High field magnetization of R2T17 compounds

Journal of Alloys and Compounds, 181 (1992) 95-109 JAL 8007

95

High field magnetization of R2T17 compounds J. J. M. F r a n s e , F. E. Kayzel, C. Marquina, R. J. R a d w a n s k i a n d R. V e r h o e f Van der W a a l s - Z e e m a n Laboratorium, Universiteit van Amsterdam, Valckenierstraat 65, 1018 X E A m s t e r d a m (Netherlands)

Abstract A summary is presented of high field magnetization studies on the ReT17 compounds (R=rare earth, T~Fe,Co or Ni). The different types of transitions that have been observed in magnetization studies on single-crystal samples along different crystallographic directions are mentioned. By analysing the transition fields, valuable information is obtained either on the strength of the R-T coupling or on the crystal field interactions of the rare earth ions. In addition, experiments are reported on powdered samples that are free to rotate in the applied magnetic field. This experimental technique provides a rather simple experimental approach to the intersublattice coupling in ferrimagnetic R-T compounds.

1. I n t r o d u c t i o n R e s e a r c h on t h e r a r e e a r t h - t r a n s i t i o n m e t a l ( R - T ) i n t e r m e t a l l i c s is v e r y m u c h s t i m u l a t e d in v i e w o f their p o t e n t i a l f o r p o s s i b l e a p p l i c a t i o n s in hardm a g n e t i c m a t e r i a l s . In o r d e r to p r o d u c e useful m a t e r i a l s at a m b i e n t t e m p e r a t u r e s , t h e s t r o n g e x c h a n g e i n t e r a c t i o n s o f t h e t r a n s i t i o n m e t a l s t h a t give rise to h i g h m a g n e t i c o r d e r i n g t e m p e r a t u r e s h a v e to b e c o m b i n e d with t h e l a r g e m a g n e t i c a n i s o t r o p y t h a t is a c h a r a c t e r i s t i c p r o p e r t y o f m o s t r a r e e a r t h m e t a l s at l o w t e m p e r a t u r e s . T h e s u c c e s s o f this c o m b i n a t i o n v e r y m u c h d e p e n d s o n t h e s t r e n g t h o f t h e R - T e x c h a n g e i n t e r a c t i o n b y w h i c h t h e large r a r e e a r t h a n i s o t r o p y c a n b e s u s t a i n e d u p to high t e m p e r a t u r e s a n d b y w h i c h t h e 3d m a g n e t i c m o m e n t is c o u p l e d to the r a r e e a r t h m o m e n t in addition. T h e c o u p l i n g b e t w e e n t h e r a r e e a r t h a n d 3d m o m e n t s is e i t h e r parallel f o r t h e first h a l f of t h e r a r e e a r t h series or antiparallel f o r t h e s e c o n d half. F o r a p p l i c a t i o n s t h e light r a r e e a r t h c o m p o u n d s a r e p r e f e r r e d b e c a u s e t h e r e s u l t i n g m a g n e t i z a t i o n is largest. F o r s t u d i e s of the R - T e x c h a n g e interaction, h o w e v e r , t h e h e a v y r a r e e a r t h c o m p o u n d s h a v e the a d v a n t a g e t h a t t h e c o u p l i n g b e t w e e n t h e t w o sublattice m o m e n t s c a n b e b r o k e n b y m a g n e t i c fields o f sufficient s t r e n g t h . A p p l y i n g t h e e x t e r n a l field a l o n g t h e e a s y d i r e c t i o n o f m a g n e t i z a t i o n , this b r e a k i n g o f t h e antiparallel c o n f i g u r a t i o n is a c c o m p a n i e d b y a f i r s t - o r d e r m a g n e t i c transition. T h e field at w h i c h t h e t r a n s i t i o n o c c u r s is d i r e c t l y r e l a t e d t o t h e c o u p l i n g s t r e n g t h b e t w e e n t h e m a g n e t i c sublattices. F o r the c o m p o u n d Ho2Co17, for i n s t a n c e , s u c h a t r a n s i t i o n h a s b e e n o b s e r v e d in m a g n e t i z a t i o n s t u d i e s at 4.2 K a l o n g t h e e a s y d i r e c t i o n in t h e h e x a g o n a l

