dynamics of the re-entrant spinglass crossover in nimn films probed via resistance fluctuations and...

~i~ Journal of magnetism and magnetic mmrlals

ELSEVIER Journal of Magnetism and Magnetic Materials 152 (1996) 317-325

Dynamics of the re-entrant spinglass crossover in NiMn films probed via resistance fluctuations and ac magnetoresistance

C.D. Keener *, M.B. Weissman

Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 6180, USA

Received 21 April 1995; revised 1 June 1995

Abstract The crossover between the ferromagnetic regime and the re-entrant ferro-spinglass regime in NiMn is investigated by

electrical noise and ac magnetoresistance in small, thin-film samples. The dependences of the noise and magnetoresistance on magnetic field indicate that the entities whose dynamics freeze out in this crossover are not individual spins but instead small clusters, at least in the thin-film material with partial short-range atomic order. These spin clusters have a significant component of magnetization transverse to the moments of the domains in which they reside. The substantial frequency dependence of the crossover temperature indicates that the crossover is a kinetic blocking, not a highly cooperative process.

1. Introduction

Several magnetic materials, including disordered NiMn, enter a re-entrant ferro-spinglass (FSG) regime upon cooling from the ferromagnetic (FM) state [1]. The nature of the re-entrant crossover or transition remains obscure, in part because magnetic susceptibility measurements are much more sensitive to the large ferromagnetic moments than to the much smaller net moments associated with the spinglass- like properties. In this paper we combine electrical noise measurements with ac magnetoresistance measurements in order to investigate the dynamical freezing that occurs at the re-entrant crossover of NiMn thin films with partial short-range atomic order (SRO).

In the mean-field solution of the infinite-range

Heisenberg spinglass (SG) model, Gabay and Toulouse [2] found a re-entrant transition in which frozen random (SG) xy order forms without break- ing the ferromagnetic z order. This transition has been suspected in some experimental re-entrant systems. However, neutron scattering in NiMn reveals spatial spin correlations [3] that are incompatible with the individual-spin transverse-SG description. Thus the questions of what change in magnetic ordering occurs at the crossover, and of whether this occurs by a true phase transition, a highly cooperative crossover, or a simple kinetic blocking, remain open. The role of random anisotropy in the crossover also has not yet been made clear.

2. Background

* Corresponding author. Present address: Department of Physics, Ohio State University, Columbus, OH 43210, USA. Fax: + 1-614- 292-4371; email: [email protected].

2.1. NiMn and its glassy freezing

Atomically disordered NiMn has a ferromagnetic phase with some disorder in the exchange field

0304-8853/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0304-8853(95)00481-5

318 C.D. Keener, M.B. Weissman /Journal of Magnetism and Magnetic Materials 152 (1996) 317-325

distribution up to the Curie temperature T c [4]. In the lower temperature range of the FM regime, some spin structure which is ordered transverse to the FM moments [3] begins to become apparent. From neutron scattering measurements when T c = 300 K, transverse-ordered spins with an average correlation length of ~ 10 ,~ [3] exist as high as 120 K, even though the re-entrant crossover appears in the susceptibility at much lower temperatures.

The re-entrant crossover temperature Tvs G will be defined as the temperature at which there is a broad cusp in the imaginary part of the ac susceptibility, X". At the same TFS G the real part of the susceptibility, X', exhibits a rapid but continuous drop. FM domain structure remains essentially unchanged through the FSG crossover, but the domain walls become less mobile below TFs G [5-8]. SG-like effects involving transverse spin components are possi- bly responsible for the domain wall stiffening. Neu- tron scattering results confirm that the Bloch walls lose mobility when canted [6].

In a field of about 40 Oe (sufficient to suppress most of the dominant response that is due to domain wall motion), X" shows a split peak near TFs G. The identity of the processes contributing to the two parts is uncertain, although it has been suggested [7] that the upper peak may be connected with transverse freezing and the lower peak with a de Almeida- Thouless-like crossover [9]. In samples with some SRO, splitting into two peaks has not been observed. In disordered samples, the upper peak overlaps with the freezing out of FM domain wall motion; the peak and freezing of FM domains was distinguishable only in the case of a partially SRO sample [10]. Although no split peak was found in either noise or magnetoresistive response in the current work, we shall see that suppression of FM fluctuations and the onset of FSG fluctuations will be clearly distinguishable in the electrical noise.

