Changeover in the order of the magnetic phase transition in the intermetallic compounds (Er1−xTbx)Co2

Journal of Alloys and Compounds 279 (1998) 117–122

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Changeover in the order of the magnetic phase transition in the intermetallic compounds (Er 12x Tb x )Co 2 F. Garcia, M.R. Soares, A.Y. Takeuchi*, S.F. da Cunha ´ , Rua Dr. Xavier Sigaud 150, 22290 -180, Rio de Janeiro, RJ, Brazil Centro Brasileiro de Pesquisas Fısicas Received 29 May 1997; received in revised form 17 November 1997

Abstract Electrical resistivity, magnetization and AC susceptibility measurements have been carried out to investigate the order of the magnetic phase transition in (Er 12x Tbx )Co 2 compounds. In this system a changeover from first- to second-order transition at about x c 50.60 was observed. This result is discussed in the framework of the generalized Inoue-Shimizu phenomenological model. Moreover, a microscope explanation about the order of the phase transition in terms of spin fluctuation and metamagnetism of the Co-3d subsystem is offered.  1998 Elsevier Science S.A. All rights reserved. Keywords: Spin fluctuations; Metamagnetism; Intermetallic compounds; First-order magnetic phase transition PACS: 75.30.Kz; 75.50.Cc

1. Introduction The investigation of the rare-earth intermetallic compounds RM 2 , with R5rare-earth and M5transition metal, is an interesting subject. Although they have the same MgCu 2 cubic Laves phase structure with very similar lattice parameters, they exhibit a wide variety of magnetic behaviours. For example, in RFe 2 compounds, where the Fermi level lies in the high density of states region, the Stoner criterion is fulfilled, and the iron ions always present magnetic moment in these compounds [1]. On the other hand, in RNi 2 , where the Fermi level lies in the flat low density of states region, the Stoner criterion is far from being satisfied, and Ni is never magnetic in this system, even in compounds with magnetic R ions [2,3]. In the compounds RNi 2 , the rare-earth moments are therefore coupled only through the RKKY interaction and consequently have low ordering temperature as compared to the Fe compounds. Finally, in RCo 2 , where the Fermi level lies in the intermediate region corresponding to a sharply decreasing density of states, the Stoner criterion is nearly satisfied. The RCo 2 compounds with non-magnetic R ions (Lu or Y) are exchange-enhanced Pauli paramagnets [4,5] and undergo a first-order metamagnetic transition under an external field exceeding a certain critical value Hc . Mag*Corresponding [email protected]

author.

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(55-21)

541-2047;

netization measurements in ultrahigh magnetic fields [6] have shown that the value of mCo jumps from zero to 0.44 mB in YCo 2 and to 0.64 mB in LuCo 2 when the applied field reaches a critical value of about 70 T. In the RCo 2 compounds with magnetic heavy rare-earth ions (except Tm) the molecular field exceeds this Hc necessary to induce a ferromagnetic order in the d-electron subsystem. The rare-earth moments are coupled mainly via strong polarization of the Co d-band. Previous studies revealed that a first-order phase transition from ferrimagnetism to paramagnetism was observed in DyCo 2 (135 K) [7], HoCo 2 (75 K) [4], ErCo 2 (32 K) [8] and TmCo 2 (3.7 K) [9], whereas a second-order transition was found in compounds with a higher transition temperature, i.e., in TbCo 2 (235 K) and GdCo 2 (395 K). Some phenomenological models have been proposed to discuss the order of the magnetic phase transitions [10,11]. The aim of the present work is to investigate the concentration dependence of the change in the order of the magnetic phase transition in the (Er 12x Tbx )Co 2 system, by means of electrical resistivity, magnetization and AC susceptibility measurements.

