Magnetic properties and giant magnetoresistance in melt-spun Co15Cu85 alloys

The structure, magnetic properties and giant magnetoresistance (GMR) of a metallic granular Co15Cu85 alloy have been investigated using an X-ray diffractometer and a SQUID magnetometer. The granular samples were fabricated by melt spinning and subsequently thermal annealing. Structural characterization confirmed that the samples consist of ultrafine Co magnetic particles embedded in the non-magnetic Cu matrix. Above the blocking temperature TB, the magnetic behaviour of Co particles can be understood on the basis of paramagnetic theory. The largest change in magnetoresistance of 43.0% was observed for the as-quenched ribbon annealed at 450 degrees C. It was confirmed that the GMR is closely correlated with the Co particle size and density, which can be optimized by controlling the annealing conditions.


Introduction
The discovery of giant magnetoresistance (GMR) in ferromagnetic granular materials has stimulated considerable interest in spin-dependent magnetotransport properties and related phenomena [1,2]. The substantial change in magnetoresistance (MR) in such a magnetic smcture has enhanced the fundamental understanding of the physical origin of GMR, as well as offering potential application in magnetoresistive devices. Now, it is widely accepted that the GMR is closely correlated with the reorientation of the magnetic moments of particles embedded in a non-magnetic mahix and can be interpreted on the basis of electron spindependent scattering [3,4]. In a granular system, the fundamental assumption underlying the G m is that the current is carried in two independent conduction channels corresponding to the spin-down and spin-up electrons. The magnetic field dependence of the resistivity is attributed to spin-dependent scattering occurring within the magnetic particles and at the interfaces of magnetic and non-magnetic entities [5,6]. The key parameters dominating the GMR are the mean free paths, the ratios of spin-dependent to spin-independent potentials, and the surfacetmvolume ratio of the magnetic clusters [5. 6].
The G M R has been discovered in various granular systems including Cu-Co [I, 21, Cu-Fe In this paper, we report the structural, magnetic and transport properties of melt-spun ColsCuss alloys. A G M R as large as 43.0% has been observed at 10 K in a magnetic field of up to 30 kOe for as-quenched ribbon annealed at 450°C for 30 min. The GMR is shown to be strongly dependent on the CO magnetic particle sizes.

Experiment
A rapidly quenched CussCo~s alloy was prepared by planar flow casting in a controlled atmosphere on a Cu-Zr drum. The samples were cut from the ribbons 5.0 x lo-' m in width and 6.0 x m in thickness and subsequently subjected to furnace annealing at different temperatures in the range 35M00"C for 30 min in a vacuum of 1 .O x mTorr, in order to control the size and distribution of the ferromagnetic CO-rich clusters. After annealing, the samples were cooled in vacuum to room temperature in about 5 min. The oxide layer of the samples was removed using diluted acid solution. Characterization of the samples was carried out on an x-ray diffractometer with Cu Kat and Cu K q radiation. The magnetic properties were obtained using a S Q m magnetometer in the temperature range 4.2-300 K.
The electrical resistivity R ( H , T) was measured using a DC four-terminal geometry in a magnetic field of up to 50 kOe and at a temperature from 10 to 300 K. The magnetic field was applied parallel to the current and to the ribbon surface. annealed states. The as-quenched sample is a single Fcc phase, with a lattice parameter of 0.3605 nm which is less than that of bulk Cu, 0.3615 nm, but larger than the lattice constant of bulk CO, 0.3545 nm. The as-quenched sample with a lattice spacing intermediate between those of bulk Cu and bulk CO is likely to be due to the substitutional effect of CO atoms in the Cu matrix. As the annealing temperature is increased, the overall x-ray diffraction patterns do not change very much until TA = 550"C, where a (111) peak begins to develop distinct shoulders. Eventually, a well resolved peak indicated by an asterisk (*) is observed, corresponding to FCC CO particles. The lattice constant calculated for the CO particles in the sample annealed at TA = 600°C is 0.3555 nm, which is larger than the lattice constant of bulk Co. This result indicates that the phase precipitated from a homogeneous Cu-Co matrix is not pure CO clusters but Co-rich particles.

