Magnetic aftereffect in CoCr filmsDaniel K. Lottis, E. Dan Dahlberg, J. A. Christner, J. I. Lee, R. L. Peterson, and R. M. White Citation: Journal of Applied Physics 63, 2920 (1988); doi: 10.1063/1.340958 View online: http://dx.doi.org/10.1063/1.340958 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/63/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetization reversal in Co/Cr multilayer films J. Appl. Phys. 73, 6353 (1993); 10.1063/1.352646 Magnetic interactions in CoCr thin films J. Appl. Phys. 73, 6671 (1993); 10.1063/1.352551 The magnetic aftereffect in CoCr films:A model J. Appl. Phys. 67, 5187 (1990); 10.1063/1.344657 Magnetization decay in CoCr films J. Appl. Phys. 63, 2923 (1988); 10.1063/1.340959 Torque analysis of the perpendicular magnetic anisotropy in CoCr films J. Appl. Phys. 63, 2914 (1988); 10.1063/1.340955

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Magnetic aftereffect in Coer films Danie! K. Lottis and E. Dan Dah!berg School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455

J. A. Christner, J. I. Lee, R. L. Peterson, and R. M. White Magnetic Peripherals Inc./Control Data Corp., Bloomington, Minnesota 55435

We have studied the relaxation or decay of the perpendicular remanent magnetization of CoCr films after the removal of a saturating magnetic field. The films have a perpendicular anisotropy and are similar to those being studied for application as perpendicular recording media. The time dependence of the decay of the magnetization was determined by measuring the magnitude of the magnetization continuously for time periods up to a thousand minutes using a SQUID magnetometer. This time dependence was studied over a range oftemperatures for each of the samples (10-300 K). The decays are found to be quasilogarithmic over at least three decades of time and have been compared to two phenomological models. A fit to one model's decay rate indicates the temperature dependence of the decay rate is nonmonotonic, i.e., the decay rate is a maximum in an intermediate temperature region for the films we have studied.

INTRODUCTION

It is well known that sputtered Co-Cr films can be pre­pared with an easy magnetization axis perpendicular to the film plane. I These films have attracted interest as possible materials for perpendicular recording systems. For their us­age in magnetic storage the stability of a recorded signal is required. We have conducted experiments in which the re­manent magnetization of samples saturated in the perpen­dicular direction were found to undergo a slow relaxation, quasilogarithmic in character, with the decay measured to times of 1000 min.

The existence of these decays should not be surprising, since many other magnetic systems, including ferromagnetic materials, have been found to display similar quasilogarith­mic relaxations. 2

-7 Although the physical mechanism of the

relaxations observed in eo-Cr films has not been deter­mined, it is clear that the demagnetizing field in the interior of a thin film with net perpendicular magnetization would tend to reverse the magnetization in the film until a demag­netized state is achieved.

The existence of quasistable remanent moments in these films would therefore seem to depend on some kind of har­riers in the free energy of the system inhibiting processes that lead to the decay of the magnetization. These barriers might be associated with the pinning of domain walls, or even with the rotation ofthe magnetization ofthe columnar crystalites which are known to characterize the microstructure of ap­propriately prepared Co-Cr films. 8

,9 In the latter case the size of the barriers would be related to the uniaxial anisotro­py constant of the material in the columns as well as to their volume lO and magnetization. The presence of the observed decays and their dependence on temperature seem to suggest that while such barriers are present, thermally activated re­versal processes are in fact occurring.

In the next section we will briefly review two phenome­nological models describing relaxations in magnetic systems with energy barriers, followed by a section describing experi-

mental details and comparing our data with the models. The last section consists of a summary and conclusions.

