Physica B 276}278 (2000) 543}546

What neutrons do tell us about the nature of (spin) glasses?

F. Mezei!,",*, G. Ehlers!, C. Pappas!, M. Russina!,", T.J. Hicks#, M.F. Ling#

!Berlin Neutron Center, Hahn-Meitner-Institnt, Post fach 390128, Glienicker Strasse 100, D-14109 Berlin, Germany"Los Alamos National Laboratory, Los Alamos, NM 87545, USA

#Department of Physics, Monash University, Clayton 3168, Australia

Abstract

A common feature of all glassy systems is the decisive role of dynamics in the evolution of macroscopic properties,while the short and eventually partial long-range order shows little di!erence between the di!erent phases. Our recentneutron scattering results on a Cu}Mn spin glass dramatically illustrate this point, and provide unambiguous evidenceagainst recent suggestions that behaviour in Cu}Mn is driven by spin density waves rather than glassy dynamics. Recent"ndings in Au}Fe provide the "rst circumstantial evidence for the theoretically predicted extremely long correlationlengths at the spin-glass transition. Recent experimental advances opened up the way to investigate dynamics in glassesand liquids on extended length scales, where only spin correlations could be studied by now. ( 2000 Elsevier ScienceB.V. All rights reserved.

Keywords: Spin glasses; Glasses; Disordered materials

The bulk of information on spin glasses comes frommacroscopic magnetic measurements, which are muchmore precise and much more easy to perform than neu-tron scattering. To some extent the same applies tohyper"ne "eld experiments too (although not to lSR).Nevertheless, neutron scattering data contribute byunique pieces of information which cannot be substitutedby other methods. Neutrons explore the generalised sus-ceptibility s(q,u) in a microscopically more relevantparameter domain than other methods and they alsodeliver details completely hidden to macroscopic suscep-tibility experiments. Macroscopic measurements corres-pond to a wave number q"0, i.e. to averages over largevolumes. In contrast hyper"ne "eld techniques directlyprobe local behaviour (r"0, i.e. the average over all q's).However, in both spin glasses and structural glasses thecentral issue is the collective behaviour of the neighbour-ing atoms and the correlations on atomic scales fromnearest-neighbour distances to a few nanometers. This is

*Correspondence address: Glienicker Strasse 100, D-14109Berlin, Germany; fax: 0049-30-8062-3094.

E-mail address: mezei@hmi.de (F. Mezei)

why the capability of neutron scattering to explore thecorresponding q range is of crucial signi"cance.

Beyond allowing us to inquire on the most relevantmicroscopic length scale, neutron scattering also deliversprecious and unique information in time, in the domainranging from characteristic microscopic times, some10~13 s, to intermediate mesoscopic times of up to some10~8 s, between the microscopic and macroscopic timescales. Actually one key feature of the glassy state is thatthe characteristic times of dynamic phenomena (prim-arily collective relaxation) span many orders of magni-tude from typical atomic collision times, or similar timesfor individual spin exchange phenomena in the paramag-netic phase far from the freezing transition, to the age ofthe universe. The particular interest in the time domaincovered by inelastic neutron scattering, if one includesboth conventional (time-of-#ight, TOF) and high-resolu-tion experiments (Neutron Spin Echo, NSE), is that itcovers the crossover range between the atomic collisiondomain to the long time relaxation domain. Actually thetype of behaviour does not change if one goes from10~10}10~8 s to eternity: on atomic scale these timeslook like eternity. For example, on this time scale, inelas-tic neutron scattering experiments (NSE) reveal charac-teristic hysteresis e!ects (see Ref. [1]), which are the main

0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved.PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 3 6 4 - 2

practical criterion for identifying spin glasses with respectto other magnetic transitions.

If one studies the hysteretic behaviour on a macro-scopic time scale, the equilibration time is comparable tothe actual time scale of the phenomena looked at and oneis in an uncertain state, where equilibration (`aginga) anddynamic relaxation processes form a complex, often inex-tricable mix (for a review see Ref. [2]). The advantage oflooking for hysteresis e!ects in the time domain coveredby inelastic neutron scattering is that on the time scale ofthe experiments, i.e. over several hours, the system canequilibrate after a change of the thermodynamic para-meters. The condition for that is that, while we arelooking at relaxation processes in the ns range, the lon-gest relaxation time in the system is shorter than somehours, so that the system can equilibrate, or age, for times12 orders of magnitude longer than the dynamic e!ectswe are looking at. In order to make this feature of in-elastic neutron scattering clearer, let us consider the rela-tion between neutron cross sections and susceptibility.