2. Experimental

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Compounds in the (Er 12x Tb x )Co 2 series were prepared

0925-8388 / 98 / $ – see front matter  1998 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 97 )00618-X

F. Garcia et al. / Journal of Alloys and Compounds 279 (1998) 117 – 122

118

Table 1 Electrical resistivity data for the Er 12x Tb x Co 2 compounds x

0.00

0.05

0.10

0.15

0.20

0.40

0.60

0.80

1.00

˚ a (A) A (10 29 ) B (10 214 ) r0 (mV cm) rsat (mV cm)

7.161 4.1 16.80 11.3 107.6

7.154 2.27 5.08 2.86 104.5

7.161 3.35 5.35 4.92 130.0

7.168 2.97 2.64 4.39 106.8

7.161 3.89 1.55 13.1 109.3

7.179 4.00 0.092 7.12 122.0

7.194 3.85 20.017 8.41 126.9

7.201 3.12 0.019 11.8 112.5

7.222 3.26 1.12 4.93 139.5

with x50.00, 0.05, 0.10, 0.15, 0.20, 0.40, 0.60, 0.80 and 1.00. The samples were prepared by arc furnace melting of the constituents elements in an argon atmosphere. To avoid the appearance of spurious phases, a 6 wt.% excess of rare-earth over the stoichiometric composition was necessary [12]. The alloys were then annealed in an evacuated sealed quartz tube for a period of one week at T58008C. The crystal structure (cubic MgCu 2 type) and the lattice parameters were determined at room temperature by X-ray powder diffractograms. All of the samples are single phase, and the lattice parameters follow approximately the linear Vegard’s law and increase with Tb concentration (Table 1). Electrical resistivity measurements were performed with the standard four point method at temperature values between 2.0 and 300 K on parallelepiped samples of 232310 mm 3 . The uncertainties in absolute value were about 2%, and reproducibility is better than 0.3%. Magnetization measurements were carried out using a vibrating sample magnetometer at temperature values between 2.0 and 300 K in magnetic fields up to 13 kOe. Samples were zero-field-cooled (ZFC) or field-cooled (FC) and measurements were always made by increasing the temperature. Isotherms with applied field up to 80 kOe were obtained for some values of temperature. Measurements of AC magnetic susceptibility were made for a fixed frequency of 128 Hz, using a mutual inductance bridge.

we can conclude that the AT 2 term dominates (see Table 1). At higher temperatures (basically T .T C ) the r (T ) curves shows a clear tendency towards saturation but with huge values ( rsat ) compared to the theoretical De GennesFriedel spin disorder resistivity of R-atoms. This additional resistivity can be attributed to some abnormal extra contribution from the Co-subsystem. For the non-magnetic RCo 2 (R5Sc, Y, Lu) Laves phase compounds, Baranov et al. [13] have shown that the pronounced saturation in r (T ) at high temperature can be well explained by spin fluctuation scattering. In RCo 2 with a magnetic rare earth, the magnetic contribution to the resistivity could be assumed to consist of two spin-dependent parts at temperature values well above T C : • scattering process of the conduction electron on the localized of the 4f moments; and • scattering on the Co 3d-electron spin fluctuation (as in LuCo 2 ). Therefore if we assume that in (Er 12x Tbx )Co 2 compounds the above scattering mechanisms are present, the magnetic resistivity behaviour can be, at least qualitatively,

3. Experimental results

3.1. Electrical resistivity In Fig. 1 we show the electrical resistivity for some concentrations in the (Er 12x Tb x )Co 2 system. For comparison, the r vs. T curve of the isostructural non-magnetic LuCo 2 compound, taken from the paper of Gratz et al. [9] is included in this figure. At first glance, we can observe in ErCo 2 , as well as for the low Tb concentration, a pronounced discontinuity at T5T C , which becomes gradually smoother for higher Tb concentrations. At lower temperatures (T ,30 K), the r vs. T curves are well fit by the expression r (T )5r0 1AT 2 1BT 5 , where r0 is the residual resistivity, AT 2 the magnon scattering and BT 5 the phonon resistivity. In this range of temperature,

Fig. 1. Temperature dependence of the electrical resistivity of the Er 12x Tb x Co 2 and LuCo 2 compounds.