THE MAGNETIC AFTEREFFECT

The delayed change of the magnetization of a material following a sudden change in the applied field is often re­ferred to as magnetic aftereffect (MA) or magnetic viscos­ityY·12 These relaxations are often found to be quasilogar­ithmic and are distinct from the shorter time-scale lag in metals due to eddy currents. An early mode14 of the phenom­enon considered a situation where the temporal evolution of the magnetization is dominated by domain processes con­sisting of thermally assisted transitions over energy barriers. Conceptually one may consider the energy barriers as asso­ciated with pinning sites for domain walls or with the rota­tion of the magnetization of single domain particles embed­ded in a nonmagnetic matrix. The nonexponential decays are understood as resulting from the presence of a distribu­tion of barrier heights. These authors showed that for a near­ly flat distribution sufficiently broad compared to kB T (i.e., equal probability for aU barrier heights up to a maximum barrier height of energy greater than k B T), the magnetiza­tion relaxation could be well approximated by

(1)

where the rate S was found to be proportional to the absolute temperature T and the value of the constant Ml depends on the units chosen for t (corresponds to the value of the mag­netization when the time t = 1 unit). Much of the later work on the magnetic aftereff'ect5,6.13,14 consisted of refining this model, and generalizing it to account for the variation of S with the value of the field at which the relaxation occurs, and the demagnetizing factor of the sample. Recent studies of magnetization decays of particulate media have been inter­preted with this model. 3

Similar considerations led to a phenomenological model of two-level systems applied to magnetization decays in spin

2920 J. Appl. Phys. 63 (8), 15 April 1988 0021-8979/88/082920-03$02.40 ® 1988 American Institute of Physics 2920

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glasses. 7,15,16 These authors show the assumption of a distri­bution of barrier heights varying slowly on a scale of kT leads to a temperature and time dependence of the decaying moment that can be combined into a single, "reduced" vari­able We' This variable has dimensions of energy and charac­terizes the distribution of barriers a time t after a relaxation has begun in a system held at a temperature T. In their model We is given by

(2)

where r is a characteristic time scale for the rate of barrier crossing. In other words, a series of relaxations at different temperatures, when plotted as a function of We' should lie on a single, "master" curve, i. e., M (t, T) = I( We ) .

The functional form of M( w,. ) depends on the shape of the distribution of barriers, and reduces to Eq. (1) for a fiat distribution. The data for the spin glasses was wen described by

(3)

where kTo is a characteristic energy for the distribution. The model is quite general, and its assumptions similar to those in Ref. 4 so that one might expect this scaling to hold for the MA in ferromagnetic systems.

EXPERIMENTAL DETAILS

The samples were prepared by rf sputtering onto alumi­num aHoy substrates films of the alloy Coso Cr20 with thick­nesses between about 0.5 and 1.5 fl..m. Measurements were performed with a SQUID magnetometer equipped with a 5-T magnet. 17 The samples had saturation magnetizations on the order of 250 G and coercivities of 250 ± 50 Oe. The coercivities were determined using sweep rates of approxi­mately 3 Oe/s. The magnetic moments of these films were found to saturate in fields of about 5000 Oe, and data at higher fie1ds were used to determine and then subtract off the paramagnetic contribution of the substrates (there was not an observable MA in the substrate material). The satura­tion moment for each sample was determined at 300 K from the intercept of a straight line fit to the high field (H> 5000 Oe) data. Attention was focused on the decay ofthe reman­ent magnetization (RM), that is, the decay of the moment following the removal of a saturating field of 30 kOe.

The decays of the RM were observed for periods of up to 1000 min, and within experimental error were found to be consistent with a logarithmic time dependence for aU sam­ples and temperatures studied. The initial value of the RM, taken as the t = 1 min value [MJ in Eq. (1)] and the decay rate S = dM I d [in (t) ] were found to depend strongly on the temperature (at 300 K the rates were similar and approxi­mately 0.36 ± 0.06 G/decade time). A few typical decays for one of the samples are displayed in Fig 1. The quantities M! and S (Fig. 2) were determined by fitting the data to Eq.1.

The most surprising feature in this data is the nonmono­tonic behavior of S which defines the decay rate of the mag­netization. This behavior is observed in all the samples we have studied. At the present time we do not know in detail why this occurs but it is apparent from the unfitted or raw

2921 J. Appl. Phys., Vol. 63, No.8, 15 April 1988

+"+++++++ 250K +.++++++., .......... . , I , , , I i ------J.._'--1-~

5 10 50 100 t (minutes)

FIG. 1. Some decays are shown for one sample which are typical of those seen in all samples. The dotted lines are least-squares fits to the logarithmic form in Eq. (l}.

data that as the samples are heated from the lowest tempera­tures the magnetization decays at an increasing rate until a sample-dependent temperature on the order of 275 K. At higher temperatures the decay rate decreases slightly for in­creasing temperatures. A nonmonotonic temperature de­pendence of S in the model of Refs. 4--6 must be absorbed into the prefactor for the temperature in their expression for S. Although the authors report observing such behavior in certain precipitation alloys, ]8 its origins were not discussed in detail.