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© 1992- Elsevier Sequoia. All rights reserved

96

plane (b axis) at a field of about 21 T, depending on the exact stoichiometry of the compound [1, 2] (Figs. 1 and 2). The transition field turns out to be roughly proportional to the net m o m e n t which depends sensitively on the cobalt-to-holmium ratio of this ferrimagnetic compound. The difference in magnetization data shown in Figs. 1 and 2 is due to a slight off-stoichiometry of sample 2. Apart from this deviation from stoichiometry, the quality of sample 2 is supposed to be superior to that of sample 1 in view of the sharpness of the transition near 21 T and the intersection of the zero-fieldextrapolated magnetization curve along the c axis. On further increasing the magnetic field along this crystallographic direction, two more transitions are expected. One of them has already been observed near 44 T in short-pulse magnetization studies on sample 2 performed at the University of Osaka, Japan [3] (Fig. 3). Along the other symmetry direction in the hexagonal plane of this compound, the a axis, another transition of the same origin as that along the b axis near 21 T appears around 28 T. One more transition BO

'

i

i

i

Ho2Coi7 T = 4.2

6O

K

~

a-axis b-axis v

o~ o

v

oo © =

c-axis

v

4o

vv

°

°°°

v

L~

v

2O

v v

v

0

,

I

0

,

I

=

20

lO

310

,

40

B [T]

Fig. 1. Magnetization data as a function of the applied magnetic field along the different crystallographic axes of hexagonal Ho2Co1~ at 4.2 K in long-pulse e x p e r i m e n t s (sample 1); data from ref. 1. 80

'

i

i

i

Ho2Co 17 BO

T = 4.2

K

:-'

~ a-axis .~

= b-axis

~.-

v

~ v v

c-axis

v

.0

v

.

/ ,,

............. ~ ............ ~

............• ..........

r

.... ,~.-p

ii

20 v v

00

'

frO

'

2LO

'

~0 ~

'

4O

B [T]

Fig. 2. Magnetization data as a function of the applied magnetic field along the different crystallographic axes of hexagonal Ho2Colv at 4.2 K in long-pulse e x p e r i m e n t s (sample 2); data from ref. 2.

97 i

i ~00

H ° 2 C o 17 T = 4.2

K

8O b-ax~.s

%

BO

L~

40

/J

2O 0

,

,

I ~0

I

,

310

20 B

zllO

50

IT]

Fig. 3. Magnetizationdata as a function of the applied magnetic field along the easy magnetization direction of hexagonal H%Co17 at 4.2 K in short-pulse experiments (sample 2); data from ref. 3. 80 DY2Co ~,7

60

4.2

K

+ a-axis O-axis

o C-8XlS CM

40

/D 20

0

,

l 10

,

210 S

,

l 30

, 40

IT]

Fig. 4. M a g n e t i z a t i o n data a s a f u n c t i o n o f t h e a p p l i e d m a g n e t i c field a l o n g t h e different c r y s t a l l o g r a p h i c a x e s o f h e x a g o n a l Dy2Co17 at 4 . 2 K i n l o n g - p u l s e e x p e r i m e n t s ; data f r o m ref. 4.

is expected along this direction before saturation is reached. Similar transitions have been observed in the easy-plane hexagonal c o m p o u n d Dy2Co,7 at 27 T and 37 T [2, 4] (Figs. 4 and 5), with the a and b axes interchanged with respect to H%Co,7. On the basis of the information concerning Dy2C%7, all "exchange-driven" transitions in the heavy R2T17 c o m p o u n d s ( T - F e , C o ) have been calculated [5] (Table 1). The calculated values for the first easyaxis transition field range from 22 T, along the easy axis in the (easy) hexagonal plane of H%COlv, to 107 T for Gd2Fel7 along the easy c axis. For an easy c axis, one single transition has to be expected in the magnetization curve before saturation is reached. The predicted values for the transition fields have been elaborated within a rather simple "two-sublattice" model in which the R - T e x c h a n g e interaction, the crystal field effect o n the rare earth ions and the magnetostatic energy compete. In fact, in predicting values for the transition fields, the crystal field effects play a minor role. The reverse is true as well. Having experimental information on the transition field values,

98 80

i

t

i

4.2K

DY2CoI7 60

.?

