the large positive spontaneous volume magne- tostriction.

Because of the low Curie temperature and the large planar anisotropy of the Fe sublattice, R2Fe17 had not been considered as a potential material for hard mag- netic applications for a long period. The discovery of the R2Fel7Nx interstitial compounds by Coey et al. in 1990 [3] has remotivated a greater interest in R2Fe17 recently. It has been found that R2Fe17 can accommodate a large amount of H, C or N atoms as interstitials (up to five H atoms and three C or N atoms

per formular unit). The interstitial atoms have a large effect on both the structural and magnetic properties of the parent compounds. The lattice parameters a and c, 3d magnetic moment and Curie temperature in- crease upon increasing the number of interstitials. The most impressive change is found in the nitride com- pounds where the increase in the cell volume by about 7% and in Curie temperature by about 400 K were reported. These facts together with the observed en- hancement of the rare earth sublattice anisotropy have made them prospective candidates for hard magnetic applications [3, 4].

RzFelaB, well known as the most powerful per- manent magnets of the present time are based on Nd2Fe14B, exhibit also large magnetovolume effects, especially a high value of 2-2.9% for the sponta- neous magnetostriction [5]. The hydrogen absorption enhances both the Curie temperature and the 3d moment [4], but drastically reduces the 3d sublat- tice anisotropy [6] and therefore degrades the hard

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392 N.M. Hong/Physica B 226 (1996) 391-398

magnetic performance of the material. The N ab- sorption, however, disintegrates the compound into components. This process, on the other hand, has important technical application in the cheap and high performance processing of the Nd2Fel4B based mag- nets (the HDDR process) [7].

Fundamentally, the introduction of interstitial atoms into the parent lattice has two effects: lattice expan- sion and contribution to the chemical bonding. While the mixing of s and p states of interstitial atoms with the Fe 3d states reduces the 3d magnetic moment, the expansion of volume, and thus the increase of inter- atomic spacing, results in narrowing the d-bands and increasing the 3d magnetic moment. The largest re- duction of the magnetization due to the strongest hy- bridization effects is found, both experimentally [8] and theoretically [9, 10], on those Fe sites which are near to the interstitials, such as 18h and 18 f in Rz Fe 17. The volume effect, however, involves all Fe sites, and on the average, it is the major contribution to the over- all Fe moment enhancement. In carbide compounds, the average magnetic moment is effectively less en- hanced [11] which may indicate a stronger effect of hybridization.

The Curie temperature of a R-Fe compound is determined by the combination of three types of exchange interactions: R-R, Fe-Fe and R-Fe. The enhancement of the Curie temperature in the inter- stitial compounds has been pointed out to be mainly due to the volume effect and relates closely to the effect of pressure on the Curie temperature [3, 4]. Analysing Curie temperatures, Coey et al. [3] reported about a large enhancement of the Fe-Fe interactions and a slight decrease of the R-Fe interactions in the R2FelTNx compounds compared to their RzFel7 counterparts. The latter is confirmed also by neutron experiments [12]. The band structure calculations pointed out that this effect is likely due to the alloy- ing effect of interstitials on the electronic structure [13].

In the present paper, a comparative analysis of the volume dependence of magnetic interactions in RzFe17 and R2Fe14B is provided. Although there are only lim- ited data on the pressure effects of a few compounds among these two series available in the literature, we will show that the analysis of the interstitial com- pounds can bring complementary information. It turns out that while the magnetic moment of the 3d sublat-

tice depends on both the volume and the hybridization, the Fe-Fe interactions depend essentially on the vol- ume, or the Fe-Fe interatomic distances. The depen- dence of the magnetovolume parameter d In Tc/d In V on the rare earth species is explained within the molec- ular field model by a negative volume dependence of the R-Fe interactions.

