Spin reorientation in (HoxY1−x)Co2 and (NdxY1−x)Co2 systems (1 ⩾ x ⩾ 0.7)

Journal of Magnetism and Magnetic Materials 29 (1982) 127-132 North-Holland Publishing C o m p a n y

SPIN

REORIENTATION

127

I N ( H o x Y t _ x)C°2 AND (Nd xYt _ x)C°2 S Y S T E M S

(1 ~>x i> 0.7) E. G R A T Z Inst. f Experimentalphysik, Technical University, Vienna, Austria

and H. N O W O T N Y Inst. f Theoretische Physik, Technical University, Vienna, Austria

A m o n g the rare e a r t h - C o 2 Laves phases, HoCo 2 and N d C o 2 show a spin reorientation at about 15 and 43 K, respectively. At low temperature in both compounds the easy direction of magnetization is [ll0]. On heating up the samples the easy direction changes to [100] at the temperatures given above. Such a spin reorientation is explained by the combined effect of crystalline field and exchange interaction. The aim of this paper is to present theoretical calculations and experimental results concerning the influence of replacing the magnetic rare earth ions in HoCo 2 and NdCo 2 by non-magnetic Y on the spin reorientation temperature. It was found that the spin reorientation temperature decreases in (Nd, Y)Co 2 and increases in (Ho, Y)Co 2 with increasing Y concentration. Experimental data obtained from resistivity measurements are compared with theoretical results.

1. I n t r o d u c t i o n

A large variety of investigations of physical properties of rare earth ( R E ) - C o z compounds are known. One of the reasons is because in some of these compounds, which crystallize in the cubic MgCu z-Structure, the magnetic transition is of first order. A first order transition exists in the heavy rare earth compounds ErCo 2 (32 K), H o C o 2 (78 K), and D y C o z (135 K), whereas the magnetic transition in the other RECo 2 compounds is of second order [ 1]. In some recent papers we have studied the influence of a first order transition in these heavy R E C o z compounds on transport phenomena such as electrical resistivity and thermopower [2]. It was found that the temperature dependence of resistivity and thermopower are both characterized by extremely pronounced discontinuities at T~. Furthermore we have also studied the pseudobinary (H0,Y I x)Co z series (0-<
the influence of the substitution of Ho by Y on the first order transition was studied. In addition we could show that the spin reorientation temperature, known in H o C o 2 at about 15 K [4], increases with increasing Y concentration. Preliminary theoretical calculations showed that such an increase of the spin reorientation temperature can be explained in the framework of a Hamiltonian consisting of a crystal field and a constant molecular field term. Furthermore we deduced from this preliminary calculation that for the isostructural (Nd, Y)Co z pseudobinary system the spin reorientation temperature should decrease as the Y content is increased. The aim of the present paper is to investigate both pseudobinary systems with respect to the variation of the spin reorientation temperature depending on the Y concentration. Experimentally this variation of the spin reorientation temperature was studied by means of resistivity measurements. Theoretically we used a Hamiltonian consisting of a crystal field and a magnetic interaction term and

© 1982 North-Holland

128

E. Gratz, 1t. Nowotny / Spin reorientation in (HoxYI x)C02 and ( N d x Y 1 x)C02 systems

3. Results

solved it in a self-consistent molecular field approximation. As will be shown, good agreement between the experiment and the theory exists.

A common characteristic feature of N d C o 2 and H o C o 2 is a spin reorientation in the ordered state detected by specific heat measurements [4,5], magnetic measurements [6,7], thermal expansion [8] etc. In a previous investigation concerning the magnetic and the transport properties of the pseudobinary (Ho, Y)Co 2 system, it was observed that the spin reorientation temperature increases with increasing Y concentration [3]. We have repeated the measurements of the temperature dependence of resistivity in the high Ho concentration region of the (Ho, Y)Co 2 system to improve the precision of the experimental data. In addition we have studied the isostructural pseudobinary (Nd, Y)Co 2 system in the same concentration range. We have found that in both systems the spin reorientation temperature is changed with increasing Y concentration, in the (Ho, Y)Co 2 system an increase and in the (Nd, Y)Co 2 system a decrease was found from experimental data. The spin reorientation temperature was obtained from resistivity measurements.

