Physica B 212 (1995) 83-87

Spin-fluctuation scattering in Y (Co, -,Al,), compounds

Nguyen Huu Duca, P.E. Brommerb* *, X. Lib, F.R. de Boerb, J.J.M. Franseb

’ Cryogenic Laboratory, University of Hanoi, 90-Nguyen Trai, Dongdu, Hanoi, Viet Nam bVan der ~aa~s-zeern~ L~5ratffri~, Universiteit van Amsterdam, ~al~ke~ie~straat 65, 1018 XE Amsterdam, The Nef~r~a~s

Received 23 November 1994

Abstract

Y (Co, -xAl,), compounds with x up to 0.2 have been studied by means of magnetization, resistivity and magnetoresis- tance measurements in the temperature range from 4.2 to 280 K and in magnetic fields up to 38 T. The paramagnetic to ferromagnetic transitions are characterized by an enhancement of both the magnetization and the resistivity, whereas at the metamagnetic transitions, observed in some of the compounds, the dis~ntinuous changes of the magne~a~on and the magnetoresistan~ are of opposite nature: the ma~eti~ation increases at the transition, whereas the magnetoresis- tance decreases. The results are discussed in terms of induced Co-magnetic moments and spin fluctuations. The absence of spin-fluctuation effects is pointed out for the weakly ferromagnetic compounds with 0.11 < x < 0.2.

The study of spin fluctuations in nearly and weakly ferromagnetic materials has been of con- siderable interest. The interaction of electrons with spin fluctuations contributes to their self-energy, gives rise to an enhancement of the effective mass and therefore, to an enhancement of the linear term, yT, of the electronic heat capacity. From this point of view, the increase of y with x in a number of Laves phase compounds such as R,Y, -,Co, (R = rare earths), Y(Col -&&, Lu(Co, -,Al,), and Lu(CO~-,G~~)~ is thought to be due to the enhancement of spin fluctuations [l-4]. In the same way, the upturn of the resistivity below the Curie temperature (T,-) has also been discussed for

*Corresponding author.

a number of R(Co, AI)2 compounds [S]. However, as suggested in Refs. [6,7], these behaviours can afso be connected to the scattering on the induced 3d-magnetic moments.

Quenching of spin fluctuations in magnetic fields has been found in low-temperature specific-heat measurements in magnetic fields up to 10 T for the strongly Pauli paramagnetic RCoz (R = SC, Lu and Y) compounds [S and refs. therein] and for the nearly ferromagnetic Lu(Co, _ XGa,)z compounds [4]. In Ref. [4], the suppression of spin fluctuations in an applied magnetic field is related to the forma- tion of the induced Co-moment, whereas the in- crease of y with x, i.e. with the enhancement of the magnetic system, is still discussed to be due to the growing extent of spin fluctuations. Recently, meta- magnetism and quenching of spin fluctuations have also been observed by means of magnetoresistance measurements for a number of the Laves phase

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84 N.H. Due et al. /Physica B 210 (1995) 83-87

intermetallics [7]. In this paper, we present mag- net~ation, el~~cal-resistivity and magnetoresis- tance measurements for the Y(Co, -,A& com- pounds, accentuating the scattering contribution from induced Co-magnetic moments and from spin fluctuations.

2. Experimental

Polycrystalline samples of Y(Co, A1)2 com- pounds with x up to 0.2 were prepared by melting stoichiometric mixtures of R (4 N), Co and Al (5 N) in a induction furnace under argon atmosphere. The melted buttons were wrapped in Ta foil, sealed under argon in silica tubes and annealed at 950°C for 60 h. The X-ray analysis shows the presence of one phase only. The magnetization was measured using the induction method. The electrical-resistiv- ity data were obtained by means of a four-terminal measuring technique on bar-shaped samples (size about 1 x 1 x 7 mm3). High-field magnetization and magnetoresistance measurements (in fields up to 38 T) were performed at the University of Am- sterdam, Netherlands. The tem~rature depend- ence of magnetization and resistivity (in fields up to 8 T) was measured at the Louis Neel Laboratory (Grenoble, France).

150

8

d

“b I40 Z

F

1

130

0 loo zoo 31

T(K)

Fig. I. Temperature dependence of the resistivity of Y(Co, -,A&), compounds. The dashed lines indicate the extra- polation applied in order to obtain the magnetic cont~bution (see text). The inset shows the temperature dependence of the magnetization for the ferromagnetic compounds.

3. Ex~~mental results and analysis

Fig. 1 presents the temperature dependence of the resistivity for the Y (Co1 -,A& compounds.

