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Insulating and metallic spin glasses: a comparative study of the dynamics by neutron scattering
Journal of Magnetism and Magnetic Materials 104- il)7 (1992) 1627-1628 North-ttolland
,M"
Insulating and metallic spin glasses: a comparative study of the dynamics by neutron scattering C. Bellouard, M. Hennion, I. Mirebeau and B. Hennion Laboratoire Leon Brillouin (CEA-CNRS), CE-Sacho', 91191 Gif-sur-Yrette cedo., France By inelastic neutron scattering, we have performed a comparative study of the spin dynamics in a metallic spin glass (Fe~t_,~Mn,)vsPI~B~,AI 3 (x = I).41) and in an insulating one, AI,MnsSi4Ot~,. in both systems, in addition to the usual behaviour observed in spin glasses, we observed a minimum close to 7"(; in the temperature dependence of the quasielastic linewidth. This minimum reveals the presence of fast fluctuations below Tc~.This feature, already observed in a dilute alloy (CuMn), seems to be characteristic of spin glass freezing. Two physical pictures are proposed to account for the surprising variation of I'. In spin glasses, the most convincing argument in favor of a genuine transition at a nonzero temperature has been provided by the divergence of the nonlinear susceptibility. D y n a m i c studies have clearly shown the existence of a large distribution of relaxation times, but have failed for a long time in determining a transition temperature. More recently, thanks to a theoretical model of fractal clusters [1,2], some of those experimcnts (lsSR, spin echo, dc susceptibility) have also been related to the occurrence of a phasc transition
tion comes from short range exchangc interactions, we observe at low angle an incrcase of the quasielastic intensity between 300 and 100 K (inset fig. 1) indicating the onset of ferromagnetic correlations. The increase of C~ in the same temperature range is related to a D e b y e - W a l l e r thcrmal variation. Below about 70 K,
1, i
~
i \
(THz]
q= 0.2 ,~
3i; \
,
i
o-1
q = O.z;5,,q/
',,
[31. Previous inelastic neutron scattering in a dilute alloy (CuMn) have shown that the mean relaxation time measured within the experimental window shows an anomalous behaviour, namely it presents a maximum at a temperature :lose to T(; [4]. Focusing on the temperature d e p e n d e n c e of this mean relaxation time, we have studied two others spin glasses: a concentrated metallic alloy and an insulating compound. These experiments were per" ~ed at O r p h e e (Saclay) using a three-axes spectrometer (4F1) and a time of flight spectrometer (Mibemol). In a neutron scattering experiment, the magnetic fluctuations yield a quasielastic signal which is usually fitted by a Lorenzian law neglecting the distribution of relaxation times. The total cross section is written as:
/+
21; /' . . . . . . .., t
"
/,
, /
tIK~ T /
/
1
q-°"x;i/
Kv
S(q, ,o)= c ' , ( q ) a ( , o ) + C , ( q ) - Ki hto/kT X exp(hw/kT)-
! 1
"rr 1 "2 +
h2(o 2"
00
kot
I 150
~ _ _ _ £ _ _ _ _
0
where K ! and K F arc the incident and final wave vector, h(w) is the energy gain of the neutron. C I is the elastic intensity, C 2 the quasielastic intensity (C 2 = F2(q)kT x(q)) and F is the energy linewidth ( F = 1 / 2 ~ r where r is the mean relaxation time measured within the experimental window). In the metallic a-FeMn sample where the frustra-
T(')
T,-
F
50
lifO
Fig. I. Temperature dependence
_
i 200
__L__
250
of the quasiela: ic linewidth
in (Fe(1 ~,IMn,)vsPv, B~,AI~ (x = 0.41) for sere" iI q values. q=0.1 A-~ and q = 0 . 2 A-~ have been peril reed with a 3-axes spectrometer (4FI), q = 0.45 ,~ ~ with t TOF spectrometer (Mibemol). In the inset is plotted th, temperature dependence of the elastic C~ and quasielastic ( intensity for
0312-8853/92/$05.00 O 1992 - Elsevier Science Publishers B.V. All rights reserved
q = (1.2,A
~
1628
(i Belhmard et al. / hzsulating and metallic spin g/asses
