Journal of Magnetism and Magnetic Materials 177 181 (1998) 602 604 Journal Of magnetism and magnetic

J H materials ELSEVIER

Moment localisation in 13-MnA1

J.R. Stewart*, A.D. Hillier, S.H. Kilcoyne, P. Manuel, M.T.F. Telling, R. Cywinski School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, Scotland, UK

Abstract

laSR has been used to map the magnetic phase diagram of 13-Mn1-xAlx and to investigate the evolution of spin fluctuations with increasing AI concentration. There is a marked change in the spin fluctuation spectrum at x = 0.08, below which simple exponential relaxation is observed, while for higher concentrations Kohlrausch relaxation, asso- ciated with spin-glass behaviour is found. This change is accompanied by a sudden increase in the magnetic transition temperature. © 1998 Elsevier Science B.V. All rights reserved.

Keywords." Itinerant electrons spin fluctuations; Magnetic moment - formation; Muon spin relaxation

[3-Mn is the only stable allotrope of elemental Mn which does not support a magnetic moment at any tem- perature. However, inelastic neutron scattering, heat ca- pacity and NMR measurements all indicate the presence of strong antiferromagnetic spin fluctuations associated with Mn moments on the verge of localisation (see e.g. Ref. [1]). Indeed partial substitution of A1 in [3-Mn re- sults in a marked narrowing of the inelastic neutron scattering linewidth, moment localisation at the Mn sites, and a the onset of a spin-glass-like state at low temper- atures [1]. This behaviour is similar to that of the C15 Laves-phase system (YSc)(Mnl _,~Alx)2, for which a quan- tum spin-liquid to spin-glass transition has been invoked [2]. Muon spin relaxation (laSR) has previously provided useful insights into the nature of spin fluctuations and moment localisation in YMn2 and related compounds [3]. Here we employ similar zero-field ~tSR techniques to study the evolution of the spin fluctuations with increas- ing A1 substitution in 13-Mn.

Alloys of Mnl xAl~ with 0 ~< x ~< 0.2 were prepared by argon arc melting. The 13-phase was stabilised at room temperature by annealing at 950°C for 24 h and quench- ing into water. The samples were powdered and phase purity confirmed by X-ray diffraction. Zero-field laSR measurements were performed at the ISIS pulsed muon facility using the EMU and RIKEN-ARGUS +g spec- trometers. The resulting ~tSR spectra, suitably nor-

* Corresponding author. Tel.: + 44 1334 463108; fax: + 44 1334 463104; e-mail: rc@isise.rl.ac.uk.

malised and corrected for background originating from muons stopping outside the sample, could all be de- scribed by the depolarisation function

P~(t) = ao[½ + ~ ( 1 - a2t2)e-('2'~/Z)Je-(a°[ (1)

The term in square brackets is the static Kubo Toyabe (KT) function which accounts for the muon depolarisa- tion due to the distribution of static nuclear dipolar fields. The second term arises from rapidly fluctuating atomic spins. In the motionally narrowed limit, the de- polarisation rate 2 is related to the second moment of the distribution of atomic fields, (B~)1/2, and the fluctuation rate of these fields, l/z, by the relation 2 = 27 .2(B.25z.

For pure 13-Mn a nuclear depolarisation rate of a = 0.32 ~t s - 1 was obtained at all temperatures indicat- ing an essentially static muon. Depolarisation due to atomic spin fluctuations also proved to be temperature independent and simple exponential in form, with [3 = 1, and 2 = 0.02 ~t s - i A temperature-independent 2 is fully consistent [3, 4] with the observation of an almost tem- perature independent inelastic neutron linewidth for 13- Mn [1]. No evidence of either local moments or a static magnetic ground state were found down to 1.6 K. As A1 is substituted into [3-Mn the KT contribution to the de- polarisation remains relatively unchanged with increas- ing concentration, whilst that arising from the fluctuating atomic moments is substantially modified. For 0 < x ~< 0.08 simple exponential relaxation (/~ = 1) is ob- served at all temperatures, but now 2 diverges towards

0304-8853/98/$19.00 ~C2) 1998 Elsevier Science B.V. All rights reserved PII S 0 3 0 4 - 8 8 5 3 ( 9 7 ) 0 0 7 0 7 - 5

J.R. Stewart/Journal of Magnetism and Magnetic Materials 177 181 (1998) 602-604 603

low temperatures, as can be seen in Fig. la where the results for the x = 0.06 alloy are shown. This again is consistent with neutron studies, which show a pronounced decrease in the inelastic linewidth with decreasing tem- perature in Al-substituted [3-Mn [1]. As 2 diverges the initial asymmetry, ao, correspondingly decreases to 13 of its high-temperature value of 0.21. This is a clear indica- tion of the onset of an essentially static magnetic ground state at low temperatures, although residual exponential depolarisation indicates the persistence of spin fluctu- ations well into the low-temperature state. The asso- ciated magnetic-transition temperatures, determined from the divergence of 2 and loss of asymmetry, are plotted on the magnetic phase diagram of Fig. 2.

