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Spin freezing in the re-entrant spin glass FeNiMn close to the frustration limit
ARTICLE IN PRESS
Physica B 397 (2007) 105–107 www.elsevier.com/locate/physb
Spin freezing in the re-entrant spin glass FeNiMn close to the frustration limit Catherine Pappasa, Jens Klenkea, Ju¨rgen Hesseb, Volker Wagnerc, a
Hahn-Meitner-Institut, Glienickerstr. 100, 14109 Berlin, Germany Institut fu¨r Metallphysik und Nukleare Festko¨rperphysik, Technische Universita¨t Braunschweig, 38106 Braunschweig, Germany c Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
b
Abstract In the invar alloy (Fe0.65Ni0.35)1xMnx we measured the magnetic form factor s(Q) and the intermediate scattering function s(Q,t) for a sample close to the critical Mn concentration (xc ¼ 0.139), at which the sample turns to a re-entrant spin glass phase. The aim was to check whether the magnetic behaviour would approach the Q-independent relaxation behaviour of a classical spin glass when x ¼ xc. The experiment showed a quite similar spin freezing as for a more ferromagnetic sample with x ¼ 0.113. The intermediate scattering function and the form factor were determined by paramagnetic NSE. The normalized scattering function S(Q,t) ¼ s(Q,t)/ s(Q) ¼ exp[(gt)n] was fitted by stretched exponential decay. As a function of temperature To200 K the inverse time constant g showed the change of more than four orders of magnitude from frozen spin glass (T ¼ 60 K to T ¼ 100 K), where the ferromagnetic phase occurred. In general, the inverse time constant is higher than in the more ferromagnetic sample as the frustration of the spins became larger. In the ferromagnetic phase S(Q,t) depended on 0.3oQo1.3 nm1, and this spin diffusive behaviour remained in the reentrant spin glass down to at least 60 K. r 2007 Elsevier B.V. All rights reserved. PACS: 75.50.L; 78.70.Nx; 75.50.Bb Keywords: Re-entrant spin glass; Spin freezing; Neutron spin echo; FeNiMn
1. Introduction In re-entrant spin glass (RSG) systems, ferromagnetic and spin glass correlations can coexist and it is well known that the latter are easily destroyed by small magnetic fields; therefore, dynamical studies can shed new light on this intriguing coexistence. In the invar alloy (Fe0.65Ni0.35)1xMnx—a well-known RSG system [1]—we measured the magnetic form factor s(Q) and the magnetic intermediate scattering function s(Q,t) for a sample close to the critical Mn concentration (xc ¼ 0.139). Upon cooling from the ferromagnetic state the sample can form a mixed spin glass containing both a ferromagnetic and a spin glass state, while for x4xc a spin glass system was expected. The aim has been to check whether the magnetic behaviour Corresponding author. Tel.: +49 531 5926550.
E-mail address: [email protected] (V. Wagner). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.02.062
would approach the Q-independent relaxation behaviour of a classical spin glass when x approaches xc. A more ferromagnetic sample with x ¼ 0.113 studied in the previous experiment [2,3] displayed a remarkable Q dependent diffusive behaviour in the RSG state. In the experiment presented here, however, a similar behaviour somewhat less Q-dependent, was observed for a ferromagnetic sample with x ¼ 0.13970.001. 2. Experimental results The experience was done with the SPAN instrument at HMI with 0.65 nm wavelength. The instrumental resolution was measured at 2 K. Decreasing the temperature the depolarization of the transmitted beam indicated that the sample was slightly ferromagnetic (TcE200 K) close to the frustration limit. This was not observed neither by neutron depolarization at smaller wavelength nor by small-angle
ARTICLE IN PRESS C. Pappas et al. / Physica B 397 (2007) 105–107
106
scattering [4]. It gradually lost the ferromagnetic order due to the onset of the freezing of the transverse components of the frustrated spins for To90 K. At 50 K the strongly irreversible RSG phase was reached. The sample was 4.9 mm thick and in a small magnetic field of about 2 A/cm. The intermediate scattering function and the form factor were determined by paramagnetic NSE techniques for 0.3 nm1oQo1.3 nm1 and 40 KoTo240 K. Fig. 1 shows the time evolution of the normalized intermediate scattering function sðQ; tÞ ¼ exp½ðgtÞn . sðQÞ
(1)
Stretched exponentials fitted to the data describe the time dependence quite well except for TX200 K, where the data are too small for decent values. The spin diffusive behaviour found in the ferromagnetic phase (200 K4T490 K) is still observed in the RSG phase (To60 K), which is a mixed phase of simultaneous ferromagnetic and spin glass order. At 40 K in the lower
a
1.0
104
40K 60K 80K 100K 120K 140K 160K 180K 200K 220K 240K
0.7 S(Q,tNSE)
40K 60K 80K 100K 120K 140K 160K 180K 200K 220K 240K
103
0.8 0.6 0.5 0.4 0.3 0.2 0.1
102 101 100 10-1 10-2 10-3 10-4 10-5 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Q / nm-1 0.1
1
Fig. 2. The inverse time constant g vs. the wave vector transfer Q. At To60 K the system is frozen. At T4100 K there is a change by a factor 104 w.r.t. low temperature. The lines are a guide to the eyes.