Since no measured parameter shows a discontinuity at TFSG, the identification of that temperature as a phase transition is not obvious. A feature in the nonlinear susceptibility at TFs 6, reminiscent of spinglasses, has been reported [11]. However, in the same work the temperature of the lower FSG peak in X differed substantially depending upon whether the measurement was made at 16 or 2400 Hz [11]. As we argue next, such frequency dependence is charac-

teristic of a very weakly cooperative blocking transition.

In many true spinglasses, the temperature T F of the cusp in the ac susceptibility is very weakly frequency dependent [1]. The spectrum of the resistance fluctuations in CuMn and (CuMn) 1_ ~Au 8 [12] also shows a weakly frequency-dependent increase near T F. Whether in ac response measurements or in noise spectra, weak frequency dependences of strongly temperature-dependent parameters indicate cooperative effects. In extreme cases they are a good indication of the presence of true phase transitions at temperatures very close to the measured freezing temperature. Such weakly frequency-dependent effects cannot arise from simple Arrhenius activated kinetics, which would require unphysically high attempt rates, e.g. near 10 300 Hz for the X' cusp in CuMn [1]. However, the reported frequency dependence of the lower-T peak in X in NiMn (e.g. at 25 Oe) [11] is consistent with Arrhenius kinetics with an attempt rate of around 5 × 1017 Hz, only slightly higher than the typical range of attempt rates for simple non-cooperative processes.

2.2. Electrical noise

It is convenient to introduce two parameters to describe the spectral density SR(f,T) of the fluctuations in resistance, R. These are

N~fSR(f,T) R2 , (1) c~(f,T) =

and

y ( f , T ) = - O l n S R ( f , T )

01nf ' (2)

where N a is the number of atoms in the sample. One of the advantages of noise measurements is

that they may be performed in such small samples as to allow either direct observation of individual co- herent units (or fluctuators) or at least some statisti- cal characterization of properties such as the volume of the fluctuators. When a noise spectrum comes from a small number of fluctuators, it will show deviations from the smooth form ( ~ 1 / f y) which characterizes a large ensemble [13]. These fluctuations around the ensemble average may either occur

C.D. Keener, M.B. Weissman /Journal of Magnetism and Magnetic Materials 152 (1996) 317-325 319

from sample to sample (in which case each sample shows persistent spectral features) or in each sample as a function of time (in which case each sample shows slow wandering of its spectral form around its average).

Under reasonably general assumptions, the excess (above the variance predicted for Gaussian noise) fractional variance v of the spectral density about the ensemble average is given by

V ~ 0 .1 /nf , (3)

where nf is the density of active few-state systems per factor of e in characteristic frequency [14]. For fluctuators which have a spread of energy asymme- tries, and hence of duty cycles, Eq. (3) applies if nf is taken to refer to all fluctuators with two states whose free energies are within about kT of one another [15]. Use of Eq. (3) will allow us to set a lower limit on the density of objects contributing to the noise peak near TFs G, and hence an upper limit on their size.

Samples ~ 300 times larger than those discussed here have been investigated by electrical noise measurements [16]. In addition to the FM domain noise, which could be suppressed in a 3.1 kOe field, a small peak in ot versus T appeared at 47 K. This peak was not suppressed in a magnetic field. Most of the FM noise seemed to freeze out below that temperature. Although we suggested that this peak might be due to SG effects, in large samples the background effects of FM domain noise made it difficult to investigate [16]. In the smaller samples discussed here, FM domain noise also appeared [17]. It exhibited non-Gaussian statistics and large spectral features, characteristic of a small number of large- volume fluctuators in the experimental frequency range. This component of the noise froze out [17] above the temperature of the ferro-spinglass contribution discussed in this work.

2.3. Complex ac magnetoresistance

Although it is not possible to measure directly the magnetic susceptibility in a very small sample, it is possible to measure a related quantity, the complex response of the resistance to an applied ac magnetic field of the form H = Hoe + HacCOS(2~rfnt). When an ac magnetic field is applied, the magnetoresis-

tance (MR) contains both in-phase and out-of-phase components, with the fractional change in R per unit ac magnetic field denoted by X,~ + i X~, in analogy to the conventional notation for susceptibility.