Microstructure esolution and x-ray analysis
The stable structure of CO at room temperature is HCP; we found that the CO particIes maintain an FCC structure to room temperature even when the sample was annealed at a temperature of up to 900°C. This phenomenon could be interpreted in terms of the annealing temperature. Thermal analyses (DSC) of phase separation in metastable C d u alloys have confirmed that the CO clusters usually start to precipitate at a temperature of 300°C [14,19]. As the as-quenched sample is annealed at temperatures above 425"C, where the Fcc phase becomes stable for bulk CO [ZO], there it is no doubt that the CO particles will be precipitated in FCC form. The CO particles are highly coherent with the Cu mamx, which may hinder the transformation of FCC CO to HCP CO as the temperature is decreased in order to maintain the 425"C, where the HCP phase becomes stable for bulk CO, the classical nucleation theory [21] (or coherent spinodal decomposition assumption [22]), indicates that the two phases, namely the mahix and precipitates, should have the same crystal structure but different compositions. Thus the CO particles will be nucleated in the same Fcc structure as the Cu matrix, and the FCC CO particles will not undergo a FCC-to-HCP transition as the samples are cooled after annealing at these temperatures. Additionally, we found that the samples are highly (200) textured in comparison with the standard bulk Cu x-ray diffraction pattern. The textured structure is not eliminated even for the sample annealed at TA = 900°C.

