Direct measurement of the dependence of granular giant magnetoresistance on the relative orientation of magnetic granules

Experiments have been designed to vary the relative angle between the magnetic moments of different Co granules in Cu80Co20 granular system. The moments of granules are mostly aligned in the same direction by field cooling to low temperature in a high magnetic field. A small field applied at an angle relative to the cooling field rotates the moments of a portion of the granules that have small particle size and coercivity. It is found that the giant magnetoresistance (GMR) varies linearly with cos φ, where φ is the relative angle between the magnetic axes of granules. This behavior disappears if the sample is cooled in zero fields, or if the rotating field is too large or small, or if the measuring temperature is higher than the blocking temperature. Our results show that the GMR in granular structures has the same angular dependence as the layered films and confirm the existing theories and recent microscopic models of granular GMR suggesting a crucial role of the relative orientations of the magnetic gr...


Direct measurement of the dependence of granular giant magnetoresistance on the relative orientation of magnetic granules
Experiments have been designed to vary the relative angle between the magnetic moments of different Co granules in Cu 80 Co 20 granular system.The moments of granules are mostly aligned in the same direction by field cooling to low temperature in a high magnetic field.A small field applied at an angle relative to the cooling field rotates the moments of a portion of the granules that have small particle size and coercivity.It is found that the giant magnetoresistance ͑GMR͒ varies linearly with cos , where is the relative angle between the magnetic axes of granules.This behavior disappears if the sample is cooled in zero fields, or if the rotating field is too large or small, or if the measuring temperature is higher than the blocking temperature.Our results show that the GMR in granular structures has the same angular dependence as the layered films and confirm the existing theories and recent microscopic models of granular GMR suggesting a crucial role of the relative orientations of the magnetic granules in determining the spin dependent scattering.© 2000 American Institute of Physics.͓S0003-6951͑00͒01326-7͔ Granular magnetic systems, where magnetic metallic particles are embedded in nonmagnetic metallic host, show a remarkable negative giant magnetoresistance ͑GMR͒.Since Berkowitz et al. 1 and Xiao et al. 2 reported the GMR found in Cu-Co granular systems in 1992, this effect has attracted a lot of interest.It is known [2][3][4][5][6] that GMR depends on granular size and distribution and is suppressed if the electron meanfree path is reduced.Generally the magnetic granules are treated as single domains and the main mechanism of GMR is usually analyzed in terms of the spin dependent scattering at the granule surfaces or within the granules.][9][10][11][12] However, more detailed theoretical works are still needed to understand the spin dependent scattering in these particlematrix systems.For example, in granular systems, the space distribution of magnetic field, the electron spin diffusion process and the spin transitions are much more complex than the multilayered systems.
Basically, GMR can be descried as the result of the alignment of magnetic granules by the external magnetic field, which reduces the spin dependent scattering of the system.A general observation is GMRϰ(M /M S ) 2 ϭ͗cos ͘ 2 , where M is the global magnetization, M S is the saturation magnetization, is the angle between the magnetic moment of a granule and the external field, and ͗cos ͘ is the average value of cos . 2,3This angular dependence has been explained by Zhang et al. 7,11 and Asano et al. 8 based on the spin dependent scattering at the granule-matrix interfaces.
The ͗cos ͘ 2 dependence also suggests 2 that the GMR is related to the relative orientations of the magnetic granules.4][15][16][17][18][19][20] It can be easily shown that, in a system of random distribution, ͗cos ij ͘ϭ͗cos ͘ 2 , where i j is the relative angle between magnetic axes of uncorrelated magnetic granules.Pogorelov et al. 12 have introduced a microscopic theory of granular GMR and have shown that the spin dependent conductance in granular systems can be sensitive to the short-range magnetic order in addition to the long-range order.It is of interest to measure directly the resistance as a function of the relative orientation of the magnetic granules and find out the relationship between the two.9][20] In those experiments, the angle between the magnetization of the two ferromagnetic layers is changed by applying a suitable magnetic field that rotates one layer but not the other.However, the same method does not work and controlling the relative angle between magnetic moments is difficult in the granular systems.
In this work, we have designed an experiment in which one can statistically adjust the relative angle between the magnetic moments of different granules in Cu 80 Co 20 .It is found that GMR varies linearly with cos .The experiments were conducted as follows.First, the granular film was field cooled ͑FC͒ down to Tϭ5 K, in a high field H 1 ϭ5 T. This way, the magnetic moments of granules were pointed in their easy axes close to the field direction H 1 and on average were aligned in the same direction as H 1 .Second, a small field H 2 was applied at an angle relative to H 1 after H 1 was removed.Since there is a size distribution of the granules with a corresponding distribution in the coercivity, granules having high coercivity may stay with the initial field H 1 and those having low coercivity rotate with H 2 .Thus, one can a͒ Also at: Department of Applied Physics, Jiao Tong University, Shanghai 200030, China.b͒ Electronic mail: jtang@uno.edurotate the magnetic moments of a fraction of the granules by choosing an appropriate value of H 2 .Figure 1 gives a schematic view of the process.One may roughly divide the granules into two groups: those rotating with H 2 and those staying in the original direction of H 1 .The angle between the moments of two groups of granules is exactly the angle between H 1 and H 2 .Here we assume the interparticle interaction is weak and ignore the effects of those granules that may not follow exactly one of the two directions.