2. Experimental procedure The samples were melted in a high-frequency furnace under an argon atmosphere and subsequently annealed at 900°C for 72h. The best result with respect to phase purity was obtained using a 6% excess of rare earths. No foreign phases were present as far as could be seen from D e b y e Scherrer patterns. For the measurements in the temperature range from 4 . 2 K to room temperature a quasi-continuous four-probe technique was applied to bar shaped samples (sample size 1 × 1 X 8 m m 3). The temperature was measured using a Au + 0.07%Fe/chromel thermocouple. The P versus T behaviour in the vicinity of the spin reorientation temperature (as shown in figs. 3 and 4 in section 3) was measured using an ac technique based on a lock-in amplifier.

teY?cml 160

100

\ .-: ~

10 A

60

8

40

~

,.

20

o

10 ~ "/"~ ~

0

,

0

J

i

i

J

50

,

,

i

l

100

=

i

i

i

i

150

,

.

i

,

~

30 T[K] i

200

~

i

,

,

,

:

250

Fig. 1. p versus T curves of (Ho, Y)Co2. The inset shows the residual resistivity P0 for different Y concentrations.

129

E. Gratz, H. N o w o t n y / Spin reorientation in ( H o x Y / _ x ) C O 2 a n d ( N d x Y I x ) C o 2 systems

140 120 100

20"/, Y

3o./. r

(Nd. Y) Co2

40 30 20

•

tO 0 tO

2O 0

20

,,i,tltl,~llll,ll,,tl*:::'~ ~

1~

30

200

250

Fig. 2. p versus T curves of (Nd, Y)Co 2. The inset shows the residual resistivity P0 for different Y concentrations.

Fig. 1 shows the p(T) behaviour of the (Ho, Y)C% samples for a temperature region from 4.2 K to room temperature. The corresponding results for the (Nd, Y)Co 2 series are given in fig. 2. Figs. 3 and 4 show the p(T) behaviour in the vicinity of the spin reorientation temperature T R for both systems. The points of inflection, which are marked by arrows in figs. 3 and 4, were taken as the spin reorientation temperatures T R. A brief discussion of the whole shape of these p versus T curves will be given later. In the following the concept for the calculation of the spin reorientation temperatures and their concentration dependence will be given. The H a m iltonian used consists of the following two terms: (i) the crystalline electric field (CEF) Hamiltonian, written in the usual notation for cubic Laves phases [9] HCEF = X H(C~F i

= E

,,~,.,%m:

13 12 11

/

(Ho,

30"/.r

Y)~'

10 9

~o

a

2o'/,~" 7,r

7 6 5

No Co2

4 3

+ w(1

(1)

i ( W and x) are crystalline electric field parameters and 0(4i), 0(6i) are linear combinations of Stevens equivalent operators [10] for the ith rare earth ion).

2 TfK] 0

12

14

16

18

20

22

24

Fig. 3. p versus T curves of (Ho, Y)Co 2 in the vicinity of the spin reorientation temperature T R (T R is indicated by an arrow),

E. Gratz, H. Nowotny / Spin reorientation in (HoxYl_x)Co2 and (Nd x YI -x)Co2 systems

130

(ii) The interaction Hamiltonian between rare earth ions in the Heisenberg form Him= ½ ~ a , s J , - Jj

(2)

i v~j

where the exchange parameters aij describe the indirect exchange between the rare earth ions due to the s electrons and the Co 3d electrons. We have solved this Hamiltonian in the mean field approximation. In the scope of this approximation one gets the following model Hamiltonian: O) H = ~, [H~e F_

a
(3)

i

where ( J ) = ( 4 ) is the thermal averaged expectation value of the total angular momentum of a rare earth ion. The parameter a in eq. (3) is given by a =

E

aij.

(4)

j(~i)

a can be considered as a molecular field parameter, which is connected with a self-consistent molecular field HMF by the relation a < S ) = gj~,BHM~.