2. Volume dependence of the Fe-Fe interactions

in this section we will confine ourselves to the R2Fe17 and R2FeI4B compounds with non-magnetic R atoms, i.e. Lu, La, or Y; in some cases, Ce and Th are also included. In such a case the magnetic properties of the compound are solely due to the 3d sublattice and within the mean field approach, the Curie temperature Tc can be written as follows (see for instant, [15]):

TC = nze-I~eCFe "~ nFe--Fe//2 ( 1 )

where nFe--Fe , CFe and #s are the molecular field coef- ficient, the Curie constant and the spontaneous mag- netic moment, respectively. We note that here we have taken CFe ~ #2 which is correct for both these two compounds and in the following discussions, we will assume that the pressure dependence of #2 is approx- imately the same as that of Cve.

In Table 1, values for the lattice parameters, mag- netic moment at 4.2 K and Curie temperature are listed for a number of R2Fe17 and interstitial compounds. It is clear that the Curie temperature of the parent com- pound depends on the species of R atoms. The dif- ference in Tc between Lu2Fe17 and Y2Fel7 has been explained to be due to the difference in their volumes [14]. Ce2Fel7 and Th2Fe17 have, however, larger vol- umes than the above two compounds, but their Tc val- ues are lower. It is worth to point out that, due to the additional 4f-3d or 6d-3d hybridization, Ce2Fel7 or Th2Fe~7, respectively, have smaller Fe magnetic mo- ment. In order to separate the different contributions to Tc from the magnetic moment and the strength of the magnetic exchange coupling, the Tc/I ~2 quantity (as first defined in [15]), which is proportional to the molecular field coefficient nFe-Ve, is used in the present analysis.

Fig. 1 is the plot Tc/IZ 2 as a function of the vol- ume per iron ion for all R2Fel7 and R2Fel7Ak (A is an interstitial atom, i.e. H, C or N) (in this way the

N.M. Hono/ Physica B 226 (1996) 391-398 393

Table 1 Structural and magnetic parameters of the R2Fel7 and their interstitial compounds. F a and F b are derived from the pressure experiment and from the comparison between the interstitial and parent compounds, respectively

Compound a (/~) c (/~) #s Tc dTc/dp F a F b Ref. (#B/f.u.) (K) (K/GPa)

Ce2Fel7 8.491 12.409 29.7 238 [ 1 ] Ce2Fel7 ~210 - 1 7 8 [43] Ce2Fel7H1 ,-~262 - 3 6 14 Ce2FeI7H 2 ~285 ~ - 4 7 17 Ce2Fel7H3 337 - 5 8 17 Ce2Fel6.5 8.484 12.39 28.8 225 [31] CezFe16.sD4.8 8.658 12.560 34.9 444 13.3 Ce2Fel7C 8.540 12.424 32.8 297 17.3 [32] Ce2Fe17Cx 8.73 12.56 - - 589 13.4 [ 19] Ce2FelTNx 8.74 12.65 - - 713 14.2 [3] Ce2Fel7Nx 8.743 12.673 36.3 700 13.6 [4]

Lu2 Fel 7 8.401 8.272 34.2 368 [ ! ] Lu2Fe17C 8.487 8.321 35.2 490 23 [32] Lu2Fel7Nx 8.57 8.48 - - 678 15.2 [3] Lu2Fe17Nx 8.576 8.475 - - 675 14.7 [33] Lu2Fe17N2.7 8.5891 8.4925 36.6 683 13.9 [30]

Y2Fe17 8.466 8.300 32.9 324 [ 1 ] 34.7 310 - 9 8 32 [14]

316 - 4 7 14.9 [41] 310 - 3 9 12.6 [17]

Y2Fel7C 8.589 12.448 35.5 502 15.1 [32] Y2 Fel 7C 8.66 8.4 - - 668 13.4 [ 19] YzFel 7C 8.65 8.44 - - 694 13.5 [3] Y2Fel7Nx 8.673 8.465 38.5 690 11.8 [33] Y2Fe17Nx 8.626 8.496 40.3 697 13.3 [39]

Th2Fel7 8.573 12.472 30.5 320 [34] 13 [16]