Like X or the noise, this ac magnetoresistance gives dynamical information. It does not necessarily probe exactly the same dynamics as appear in the noise: Those magnetization fluctuations which cou- ple to the resistivity with random signs (e.g. via universal conductance fluctuations, UCF [18]) will contribute to the noise but will not give a systematic magnetoresistive response to an applied field. The dynamics probed are also somewhat different than those measured by X, since 180 ° rotations of anisotropic domains show up in X but not in XR. In fact, by symmetry the linear magnetoresistive response vanishes in unmagnetized samples at zero field, while neither the noise nor the linear susceptibility does. We shall make use of the difference between the noise and the MR sensitivities to different components of the magnetization to help distinguish between transverse and longitudinal contribu- tions to the noise (where we define transverse and longitudinal in relation to the direction of the local FM moment).

XR may be used to characterize the anisotropy of the domains which give rise to it. Qualitatively, for purely uniaxial anisotropy there is a discontinuity in Xn versus field at zero field; it switches sign between its maximum absolute values, as all the domains rotate 180 ° . In practice, one expects some hysteresis in this sign reversal. For purely unidirectional anisotropy, however, XR goes smoothly through zero, with no particular difference between the hysteresis there and at other fields. We shall see that the data closely resemble the prediction for uniaxial anisotropy.

Like other dynamical probes, XR provides a way of checking if large changes in response as a function of T are due to cooperative transitions. In complete analogy with similar arguments for X [19,20], one can derive from the Kramers-Kronig relation a ' 7 / 2 rule', as long as there is a broad distribution of relaxation rates [21]:

= (4) 2 d l n w

3 2 0 C.D. Keener, M.B. Weissman /Journal of Magnetism and Magnetic Materials 152 (1996) 317-325

If the characteristic rates are activated with some attempt rate too, then Eq. (4) can be converted to a relation between X~ and the temperature derivative of X~ (assuming that the T derivatives are domi- nated by kinetic effects, not by, for example, overall changes in the MR strength):

1 'rr dx~

X'~= ln( to0/ to ) 2 d l n T " (5)

When Eq. (5) cannot be fitted with a physically reasonable too, then the T-dependence cannot be due to simple Arrhenius blocking, and when a highly cooperative crossover is present, very large deviations from Eq. (5), generally requiring unphysically large too, are expected.

3. Sample characterization and susceptibility

A Ni0.77Mn0.23 film was deposited onto a sap- phire substrate by dual electron beam evaporation at 3 × 10 -8 Torr base pressure, at a rate near 3 A / s . Samples were fabricated into five-point resistance bridges by standard optical lithography. The film was etched by ion milling in an Ar atmosphere of 3 × 10 - 4 Torr. To minimize contact resistance, Ag was evaporated onto the contact areas, and then Cu wire was connected by using pressed In pads. The samples were 32 ixm long and 55 nm thick. Sample 1 was 1.8 Ixm wide, and sample 2 was 2.0 tim wide. The volumes of these samples were 300 times smaller than those used previously [16].

The Mn concentration was determined by the inductively coupled argon ion plasma (ICP) tech- nique to be 23 at%. The two samples were fabricated from the same film at different positions on the substrate. A sample for dc magnetization ( M ) and ac susceptibility (X) measurements, lm, was grown on a glass substrate.

Fig. 1 shows X' versus T of sample 1 m for three different dc fields and two different ac probing fields. X" was not accurately measurable for these small- volume samples. Three features are prominent in Fig. 1.

First, a peak marking the onset of FM order is obvious at (320 _ 5) K in 20 Oe and (310 +__ 5) K in 10 Oe. We estimate T c , the temperature at which the

6 t I I I I

. . . . . . . 0 o e

~.~ ~ I - - ~ - - l o o ~

0 ~ I t t I , " e ' t ~ , ( a i 0 5 0 100 150 200 250 300 350 400

T(K) 6 I I I I I I I

ITi ....... i ooo I O, , 1ooe(aczoe)l ..I,4 . . ' " . ~ 4 m 2 0 0 e l ~ ' ~ . - ' ' ~ ' " -

%

(b) 0 I I I I I I I

0 2 0 40 60 80 100 120 140 T(K)

Fig. 1. X' versus T of sample El,.. The dc field is given in the legend. The ac field amplitude was 5 Oe, except for the data labeled 2 Oe. All data were taken while warming, having cooled in zero field, except for the curve labeled with an arrow to indicate that it was measured while cooling in 10 Oe. (b) Ex- panded view of the data, showing the FSG knee region.

peak would appear if H were zero, to be about (290 + 15) K. The dc magnetization and hysteresis loops also were measured, and T c agreed with that obtained from X measurements. In samples 1 and 2 T c was probably higher due to annealing at 90°C during fabrication; this annealing could have increased the amount of atomic short-range ordering.