F. Garcia et al. / Journal of Alloys and Compounds 279 (1998) 117 – 122

119

to be the spin disorder contribution. However, as the r (T ) data for LuCo 2 was obtained with large uncertainties Dr shows variations from one sample to the next. For T ,T C we observe negative values of Dr. However, this result is not surprising if we remember that in LuCo 2 that the spin fluctuations scattering contribution is always present, whereas in (Er 12x Tb x )Co 2 compounds, the spin fluctuations below T C are quenched by the molecular field of the R ions. Therefore, in this range of temperature (T ,T C ), we can conclude that the spin fluctuation contribution to the resistivity is significantly larger than the magnetic scattering of Er or Tb by s-electrons.

3.2. Magnetization and AC susceptibility

Fig. 2. Temperature dependence of Dr 5 ( r (T ) 2 r0 ) Er 12x Tb x Co 2 2 ( r (T ) 2 r0 ) LuCo 2 . Arrows indicate T C .

obtained by subtraction of the r (T ) of a non-magnetic compound reference. Results obtained from this approximation by using LuCo 2 as the reference compound are shown in Fig. 2. As we can see, this excess resistivity Dr 5( r [(Er, Tb)Co 2 ]2 r [LuCo 2 ]) is characterised by a sharp change at T C . Above the magnetic ordering temperature, Dr presents two distinguishing behaviours: for x#0.40, Dr decreases as the temperature increases, whereas for x$0.60, Dr is almost temperature independent. Moreover, the sharp drop of resistivity at T C becomes smoother in the higher Tb concentration region (x$0.60). These results are clearly an indication that the scattering mechanism involved in the two regions are different. At room temperature, the resistivity Dr shows a strong saturation tendency for all Tb concentrations. This saturated resistivity could be assumed

The magnetization temperature dependence of the (Er 12x Tb x )Co 2 compounds was measured in different applied magnetic fields. In a field of 0.1 kOe, this system presents a difference between the (FC) and (ZFC) measurements for T ,T C , which collapses under higher applied fields (5 kOe). This thermal irreversibility can be related to domain wall motion in the crystal. The saturation moments per formula unit, msat , of these compounds were estimated by extrapolation of the magnetization at infinite field, from the M vs. H 21 curves performed at 4.2 K, in fields up to 80 kOe. In this system it was found that the results agree with the model of antiparallel coupling between the rare earth magnetic moment [14], mR 5,gJ.59 mB for Tb and Er, and the cobalt moment of approximately 1 mB ). As noted before, this moment is assumed to be induced by the exchange field from the localized 4f magnetic moments. As can be seen in the Fig. 3, the temperature dependence of the AC susceptibility ( xAC ) for (Er 12x Tb x )Co 2 shows a clear change of behaviour near the critical

Fig. 3. Temperature dependence of x /xmax of the Er 12x Tb x Co 2 compounds x50.40 and x50.60.

F. Garcia et al. / Journal of Alloys and Compounds 279 (1998) 117 – 122

120

temperature as a function of Tb concentration. For x#0.40 we can observe a sharp drop just below T C in the susceptibility curves, which is characteristic of a first-order transition. For x$0.60 the x vs. T curves present a behaviour characteristic of a second-order magnetic phase transition. These results are a clear evidence that this system presents a change from first- to second-order magnetic phase transition around x50.60.

4. Discussion It can be concluded from the resistivity, magnetization and AC susceptibility measurements in the (Er 12x Tb x )Co 2 compounds that samples with x#0.40 (T C #113 K) exhibit first-order magnetic phase transition and those with x$ 0.60 (T C $156 K) a second-order phase transition. Therefore, the crossover of the order of the transition takes place for T C between 113 K and 156 K. This dependence of T C which determines the order of the magnetic transition was first described by Bloch et al. [11]. They connected the occurrence of the first-order phase transition to a negative sign of the coefficient a 3 in the free-energy (Fd ) expansion for the 3d-subsystem: 1 1 1 Fd (Md ) 5 ] a 1 M 2d 1 ] a 3 M 4d 1 ] a 5 M d6 2 4 6

(1)

where Md is the 3d subsystem magnetization. Otherwise the phase transition is of second-order. The temperature dependence of a 3 is, approximately:

F S DG

T a 3 (T ) ¯ a 3 (0) 1 2 ] T3

2

,

Fig. 4. Dependence of the susceptibility xd of Co on the Curie temperature T C .