wc observe a t'urther increase of C t concomitantly with a decrease of C, which is as usual attributed to a freezing process [4]. As the spins frcczc, a part of the quasiclastic signal becomes resolution limited and is thus transferred to the elastic peak. The temperature where this transfer occurs depends on the resolution of the spectrometer. At this temperature, the maximum relaxation time of the distribution becomes larger than the neutron time scale (1 x 10- ~ s for a resolution of 0.014 Tl4z). The quasielastic linewidth F (fig. 1) firstly decreases with decreasing temperature. In a metallic spin glass, this can be related to the coupling with conduction electrons (Korringa effect) or to the freezing process. Then F goes through a minimum and increases steeply at low temperature. This is very reminiscent of the shallow minimum observed in CuMn [4]. The tetrlperature of the occurrence of the minimum seems to bc q-dependent and is slightly higher than T¢~ ( = 35 K). This increase of F at low temperature reveals the existence of fast fluctuations which coexist with the spin freezing as indicated by the variation of C I and C.~. In the insulating sample AI2MnsSi4OI,, the q-dependence of the magnetic intensity is rather different tllan in the metallic sample. Wc observe a diffuse peak at q = i.5 ,~,-= characterizing short range antifcrromagnetic correlations. Energy scans performed for q = 1.5 A-= could be fitted by a Lorcntzian shape, except for temperatures around 20 K. This could bc duc to a deviation of the magnetic signal from the Lorentzian ~hapc or to an experimental problem. These points have not bccn mentioned in fig. 2. The temperature dependence of (?~ and the quasiclastic intensity indicates a freezing process as in the metallic sample. Thc distribution of relaxation times enters the resolution window below 15 K. With decreasing temperature, F firstly decreases in agreement with an Arrhenius law F = ['. e x p ( - E / k T ) with 1~ = 1.19 THz (~-. = 1.3 × 10 13 s) and E = 3.3 meV (inset fig. 2). Below 15 K, whereas the distribution of relaxation times enters the resolution window, F goes through a large minimum close to TG (= 5.3 K) (fig. 2). In a previous work on a similar sample [5], the spin freezing was described by an Arrhenius law even bclow To; although a distribution of relaxation times was suspected. The present study is in good agreement in the high tcmperature ,,-g . . . . . u,.,,.,,-p,t,,~, . . . . . s. at. .IOW . .*. . . .p. . . . . ~. .... . . . is duc to the higher resolution of the spectrometer used in [5] which prevented the exploration of a sufficiently large energy window. The variation of F below TG, as evidenced in several spin glasses, reveals the presence of fast fluctuations in the spin glass state which could be explained by a dclormation of the distribution of relaxation times. The fractal cluster model gives a physical picture for
0.4
_.= .....
=_
...........
1 :"~:,e.~
, Ki=2.a62A'I :\
K i=l.~:i't
/
0,3
"r-
0,1
1/T~( ~ K ~" )
-
~.,,~,,0.2
o.o---2oi04
o
f ~
. o.o6
~" o.d~//
L_ "
1"
/
0.1
÷
& 0
I
0
Ki:1.4A'1
Temperature (K) ~0
,
I
20
f
I
30
, 40
Fig. 2. Temperature dependence of the quasielastic linewidth I" in AI2Mn.~Si40,,, for q= 1.5 ,~--t (performed with a 3-axes spectrometer). K ! = 1.4 ,~-i corresponds to a resolution of I).015 THz, K I = 2.66 ~,- t to 0.12 THz. The straight line in the inset corresponds to the fit with an Arrhenius law between 15 and 300 K. this dct'ormation [1,2]. The spins arc supposed to bc rigidly coupled in uncorrelatcd clusters; the relaxation time of each cluster is directly related to its size. Above TG, with decreasing temperature, the clusters grow and their relaxation times increase. At TG, the maximum relaxation time diverges with the formation of a percolating "infinite" cluster. Below Tc;, as this static percolating cluster grows, the size of the remaining dynamic clusters decreases as well as their relaxation time,,. By taking into account the influence of the experimental window, we expect a maximum of the averaged mcasurcd relaxation time ncar T~;, and thus a minimum of I'. This model has bccn quite satisfactorily applied to spin echo and t~SR mcasurcmcnts [3]. Wc arc currcnlly t13,ing to apply it to our results. In an other picture, already proposed by Murani [4], the fast fluctuations at low temperature could be due to excitations of the spins which fluctuate around their mean equilibrium position as soon as the relaxation of the cluster is too slow for the neutron probe. F below TG could thcn bc a measure of the stiffness of the system. We arc thankful to J. Prcjean and to M. Oci(~ fi)r helpful discussions and for providing us samples. Relerences
[1] A.P. Malozemoff and B. Barbara, J. Appl. Phys. 57 (1985) 341(I. [2] P. Beauvillain, J.P. Renard, M. Matecki and J.J. Prejean, Europhys. Left. 2 (1986) 23. [3] H. Pinkvos, A. Kalk and Ch. Schwink, Phys. Re~,. B 41 (1990) 540. [41 A.P. Murani J. de Phys. 39 (1978) 1517. [5] W. Nagele, Z. Phys. B 42 (1981) 135.