Upon cooling, the second peak encountered in all zero-field-cooled data is the large one that varied significantly with different applied fields, both ac and dc. This sharp dependence upon field probably appears because of some coercive field being crossed; i.e. the peak is a response of the FM domains.

The third major feature in X' is the more subtle knee found to be centered around 75 K, extending from about 40 K to about 110 K. Like the peaks in susceptibility [4,7] at T~s o in bulk disordered re-entrant SG samples, this knee was not very field depen-


dent. A comparison with standard data on bulk samples [22] suggests that TFs 6 is between about 55 and 60 K.

The question has been raised as to whether the partially ordered thin-film system really has true long-range FM order for T > TFS o. Arguments from Lorentz microscopy images [5] (the samples probably had SRO due to the minimum amount of time required at room temperature to electropolish [23]), our own images of FM domains at room temperature [16], and noise and transport measurements all agree that FM ordering is present in such samples.

4. Results A peak in the resistance noise appeared at almost

exactly the same temperature, about 41 K, in both samples 1 and 2, which were fabricated on different parts of one NiMn film. The sizes of the peaks were identical in the two samples, within the calibration uncertainty (see Fig. 2). The magnitude of the resistance noise peak was independent of whether ac or dc probe currents were used.

This noise varied reproducibly with H, as shown in Fig. 3. From the significant dependence on H, we conclude that the fluctuators were magnetic. No- tably, for low H, the temperature of the peak in a increased, up to 48 K for H = 400 Oe.

The peak was much broader in frequency than a Lorentzian that would arise from a two-state system. Together with the peak's reproducibility between samples, this breadth in frequency suggests that the

10-

"0. ..

• Sample 1 I 10 -4

0 10 20 30 40 SO 60 70 80 T(K)

Fig. 2. a versus T of samples 1 and 2 at 7 Hz near Tvs G.

48

46 ,,e''" " ~ ' ' ' ' e

~'= 44 I ,,e

. . : I ' . : I ' , : ' , ' : ' , I : : : . o .

?-- ....... [ o % / " "'""-. K) ~-8 ~ , ~ .

6

(b)~ 4 , , , i , , , i , , , i , , , i , , ,

0 2 O0 400 600 800 1 000 H(Oe)

Fig. 3. (a) Tp, the temperature of the peak in a, as a function of H. (b) ap, the magnitude of the peak in ot at 7 Hz, and ot at T = 50 K, as a function of H.

noise came from a large number of small objects. To test this hypothesis, we looked for small deviations from smooth spectral forms, which can reveal the presence of discrete fluctuators that are too small to resolve individually. No such deviations were found; within experimental uncertainty, v < 4 × 10 -4 from the lack of spectral features in the average of 2000 consecutive 1024-point Fourier transforms. We also checked the variance of the spectral density in time, using the same 2000 Fourier transforms. The variance was Gaussian, to within the accuracy of the measurement, which sets an upper limit on the fractional temporal variance of also about 4 X 10 -4. The net excess fractional variance is then also zero, with uncertainty extending to about 6 X 10 -4.

Spectral slopes and o~ were fit to the Dutta-Horn equation [24]. The fit was excellent (see Fig. 4) and yielded an attempt rate of 6 x 10 ~s Hz and peak E a of 0.12 eV.

X,~, shown in Fig. 5 as a function of T, peaked at around 50 K, roughly comparable to the temperature of the a peak. X,~ exhibited a broad feature from 40


1.05

1 . 0 0

I I I I

D "'" " ° ' ' " 4 " '¥

:"- 0.95

0.90 ........ DDH "¢ "

0 . 8 5 ' I i " I I I u

0 1 0 20 30 40 50 60 T(K)

Fig. 4. Dnt ta -Dimon-Horn plot: Y versus T, and 3' calculated from the temperature dependence of SR(f,T), using Ref. [24], labeled DDH y. The agreement is within experimental uncertain- ties.

to 100 K, similar to the bump in X'. The magnetoresistive response at 2fn was much smaller than the linear response. For comparison with Eq. (5), in Fig. 5 we plot X~ along with K(dx'n/dln T), where K is "rr/[21n(fo/f)], with f = 18 Hz and f0 = 1022 Hz. A small correction to the w /2 rule, due to the deviation of the spectral slope in this regime from 1/f, requires a slightly larger f0, 5 × 1022±2 Hz [21].