As it is well known, the inelastic neutron scatteringcross-section is proportional to the imaginary part of thesusceptibility s(q,u), while the macroscopic susceptibilitycorresponds to the real part at q"0 and for x, which canbe varied in a limited range corresponding to times fromtypically some ls to hours. The Kramers}Kronig rela-tion between the imaginary and the real parts can almostnever be evaluated, since one rarely knows the suscepti-bility for all u's. However, if we consider relaxationprocesses only, i.e. correlation functions monotonicallydecaying in time, and NSE experiments, where integra-tion over u is involved, one can write in good approxi-mation that

Re s(q, u)JS(q)[1!s(q, t)]/k¹, (1)

where S(q)": S(q, u)du is the magnetic structure factor,s(q, t)" : S(q, u) exp(!iut)du/S(q) is the intermediatescattering function measured directly in NSE andt+1/u [1]. The meaning of this equation is quite simple:s(q, t) is the fraction of the total magnetic response S(q)which does not relax before the time t, in other wordss(q, t) is the part of S(q) which cannot respond to a driving"eld of frequency 1/t.

We have to stress that neutrons deliver both S(q) ands and thus give more information than susceptibilitymeasurements. The static part of S(q) (more preciselystatic with respect to a given time t) does not contributeto the susceptibility at all, it remains fully hidden formacroscopic susceptibility experiments and it is also ex-cluded when applying the Kramers}Kronig analysis.Neutrons on the contrary can reveal not only the tem-perature dependence of the susceptibility but also itsmechanism: does it come from the change of the static(instantaneous) order re#ected in S(q) or from the dynam-ics re#ected in s(q, t) or from both. A typical example is

the peak in the susceptibility at the NeH el point, which isentirely due to the change of S(q"0): the antiferromag-netic order reduces the magnetic structure factor at smallq's. In spin glasses, however, it has been shown [1] thatthe characteristic sharp cusp in the susceptibility can alsobe observed at frequencies of the order of 100 MHz,accessible to NSE, and that its origin is fully dynamicwith no essential change in S(q). This is an evidence forfreezing (hysteresis) on the ns time scale. We note thathysteresis is understood here on the time scale: within thelinear response regime, knowing the time relaxation func-tion allows us to determine the response to a perturba-tion with an arbitrary time pro"le. Neutrons cannot seethe non-linear susceptibility, the thermal #uctuationsthat they normally probe remain within the linearresponse regime.

A recent discovery of spin density wave (SDW) typeantiferromagnetic short-range order in single-crystallineCu}Mn alloy [3,4] lead to speculations that the magneticbehaviour of these alloys might be governed by antifer-romagnetic ordering and not by the spin-glass transition[3]. In order to check this suggestion we determined thetemperature dependence of the magnetic scattering ofa single crystalline CuMn 4.7% sample around q"0, i.e.in the range most relevant to the macroscopic suscepti-bility. We used conventional three directional neutronpolarisation analysis [5] only at low temperatures, wherecorrections due to the inelasticity of the magnetic signalare negligible. The experiments were done at the coldneutron NSE spectrometer IN15 of the ILL with incidentwavelengths of 8 and 15 As and for 0.04 As ~1)q)0.31 As ~1. Separate measurements of a vanadium speci-men were used to obtain the absolute values of thescattering cross sections from the data. At temperatureswell above the spin-glass temperature we identi"ed themagnetic signal using time-of-#ight spectroscopy.

The TOF measurements were done at the spectro-meter SPAN of BENSC [6]. The incident wavelength of5.5 As was selected by a system of four choppers and theresolution of the spectrometer was 0.55 meV FWHM.One of the three detector banks of the spectrometer, withan opening of 253, was centred at the incident beam andthe spectra were collected for positive as well as fornegative scattering angles (0.08 A~1)q)0.27 As ~1).The resolution was determined from separate measure-ments on a reference vanadium sample, which hada thickness of 1 mm and the same area in the beam as theCuMn sample. The vanadium spectra were also used forthe calibration of the spectrometer, i.e. the determinationof the neutron scattering cross section from the countingrate. The background contribution was estimated fromseparate measurements of a cadmium sample and of theempty sample container.

Well above the spin-glass temperature, ¹'"27 K, the

TOF spectra of CuMn 4.7% are a superpositionof a strong elastic non-magnetic contribution and of

544 F. Mezei et al. / Physica B 276}278 (2000) 543}546

Fig. 1. Magnetic scattering cross section of a single-crystallineCuMn 4.7% sample around q"0. The result at 2 K (closedcircles) was obtained with three directional neutron polarisationanalysis at cold neutron NSE spectrometer IN15 at ILL. Thedata for 100 K (open rhombi) were determined with TOF spec-troscopy at the spectrometer SPAN of BENSC. Also shown isthe q"0 cross section from the bulk susceptibility at ¹'¹

'(closed square) and previous data from [7] (closed triangles).The line is a guide to the eyes.