%

::

. . . . . . . . ~ : : ..............; . :

4o

a-axls

b

~:-,-~

........-.

b--aXlS

2O

0

i

0

I

l0

*

i

i

20

I

30

i

I

40

B [T]

Fig. 5. Magnetization d a t a a s a f u n c t i o n of the a p p l i e d m a g n e t i c field a l o n g t h e c r y s t a l l o g r a p h i c directions in the e a s y p l a n e o f h e x a g o n a l Dy2ColT at 4.2 K in s h o r t - p u l s e e x p e r i m e n t s ; data f r o m ref. 2.

TABLE 1 Calculated v a l u e s f o r t h e t r a n s i t i o n fields (in tesla) t h a t are c o n n e c t e d w i t h the b r e a k i n g o f the f e r r i m a g n e t i c s t r u c t u r e of R2Tlz c o m p o u n d s ; data f r o m ref. 5 R

E a s y axis in plane

H a r d axis in plane

c axis

T-=Fe Gd Tb Dy Ha Er Tm

75, 54, 46, 41, -

95, 70, 62, 58, -

107 56

T------Co Gd Tb Dy Ha Er Tm

42, 81, 190 27, 51, 130 22, 44, 94 -

160, 2 6 0 102, 190 97, 135 85, 120

200 150 125 100

54, 105 37, 80 29, 55 -

79 42 48

an accurate value can be obtained for the R - T exchange parameter without having detailed knowledge of the crystal field interactions. In Section 2, the model will be discussed in more detail. To verify the m o d e l predictions collected in Table 1, one needs, apart from a facility for magnetic fields well above 20 T, well-oriented singlecrystal samples with sufficient mass in order to perform the magnetization studies. For most of the compounds collected in Table 1, single-crystal batches with a volume of approximately 1 cm 3 have been produced by the Czochralski technique [6]. In the reported investigations, spheres with a diameter of 3 mm have been spark eroded out of the single-crystal batches.

99 Magnetization studies have been p e r f o r m e d along the three main crystallographic axes. In a full analysis of these magnetization curves, not just restricted to the analysis of the transition fields, additional information is obtained on the magnetic anisotropy and the underlying crystal field interactions o f the rare earth ions in particular. In the above-given summary of the experimental a p p r o a c h to exchange and crystal field interactions in the R - T intermetallics, high field facilities and single-crystal growth are emphasized. Needless to say, the present longpulse (up to 40 T) and short-pulse (up to 60 T) facilities do not provide the necessary field range to study the exchange p h e n o m e n a in the R - T intermetallics in full detail. Furthermore, single-crystal growth turns out to be not always successful. In order to study exchange interactions for those systems for which either no single-crystal material could be p r o d u c e d or the transition fields are outside the available field range, special solutions have been worked out. In the latter case we have to consider possibilities for changing the balance between the exchange interactions and the magnetostatic energy since these are the two quantities that mainly determine the value of the transition field. This balance can be effected in the desired direction by, for instance, substitutions that lower the magnetic m o m e n t of the sublattice with the largest magnetic moment. The gain in magnetostatic energy at a reorientation of the magnetic m om e nt s of a ferrimagnetic c o m p o u n d of the type discussed above is largest in the case where the two sublattice m om ent s are almost equal. As an example of the manipulation of the transition field we refer to the c o m p o u n d Ho2Co14Fea. On substituting cobalt by iron the dominant magnetic m o m e n t of the 3d sublattice further increases and the difference between the values of the 3d and holmium sublattice moments b eco mes larger. The easy-axis transition field increases by this substitution from 21.5 T to 29.5 T [7]. On the contrary, by lowering the 3d m o m e n t by appropriate substitutions, the value for the transition field decreases as observed, for instance, in the Ho2(Fedkl)17 system. In cases where no singlecrystal material is available, the R - T exchange interaction can be studied satisfactorily on finely pow de r ed material that is free to rotate in the sample holder under the action of the applied magnetic field. The concept behind this meth o d is that the individual pow der particles can be considered to be monocrystalline. In order to demonstrate the magnetic characteristics of such a sample in high field magnetization studies, we present in Fig. 6 the magnetization curve of a monocrystalline Ho2Co17 sphere of 3 m m diameter that is free to rotate in the sample holder [8]. In the low field regime, the magnetization is constant and equal to the low field magnetization along the easy axis. Just below 20 T, there is a kink in the magnetization curve, followed by a trajectory with a constant differential susceptibility. The kink field as well as the slope of the cr v s . B curve above this field are again largely determined by the value of the R - T exchange parameter. At the kink field, the antiparallel m o m e n t configuration of the rare earth and 3d m om ent s is broken. In the canted configuration above the kink field, the sublattice m o m e n t s gradually bend to the field direction, reaching saturation far outside