2

(NA mB ) 2 T C 5 ]]] J R2Co G¯ m0 xd (T C ) 3R

(4)

where NA , R, m0 and mB have their usual meaning, G¯ is the averaged De Gennes factor, xd is the temperature-dependent susceptibility of the 3d-electrons and, finally, JR-Co is the effective exchange constant and represents the interaction between a 4f-spin and a 3d-spin, and is connected to the molecular field constant n di through: JR2Co ( gi 2 1) n di 5 ]]]] gi

(5)

(2)

where T 3 is a constant. Inoue and Shimizu [10] improved the model by expanding the free energy in terms of the total magnetization (M), given by M5Md 1MR , where MR is the rare earth subsystem magnetization: 1 1 1 F(M) 5 ] c 1 M 2 1 ] c 3 M 4 1 ] c 5 M 6 2 4 6

(3)

The character of the phase transition is now determined by the sign of c 3 (T C ). The Inoue-Shimizu model was generalized by Brommer [15] to pseudo-binary compounds. In this case, the Curie temperature can be written as:

where gi is the Lande´ g-factor for the rare earth ion R i . From Eq. (4) with JR-Co 518.5310 26 mol / m 3 taken from GdCo 2 [11] and T C obtained experimentally, we have calculated the xd ’s (see Table 2). In Fig. 4, it is shown that the resulting temperature dependence appears to be similar to that one for YCo 2 and LuCo 2 , as expected. In the generalized Inoue-Shimizu model [15,16] the coefficient c 3 (T C ) can be expressed as:

O F G

n di 4 a 3 (T C ) 1 x i b 3i ] b 1i i c 3 (T C ) 5 ]]]]]]] 4 q

(7)

Here, q is given by:

Table 2 Coefficients obtained using the Inoue-Shimizu model for Er 12x Tb x Co 2 x

0.00

0.05

0.10

0.15

0.20

0.40

0.60

0.80

1.00

T C (K) G¯ xd (10 29 ) q a3 c 3 (10 24 )

31.1 2.6 22.2 213.71 24.61 20.57

43.8 3.00 24.8 211.75 24.52 21.19

47.4 3.39 26.6 210.34 24.42 21.81

55.8 3.79 27.4 29.29 24.29 22.77

65.1 4.18 28.9 28.35 24.12 24.14

113.0 5.76 36.5 25.35 22.84 298.08

156.0 7.34 41.4 23.89 21.10 0.0047

195.0 8.92 41.5 23.34 0.95 124.8

229.0 10.50 40.5 23.00 3.54 449.7

F. Garcia et al. / Journal of Alloys and Compounds 279 (1998) 117 – 122

xn O ]] b i di

q511

i

(8)

1i

b 1i and b 3i are the coefficients of the subsystem of the rare earth R i in the binary compounds R i Co 2 and are determined by: 3RT b 1i 5 ]]]]]] 2 (NA mB ) [g 2 J(J 1 1)]

(9)

and 9RT (2J 1 1)2 1 1 ]] ]]]]]]] b 3i 5 20 (NA mB )4 [g 4 J 3 (J 1 1)3 ]

(10)