(5)

The parameters W, x, and a (together with the known value of J for the ground state multiplet of the rare earth ions) determine self-consistent solutions of the model Hamiltonian, eq. (3). There exists not only one self-consistent solution, because for a cubic crystalline electric field an initially selected direction of ( . I ) in one of the crystallographic [100], [110], or [111] directions will not be changed by the self-consistent solving procedure. For that reason we get for each of these directions a self-consistent solution. To obtain the physically stable ( J ) - d i r e c t i o n one than has to compare the corresponding free energies F. Because of the lack of theoretically calculated values for the crystal field parameters W and x it is necessary to use experimental data for the boundary compounds HoC% and N d C o 2. For HoC% Gignoux et al. [7,11] determined the crystal field parameters W and x from the spin reorientation temperature and the free energy difference F [ l l 0 ] - F [ 1 0 0 ] using a constant molecular field model Hamiltonian. The results are: W = 0 . 6 K

and x = - 0 . 4 6 9 . In order to get the same free energy difference F [ I 1 0 ] - F[100] and a spin reorientation temperature T R = 15.6K (obtained from our experimental data in fig. 3) in our self-consistent calculations we have to use the crystal field parameters W = 0.6 K and x = - 0 . 4 6 together with a = 5.2 K. In contrast t o H o C o 2 for N d C o 2 n o free energy difference F[110] - F[100] was available. Gignoux et al. [7] determined the crystal field parameters W and x for NdC% using neutron diffraction and magnetic measurements. Using a molecular field of HMv= 1100 kOe they get W = 2 . 9 K and x = - 0 . 1 8 . To determine the three parameters W, x, and a for our model Hamiltonian the knowledge of HMF= 1100 kOe and T R = 4 3 . 3 K (see fig. 4) are not enough. As an additional input we used the entropy gap at T R. Within the constant molecular field model Gignoux et al. [7] obtained for the entropy gap in H o C o 2 1.6 J K l m o t - I in good agreement with an experimental value of 1.4J K - i m o l - 1 [4], whereas the calculated entropy gap for NdC% is 0.6 J K ]mol-I. We have recalculated the entropy gap for H o C o 2 within our self-consistent model and obtained the smaller value 1.2J K - I m o 1 - 1 , which is roughly in the same agreement with the experimental data. We have also taken this model dependent reduction into account in the case of N d C o 2 and reduced the value of the entropy gap from 0.6 J K l m o l - i to 0.45 J K - l m o l - 1 . This reduced value was used together with T R and HMV for the determination of the parameters W, x, and a. The results are W = 4 K , x = - 0 . 2 0 and a = 17.2 K. If we now substitute non-magnetic Y ions for the magnetic rare earth ions Ho or Nd, the most important change in the set of the model parameters can be expected for the molecular field parameter a, because the sum in eq. (4) is only over magnetic rare earth ions. To a first approximation the pseudobinary systems (Ho, Y ) C o 2 and (Nd, Y)C% can therefore be described by the model Hamiltonian of eq. (3) using the same values W and x as for the boundary compounds, but with linear decreasing a-values as the Y content is increased. In this way we have calculated within the self-consistent procedure the spin reorientation temperature T R as a function of the Y concentra-

E. Gratz, H. N o w o t n y / Spin reorientation in (Hox Yz _ x)Co2 and ( N d x Yz _ x )Co : systems

131

r~t~ 30*/, Y 44

[100]

~

50 42 48

~..~(Nd.Y)

46

Co2

[tto]

Z,O 20 */, Y

44 ÷ (No. Y) Co2

20

42 40

10 */, Y

/

~

[ttO]

15

38 36

14

NdCo2

34

o

,b

j0

=

%Y 32 30 0

T[K]

o

"

38 3'9 ,;o 41 45 4'3 4. 45

-'-

Fig. 4. p versus T curves of (Nd, Y)Co 2 in the vicinity of the spin reorientation temperature T a (T R is indicated by an arrow).

tion. The results of the numerical calculations together with the experimental measured values of T R for (Ho, Y)Co 2 and (Nd, Y)Co 2 are shown in fig. 5. Although the calculated and the experimental results are not fully identical, there is a good overall agreement. The magnitude and the sign of the slope of the TR(%Y)-function are both correctly described by our theoretical calculations. This implies, that for the spin reorientation in such cubic compounds, the most important parts of the Hamiltonian describing the complete system are included in the model Hamiltionian given by eq. (3). Similar investigations performed on the isostructural Ho(Co, AI) 2 system show that with increasing AI content the spin reorientation temperature decreases [12]. Such a decrease follows directly from the Hamiltonian, eq. (3), if one takes into account, that the substitution of Co by AI

Fig. 5. The spin reorientation temperature T R as a function of Y concentration for (Ho, Y)Co 2 and (Nd, Y)Co 2 (the experimental results are given by the dots and the theoretical results are shown by the lines).

increases the molecular field, which results in an increase of the molecular field parameter a. This increase is opposite to the decrease of a caused by the substitution of magnetic rare rearths by Y.