100 70

i

Ho2CoI 7 T=

6O

5o

:/

4.2K

o free

sphere

* free

pauper

L~ 40

30

0

i ~0

,

t 20 B [T)

,

3tO

40

Fig. 6. Magnetization data at 4.2 K of a single-crystal s p h e r e (diameter, 3 ram) of Ho2Col7 that is free to orient itself in the applied magnetic field in long-pulse experiments; for comparison the results are s h o w n for a powdered polycrystaUine sample with powder particles t h a t are free to orient themselves in the applied field; data from ref. 8.

the available field range for this particular compound. The magnetic anisotropy of the compound has only a minor effect on these processes just as in the case of the transition field for a fixed monocrystalline sample along the easy direction. The analysis of this type of magnetization measurements is further elaborated in Section 2. In order to prove the relevance of this method, polycrystalline Ho2Co17 material has been powdered down to particle sizes of the order of 10 /zm. The powder has been loosely stacked in the sample holder for high field magnetization studies. Experimental results are shown in Fig. 6 as well and deviate slightly from the single-crystal result, in particular below and around the kink field. The slopes well above the kink field, however, are almost identical in the two experiments. The deviations at lower fields indicate that in the polycrystalline powder not all particles are fully monocrystalline. This powder method has been found to be extremely successful in the study of the R-T exchange interaction and a large series of R-T compounds has recently been investigated [9].

2. T h e o r e t i c a l c o n c e p t s and m o d e l c a l c u l a t i o n s Magnetism of the R-T intermetallics is often discussed in terms of an itinerant picture for the transition metal magnetism and a single-ion local m o m e n t approach of the rare earth partner. In general, the magnetic properties of the transition metal are taken from a c o m p o u n d with a non-magnetic rare earth partner. For the low temperature magnetic behaviour of the transition metal sublattice, the spontaneous magnetization, the differential high field susceptibility and the magnetic anisotropy constants are the relevant parameters. These parameters are assumed not to change drastically over a given series of rare earth compounds such as, for instance, the 2:17 series. In describing the magnetic properties of the rare earth ions, the following hamiltonian is used:

101

HR = H c +H~_o + H~ch +HcF +Hz

(1)

Hc represents the intra-atomic Coulomb interaction that results in energy states with well-defined orbital and spin quantum numbers; H,_o represent the spin-orbit interaction - A L . S by which the spin and orbital moments are coupled to a total angular m o m e n t u m J. In the case that the spin-orbit interaction is much larger than the following energy terms in eqn. (3), the total angular m o m e n t is a good quantum number and Hund's rules can be applied. Hexch describes the exchange interactions of the 4f spins with the surrounding unpaired 3d spins and with the electron spins of the surrounding rare earth ions; HCF accounts for the electrostatic interaction of the 4f electrons with the neighbouring charge distribution and Hz represents the Zeeman energy. Since the spin--orbit energy in most of the discussed compounds is at least one order of magnitude larger than the exchange and crystal field interactions, we restrict ourselves to the lower multiplet J of the 4f ion. The exchange interactions are assumed to be of the Heisenberg type: H~¢h= -- ~ ~ 2JijS~ .~.