The magnetic properries and the sue of CO particles
The 295 K magnetization curves for various samples are shown in figure 2. For the sample annealed at temperatures above 6OO0C, the magnetization was found to be easily saturated using fields of just a few kilo oersteds. For the samples in the as-quenched state or annealed at a temperame below 550°C, the magnetization does not saturate even in fields up to 30 kOe. In comparison with as-quenched ribbon, the sample annealed at TA = 350°C has a lower M, (see figure 2). This phenomenon has been observed many times by different groups, but its physical origin is not clear at present. As the annealing temperature is increased, successive nucleation and growth of magnetic CO particles will increase the volume fraction of the CO magnetic particles and the saturation magnetization. The largest saturation magnetization of 147.38 emu g ; : was observed for the sample annealed at a temperature of 550°C. This value does not reach the M,-values of 175 emu g-' [23] and R H Y u e t a l the CO particles contain some Cu atoms and because some CO atoms are dissolved in the Cu matrix. Very small CO particles may lose their magnetic moments owing to electron hybridizations [GI. A decrease in M, occurs for the sample annealed at a temperature of 600°C. This was interpreted as the increased diffusion of CO atoms back to the Cu matrix at this high temperature as assumed by Childress and Chien [25].
The particle size and distribution are important parameters of an assembly of ultrafine ferromagnetic particles. In addition to microstructural characterizations, they can be determined by analysing the magnetization curve in the superparamagnetic state. If pa is the moment of a CO atom and the cluster has m atoms, the total CO cluster moment will be m p a . In reality, the magnetic cluster moment will be affected by the geometry of the clusters and also by the demagnetization effect. For a small magnetic anisotropy, the CO cluster moment will exhibit a Boltzmann distribution of the orientation with respect to the magnetic field H at thermal equilibrium. The magnetization M of a non-interacting superparamagnetic system with uniform particle size due to a ctassical elemental moment p is described by a Langevin function [26,27] L(a) = cotholl/m: where ke is Boltzmann's constant, N is the number of elemental moments, p = M s V is the magnetic moment of a single particle with volume V, and H is the external magnetic field. Using the data only for a temperature of 295 K, a least-squares fit to the magnetization data, i.e. the magnetic moment p, can be calculated. Again, using the 5 and 412 K values of saturation magnetization for pure FCC Co. 175 emu g-' (1.545 x lo3 emu cm-') 1231 and 155.2 emu g-' (1.371 x IO3 emu [24], respectively, we fitted the experimental data to equation (1); the CO particle size can be estimated. However, unsatisfactory fitting results are shown in figure 2(a). In real granular systems, there is a distribution of particle sizes, and consequently of p. Without knowing the exact distribution of CO particle sizes, the magnetization should roughly be described by where n represents the CO particles with the same size. Fitting the 295 K experimental M ( H ) data to equation (2) (here we selected n = 20). the average CO particle sizes were determined as shown in figure 3 and table 1. The theoretical results are in good agreement with the experimental data (see figure Z(b)). It should be noted that we use M, for pure FCC CO in the calculation; in reality, the calculated CO particle sizes should be smaller than the real particle size owing to the lower saturation magnetization for the Co-Cu samples as demonstrated above. By analysing the data obtained for the CO magnetic particles, we have confirmed that the CO particle size distribution follows a log-normal form as discussed in [ZS,29]. It should be noted that the magnetization is easy to saturate for the sample annealed at 600°C. In this case, the sample shows a complicated beha\viour which may be re-entrant magnetic behaviour [23]. Here, we present the fitting result of this sample just for comparison. in the ZFC data do not change very much. The sample annealed at T = 600°C has a very broad peak near 150 K. In this annealing condition, some CO particles are still in the superparamagnetic regime, but some larger CO particles show re-entrant magnetic or ferromagnetic behaviour 1231. The higher fiwzing temperatures reflect the CO particle growth during annealing. As observed for sputtered samples [1,8] and melt-spun Co-Cu alloys [30], a large thermal hysteresis is observed below a characteristic freezing temperature (above 320 K in figure 4). where the ZFC and Fc curves diverge. The observation of thermal hysteresis much above the peak of the ZFC curves indicates the existence of a broad distribution in the sizes and shapes of the magnetic CO particles. As shown in figure 2 and figure 4(a), the as-quenched sample shows a large saturation magnetization and large thermal hysteresis between the ZFC and FC data. These results indicate that some CO clusters have already been formed during rapid solidification from the melt state. As reported in 123,301, metastable CozCul, alloys with x 6 0.20 exhibit a rather complex magnetic behaviour i.e. a mixture of paramagnetic and cluster-glass behaviours. The superparamagnetic contribution is associated with the very finely dispersed small CO clusters, and the cluster-glass contribution comes from the larger ferromagnetic CO clusters which are randomly dis~buted in the Cu matrix.
At a sufficiently high temperature (above the blocking temperature TB), the magnetic anisotropy energy barriers of the singledomain particles are overcome by thermal fluctuation, and superparamagnetism occurs. Superparamagnetic behaviour can be observed using an instrument with a characteristic measuring time rj at the temperature above the blocking temperature TB, which is defined as As the annealing temperature reached 600°C. the growth of the CO particles results in an increase in the distance between the CO particles, and the magnetic CO particles are weakly interacting. In this case, the CO magnetic particles behave as non-interacting granules. This result was also verified by the good magnetization fitting using the Langevin equation using only single CO particles for the as-quenched sample annealed at a temperature of 600°C ( figure 2(a)). For a typical paramagnetic system with atomic moments, x follows the well known Curie-Weiss law x = n p : # . ; / 3 k~T . Thus, I/x will be linear in T as shown in the inset of figure 4(d). where H , , is the maximum magnetic field. The field required to saturate the magnetoresistance is quite high for the sample in the asquenched state and annealed at temperatures below 500°C M ( H ) and MR are not saturated even in fields of 50 kOe. Here, we show only the GMR data in a maximum field of 30 kOe for comparison. We focus on the GMR at a low temperature (10 K), where the phonon and magnon conb5butions to the resistance are negligible.