Th2Fel7C0.3 8.602 12.485 30.5 343 9.2 [34] Th2Fel7C0.6 8.637 12.495 31.8 396 13.1 [34] Th2Fel7C0.9 8.663 12.500 32.3 418 [34] Th2Fel7Ci.2 8.694 12.509 34.3 462 [34] Th2Fe17Cl.5 8.712 12.509 33.9 482 11.8 [34] Th2 Fel 7 C2.6 8.798 12.703 37.7 747 12.0 [34]

different R2Fel7 compounds with hexagonal or rhom- bohedral structures can be compared). It is striking that there exists a systematic increase o f the Fe-Fe exchange interactions upon increasing the volume in various R2Fe17 and R2FelTAk compounds despite the fact that these compounds possess different magnetic moments and Curie temperatures. In other words, the Fe--Fe interactions in R2Fe17 increase largely upon in- creasing the unit cell volume, or the Fe-Fe atomic separation. From the slope of the Tc/lt 2 (V) plot, we obtain A In nFe--Fe/A in V = 8.

As mentioned, the interstitial atoms play the major role of a negative pressure which extends the lattice volume V and consequently increases the Curie tem- perature through the magnetovolume coupling. The value for F = d In Tc/d In V can approximately be de- termined by the comparison of Tc and V values of the interstitial and corresponding parent compounds (i.e., F -- A(ln Tc)/A(ln V)). The obtained values are col- lected in Table 1.

The pressure dependence of the Curie temper- ature has been measured on a number of R2Fe17

394 N.M. Hong / Physica B 226 (1996) 391-398

200 c,/

180

~ . 160

I

: ~ 140

b" 120

100

80

140 Ib--_ ~ . •

130 .... "~_

100 ©

i 18.0 16,5

R2Fel4B 17.0

/ 17.5 ~.~

/

tJ )¢~"'2 )r ©

/ V /

/v<~ "© ©

/

, i 15 .0 15.5

ReFex7

50

i J i

14.0 14.5 16 ,0 16.5 17 .0

Volume (~a /Fe-a t . /

Fig. 1. Volume dependence of Tc/# 2 (volume is calculated for one iron atom) in the RzFel7 compounds ( 0 Lu, Q) Ce, [] Y and • Th). The corresponding data for the R2Fel4B are drawn in the inset ( 0 Lu, Q) Ce, [] Y, • La and • Th).

compounds as quoted in Table 1 (for R = Ce, Y and Th) and Table 3 (for magnetic R). Knowing the compressibility ~, one obtains F = d ln Tc/d In V = --(l/K) d In Tc/dp. We note that the experimental val- ues for ~: varies from 0.8 × 10 -2 GPa -1 for Er2Fe17 [16] to 1.16 × 10-2GPa -~ in Nd2Fe17 [17]. For the following discussion, we use a mean value of x = 1.0 × 10 -2 GPa -1.

The F values thus obtained from pressure exper- iment are in agreement with those obtained from interstitial compounds which indicates indeed the major role of the volume effect on the Curie temper- ature in the interstitial compound. As can be seen in Table 1, within the experimental error, the F value is not very sensitive to the R species, or in other words to the Tc value of the corresponding compound. In the following discussion, we take the average value F = 15 for the whole R2Fel7 series which, in fact, coincides with the pressure result obtained by Nikitin et al. for Y2Fel7 [41].

From Eq. (1), the volume dependence of the Fe-Fe interactions can be written as follows:

F = d In nFe--Fe/dln V + 2d ln#s /d In V. (2)

Taking F = 15 and d In nFe--Fe/d In V = 8 obtained above, we derive d In #s/d In V = 3.5.

From a forced magnetostriction measurement on Y2FeI7, Armitage et al. [18] obtained a magnetostric- tion value d In V/dB = (43 ± 4) x 10 -6 T -1 or ther- modynamically equivalent to a value d lnps/dp = -4.16 × l0 -2 GPa - l for the pressure dependence of the magnetization. Taking x = 1 × 10 -2 GPa -1, we have d ln/~s/dln V = 4.2. A direct pressure experiment [15, 20] yields d In ps/d In V = 2.8. Thus there is an agreement between our derived value of 3.5 and those obtained from the experi- ments, implying that the volume effect plays a ma- jor role in the variation of the Fe-Fe interaction in RzFe17 due to either interstitial atoms or pressure.