For all samples, the resistivity tends to saturation above 100 K and the obtained resistivity value at 280 K is about 150 @ cm. The x = 0.075 com- pound appears to exhibit a somewhat stronger tem- perature dependence than the other compounds. For the compounds with x >, 0.145, for which weak ferromagnetism occurs [9], an upturn of the resis- tivity is observed at low tem~rature. The residual resistivity values ( po) are listed in Table 1. We note that p. increases with increasing x and reaches a maximum value of 137.6 pR cm at x = 0.16. This

Table 1 The residual resistivity (p& the magnetic cont~bution to the resistivity (A&, the spontaneous ma~eti~tion (Me), the ratios A&,/p0 and A~~pe~~ for the Y(Cor -XA1X)2 compounds at ‘I’ = 0 K

X 0.0 0.075 0.11 0.145 0.160 OS85 0.20

PobQ 4 10* 128 131 134.3 137.6 133.5 132 4~AQcm) - - - 2.2 3.2 - 0.3 &ho - - - 0.01 0.023 - 0.002 MO@B/f.U.) - - - 0.16b 0.19” 0.15s 0.06b h,l~oMB&~) - - - 0.64 0.61 - 0.63

*Data taken from Ref. [I], bData taken from Ref. [9].

N.H. Due et al. /Physica B 210 (1995) 83-87 85

variation of p. is rather similar to that of the electronic heat capacity [2, 31, the 3d-magnetic moment and the ordering temperature [9]. Thus, it might be that peculiarities in the band structure (such as peaks in the density of states) may not only be the origin of the effect of the Al-substitution on the 3d-magnetism, but may also contribute both to the specific heat and to the resistivity (because of the increase of the number of states into which the carriers can be scattered).

Following Ref. [7], the resistivity is written as

PW, T) = POW + P,(T) + NW T2. (1)

The first term in Eq. (l), the residual resistivity, includes the (zero-temperature) spin-fluctuation contribution (see below) along with the usual con- tributions due to impurities and lattice defects; the second term is a contribution due to phonon scat- tering whereas the third term is due to both elec- tron-electron scattering and spin fluctuations. In strongly enhanced materials containing transition metals, the temperature dependence of p is mainly governed by the third term (i.e. T 2-term). From this point of view, the observed decrease of the vari- ation of the resistivity with temperature would indicate a decrease of the A-coefficient and, consequently, a decrease of the spin-fluctuation contribution with increasing x.

The residual resistivity, p. can be expressed by the following equation [7]:

p. = m*/ne2zo, (2)

where m*, n and e are the effective mass, the con- centration and the charge of the carriers, respec- tively, and where to is the relaxation time of the scattering due to impurities, lattice defects and other imperfections. Since the effective mass m* is also proportional to the mass-enhancement factor due to spin fluctuations, the enhancement of y as well as p. in Y(Co, Al)z may be thought to have the same origin, i.e. peculiarities in the band structure. Previously, the enhancement of y and p. was con- sidered as an indication of the growing extent of spin fluctuations as a result of a volume expansion. In Ref. [lo], however, it seems that the enhance- ment of p. is related to the variation of the spontan- eous magnetization of the 3d-subsystem in the R(Co, Al)a compounds. Thus, we expect that the

3d-magnetism may play an important role in the resistivity behaviour of these compounds. In order to confirm this expectation, magnetization and magnetoresistance measurements have been car- ried out.

Fig. 2(a) shows the high-field magnetization curves at 4.2 K for the investigated Y(Co, -XAl,)z compounds. The results are in good agreement with those reported previously [9], concerning (i) the metamagnetic transition in the compounds with x < 0.11 and (ii) the strong increase of the magnetization with increasing applied field charac- terizing the weakly itinerant-electron ferromagnetic behaviour in the compounds with 0.11 < x < 0.2. The magnetoresistance data of these compounds are presented in Fig. 2(b) in a plot of AR/R(O) = [R(B) - R(O)]/R(O) versus B, where R(0) and R(B) are the resistance in zero field and applied field, respectively. It can be seen from this figure that upon applying external magnetic fields the resistance initially increases for all samples. At B = 10 T, we obtain values for AR/R(O) of 1.25%, 2.5% and 5% for x = 0.075,0.11 and 0.145, respec- tively. This increase in the resistivity with field is in contrast to the reduction of the low-temperature

B(T)

a 0.05

E 5.2 0 a

Fig. 2. High-field magnetization (a) and magneto&stance (b) for Y(Co, -,Al,), compounds at 4.2 K.

86 N.H. LIuc et al./Physica B 210 (1995) 83-87

specific heat with field. For LuCoZ, the electronic- specific-heat coefficient is suppressed by 10.8% in a field of 10 T [7]. In a thermodynamic analysis of the magnetization data, a similar reduction of y was also found for Y(Co 0.89A10.1 I)2 [ 111. The resist- ance continues to increase with increasing field for the compound with x = 0.145. For the compounds with x = 0.075 and 0.11, a reduction of AR/R(O) is observed above a field of about 20 and 14 T, respec- tively, followed by a sharp suppression at the field that corresponds with the metamagnetic transition. It is worthwhile to mention that in the para-fer- romagnetic transition at T,, both magnetization and resistivity are enhanced (see also the inset in Fig. l), whereas at the metamagnetic transition the magnetization increases and the magnetoresistance decreases.