(2)

where J~j is the exchange parameter representing the exchange interaction between the spins S~ and Sj. Since three different type of spin pairs can be distinguished we are dealing with three different types of exchange parameters: Jrr, JRT and JRR. In discussing the low temperature magnetization curves, we can restrict the analysis to the parameter JRT since it is j u s t this parameter that governs the mutual configuration of the rare earth and transition metal spins. V~rlthin a mean field approach, the R-T exchange interaction is related to the molecular field acting on the rare earth ion and produced by the transition metal subsystem. The molecular field is usually expressed as BmolR = nRTMT

(3)

with nRw the inter sublattice molecular field coefficient. On considering nearestneighbour interactions only and taking the exchange interaction to be spatially isotropic, the following relation between the parameters JRT and nRT has been derived [10]: ZRTJRT = ~ B 2 N T n R T g R / ( g R -- 1)

(4)

where ZRT is the number of nearest transition metal neighbours of a rare earth atom, NT is the number of transition metal atoms per unit of mass and gR is the Landd factor of the rare earth element in question. Expressing in the same approximation the exchange field Be~R as BexR= - ZRT ST JRT//~B

(5)

we arrive at the following relation between BmolR and B~xR:

B~,:R =BmolRgR/2(gR-- 1)

(6)

9

102 The crystal field hamiltonian for the R2T17 compounds with the hexagonal Th2Nil~ s y m m e t r y can be expressed as

HCF =B2°O20 +B4°Oa ° +B6°O6 ° +B66068

(7)

for each of the two different rare earth sites. The coefficients B~m are the crystal field parameters and O~m the Stevens operators. The crystal field parameters carry information about the multipole moment of the 4f ion as well as about the crystal field potential associated with the neighbouring charge distribution. In first approximation we can write

B~m= O ~ ( r 2 ) A ~

(8)

where 0, is the appropriate Stevens factor, r4f the 4f radius and Anm the crystal field coefficients that characterize the surrounding charge distribution of the appropriate site. Values for the product On(r4~) for the different rare earth elements have been collected in ref. 11. Since the coefficients A~m are supposed not to change drastically within a given series of compounds, the crystal field parameters B~m have to follow in first approximation the numbers for this product. Crystal field interactions are responsible for the huge magnetic anisotropy of the rare earth ions. For compounds with the rhombohedral TheZn~7-type of structure two additional terms, B43043 and B68063, have to be added to the right-hand side of eqn. (5). For this type of compound there is only one single rare earth site. The rare earth contribution to the magnetic anisotropy energy for compounds with hexagonal symmetry can be described by the following phenomenological expression:

EAR~- K20p20+ K4°P40+ K6°P6° + K66P66 cos(6~b)

(9)

with r~"~ the anisotropy coefficients, and p m the Legendre functions. The set of Legendre functions employed in the analysis of the 2:17 compounds has been presented in ref. 11. Since the Legendre functions are the classical equivalents of the Stevens operators, relations exist between the crystal field parameters B=m and the anisotropy parameters r~".

K2°=2J2B2O, K4° = 8J4B40,

K60~-16J6B60, K66= JfB66

(10)

Values for J~ for the trivalent rare earth ions can be found in ref. 11. The magnetic anisotropy of the transition metal sublattice can be approximated by an expression similar to eqn. (9). In general, only the first two coefficients are relevant. In analysing high field magnetization curves of the R-T intermetallics we start with the following free energy expression:

E =EAR + E w + nrrrMa" MT - - B "Ma - B . M w

(11)

In the case of the hexagonal TheNi17 structure with two different rare earth sites, only the m e a n value of the anisotropy coefficients over the two different sites can be determined from the macroscopic magnetization measurements. Subsequently, the following set of parameters has to be evaluated: four crystal

103

field parameters corresponding to mean values over the two different sites of the rare earth ion, two anisotropy coefficients of the transition metal system, the molecular field coefficient nRw and the sublattice moments MR and .)~rw. The transition metal parameters are taken from the Y-T compound; for M R the full m o m e n t of the trivalent rare earth ion is taken. The five remaining parameters should follow from fitting the magnetization curves along the different crystallographic directions. As we have mentioned already in section 1, the parameter nRw Can be determined rather independently for ferrimagnetic compounds, either from a study of transition fields in monocrystalline samples or by investigating the kink field in the magnetization curves of finely powdered samples that are free to rotate in the applied field. When 3d anisotropy is negligible compared with the rare earth anisotropy, the rare earth moment of a free particle will be along the easy magnetization direction for any field strength. In that case the free energy expression reduces to

E

= nRTMR "MT - B "M R-B

"MT

(12)

The resulting magnetic m o m e n t M of a free powder particle will always be along the field direction; its magnitude is given by