Similar analysis can also be performed for R2Fei4B and the interstitial (non-magnetic R) compounds. Values for the lattice parameters, magnetic mo- ment, Curie temperature and F derived from the interstitial compounds are collected in the Table 2. The F values from various pressure experi- ments are obtained using t¢=0.7 × 10-ZGPa -1 [20]. We note that there exists a large difference between the F values obtained from the pressure effect and those from the interstitial compounds for YzFel4B.

The Curie temperature for YzFeI4B is larger than those for Lu2Fel4B and La2FeI4B, which is not ex- pected in terms of differences in their volumes as mentioned above for R2FeI7. It is striking enough, however, that the correlation between the strength of the Fe-Fe exchange interactions and the volume still holds except for the case of CezFel4B (see inset of Fig. 1 where the volume per iron ion is still used in the Tc/p~ (V) plot for the sake of comparison with RzFel7). In contrast with RzFe17, here the Fe-Fe in- teractions decrease with increasing volume. From the inset, we obtain din nF¢--F¢/d In V = - 1.8.

Measurement of the pressure dependence of spon- taneous magnetization performed on a Y2FeI4B single crystal [15,20] yields d l n / ~ s / d p = - 2 . 0 x l0 -2 GPa -1 or din/Is /din V = 2.86 (taking again K ----" 0.7 × 10 -2 GPa -I ). Then making use of Eq. (2) we have F = 3.9. This value is close to those de- rived from the interstitial compounds but significantly smaller than the one obtained from the pressure exper- iment. An unambiguous analysis, however, requires thorough pressure experiments to be performed on these compounds.

N.M. Hong / Physica B 226 (1996) 391-398 395

Table 2 Structural and magnetic parameters of the R2Fe14B (values for a and c are taken from Ref. [3] except those for the Th compound from Ref. [46]) and their interstitial compounds. F ~ and F b are derived from the pressure experiment and from the comparison between the interstitial and parent compounds, respectively

Compound a (/k) c (/k) #S TC dTc/dp r a /-'/' Ref. (#a/f.u.) (K) (K/GPa)

Ce2Fe14B 8.75 12.09 29.4 422 [4] 464 - 4 6 + --83 14 -- 26 [42]

Lu2Fe14B 8.712 11.883 28.5 534 [36] Lu2Fel4 B 8.710 11.876 543 [25] Lu2 Fe14H2.3 8.764 11.958 ~30 582 4.7 [25]

Y2FeI4B 8.757 12.026 29.9 571 [36] 564 - 3 4 + - 7 2 8.6 + 18 [42]

Y2FeI4BH3.6 8.849 12.148 ~32 639 3.6 [25] Y2FelgBH3. 4 8.7857 12.142 31.6 614 2.4 [37] Y2Fe14BH3.37 8.8377 12.141 32.3 629 3.5 [38] YEFe14BNx 8.798 12.075 - - 628 7.0 [26]

La2Fe14B 8.822 12.333 30.8 542 [36]

Th2Fel4B 8.805 12.187 27.0 487 [46]

3. Volume dependence of the R-Fe interactions

In this part, we consider the variation of the para- meter F ---- d In Tc/d In V within a series of isostruc- rural compounds. For R2Fel7, the corresponding F values derived from pressure experiments and from interstitial compounds are rather consistent as shown in the Fig. 2 where F values are plotted with respect to Tc of the corresponding parent compounds.

Upon increasing the Curie temperature, F has the tendency to decrease. Such a tendency observed for various RnFem and RnCom compounds had been ex- plained by Brouha et al. [16] in the framework of the itinerant electron theory of magnetism [21 ] by the fol- lowing expression:

r = + b / r L (3)

The value b = 1.25 × 106 K had been obtained for RnFem [16]. We note that the F values calculated ac- cording to Eq. (3) with the mentioned b value, drawn as curve (1) in Fig. 2, describe poorly the observed data for the R2Fe17 compounds.