tNSE / ns
b
In Fig. 2, the observed inverse correlation time g is shown as a function of scattering vector Q. Obviously the sample seems to be ferromagnetic, when observed with long wavelength neutrons close to the frustration limit in a small field, and the same behaviour is found as for x ¼ 0.113 [3]. It appears that the mean inverse correlation time g has been increased by more than an order of magnitude in comparison with the ferromagnetic sample x ¼ 0.113 [3]. This fact is due to the smaller size of correlated spins in a mean domain size. Also the difference between the strongly irreversible RSG phase and the ferromagnetic phase has become larger by about a factor of 104, showing the influence of a large difference of ferromagnetic and spin glass phase and the effect of the spin freezing in the more dilute sample.
Q = 0.495 nm-1
0.9
0.0 0.01
3. Discussion
/ns-1
SðQ; tÞ ¼
mixed phase the spins are almost completely frozen within the time window observed in the experiment.
Q = 1.037 nm-1 1.0 0.8
S(Q,tNSE)
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.01
1
0.1 tNSE / ns
Fig. 1. The normalized intermediate scattering function S(Q,tNSE) of (Fe0.65Ni0.35)0.86Mn0.14 weakly depends on the scattering vector: (a) Q ¼ 0.495 nm1 and (b) Q ¼ 1.037 nm1. The lines result from fitting Eq. (1) to the data.
1.0 60K 80K 100K 120K 140K 160K 180K 200K
0.8 0.6 n
40 K 60 K 80 K 100K 120K 140K 160K 180K 200K 220K 240K
0.9
0.4 0.2 0.0 0.2
0.4
0.6
0.8
1.0 Q/
1.2
1.4
1.6
1.8
nm-1
Fig. 3. Dependence of the exponent n of the normalized intermediate scattering function S(Q,t) ¼ exp[(gt)n] on the wave vector transfer Q. The lines are a guide to the eyes.
ARTICLE IN PRESS C. Pappas et al. / Physica B 397 (2007) 105–107
The effects of the Q dependence is seen by the increase in g by a factor of 10 from the smallest scattering vector to the larger ones, i.e. from large spatial correlations to the smaller ones due the fall-off of the correlated regions. There are also contributions to the stretching exponent n of the function from 1 to smaller values, which however are affected by rather large errors (cf. Fig. 3). Altogether they show a Q dependence for the ferromagnetic phase and not the Q-independent behaviour which can be seen in classical glasses [5,6] or in the paramagnetic phase of ferromagnetic CdCr1.9In0.1S4 [7]. Thus, the behaviour is similar to the reentrant RSG of EuSrS studied by Shapiro et al. [8] and to the nearly percolating frustrated CdCr1.8In0.2S4 [9]. 4. Conclusion In summary the same behaviour of the spin dynamics was observed for the two Mn concentrations studied in the previous and the present experiment. Spin diffusion resulting in a Q dependence of S(Q,t) is present and appears to be inherent to a mixed RSG phase of FeNiMn. However, the present sample is so close to the frustration
107
point that the inverse correlation time g is increased unlike in the more ferromagnetic sample with x ¼ 0.113, by more than an order of magnitude.