,M"
Insulating and metallic spin glasses: a comparative study of the dynamics by neutron scattering C. Bellouard, M. Hennion, I. Mirebeau and B. Hennion Laboratoire Leon Brillouin (CEA-CNRS), CE-Sacho', 91191 Gif-sur-Yrette cedo., France By inelastic neutron scattering, we have performed a comparative study of the spin dynamics in a metallic spin glass (Fe~t_,~Mn,)vsPI~B~,AI 3 (x = I).41) and in an insulating one, AI,MnsSi4Ot~,. in both systems, in addition to the usual behaviour observed in spin glasses, we observed a minimum close to 7"(; in the temperature dependence of the quasielastic linewidth. This minimum reveals the presence of fast fluctuations below Tc~.This feature, already observed in a dilute alloy (CuMn), seems to be characteristic of spin glass freezing. Two physical pictures are proposed to account for the surprising variation of I'. In spin glasses, the most convincing argument in favor of a genuine transition at a nonzero temperature has been provided by the divergence of the nonlinear susceptibility. D y n a m i c studies have clearly shown the existence of a large distribution of relaxation times, but have failed for a long time in determining a transition temperature. More recently, thanks to a theoretical model of fractal clusters [1,2], some of those experimcnts (lsSR, spin echo, dc susceptibility) have also been related to the occurrence of a phasc transition
tion comes from short range exchangc interactions, we observe at low angle an incrcase of the quasielastic intensity between 300 and 100 K (inset fig. 1) indicating the onset of ferromagnetic correlations. The increase of C~ in the same temperature range is related to a D e b y e - W a l l e r thcrmal variation. Below about 70 K,
1, i
~
i \
(THz]
q= 0.2 ,~
3i; \
,
i
o-1
q = O.z;5,,q/
',,
[31. Previous inelastic neutron scattering in a dilute alloy (CuMn) have shown that the mean relaxation time measured within the experimental window shows an anomalous behaviour, namely it presents a maximum at a temperature :lose to T(; [4]. Focusing on the temperature d e p e n d e n c e of this mean relaxation time, we have studied two others spin glasses: a concentrated metallic alloy and an insulating compound. These experiments were per" ~ed at O r p h e e (Saclay) using a three-axes spectrometer (4F1) and a time of flight spectrometer (Mibemol). In a neutron scattering experiment, the magnetic fluctuations yield a quasielastic signal which is usually fitted by a Lorenzian law neglecting the distribution of relaxation times. The total cross section is written as:
/+
21; /' . . . . . . .., t
"
/,
, /
tIK~ T /
/
1
q-°"x;i/
Kv
S(q, ,o)= c ' , ( q ) a ( , o ) + C , ( q ) - Ki hto/kT X exp(hw/kT)-
! 1
"rr 1 "2 +
h2(o 2"
00
kot
I 150
~ _ _ _ £ _ _ _ _
0
where K ! and K F arc the incident and final wave vector, h(w) is the energy gain of the neutron. C I is the elastic intensity, C 2 the quasielastic intensity (C 2 = F2(q)kT x(q)) and F is the energy linewidth ( F = 1 / 2 ~ r where r is the mean relaxation time measured within the experimental window). In the metallic a-FeMn sample where the frustra-
T(')
T,-
F
50
lifO
Fig. I. Temperature dependence
_
i 200
__L__
250
of the quasiela: ic linewidth
in (Fe(1 ~,IMn,)vsPv, B~,AI~ (x = 0.41) for sere" iI q values. q=0.1 A-~ and q = 0 . 2 A-~ have been peril reed with a 3-axes spectrometer (4FI), q = 0.45 ,~ ~ with t TOF spectrometer (Mibemol). In the inset is plotted th, temperature dependence of the elastic C~ and quasielastic ( intensity for
0312-8853/92/$05.00 O 1992 - Elsevier Science Publishers B.V. All rights reserved
q = (1.2,A
~
1628
(i Belhmard et al. / hzsulating and metallic spin g/asses
wc observe a t'urther increase of C t concomitantly with a decrease of C, which is as usual attributed to a freezing process [4]. As the spins frcczc, a part of the quasiclastic signal becomes resolution limited and is thus transferred to the elastic peak. The temperature where this transfer occurs depends on the resolution of the spectrometer. At this temperature, the maximum relaxation time of the distribution becomes larger than the neutron time scale (1 x 10- ~ s for a resolution of 0.014 Tl4z). The quasielastic linewidth F (fig. 1) firstly decreases with decreasing temperature. In a metallic spin glass, this can be related to the coupling with conduction electrons (Korringa effect) or to the freezing process. Then F goes through a minimum and increases steeply at low temperature. This is very reminiscent of the shallow minimum observed in CuMn [4]. The tetrlperature of the occurrence of the minimum seems to bc q-dependent and is slightly higher than T¢~ ( = 35 K). This increase of F at low temperature reveals the existence of fast fluctuations which coexist with the spin freezing as indicated by the variation of C I and C.