In a compound of the magnetic rare earth, the Curie temperature is not determined merely by the Fe-Fe interaction, but also by the R-Fe and R-R interac- tions. F in that case should reflect also the volume

2 0

15

% [...

"~ 1 0 II

• ~<~p<~) RzFet7

,,o

(1) " ' - . . . .

0 i i 2 0 0 3 0 0 4 0 0

RzFel4 B

C,<>

i i

5 0 0 6 0 0 7 0 0

To (K)

Fig. 2. Dependence of F on the Curie temperature of R2FeI7 and R2FelaB: • derived from data for R2Fel7Nx reported by Coey et al. [3], C) from data for R2FeI7N/reported by Buschow et al. [33], • from data for R2FelTCx reported by Hong Sun et al. [40], • from data for R2FelaHx reported by Zhang et al. [26], and O is the pressure experiment data as quoted from various sources in Tables 1, 2 and 3. The curve (1) is the result of calculation according to Eq. (3) with b = 1.25 × 106 K 2 [16]; curves (2) and (3) are results of calculations for R2Fe17 according to Eq. (5) with d In n Rre/d In V = --2.8 and d In nRFe/d In V = 0, respectively; and curve (4) is the corresponding calculation for R2Fe14B with F = 3 and dlnnRFe/dln V = --2.86.

396 N.M. Hono / Physica B 226 (1996) 391-398

dependence of the R-Fe and R-R interactions and Tc in Eq. (3) should be considered as TEe characterizing for the Fe-Fe interaction only, and thus varies little within a series of compounds. In the framework of the two sublattice molecular field model, the Curie tem- perature can be expressed as follows (see for instance [22]):

Tc = 0.5{TR + TEe + [(TR -- TEe) 2 q- 4T2RFe] 1/2 } (4)

where TR = nRRCR, TF¢ = nve-veCFe, TRFe = nRFc(CRCve)I/2; nil or nij is the molecular field coef- ficient, Ci is the Curie constant of the corresponding sublattice.

In the hard magnetic compounds like R2Fel7 and R2FeI4B, Tc is high and thus the contribution of TR to Tc is usually small which can be neglected in the following discussions. We obtained from Eq. (4) the volume dependence of the Curie temperature as follows:

r = (2Tc/TFe- 1)-I[FFe + 2(Tc/TFe- 1)rRvd (5)

where FFc = d In TFJd In V and Fp,.ve = d In TREe/ d In V. Neglecting the volume dependence of the rare earth magnetic moment, one can write:

FREe = d In nRF¢/d In V + d In #ve/d In V. (6)

FFe and din #v~/d In V can be considered, respec- tively, the same as F and d in#s /d in V for non- magnetic rare earth compounds discussed in the previous section.

In order to use Eq. (5), the TF~ value should be de- termined for each R2Fe17 compound. It is suggested that TEe can be obtained by interpolating between the Tc values of the Lu- and La-compounds [22]. La2Fe17 does not exist but fortunately values for the inter- sublattice interaction coefficient ne4~ have been deter- mined from the studies on the magnetization process on single crystals of heavy rare earth compounds (see [23, 24] and references therein). Then making use of Eq. (4) the TFe values are obtained. Using FFe = 15, independent of TEe value, the F value can be calculated with a variable parameter F ~ . In fact, because of the large scatter of the F value, the fit can be obtained with 0 < FRye < 2 (see Fig. 2). Using the experimental value d In/*v~/d In V = 2.8 mentioned in the previous section, we obtain -2 .8 < d In nRFe/d In V < --0.8. This result indicates clearly the negative effect of the

Table 3 Pressure experiment data on R2FeI7 and R2Fel4B, dlnTc/dln V was calculated using x = lxl0 -2 GPa- l and 0.7x 10 -2 GPa-1, for R2Fel7 and R2Fel4B, respectively (see text for details)

Compound Tc(K) dTc/dp ira = d In Tc/d In V Ref. (K/GPa)

Nd2Fel7 330 -36 10.9 [17]

Er2Fe17 299 -43 14.4 [17] 320 --54 16.9 [44] 310 -37 11.9 [16]

Nd2FelaB 585 -26 6.3 [45] --35 -- -100 8.6 + 24 [42]

Er2Fe14B 560 --24 6.1 [17]

volume on the R-Fe intersublattice interaction of the compounds.