With a constant T of 49.7 K (near TFs6), XR versus Hd~ is shown in Fig. 6. As required by symmetry, X~ and h'~ passed through zero for small

~ X R " × K d x R ' / d l n T

1 2 , , , ~ , , , ~ , , , ~ . , , ~ , , . , , , , 4

"7, oO 1 ~ e e ×

× x

0 ' ' ' I . . . . . . 0 0 2 0 40 60 80 1 O0 20

T(K)

Fig. 5. XR and XR versus T; R is the resistance at H = 0. Hac = 7 . 7 0 e , Hdc = 0 , and fu = 1 8 Hz. Also, K(dx'R/dlnT)is plotted; K is described in the text. The best fit for K yielded an attempt rate of 1022 ± 2 Hz, slightly above realistic Arrhenius values.

'~ 0 ©

o - 5

- 1 0

- 0

%

. . i - , ~ . : . . . . , . . . , . . . , . .

0 -40 -20 0 2 0 40 60 H D c(O e)

O O'e / t,w

- 1 - 5 0 0 (

8

co 4 ~

0 ~,

- 4

2

- 2 0 0

0 3 ¢D,

H~ c(Oe)

Fig. 6. X~ and X~ versus Hdc with T = 49.7 K. (a) LoW-Hdc response. Hac = 7 . 4 0 e , and fn = 18 Hz. (b) High-Hale response. Hac = 8 . 3 0 e , and fn = 10 Hz.

Hdc, with hysteresis similar to that of M. Little hysteresis was found at larger fields. Comparison with the predictions for uniform-strength uniaxial or unidirectional anisotropy shows a strong similarity to the uniaxial prediction and a qualitative dissimilarity to the unidirectional prediction, probably not surpris- ing since the temperature is not far below Tc, so no unidirectional anisotropy is frozen in.

In contrast with the low-field response, when Hac was large, FM domain motion produced substantial in-phase and out-of-phase response because the larger field surpassed the coercive field. This non-linear effect gives a response at both fn and 2fH.

5. Discussion

Neither the noise nor the ac MR show a strongly cooperative blocking at TFs c, much less anything


like a phase transition. The attempt rate of 6 × 1015 Hz needed to fit the noise is only marginally high for Arrhenius kinetics. The MR response (probing different objects in a slightly higher range of T) is somewhat cooperative (fo ~ 5 × 1022 Hz), but the attempt rate is still closer to the plausible physical range than even that found in the noise of re-entrant FeZr films [25]. In NiMn films we see a weakly cooperative crossover into the ferro-spinglass regime. These results would be hard to explain if long-range SG order were forming in the plane transverse to the FM moment.

The interesting question becomes just what sort of entities are freezing. The noise statistics allow us to set a lower bound on the density of the fluctuating objects of nf >_ 175, using Eq. (3) and the net non- Gaussian fractional variance of < 6 × 10 -4. Given the width (in T) of the peak, it must be spread over at least 20 factors of e in f (using an Arrhenius equation with f0 = 6 × 1015 Hz). Then at least 3500 fluctuators are contributing to the noise peak in this sample. If the entire sample consists of fluctuators with two nearly equal energy levels, the upper limit on the average fluctuator volume would then be 0.8 × 10 -15 cm 3. In the far more likely case that there is a wide distribution of local fields, only a small fraction of the sample would be distributed among those > 3500 units, so that the typical volume would be much smaller. These fluctuating units are clearly very different from the large domains and domain cluster that constitute the main noise source at higher temperatures and, occasionally, at lower temperatures [16,17].

Since the noise appears to involve fluctuations of some sort of spin cluster whose properties are not anomalously temperature sensitive, a true phase boundary does not seem to lie nearby. Thus it makes sense to analyze the field dependence on the assump- tion that clusters of well-defined moments are its source. We may then use the scale of the noise field dependence to obtain a lower estimate for the typical size of the fluctuating entities. By 800 Oe, the noise magnitude is significantly reduced from its maximum, suggesting that the typical magnetic moment of the fluctuator, /.t > kT/800 Oe --~ 1000/z B. Given that the saturation magnetization per atom was about 0.2/z B, fluctuating cluster sizes seem to be at least about (4 nm) 3.