4. Discussion

The spin reorientation temperature T R is visible by a step-like increase of p(T) at this temperature (see figs. 3 and 4). This behaviour of p(T) at T R can be understood by the assumption that due to the spin reorientation the spin wave spectra will also be changed [4, 13, 14]. We feel that such a sudden change of the spin waves at T R gives rise to a change of the magnetic scattering rate of the conduction electrons. It is of interest to note that in both systems the sharpness of this step increases with increasing Y content. The most striking difference in the shape of the p versus T curves of the Ho and the Nd pseudobinary systems is the appearence of the pronounced

132

E. Gratz, H. Nowotny / Spin reorientation in (HoxY1 x)Co 2 and ( N d x Y1 x)Co 2 systems

discontinuities at T~ in the Ho system. This is caused by the magnetic transition which is of first order in H o C o 2 and also in (Ho, Y)Co 2 in the concentration range under investigation [3], whereas the magnetic transition is of a second order in the Nd compounds (see ref. [1], where a general discussion of the magnetic properties of R E C o 2 compounds have been given). As was discussed in ref. [2] the pronounced discontinuity in the p(T) behaviour in the case of the first order transition can be understood by the disappearence of the order in the arrangement of the local 4f moments within a few tenths of a degree at T~. Furthermore, in connection with this disappearence of the order, the d-band polarization suddenly becomes zero. This is in contrast to a second order transition where the alignment of the 4f moments continuously vanishes on heating the sample leading to a continuous shape of the to versus T curve. In the paramagnetic temperature range the to versus T curves of both systems exhibit a saturation tendency. Such a flat slope was found in nearly all the R E C o 2 c o m p o u n d s ( Y C o 2 included) [15]. Because of the similar behaviour of non-magnetic Y C o 2 to those compounds under consideration above Tc one can conclude that scattering processes of the conduction electrons on the disordered localized magnetic moments give rise to a temperature independent contribution to the total resistivity.

References [1] D. Bloch, D.M. Edwards, M. Shimizu and J. Voiron, J. Phys. F5 (1975) 1217. [2] E. Gratz, H. Sassik and H. Nowotny, J. Phys. FI1 (1981) 429. [3] W. Steiner, E. Gratz, H. Ortbauer and H.W. Camen, J. Phys. F8 (1978) 1525. [4] J. Voiron, A. Berton and J. Chaussy, Phys. Lett. 50A (1974) 17. [5] C. Deenadas, R.S. Craig, N. Marzouk and W.E. Wallace, J. Solid State Chem. 4 (1972) 1. [6] R. Lemaire, Cobalt 33 (1966) 201. [7] D. Gignoux, F. Givord and R. Lemaire, in: Crystal Field Effects in Metals and Alloys, ed. A. Furrer (Plenum, New York, 1977) p. 335. [8] E.W. Lee and F. Pourarian, Phys. Stat. Sol. (a)33 (1976) 483. [9] K.R. Lea, M.J.M. Leask and W.P. Wolf, J. Phys. Chem. Solids 23 (1962) 1381. [10] M.T. Hutchings, Solid State Phys. 16 (1966) 227. [11] D. Gignoux, F. Givord and R. Lemaire, Phys. Rev. B12 (1975) 3878. [12] D. Gignoux, F. Givord, R. Lemaire and N. Nguyen van Tinh, in: Rare Earths and Actinides 1977, Inst. Phys. Conf. Ser. No. 37 (Institute of Physics, Bristol, 1978) p. 300. [13] J.J. Rhyne, N.C. Koon and B.N. Das, J. Magn. Magn. Mat. 14 (1979) 273. [14] N.C. Koon and J.J. Rhyne, in: Crystalline Electric Field and Structural Effects in f-Electron Systems, eds., J.E. Crow, R.P. Guertin and T.W. Mihalisin (Plenum, New York. 1980)p. 125. [15] E. Gratz and M.J. Zuckermann, in: Handbook of the Physics and Chemistry of Rare Earths, Vol. 5, chap. 42, eds. K.A. Gschneider, Jr. and L.Eyring (North-Holland, Amsterdam, 1982)p. 117.