The effect of hydrogen absorption on the crystal- lographic and magnetic properties of R2Fel4B com- pounds has been studied earlier (see, e.g. [25, 26]). The nitride compounds were also studied [27]. Un- fortunately, the numerical values for the lattice pa- rameters and the corresponding Curie temperature are rarely available. In the high temperature part of Fig. 2 the F values derived from Ref. [26] are plotted as a function of the Curie temperature of the REFelaB parent compounds. We note again that the pressure experiment derived F values (see Table 3) are by a factor of 2 larger than the corresponding values de- rived from the hydride compounds. There are only few compounds that were studied under pressure and there is only one set of hydride data available. For an unambiguous explanation of this discrepancy, further pressure experiments are again required. The calculated curve is thus obtained for the hydride data using fiFe = 3 and FRFc = 0 or d lnnRFe/dln V = - d In #Fe/d In V = -2.86. It turns out again that the volume effect on the intersublattice exchange interac- tion is also negative in the R2FeI4B compounds.

In our calculation, FFe is assumed independent of the species of the rare earth atom. In practice, it is expected that FF¢ changes with changing TFe. How- ever, the change of TFc within a series of compounds is considerably smaller than Tc. For R2Fe14B, TF~ in- creases by 1.5% going from Lu to La, while Tc gets a maximum value of 22% higher at Gd. For R2Fe17 the change of TEe is larger, but the corresponding change

N.M. Hon9 / Physica B 226 (1996) 391-398 397

in FFe is not likely to be as much as that predicted by Eq. (3) and our above conclusion about a nega- tive volume dependence of the R-Fe interaction is still valid even if a slight decrease of the /'Fe value with temperature is taken into account.

It is appropriate to note here that on the basis of the so-called s-d model, in the case when the temperature dependence of the 3d sublattice susceptibility follows the Curie-Weiss law, Inoue and Shimizu [28] also arrived at an expression similar to Eq. (5). The dif- ference is that they assumed FRFe = d In nRFe/d In V, while in our Eq. (6) besides this term, FRFc com- poses also the contributions from the 3d magnetiza- tion, d In//Fe/d In V. As pointed out above, although the analyses for both R2Fel7 and R2Fe14B provide positive or zero FRFe values, we obtain negative d In nRFe/d In V values.

4. Concluding remarks

It is evident from the present analysis that the Fe- Fe interactions in REFe17 and REFe14B depend largely on the volume or the interatomic spacings in the com- pound. The difference in the signs of d In nFe--Fed In V in R2Fel7 (positive) and REFe14B (negative) reflects the difference in their d-band structures. Phenomeno- logically, the distance dependence of the 3d-3d in- teraction is illustrated by the Neel-Slater curve. As the average Fe-Fe interatomic distances in R2Fel7 are

smaller than that in R2Fe14B, the former compound can be assumed to be on the left side while the latter on the right side of the curve.

The volume dependence of the Curie tempera- ture in the compounds with magnetic rare earths can be explained in terms of the molecular field model. In both two types of compounds the R- Fe interaction becomes weaker with increasing volume. From the band structure calculation for RFe2, Brooks et al. [29] pointed out that the 3d- 4f interaction is mainly due to the 5d-3d hy- bridization and the local 4f-5d exchange interac- tion. The latter is expected to be insensitive to the change of the environment around the rare earth ion. The observed reduction of the R-Fe interac- tion, therefore, might be explained to be due to the reduced 3d-5d hybridization with increasing volume.

Acknowledgements

The author expresses his thanks to Prof. V. Se- chovsky, Prof. A.V. Andreev and Dr. L. Havela for critical reading and correcting the manuscript and to Prof. G. Hilscher and Dr. D. Givord for sug- gestive discussions and encouragement. The work is supported in part by the Czech Grant Agencies under the grants no. 202/96/0207, A1010614 and A1010622.