M = (MR2 +MT 2 + 2MRMT COS a) 1/2

(13)

where a is the angle between the sublattice moments. There are two critical field values: Befit (I) = nRw I M R - MT]

and Bcrit (2) ~- n R T ( M R + M T )

(14)

below and above respectively the resulting magnetization is constant. In the intermediate field regime the magnetization is given by

M----B/nuT

(15)

In Figs. 7-9, a few examples are given of "free powder" measurements on powdered Ho2(Fel_~,lx) samples [12] on a collection of monocrystalline spheres (diameter, 3 mm) of R2T17 (R----Dy, Ho, Er; T--Fe, Co) compounds that are free to rotate in the sample holder [2] and on powdered R2Ni17 (R--Dy, Ho, Er) samples [13]. The value for nRT of 0.52 T kg A -1 m -2 that can be derived from the data of Fig. 7 for the Ho2(Fe, A1)17 system is very much the same as the value reported in Table 2 for Ho2Colv that has been derived from experiments on a monocrystalline sample of Ho2Colv. The variation in the value of n~r over the different rare earth elements as shown in Table 2 is clearly reflected by the different slopes of the magnetization curves of Fig. 8 in the higher field region. In Ho2Ni~7 and Er2Nil~, both critical fields of eqn. (14) can be observed; see Fig. 9. For Dy2Ni~7 the second transition is expected at 42 T, above the field range of the Amsterdam High Field Installation. Values for the molecular field coefficient nRT derived from these experiments are collected in Table 2. The free powder method is only applicable to the ferrimagnetic compounds. For the light rare-earth compounds, all five parameters (four crystal field and one molecular field)

104 B0 H02Fel7_xAl x 6O

so oo

o o.o,©.o,o

-o

• oo...o,

o

-

¢~E 40

4.2

K

o ........ o ......

a::

o x=i

~,$

o x=2 ~x=3

a A

Lo

2O

-

0

aa v v

v 'xffi,4

vvvvv.v v~v v ,+

, 0

.......

* x=5

I CO

,

210

,

I

,

30

I

40

B [T] Fig. 7. Magnetization data at 4.2 K of powdered polyerysta]line samples of Ho2(Fel_=Al=)17 with powder particles that are free to orient themselves in the applied field in long-pulse experiments; data from ref. 12.

100 80

........... • .........

6O ,40 ..............

•

l~

- Ho2co~7 v

20

H02Co

Er2Fe 17 DY2COl 7

o o

0

14Fe3

" Er2C° I7

0

,

I

l0

,

210

S

,

I

30

,

40

[T]

Fig. 8. Magnetization data of single-crystal spheres (diameter, 3 ram) of a series of R2T)~ compounds in long-pulse experiments; the samples are free to orient themselves in the applied magnetic field; data from ref. 2.

should be determined from an analysis of the magnetization curves on monocrystalline samples, to be discussed in the next section.

3. High f i e l d m a g n e t i z a t i o n c u r v e s a l o n g d i f f e r e n t crystallographic directions High field experiments on oriented monocrystalline samples have been performed along different crystallographic directions at liquid helium temperatures for an extended series of R2T17 compounds: T--Fe, R--Y, Gd, Tb, Dy, Ho and Er; T--=Co, R--Y, Pr, Nd, Gd, Tb, Dy, Ho and Er. Magnetization measurements on Y2FeI~ up to 21 T reveal an appreciable anisotropy; saturation is reached above 6 T [14]. The spontaneous magnetic moment corresponds to 174.2 A m 2 kg -1, resulting in a value of 2.07 ~b per ion atom, assuming exact stoichiometry. The saturation magnetization

105 i00

i

i

i

80

o

% <

OY2Ni 17 4.2 K

,40

l~

o

2O

~

~00

"~

60

•~

40

1~

20

%

,

f

I

~

/ ~

~ H°2N± J.7

4.2K

'

100 ,~

I

I

I

I

'

I

'

8O

~

% <

40

I~

2O

ErpNi17 4.2 K

10

20

30

40

S [T]