Fig. 2. Temperature dependence of the line width C (HWHM) ofthe broad quasi}elastic magnetic scattering as seen in the TOFspectra of the single-crystalline CuMn 4.7% well above itsspin-glass temperature ¹

'. The result is comparable to that

found on polycrystalline CuMn 8% [8].

a broad quasi-elastic magnetic part. Within the q-rangecovered by these measurements we did not "nd anysigni"cant q-dependence of the inelastic line width andline shape, which was consistent with a Lorentzian form.The q dependence of the magnetic signal S(q) was deter-mined by assuming a common Lorentz function in en-ergy with a common C over the covered q range. Theresults in Fig. 1 show that S(q) is practically independentof the temperature between 2 K (where quasi-elasticpolarisation analysis works well) and 100 K (where TOFis a reliable approach). The S(q) data are in agreementwith previous results for q*0.3 As ~1 [7] and extrapolateon qP0 to the value expected from the macroscopicsusceptibility of the very same sample at ¹'¹

'. As

pointed out previously, below ¹'

the susceptibility ofspin glasses does not see the whole magnetism, thereforeit cannot be compared with S(q) at 2 K. The temperaturedependence of the line width C (HWHM) is shown inFig. 2 and is comparable to that found on a polycrystal-line CuMn 8% sample [8].

These results strikingly con"rm that in single-crystal-line Cu}Mn alloys there is the same amount of ferromag-netic short-range order as in the better homogenised,quenched polycrystalline ones and it coexists with theantiferromagnetic SDW like short-range order. The fer-romagnetic short-range order is impressively temper-ature independent below 100 K. The only thing thatchanges with temperature is the dynamics and the resultis very similar to that obtained by earlier NSE investiga-tions on a polycrystalline CuMn 5% sample [1]. It is

therefore unambiguous that the cusp in the susceptibilityaround 27 K is due to the slowing down of the dynamics,expressed by s(q, t), and not to the build up of an antifer-romagnetic short-range order, which would lead to adecrease of S(qP0) by the NeH el mechanism. In otherwords the macroscopic magnetic behaviour of Cu}Mnsingle crystals (at least in the 5% concentration range) isdominated by the spin-glass nature of these samples andde"nitely not by the SDW short-range order suggested inRef. [3].

The existence of a complex short-range order witha weak temperature dependence, while the macroscopicproperties vary vastly due to changes in dynamics, isa common feature of spin glasses and ordinary (struc-tural) glasses. There is, however, a systematic di!erencein the evolution of the glassy slowing down. In glasses,over a broad range of temperatures, the relaxation func-tion s(q, t) tends to have the same functional shape, whichis described by a constant Kohlrausch exponent b(1characterising the stretching of the relaxation [9]. In spinglasses, on the other hand, above ¹

'the relaxation line

shape is consistent with a distribution of Arrhenius ac-tivation energies ranging from 0 to about 10 k¹

'[1]

s(q, t)+Pe~t@q %91(E@kT) dE, (2)

where q is a constant. This corresponds to a rapiddecrease of the e!ective Kohlrausch exponent b withdecreasing temperature from 1 at ¹A¹

'to about 0.3 at

¹'[10]. Below ¹

'the slowing down of relaxation is more

rapid than the one predicted by Eq. (2).Another common point of interest in the neutron stud-

ies of both spin glasses and ordinary glasses is in thelength scale of collective glassy behaviour. Experiments

F. Mezei et al. / Physica B 276}278 (2000) 543}546 545

and their interpretation are quite di$cult since, in theabsence of a long-range (magnetic or structural) order,correlations are of a dynamic nature. Recent progress inextending the q range of inelastic neutron scatteringexperiments in structural glasses showed indeed thatthere are substantial dynamic correlations on an inter-mediate length scale, several times longer than the distan-ces between nearest neighbours [11]. In spin glasses wefollowed an indirect approach and examined the ferro-magnetic critical correlation lengths in Au}Fe alloys,with a composition very close to the percolation thre-shold, where ferromagnetism is replaced by a spin-glassphase. The surprising result was that the disorder enhan-ces the range of critical #uctuations instead of sup-pressing them [12]. The correlation length and the vol-ume susceptibility are much larger in the disorderedAu}Fe systems than in ordinary ferromagnets. This leadsto an exceptionally wide critical region and reminds oneof the situation in spin glasses [13], suggesting that thedynamic correlation lengths in spin glasses might e!ec-tively also be very long, maybe 100 As or more, and thusproviding the "rst circumstantial evidence for the theor-etically predicted extremely long correlation lengths atthe spin-glass transition [14].

References

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[5] F. Mezei, in: F. Mezei (Ed.), Neutron Spin Echo, Springer,Heidelberg, 1980, p. 3.

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