The samples used in our experiments are typical GMR granular Cu-Co films.Cu 80 Co 20 films were deposited by vacuum magnetron sputtering from a composition target.The film thickness was 80 nm and the GMR value was ϳ10% at Tϭ5 K. Samples were cut into 1 mmϫ4 mm rectangles.Four-terminal direct current resistivity measurement was performed using a Quantum Design physical properties measurement system.Magnetic susceptibility and magnetization measurements were made with a Quantum Design superconducting quantum interference device.Figure 2͑a͒ shows the susceptibility versus temperature T curves for both zero filed cooled ͑ZFC͒ and FC runs.It indicates a blocking temperature T B of about 40 K and implies the existence of size distribution of the Co granules with small and large particles.The inset shows the MR ratio of the Cu 80 Co 20 granular film at 5 K.It does not saturate even in a high field of Hϭ6 T, which suggests the Co granules have a wide size distribution.Figure 2͑b͒ shows the magnetization curve at 300 K, above the blocking temperature.The shape of the curve is consistent with the Langevin function associated with a distribution of granule size.The inset gives the low field hysteresis loop at 5 K, and it indicates coercivity H C of about 200 Oe.
In Fig. 3, the solid line and symbol shows the MR dependence on angle .The experimental data fit well to the cos function in the entire range between 0°and 180°, and the inset shows the resistance is linearly dependent on cos .The resistance of the sample R can be expressed as RϷ31.201ϩ0.065͑1Ϫcos͒͑⍀͒.͑1͒ The same measurement has been repeated for a ZFC sample, and it is found that the cos dependence of the GMR disappears, as shown in Fig. 3 ͑dashed line͒.Since the moments of the ZFC sample are blocked in random directions, a cos dependence is not expected.Rather the MR should be independent of , which is consistent with our experiment.This result lends support to that the cos dependence of GMR for FC is due to the change in the angle between the moments of those granules rotating with H 2 and those fixed in H 1 .Our result confirms that the GMR depends on the relative orientations of the magnetic granules.The field strength of H 2 has been varied and the earlier experiment repeated.It is found that when H 2 is either too low or too high the cos dependence of the GMR is weak, and the optimal field of H 2 is around H 2C Ϸ650 Oe at which the GMR is most sensitive to the change of .This is not difficult to understand: when H 2 is too small ͑Ͻ100 Oe͒, only a small portion of the granules with very small particle sizes can be rotated and most of the granules stay in the initial orientation of H 1 .The MR change is small due to the small number of those involved in the scattering associated with the angle change.On the other hand, when H 2 is too large ͑Ͼ1000 Oe͒, most of the granules will align with the rotating H 2 and it also reduces the contribution from the scattering due to the relative orientations of the granules.Figure 4 shows the ⌬RϭR()ϪR(ϭ0) as a function of measured at different rotated field H 2 .One can see that the cos dependence of GMR weakens when H 2 is greater than H 2C .This result is significant in that it indicates the angle one measures in our experiment is that between the moments of two groups of the magnetic granules and GMR varies linearly with the cosine of that angle.In order to observe a significant cos dependence of the GMR, one needs to chose a rotating field H 2 of reasonable strength and try to balance the number of granules of the two groups: those staying in the initial field direction H 1 and those rotating with H 2 .
It has been found in our experiment that the cos dependence of the GMR becomes weaker when the temperature is higher and disappears when temperature is higher than the blocking temperature.Figure 5 shows the GMR as a function of at different temperatures with H 2 ϭ600 Oe.This result is expected considering that the coercivity of the system in the blocked state decreases with increasing temperature and becomes zero at the blocking temperature.Raising the temperature is equivalent to increasing the rotating field H 2 in that it is easier to rotate the majority of the magnetic granules.
In summary, using a uniquely designed experiment, we have demonstrated a linear dependence of granular GMR on the cosine of the relative orientation between the magnetic axes of granules in the particle-matrix systems.This is similar to the linear dependence found in layered films, where the relative angle between the magnetic layers is easily controlled.The result confirms the existing theories and recent microscopic models of granular GMR and provides direct experimental proof that the relative orientations of the magnetic moments of the granules is a crucial factor in determining the spin dependent scattering in granular GMR materials.
Dai a) and Jinke Tang b) Advanced Materials Research Institute and Department of Physics, University of New Orleans, New Orleans, Louisiana 70148 ͑Received 22 March 2000; accepted for publication 28 April 2000͒

FIG. 1 .
FIG. 1. Illustration of changing the relative orientations of magnetic granules.