The fact that a and X~ peaked at comparable temperatures suggests a common source. Both quantities are also strongly affected by fields in the range of hundreds of Oe, again suggesting that both reflect the dynamics of similar entities. In fact, the fluctua- tion dissipation theorem (FDT) [26] gives a relation between two relevant quantities SM(f) and X". Since M is a vector and R is determined by one diagonal term in a resistivity tensor, however, the relationship between SR(f) and h',~ is obtained only indirectly through SM(f) and X" for certain conditions of applied magnetic field. We shall argue that the de- tailed field dependence of these two quantities indicates that the noise is in large part the result of transverse magnetization fluctuations.

We define the z-direction as parallel to the applied magnetic field (and approximately to the current in this case), and the longitudinal direction locally as parallel to the ferromagnetic moment within a given domain. XR probes a change in the z-component of magnetic moments (systematic collections of spins) via the anisotropic magnetoresistance. S t ( f ) arises from magnetization fluctuations not only via these systematic magnetoresistance effects, but also from random interference terms which are sensitive to all components of M.

If Hdc is large and the sample becomes nearly single-domain, the longitudinal and z-directions will approximately align throughout the sample. Under the condition of high Hdc, therefore, the longitudinal contribution to S t ( f ) will coincide with the z-component, which will be proportional to SM(f). The nearly complete absence of X,~ for H > 400 Oe indicates that slow fluctuations in M z are suppressed. Although a continues to fall off with in- creasing H in this regime, it is far from completely suppressed. We believe that the obvious explanation is that the noise comes largely from transverse fluctuations, which are not related by the FDT to X,~ and should persist to higher fields.

Given that the fluctuating entities are substantially larger than individual spins, and cannot be large domains, it is most reasonable to compare them with the transverse-ordered FSG spin clusters that have been found with neutron scattering [3] to have a correlation length of ~ 1 nm at around 10 K, and apparently only a bit larger at higher T. Clusters of this size are shorter than an inelastic electron diffu-


sion length, so that fluctuations of their magnetization along any axis would be expected to show up in Sn(f) via the UCF mechanism. The difference in the field dependences of a and X~ is consistent with UCF being the noise coupling mechanism.

Unless the correlation length of the transverse magnetization is significantly larger near TFS6, in our samples than near 10 K in those used for neutron scattering, the apparent fluctuator moment inferred from the field dependence of the noise is too large to be that of a single correlated region. Together with the partial cooperativity of the blocking transition, that result suggests that there may be cooperative clusters including several correlation volumes in a glassy arrangement.

The difference in temperature between the peaks in a and X,~ is reasonable, given our explanation of the data. X~ peaks somewhat higher in T (50 K) because X~ depends on both the magnetic moment and the volume of the contributing anisotropic re- gions, a depends on interference terms in scattering among nearby clusters; these saturate for large clusters. Thus a tends to pick up motion of smaller clusters, which thermally block at lower temperatures. Judging from X', X" apparently peaks at slightly higher temperatures than X~ consistent with the same pattern. It is interesting that more cooperativity shows up in the higher-T part of the crossover.

We have not been able to use identical samples to those used by others for susceptibility measurements. Because we used thin films that were partially SRO, one could argue that the lack of a transition in our films tells little about the re-entrant crossover in the bulk. A recent comparison of disordered films and bulk samples [23], however, found little difference in the susceptibility's main features until the films be- came thin enough to exhibit finite size effects. Our films, which have SRO, should be comparable with bulk samples with SRO. At any rate, the only frequency-dependent susceptibility measurements we have encountered on fully disordered material also indicate a strongly frequency-dependent re-entrant crossover. It might also be worthwhile to investigate the frequency-dependence of X at the non-re-entrant spinglass crossover in disordered samples (Mn concentration > 24 at%) in order to see if it indicates a true spinglass transition or a weakly cooperative kinetic crossover.

Acknowledgements

This work was supported by the NSF through grant DMR 93-05763 and, through the facilities and staff of the Materials Research Laboratory, under grant DMR 89-20538.

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dynamics of the re-entrant spinglass crossover in nimn films probed via resistance fluctuations and...

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