Giant magnetoresistance and relation to CO cluster sue
In the as-quenched state the MR changes by as much as 16.0% in magnetic fields up to 30 kOe. Annealing of the as-quenched ribbons drastically increases the GMR as shown in figure 5. The maximum in the M R change of 43.0% was achieved for the sample annealed at 450°C for 30 min. and a large slope d(AR)/dH was observed even in a field of 30 kOe.  where rpi is the angle between the magnetization axis of a particle and the external field, (cosrpi) is averaged over many ferromagnetic entities, and the relation between the GMR and global magnetization was roughly established. We found that this relation describes the experimental results in the magnetic fields of less than 2 kOe well, except for around H = H,.
The dependence of the GMR on the annealing conditions is related to the change in the microstructure in the sample upon ageing, mainly the size o f CO clusters and its distribution in the Cu matrix. The results in [Z] show that there was a small change in MR (0.5%) in the homogeneous as-deposited samples of Co~Cuso with magnetic fields of up to 50 kOe. At -10 K, however, we found that a MR change of as much as 16.0% was observed in the asquenched ribbons. On the basis of the structural characterization using 295 K magnetization data, we assume that some magnetic domains with relatively low CO atom concentrations were formed during the rapid solidification, to which the MR change is attributed. Annealing the sample at a temperature below 500°C. ultra-fine single-domain CO particles were nucleated in the CO-rich regions, and superparamagnetic behaviour appears. Annealing the as-quenched ribbon at 450°C is appropriate for obtaining a higher GMR. At this temperature (450"C), we can probably assume that the sample has higher magnetic particle surfacetovolume ratios which act as the conduction electron spin-dependent scattering centres. On further increase in the annealing temperature, the CO particles grow to a larger size; thus the GMR decreases owing to the reduction in the particle surface-to-volume ratios. Figure 6 shows the relation between the MR and average CO particle size obtained from calculating the blocking temperature of CO magnetic particles. The fundamental assumption underlying models of GMR is that the current is carried in two independent conduction channels corresponding to spin-up and spin-down electrons. The field dependence of the resistivity is attributed to the spin-dependent scattering occurring within the magnetic   figure 6, the MR increases with increasing psv, where psv is a measure of the surfaceto-volume ratio of CO clusters and is proportional to (4nr2)/(4xr3/3) = 3/r, where r is the radius of CO particles. According to the phenomenological models described in [5,6], the MR should scale approximately as the magnetic particle surface-to-volume ratio if interfacial spin-dependent scattering is the dominant mechanism for GMR in granular systems. Alternatively, if the spin-dependent volume scattering is dominant, then the MR should weakly depend on the magnetic particle size. We have examined the MR dependence upon CO cluster size by a representative model [5] where

a ( H ) = M ( H ) / K (5d
where c is the concentration of magnetic particles per unit volume, rm is the average radius of the particles, pb and p s represent the ratios of spin-dependent to spin-independent scattering potentials in the magnetic particles and at the interfaces, A. , is a parameter representing the interfacial roughness, and Am and A. , are the mean free paths for magnetic particles and the non-magnetic makix, respectively. Fitting the MR data to equation (4), we obtain pb = 0.18, Ps = 0.66 and As = 3.5%. and the fitting results are shown in figure 6. This analysis ( p , > Pb) provides quantitative coniirmation that the interfacial spin-dependent scattering plays an important role underlying the GMR in the C&u granular systems. According to equation (3), the key parameters are the mean free path, the ratio of spin-&pendent to spin-independent scattering potentials, and the interfacial roughness. For the small magnetic particles, they will be subject to thermally activated magnetization which adversely affects the MR change [I], The magnetic particle size dependence of GMR should exhibit a peak behaviour.

Conclusions
We have investigated the microstructure, magnetic properties and GMR of c o t s c u 8 s samples in the as-quenched state and annealed at different temperatures. The materials consist of nanometre-sized CO magnetic particles embedded in a Cu nonmagnetic matrix. The M R change with magnetic field is closely correlated with the CO particle size and density.
The average CO particle diameter ranges from 3.5 to 8.0 nm for the sample annealed at temperatures below 60O0C, which results in a change in the magnetic properties and a change in the value of the GMR. The GMR decreases with increasing CO particle size. The largest G m occurs for the sample annealed at 450°C for 30 min, which results in an average CO particle size of 4.0 nm. In our experiment, a universal variation in GMR with particle size has been revealed. The phase separation is crucial for the GMR in magnetic granular systems.