References

[1] K.H.J. Buschow, in: Ferromagnetic Materials, Vol. 1, ed. E.P. Wohlfarth (North-Holland, Amsterdam, 1980) p. 297.

[2] A.V. Andreev, Handbook of Magnetic Materials, Vol. 8, ed. K.H.J. Buschow (North-Holland, Amsterdam, 1995) p. 59.

[3] J.M.D. Coey, HongSun and Y. Otani, Proc. 6th Int. Symp. Magn. Anis. Coerc. RE-TM Alloys, Pittsburgh, PA, 1990, ed. S.G. Sankar (Carnegie Mellon Univ., Pittsburgh, PA, 1990) p. 36; J.M.D. Coey, Hong Sun and D.P.F. Hurley, J. Magn. Magn. Mater. 87 (1990) L251.

[4] K.H.J. Buschow, Rep. Prog. Phys. 54 (1991) 1123; G. Wiesinger and G. Hilscher, Handbook of Magnetic Materials, Vol. 6, ed. K.H.J. Buschow (North-Holland, Amsterdam, 1991) p. 511.

[ 5] D. Givord, H.S. Li, J.M. Moreau, R. Piere de la Bethie and R du Tremolet de Lacheisserie, Physica B 130 (1985) 323; A.V. Andreev, A.V. Deryagin, S.M. Zadvorkin and S.V. Terent'ev, Sov. Phys. Solid State 27 (1985) 987; H. Fujii, H. Nagata, Y. Uwatoko, T. Okamoto, H. Yamamoto and M. Sagawa, J. Magn. Magn. Mater. 70 (1987) 331; K.H.J. Buschow and R. Groessinger, J. Less-Common Met. 135 (1987) 39.

[6] F. Pourarian, M.Q. Hoang and W.E. Wallace, J. Less-Comm. Met. 120 (1986) 63.

[7] T. Takeshita and R. Nakayama, Proc. Int. Workshop on Rare Earth Magnets, Pittsburgh, PA, 1990, ed. S.G. Sankar (Carnegie Mellon University, Pittsburgh, PA, 1990) p. 49.

[8] O. Isnard and D. Fruchart, J. Alloys Compounds 205 (1994) 1. [9] R. Coehoorn, Phys. Rev. B 39 (1989) 13072.

[10] T. Beuerle, P. Braun and M. Faehnle, J. Magn. Magn. Mater. 94 (1991) LI1.

[11] R.J. Zhou, Th. Sinnemann, M. Rosenberg and K.H.J. Buschow. J. Less-Comm. Met. 171 (1991) 263.

[12] M. Loewenhaupt, P. Tils, D.P. Middleton, K.H.J. Buschow and R. Eccleston, J. Magn. Magn. Mat. 129 (1994) LI51.

[13] T. Beuerle, M. Liebs, K. Hummler and M. Faehnle, J. Magn. Magn. Mat. 132 (1994) L1.

[14] D. Givord, F. Givord and R. Lemaire, J. de Phys. Coll. C1, 32 (1971) C1-668; D. Givord, R. Lemaire, IEEE Trans. Mag. MAG-10 (1974) 109.

[15] J.P. Gavigan, D. Givord, H.S. Li and J. Voiron, Physica B 149 (1988) 345.

398 N.M. Hong / Physica B 226 (1996) 391-398

[16] M. Brouha, K.H.J. Buschow and A.R. Miedema, IEEE Trans. Mag. MAG-10 (1974) 183.

[17] Z. Arnold, J. Kamarad, P.A. Algarabel, B. Garcia-Landa and M.R. Ibarra, IEEE Trans. Mag. 30 (1994) 619; Z. Arnold, M.R. Ibarra, L. Morellon, P.A. Algarabel and J. Kamarad, paper presented at the EMMA'95 Conf., Vienna, 1995.

[18] J.G.M. Armitage, T. Dumelow, P.C. Riedi and J.S. Abell, J. Phys.: Condens. Matter 1 (1989) 3987.

[19] J.M.D. Coey and D.P.F. Hurley, J. Magn. Magn. Mater. 104 -107 (1992) 1098.