As the inelastic neutron scattering linewidth of [3-MnA1 alloys is only weakly dependent upon scattering vector [1] it is possible to describe 2(T) within the framework of a model originally established for Y(MnAI)2 [3, 4] in which an Arrhenius-like activation of spin fluctuations and a Curie-Weiss-like local (i.e. Brillouin zone-averaged) susceptibility is assumed. The fit of this model to 2(T) is shown in Fig. la for the x = 0.06 alloy. The significance of this behaviour will be discussed in detail elsewhere.

For A1 concentrations beyond x = 0.08, the muon depolarisation arising from the atomic spin fluctuations exhibits a distinct change of character. The full stretched exponential form of the depolarisation function is now required to describe the spectra, fl is found to decrease slowly from unity at high-temperatures reaching approx- imately 0.3 at the transition temperature. Such a response is characteristic of concentrated spin-glass systems, and reflects a non-exponential or Kohlrausch spin autocorre- lation function associated with a broadening distribution of spin-relaxation rates as the temperature is lowered [3 5]. Over the range 0.08 < x ~< 0.20 the temperature dependence of 2 has a similar modified Arrhenius form to that determined for x ~< 0.08, as can be seen in Fig. lb for the x = 0.15 alloy. However, it should be noted that the transition temperatures associated with the divergence of 2 are now considerably higher than those obtained at lower concentrations.

These pSR experiments provide clear evidence of mo- ment localisation in [3-Mn resulting from A1 substitution. Such localisation leads to a marked reduction in the spectral width of spin fluctuations in the paramagnetic state and to the onset of a magnetic ground state at low temperatures. Although this ground state appears to be largely static, at least on the time scale of the pSR technique, there is clear evidence of spin fluctuation per- sisting to the lowest temperatures. The dramatic change in the character of the spin-fluctuation spectrum close to 8 at%A1 is quite remarkable: simple exponential relax- ation gives way to Kohlrausch relaxation with a corres- ponding marked increase in the magnetic transition temperature. It is tempting to interpret such behaviour in terms of a quantum spin-liquid to spin-glass transition.

0.4

0.3

0.2

0.1

0.0 0

~ ~ 1.4

0.20 i ~ • 5K : 1° K 1.2

i o15

1.0

o.oo 0.6

0.4

0.2

a) . b ) ~ 0.0 10 20 30 40 50 60 0 50 100 150 200 250

Temperature (K)

Fig. l. Temperature dependence of the depolarisation rate 2 for [3-Mnl xMnx with (a) x = 0.06 and (b) x = 0.15. The solid line in both figures shows the fit of the modified Arrhenius law to the data. The insets show the pSR spectra for each sample at several temperatures. The solid lines are a fit of Eq. (1) to the spectra.

50

4O 9

30

I-- 2O

10 I--

0 0

I I I I I I I I I

"Simple Exponential" X

i , , , , ~ , , , ,

"Stretched Exponential" i

k , , , i h i i i I r i i i 5 10 15 20

AI C o n c e n t r a t i o n (a t .%)

Fig. 2. The magnetic phase diagram of [~-Mnl xAlx determined by the pSR measurements. The transition from simple to stretched exponential muon spin depolarisation is indicated by the dotted line.

Within this model simple exponential relaxation, asso- ciated principally with longitudinal (amplitude) spin fluc- tuations, dominate the muon depolarisation at low A1 concentrations. At higher concentrations the muon re- sponse is dominated by a broad distribution of relaxation rates. It is likely that these arise from the increasingly well localised, interacting, but topologically and exchange frustrated Mn spins which, at low temperatures, form a concentrated spin-glass-like state. The precise nature of the magnetic ground state in the range 0 ~< x ~< 0.2 re- mains unclear. Our own neutron polarisation analysis measurements on 13-Mnl xAlx exclude the possibility of long-range magnetic order at any concentration and do not reveal any marked change in static short-range spin correlations as the x = 0.08 boundary is crossed.

604 J.R. Stewart~Journal of Magnetism and Magnetic Materials 177-181 (1998) 602 604

References

[1] M. Shiga, H. Hiroyuki, M. Nishi, K. Kakurai, J. Phys. Soc. Japan 63 (1994) 1656.

[-2] M. Shiga, K. Yoshimoto, H. Nakamura, H. Wada, J. Phys. Soc. Japan 62 (1993) 1329.

[3] R. Cywinski, B.D. Rainford, Hyperfine Interactions 85 (1994) 215.

[4] B.D. Rainford, R. Cywinski, S.J. Dakin, J. Magn. Magn. Mater. 140-144 (1995) 805.

[5] I.A. Campbell, A. Schenck, D. Herlach, F.N. Gygax, A. Amato, R. Cywinski, S.H. Kilcoyne, Phys. Rev. Lett. 72 (1994) 1291.