Turning now to the other model,7 Fig. 3 shows the data over an extended temperature range plotted with a fitted "master curve" as predicted by Eq. (2). It was not possible to find a value of 1" for which the data from decays at different temperature lay on a single smooth curve. The "master curve" was generated using the parameters r and To ob­tained from a best fit to Eq. (3), and illustrates the difficulty in "aligning" the various runs with a single curve. On the other hand, the value of To obtained (12000 K) is clearly consistent with the assumption of a distribution wide com-

, , , I

,

' '1 ,-.. El , T

III (J 40 (J n. .·f·· .. I.

'-.. , I ~ , )i~ -1 -"

S 30 ,

~ 'a

:f '" , , "'1J...--. a ..... en 20 ~~ M f

, , 'E_ --0

0 ± 100 X S

~ 0 .... 10 oM!.

IJ ..... ::.1

0 , , , I , 0 100 200 300 400

T (kelvin)

FIG. 2. Temperature dependence ofthe least-squares parameters obtained by fitting the data from decays on one typical sample to the logarithmic form in Eq. (l). Note in this figure it is the absolute value of S which is plotted (S is n.egative since the magnetization decays) and has been multi· plied by 100 (and corresponding error bars) for easy comparison with M, . The values plotted represent averages over several decays at each tempera­ture.

LoUis et al. 2921

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30

20

~OK

'WOK

10 ~ ~. ~,~~~,~I~,~~, ~,~I-L'-kJ_~L-~ o 5000 10000 15000

We (kelvin)

FIG. 3. A fit of the data for one sample to the concept of a master curve as defined by Eq.(3) (see text). The dotted line is a least-squares fit of the data to Eq. (3) with M() = 36.1 G, 1'.0 = 11 944 K, and r = 10-". For simpli­city, We is shown in K, i.e., we set k n = I.

pared to k R T and is not unreasonable if one considers macro­scopic regions of the sample to be involved. The constant 1" is found to be at least an order of magnitude smaller than the commonly accepted values for this quantity.

SUMMARY AND CONCLUSIONS

'Ve have found the remanent magnetization of CoCr films with a perpendicular anisotropy to decay with time. The quantity S = dM / dIn (t) used to characterize the decay is found to be essentially a constant for times from 1 to 1000 min, at fixed temperatures over the range from 10 to 300 K. While the basic features of our data may be characterized by either of the two phenomenological models we considered, there are some unresolved problems. The non monotonic be­havior of the rate S is awkward to deal with in the model of Ref.,. 4-6. It can be understood in terms ofthe second model as arising naturally from an appropriate "Master curve" function M ( We ),11> however, our data is not well described by such a curve.

A better understanding of the our data might be ob­tained by noting that the parameter MI , which is a measure of the initial remanence, varies by almost a factor of 3 over the temperature range studied. The demagnetizing field in the sample therefore is not constant for the rates plotted in Fig. 2, but varies over a range of several hundred Oe. Since

2922 J. Appl. Phys., Vol. 63, No.8, 15 April 1988

this field is clearly driving the sample to a demagnetized state its magnitude variations are similar to measuring the decay in different reversed magnetic fields. The simpler ver­sions of either model describe only the variation of S with T for decays at a fixed value of the field, and even the later papers do not deal satisfactorily with the temperature depen­dance of a demagnetizing field.

On more general grounds, one might accept a priori that thermal activation over some form of energy barriers drives the relaxation of the system and recognize that for a magne­tization perpendicular to the plane of a thin film there is a demagnetizing field which determines the energy of the sys­tem. Given these two conditions, then, the relaxation of the system depends on the detailed relationship between the temperature, which provides the energy for barrier hopping, and the internal magnetic field, which alters the distribution of energy minima and barriers in the system. In other words, the maximum in the decay rate may be due to the competi­tion between an increase in the thermal excitations with in­creasing temperature and a decrease in the driving field, the demagnetization field forcing the system to relax.

The authors (D.K.L. and E.D.D.) gratefullyacknowl­edge receipt of a funding from the Control Data Corp. for this research.

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