~. In the insulating sample AI2MnsSi4OI,, the q-dependence of the magnetic intensity is rather different tllan in the metallic sample. Wc observe a diffuse peak at q = i.5 ,~,-= characterizing short range antifcrromagnetic correlations. Energy scans performed for q = 1.5 A-= could be fitted by a Lorcntzian shape, except for temperatures around 20 K. This could bc duc to a deviation of the magnetic signal from the Lorentzian ~hapc or to an experimental problem. These points have not bccn mentioned in fig. 2. The temperature dependence of (?~ and the quasiclastic intensity indicates a freezing process as in the metallic sample. Thc distribution of relaxation times enters the resolution window below 15 K. With decreasing temperature, F firstly decreases in agreement with an Arrhenius law F = ['. e x p ( - E / k T ) with 1~ = 1.19 THz (~-. = 1.3 × 10 13 s) and E = 3.3 meV (inset fig. 2). Below 15 K, whereas the distribution of relaxation times enters the resolution window, F goes through a large minimum close to TG (= 5.3 K) (fig. 2). In a previous work on a similar sample [5], the spin freezing was described by an Arrhenius law even bclow To; although a distribution of relaxation times was suspected. The present study is in good agreement in the high tcmperature ,,-g . . . . . u,.,,.,,-p,t,,~, . . . . . s. at. .IOW . .*. . . .p. . . . . ~. .... . . . is duc to the higher resolution of the spectrometer used in [5] which prevented the exploration of a sufficiently large energy window. The variation of F below TG, as evidenced in several spin glasses, reveals the presence of fast fluctuations in the spin glass state which could be explained by a dclormation of the distribution of relaxation times. The fractal cluster model gives a physical picture for
0.4
_.= .....
=_
...........
1 :"~:,e.~
, Ki=2.a62A'I :\
K i=l.~:i't
/
0,3
"r-
0,1
1/T~( ~ K ~" )
-
~.,,~,,0.2
o.o---2oi04
o
f ~
. o.o6
~" o.d~//
L_ "
1"
/
0.1
÷
& 0
I
0
Ki:1.4A'1
Temperature (K) ~0
,
I
20
f
I
30
, 40
Fig. 2. Temperature dependence of the quasielastic linewidth I" in AI2Mn.~Si40,,, for q= 1.5 ,~--t (performed with a 3-axes spectrometer). K ! = 1.4 ,~-i corresponds to a resolution of I).015 THz, K I = 2.66 ~,- t to 0.12 THz. The straight line in the inset corresponds to the fit with an Arrhenius law between 15 and 300 K. this dct'ormation [1,2]. The spins arc supposed to bc rigidly coupled in uncorrelatcd clusters; the relaxation time of each cluster is directly related to its size. Above TG, with decreasing temperature, the clusters grow and their relaxation times increase. At TG, the maximum relaxation time diverges with the formation of a percolating "infinite" cluster. Below Tc;, as this static percolating cluster grows, the size of the remaining dynamic clusters decreases as well as their relaxation time,,. By taking into account the influence of the experimental window, we expect a maximum of the averaged mcasurcd relaxation time ncar T~;, and thus a minimum of I'. This model has bccn quite satisfactorily applied to spin echo and t~SR mcasurcmcnts [3]. Wc arc currcnlly t13,ing to apply it to our results. In an other picture, already proposed by Murani [4], the fast fluctuations at low temperature could be due to excitations of the spins which fluctuate around their mean equilibrium position as soon as the relaxation of the cluster is too slow for the neutron probe. F below TG could thcn bc a measure of the stiffness of the system. We arc thankful to J. Prcjean and to M. Oci(~ fi)r helpful discussions and for providing us samples. Relerences
[1] A.P. Malozemoff and B. Barbara, J. Appl. Phys. 57 (1985) 341(I. [2] P. Beauvillain, J.P. Renard, M. Matecki and J.J. Prejean, Europhys. Left. 2 (1986) 23. [3] H. Pinkvos, A. Kalk and Ch. Schwink, Phys. Re~,. B 41 (1990) 540. [41 A.P. Murani J. de Phys. 39 (1978) 1517. [5] W. Nagele, Z. Phys. B 42 (1981) 135.