Fig. 9. Magnetization data at 4.2 K of powdered polycrystalline samples of R2Ni17 compounds (R=-Dy, Ho, Er) with powder particles that are free to orient themselves in the applied field in long-pulse experiments; data from ref. 13. TABLE 2 Values for the molecular field coefficient nRT (T kg A -1 m -2) and for the exchange parameter JRT ( × 10 -22 J) for the R2T~7 compounds; data from refs. 2, 13 and 14 Values for the following R Pr

Nd

Gd

Tb

Dy

Ho

Er

1.6 1.17

0.88 0.96

0.66 0.96

0.52 0.94

0.41 0.89

-

1.06 1.11

0.72 1.01

0.54 0.94

0.40 0.83

0.45 0.64

0.33 0.58

0.26 0.55

T-~Fe nRw

JRT T~-Co nRT

JRT

0.80 1.15

1.05 1.0

T--=Ni nRT

JRT

t u r n s out to be slightly anisotropic. The difference for fields parallel a n d p e r p e n d i c u l a r t o t h e c a x i s , h o w e v e r , is n o t m o r e t h a n 2%. F r o m a S u c k s m i t h - T h o m p s o n p l o t t h e a n i s o t r o p y c o n s t a n t s K1 a n d K2 i n t h e e x p r e s s i o n

EA=K1 s i n 2 0 + K 2 sin40+Ka s i n 6 0 + K 4

s i n 6 0 cos(6~b)

(16)

w e r e f o u n d t o b e - 4 2 7 J k g -1 a n d 3 5 J k g -1 r e s p e c t i v e l y . T h e s e r e s u l t s for the iron moment and the iron anisotropy have been employed in the a n a l y s i s o f t h e r e m a i n i n g R2Fe~7 c o m p o u n d s f o r w h i c h w e w r i t e

106

Ki =K~T+KIR

(17)

Between the anisotropy constants KiR and the anisotropy coefficients ~ m of eqn. (9), the following relations exist: K, R-- - ½(3K2° -}- 10K4° + 21 r~°) K2R= (1/8)(35K4 ° + 189r~ °) K~R= - ( 2 3 1 / 1 6 ) ~ ° K4 R -- K66

(18)

Magnetization curves of a spherical monocrystalline Y2Co,z sample (diameter 3 mm) have been measured at 4.2 K in fields up to 22 T [14]. The spontaneous magnetic moment along the easy magnetization direction amounts to 132.5 A m 2 kg -1, corresponding to a cobalt m o m e n t of 1.65~B, assuming perfect stoichiometry. The differential high field susceptibility is equal to 0.09 A m 2 kg-1. The anisotropy constants K, and K2 have been determined by the Sucksmith-Thompson method resulting in the value - 6 1 J kg -1 and - 2 . 7 J kg-1 respectively. Magnetic torque studies in the (a,b) plane yield a value for IK4] of 0.026 J k g - ' , negligibly small compared with the values of the first two constants [5]. In fact the measured values for the 3d anisotropy constants in Y2Fe~z and Y2Co,7 also represent mean values over the four different 3d sites; see, for instance, ref. 16. Experimental results for the high field magnetization of the remaining R2T,7 compounds have been published in a series of papers: Gd2Fe~7 [2], Tb2Fel~ [14, 17], Dy2Fe17 [14], Ho2Fe17 [7], Er2Fe17 [14, 18], Pr2Colz [14, 19], Nd2ColT [14, 19], Gd2Co17 [14], Tb2Co1~ [14, 18], Dy2COlT [4, 14], Ho2Co17 [1, 14], Er2Co17 [14]. The results for Ho2Co17 and Dy2Co17 have already been shown in Figs. 1 and 4 respectively of this paper. As another example we show in Fig. 10 the magnetization curves of Nd2Cos~ in fields up to 35 T. These magnetization data have been analyzed in ref. 20 and have resulted in a set of values for the crystal field parameters Bnm and the molecular field coefficient. The value of the parameter nRw for Nd2Co~7 is certainly less accurate than those reported for the ferrimagnetic compounds.