In Ref. [7], the magnetoresistance is written as

AR(H, T) = AR,(H, T) + AR,,(H, T), (3)

where ARc(H, T) is a positive contribution, as- cribed to the cyclotron motion of the conduction electrons, and where AR&H, T) is a negative con- tribution due to the quenching of spin fluctuations. In our measurements, a positive contribution is clearly observed at low magnetic fields. This positive contribution might be connected to the increase of the magnetic moments. For the fer- romagnetic compound with x = 0.145, a linear re- lationship between AR/R(O) and MZ is found in fields up to 38 T (see Fig. 3). We note that such a relationship is expected in the case of a pure volume effect. Then, one expects that also in the magnetically ordered state the same relation be- tween resistivity and spontaneous magnetization would hold. To check this, we determined the extra magnetic contribution Apm by extrapolation of p(T) from the paramagnetic region down to T = 0 K (see Fig. 1). The results obtained for Apm at T = 0 K are listed in Table 1. Note that, for the considered samples, the values of Ap,,JpoMt are almost constant. The values of Ap,JT) at finite temperatures are also included in Fig. 3 as a func- tion of the spontaneous magnetization. The uncer- tainties in the extrapolation procedure inhibit a more detailed analysis. We conclude that the experimental data are consistent with a quadratic dependence on the magnetization (as expected for

0.12

0.10

-0 g 0.08

2

a 0.06

0.04

0.02

0.00

M’(P~‘) Fig. 3. AR/R(O) versus M* for Y(CO~.~~~AI~.~~~)~: (o), M being the magnetization induced by an applied magnetic field; ( + ), M being the spontaneous magnetization. See text for the deter- mination of AR/R(O) .

a pure volume effect), both for the spontaneous magnetization and for the induced magnetization,

For the exchange-enhanced paramagnetic com- pounds (i.e. x < 0.1 l), we observe a magnetoresis- tance discontinuity, which appears to become less pronounced with increasing Al-content. This obser- vation is consistent with the decrease of the thermal variation of the resistivity noted above. The effect may be described by stating that the resistivity in the “low spin state” (or “spin fluctuation state”) is larger than that in the “high spin state” (or “strong- ly ferromagnetic state”). In so far as this difference is ascribed to a suppression of spin fluctuations, the magnitude of the drop in resistivity at the metamagnetic transition can be regarded as a measure for the amplitude of the spin fluctu- ations. Obviously, the drop ascribed to the fluctu- ations is much larger than the increase expected on the basis of the contribution proportional to M2 (or the volume) discussed above. Finally, we feel that alloying with Al must have an influence of its own, presumably due to peculiarities in the band struc- ture. With respect to the paramagnetic compounds, the main part of the increase of p. from the value of 10 p!J cm in YCo2 to 131 fl cm in Y(CO~.~~A~~.~~)~) may be ascribed to the increased exchange enhancement of the magnetic system, leading to

N.H. Due et al. /Physica B 210 (1995) 83-87 87

enhanced spin fluctuations [2,3]. Nevertheless, the maximum value of p. is found for the ferromagnetic compound with x = 0.16. At still higher Al-concen- tration the peculiarities are “averaged out”: the compound with x = 0.2 (extrapolated to the “low spin state”) does not appear to be much different from that with x = 0.075. This is consistent with the band-structure calculations by Aoki and Yamada [ 123 in the sense that the sharp peak in the density of states of Co is appreciably destroyed when Co is substituted by Al to form Y(Co, -,Al,), com- pounds.

4. Concluding remarks

In conclusion, the main results can be sum- marized as follows:

(i) Metamagnetic transitions are observed by sharp changes in both the magnetization and the magnetoresistance.

(ii) The magnetism of the 3d-electrons plays an important role with respect to the resistivity beha- viour. The enhancement of the resistivity due to the formation of the magnetic moments, in applied fields as well as at decreasing temperature below Tc, is well described by a linear relationship be- tween A.p/p(O) and M', and thus may be related to an expansion of the lattice.

(iii) The resistivity in the “low spin” or “spin fluctuation state” is larger than that in the “strongly ferromagnetic state”. The decrease of the resistivity

at the metamagnetic transitions is therefore due to the quenching of spin fluctuations.

(iv) Finally, our analysis suggests that, with in- creasing Al-concentration, in addition to the trend reported in Refs. [2,3] about the growing extent of the spin fluctuations due to lattice expansion, pecu- liarities in the band structure may cause an increase of p. (in the ferromagnetic compounds). The de- crease of p. at still higher Al-concentration points to a washing out of these peculiarities.

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