[20] J.P. Gavigan, Thesis, University of Dublin, 1988. [21] E.P. Wohlfarth, Phys. Lett. A28 (1969) 569. [22] E. Belorizky, J.P. Gavigan, D. Givord and H.S. Li, Europhys.

Lett. 5 (1988) 349. [23] S. Sinnema, Thesis, University of Amsterdam, 1988. [24] R. Verhoefi Thesis, University of Amsterdam, 1990. [25] Ph. L'Heritier and R. Fruchart, J. de Phys. Coll. C6, 46

(1985) C6-319. [26] L.Y. Zhang, F. Pourarian and W.E. Wallace, J. Magn. Magn.

Mat. 71 (1988) 203. [27] Y.C. Yang, S.L. Ge, X.D. Zhang, L.S. Kong, Q. Pan,

Y.T. Hou, S. Huang and L. Yang, Proc. 6th Int. Symp. Magn. Anis. Coerc. RE-TM Alloys, Pittsburgh, PA, 1990, p. 190.

[28] J. Inoue and M. Shimizu, J. Magn. Magn. Mater. 54-57 (1986) 991.

[29] M.S.S. Brooks, T. Gasche, S. Auluck, L. Nordstrom, L. Severin, J. Trygg and B. Johansson, J. Magn. Magn. Mater. 104-107 (1992) 1381.

[30] G. Zouganelis, M. Anagnostou and D. Niarchos, Solid State Commun. 77 (1991 ) I I.

[31] O. lsnard, S. Miraglia, D. Fruchart and J. Deportes, J. Magn. Magn. Mater. 103 (1992) 157.

[32] X.-P. Zhong, R.J. Radwanski, F.R. de Boer, T.H. Jacobs and K.H.J. Buschow, J. Magn. Magn. Mater. 86 (1990) 333.

[33] K.H.J. Buschow, R. Coehoom, D.B. de Mooij, K. de Waard and T.H. Jacobs, J. Magn. Magn. Mater. 92 (1990) L35.

[34] T.H. Jacobs, Gary J. Long, O. Allan Pringle, F. Grandjean and K.H.J. Buschow, J. Appl. Phys. 70 (1991) 5983.

[35] J.F. Herbst, in: Supermagnets Hard Magnetic Materials, eds. Gary J. Long and F. Grandjean (Kluwer Academic Publishers, Dordrecht, 1991 ) Chap. 5.

[36] H.S. Li, Thesis, Grenoble, 1988. [37] M.I. Bartashevich and A.V. Andreev, Physica B 162 (1990)

52. [38] J.M.D. Coey, A. Yaouanc and D. Fruchart, Solid State

Commun. 58 (1986) 413. [39] M.Q. Huang, B.M. Ma, W.E. Wallace, S.C. Sankar, Proc. 6th

Int. Symp. Magn. Anis. Coerc. RE-TM Alloys, Pittsburgh, PA, 1990, p. 204.

[40] Hong Sun, Y. Otani and J.M.D. Coey, J. Magn. Magn. Mater. 104-107 (1992) 1439.

[41] S.A. Nikitin, A.M. Tishin, M.D. Kuz'min and Yu.I. Spichkin, Phys. Lett. A 153 (1991) 155.

[42] H. Nagata, S. Hirosawa, M. Sagawa, A. Ishibashi and S. Endo, J. Magn. Magn. Mater. 70 (1987) 334.

[43] O. Isnard, R. Zach, S. Niziol, M. Bacmarm, S. Miraglia, J.-L. Soubeyroux and D. Fruchart, J. Magn. Magn. Mater. 140-144 (1995) 1073.

[44] Z. Arnold, J. Kamarad, P.A. Algarabel and M.R. Ibarra, J. Magn. Magn. Mater. 140-144 (1995) 951.

[45] J. Kamarad, Z. Arnold and J. Schneider, J. Magn. Magn. Mater. 67 (1987) 29.

[46] A.V. Andreev and M.I. Bartashevich, J. Less-Comm. Met. 167 (1990) 107.