4. D i s c u s s i o n

The magnetization curves of all 2:17 compounds studied have been analyzed in terms of the molecular field parameter nRW and the anisotropy constants K1 R, Kua and K4R. Assuming that the exchange parameter J~w is constant over an isostructural series of rare earth compounds, we expect the parameter nRT to vary as (gR-- 1)/gR over a given series. In Table 2, the values for the parameters nRT and JRT are presented for the compounds discussed in this paper. Examining these results we note that there is a tendency for the parameter JRT to decrease with increasing number of 4f electrons. As has been proposed by Beloritzky et al. [21l, this decrease is

107

i

N~2Co~7

d

4.2 K

150

%

~00 v

50

~

a

o

~-a×is

axis

tree

I

l0

I

20 B [T]

I

3O

Fig. 10. Magnetization data as a function of the applied magnetic field along the different crystallographic directions of rhombohedral Nd2Co~? at 4.2 K in long-pulse experiments; data from ref. 19.

related to the lanthanide contraction and reflects a weakening of the indirect R - T e x c h a n g e that p r o c e e d s via the intraionic 4 f - 5 d interaction of the rare earth ions and depends on the radius of the 4f shell. A discussion of the rare earth anisotropy constants is h a m p e r e d by the two different rare earth sites that occur in the hexagonal Th2Znl~ structure that, in general, is found for the heavy R2TI~ compounds. For the light R2T17 c o mp o u n d s , the r hom bohe dr al Th2Nil~ structure is m o r e c o m m o n with only one single rare earth site. For this type o f structure additional param et ers a p p e a r in the crystal field hamiltonian that cannot be evaluated on the basis of the m a c r o s c o p i c magnetization measurements. These different structures and the two different rare earth sites of the Th2Zn~7 structure in particular, make a systematic study of the variation in the anisotropy constants over a given rare earth series on the basis of magnetization studies rather difficult. The best that can be done is to predict the variation in the param et ers _ElR and K4R (under the assumption that in eqn. (9) the coefficients K4° and K8° are zero and that there is only one rare earth site) and to com pare the calculated results with the experimental data. These predicted values, as calculated by Sinnema [ 14 ], are collected in Table 3. Comparing these results with the fitting p a r a m e t e r s that have be e n obtained for the individual compounds, we note that, in general, the variation in sign of the anisotropy constants is well predicted. Although less accurate, the variation in the absolute values of the calculated coefficients follows the trends observed in the experiments. Inelastic n e ut r on scattering experiments on Ho2Co17 [22] and Dy2Co~7 [23] confirm the results for the anisotropy and exchange p a r a m e t e r s collected in Table 2. Specific heat experiments on Ho2Co,7 are in agreem ent with the p a r a m e t e r values and the subsequent energy level schem es deduced from these p a r a m e t e r s [24].

108 TABLE 3 Values for the anisotropy constants K , R ( × 102 J kg -~) derived from fitting the high field magnetization curves of a series of R2T~7 compounds; "calculated" values for K1R and K4 R follow the first- and third-order Stevens factors 02 and e6 respectively; data from ref. 1 Values for the following Pr Tw-Fe K1R

-

K2 R

.

K4R

-

T-~Co KI R

Nd

-

.

. -

R

Gd

Tb

Dy

0

-

-- 12

. -

0.3

-

Ho

Er

6.5

12 7.8

1.5

2.0

-

4.2 - 3.5 -

1.0

15 3 --0.9

- 14 3 4.8

--

- 18 0 0.15

- i0 2.6 -2.0

- 17.5 6.4 1.9

14 -- 1.9 -

C a l c ~ a t e d results -15 K4 R --5.1

-9.5 5.1

0 0

-20

-19.3 --1.2

-7.4 2.0

6.8 --1.9

K2a K4a

-

gl R

0.4

A c k n o w l e d g m e n t

The authors acknowledge the support by the Commission of the European Community within its BRITE/EURAM Research and Development programme.

R e f e r e n c e s

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109 13 C. Marquina, F. E. Kayzel, T. H. Anh, R. J. Radwanski and J. J. M. Franse, submitted to

J. Magn. Magn. Mater. 14 S. Sinnema, Thes/s, Amsterdam, 1988. 15 B. Matthaei, J. J. M. Franse, S. Sinnema and R. J. Radwanski, J. Phys. (Paris), Colloq. C8, 4P (1988) 533. 16 N. P. Tbuy and J. J. M. Franse, J. Magn. Magn. Mater., 54-57 (1986) 915. 17 R. Verhoef, P. H. Quang, R. J. Radwanski, C. Marquina and J. J. M. Franse, submitted to

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