In this model, the order of the magnetic phase transition is determined by the sign of c 3 (T C ). In practice, however, this sign has a strong dependence on that of a 3 (T C ). In order to analyze our results for the (Er 12x Tb x )Co 2 compounds, we present the calculated data for xd (T C ), q and c 3 adopting a 3 (0)5 24.76 (mol /Am 2 )3 and using the parameters deduced by Duc et al. [16,17] for the (Er,Y)Co 2 compounds. Consistent with the experimental results, these data show that the value of the coefficient c 3 (T C ) in the free energy expansion becomes positive at x50.60, i.e., the initially first-order transition becomes second-order for concentration exceeding ¯60 at %Tb. The microscopic explanation of the occurrence of firstorder phase transition in these compounds can be made in terms of the metamagnetism of the Co-3d-subsystem. In this system, at 0 K, the cobalt moment is induced by the molecular field of the 4f localized moments (which interact via the cobalt polarization). As the temperature increases, the molecular field due to the rare earths moments decreases until a critical value HC (¯70T), beyond which there is a sudden disappearance of the moment on the Co site (i.e. a first-order metamagnetic transition). As the RKKY exchange interaction between the well localized moments is weaker than the 3d–3d interaction, the sudden disappearance of the cobalt moment in the (Er 12x Tb x )Co 2 system will also cause a misalignment of the rare earth moments and will lead to a first-order magnetic phase transition. In this case, a pronounced discontinuity will occur in the temperature variation of the physical parameters such as magnetization, specific heat, resistivity, susceptibility, etc. From the foregoing remarks we would expect a first-order transition in all of the concentration range of the (Er 12x Tb x )Co 2 system. However, as we have seen, this system undergoes a changeover from first- to second-order transition as the Tb content increases, indicating that a new magnetic mechanism appears in compounds with higher T C . As we will see later, this mechanism is due to the appearance of the localized spin density fluctuation. It is worthwhile mentioning that the electrical resistivity is very sensitive to the spin fluctuation dynamics in the Co-d-electron subsystem. As stated previously, this scatter-

121

ing is present in RCo 2 (R5Sc, Y, Lu), as well as in the Er 12x Tb x Co 2 compounds. Therefore, the large discontinuity in the Dr vs. T curves at T C (Fig. 2) observed for Er 12x Tb x Co 2 with x#0.40 compounds is caused by the quenching of the spin fluctuations due to the onset of long-range magnetic order [18]. Moreover, the pronounced peak at T C , observed in this range of the Tb concentration can be attributed to the short-range correlation between 4f moments that enhances the spin fluctuations in the delectron subsystem via an f–d exchange interaction. This enhancement decreases with increasing temperature and at T $160 K, the Dr curves becomes nearly temperature independent. In Fig. 2 we can observe that at low Tb concentrations, the minimum in the Dr curve, just below T C , is characterized by a sharp change and becomes gradually smoother with increasing Tb concentration. This difference is due to the appearance of the extra scattering mechanism that becomes effective in the high-temperature regime. This new scattering could be related to the existence of localized spin density fluctuations of the Co sub-system in the long-range order regime. Baranov et al. [19,20] derived evidence from their experiments for the coexistence of long- and short-range magnetic order in the (Er,Y)Co 2 and (Ho,Y)Co 2 system near the critical concentration and in the low-temperature regime. The existence of clusters with a short-range order in the R subsystem was attributed to an inhomogeneous distribution of Y over the lattice (alloying effect) that produces fluctuations in the local molecular field. A similar effect can also occur in the high Tb concentration range of the (Er 12x Tbx )Co 2 system. In this case, as the critical temperature is higher than in the former, it seems reasonable to assume that the thermal excitation in our system is high enough to create similar fluctuations in the local molecular field. Consequently, the localized spin density fluctuation of the Co subsystem in the long-range order regime can be responsible for the changeover of the first- to second-order phase transition in our compounds.

5. Conclusions In this paper, we have performed an experimental investigation of the (Er 12x Tbx )Co 2 compounds by electrical resistivity, AC magnetic susceptibility and magnetization measurements. In this system, the order of the magnetic transition changes from first to second around x c 50.60. A satisfactory agreement between the calculation within the InoueShimizu model and our experimentally observed first-order and second-order phase transitions changeover in these compounds was obtained. However, this critical concentration is higher compared to those observed in other compounds: Er 12xYx Co 2 (x c 50.30) [17], Ho(Co 12x Ni x ) 2 (x c 50.09) [21] and Er(Co 12x Ni x ) 2 (x c 50.20) [22]. These

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F. Garcia et al. / Journal of Alloys and Compounds 279 (1998) 117 – 122

lower values can be attributed to the substantial decrease of the cobalt magnetic moment. The existence of the spin density fluctuations in this compounds, claimed to explain the changeover, was deduced by analogy with the isostructural compounds, this should be confirmed by others measurements such as neutron diffraction. Nevertheless, we may conclude that there is a close relationship between the spin fluctuation behaviour and the metamagnetic transition in this system.

Acknowledgements F. Garcia and M.R. Soares acknowledge the financial support from CAPES and CNPq (Brazil).

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