Acknowledgment The allocation of beam time and the technical support by the staff of HMI are gratefully acknowledged.
References [1] [2] [3] [4] [5] [6] [7]
J. Hesse, Hyperfine Interact. 47 (1989) 357–378. V. Wagner, et al., BENSC Experimental Reports PHY 03-0223, 2003. V. Wagne, et al., Physica B 350 (2004) e1051–e1054. J. Klenke, Thesis ISSN 0177-316X, 1999, p. 71. F. Mezei, J. Appl. Phys. 53 (1982) 7654. C. Pappas, et al., Appl. Phys. A 74 (Suppl.) (2002) S907. M. Alba, C. Pappas, BENSC Experimental Reports PHY-03-0331, 2005, p. 55. [8] S.M. Shapiro, H. Maletta, F. Mezei, J. Appl. Phys. 57 (1985) 3485–3487. [9] S. Pouget, M. Alba, Physica B 267–268 (1999) 304–307.
Physica B 397 (2007) 105–107 www.elsevier.com/locate/physb
Spin freezing in the re-entrant spin glass FeNiMn close to the frustration limit Catherine Pappasa, Jens Klenkea, Ju¨rgen Hesseb, Volker Wagnerc, a
Hahn-Meitner-Institut, Glienickerstr. 100, 14109 Berlin, Germany Institut fu¨r Metallphysik und Nukleare Festko¨rperphysik, Technische Universita¨t Braunschweig, 38106 Braunschweig, Germany c Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany
b
Abstract In the invar alloy (Fe0.65Ni0.35)1xMnx we measured the magnetic form factor s(Q) and the intermediate scattering function s(Q,t) for a sample close to the critical Mn concentration (xc ¼ 0.139), at which the sample turns to a re-entrant spin glass phase. The aim was to check whether the magnetic behaviour would approach the Q-independent relaxation behaviour of a classical spin glass when x ¼ xc. The experiment showed a quite similar spin freezing as for a more ferromagnetic sample with x ¼ 0.113. The intermediate scattering function and the form factor were determined by paramagnetic NSE. The normalized scattering function S(Q,t) ¼ s(Q,t)/ s(Q) ¼ exp[(gt)n] was fitted by stretched exponential decay. As a function of temperature To200 K the inverse time constant g showed the change of more than four orders of magnitude from frozen spin glass (T ¼ 60 K to T ¼ 100 K), where the ferromagnetic phase occurred. In general, the inverse time constant is higher than in the more ferromagnetic sample as the frustration of the spins became larger. In the ferromagnetic phase S(Q,t) depended on 0.3oQo1.3 nm1, and this spin diffusive behaviour remained in the reentrant spin glass down to at least 60 K. r 2007 Elsevier B.V. All rights reserved. PACS: 75.50.L; 78.70.Nx; 75.50.Bb Keywords: Re-entrant spin glass; Spin freezing; Neutron spin echo; FeNiMn
1. Introduction In re-entrant spin glass (RSG) systems, ferromagnetic and spin glass correlations can coexist and it is well known that the latter are easily destroyed by small magnetic fields; therefore, dynamical studies can shed new light on this intriguing coexistence. In the invar alloy (Fe0.65Ni0.35)1xMnx—a well-known RSG system [1]—we measured the magnetic form factor s(Q) and the magnetic intermediate scattering function s(Q,t) for a sample close to the critical Mn concentration (xc ¼ 0.139). Upon cooling from the ferromagnetic state the sample can form a mixed spin glass containing both a ferromagnetic and a spin glass state, while for x4xc a spin glass system was expected. The aim has been to check whether the magnetic behaviour Corresponding author. Tel.: +49 531 5926550.
E-mail address: [email protected] (V. Wagner). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.02.062
would approach the Q-independent relaxation behaviour of a classical spin glass when x approaches xc. A more ferromagnetic sample with x ¼ 0.113 studied in the previous experiment [2,3] displayed a remarkable Q dependent diffusive behaviour in the RSG state. In the experiment presented here, however, a similar behaviour somewhat less Q-dependent, was observed for a ferromagnetic sample with x ¼ 0.13970.001. 2. Experimental results The experience was done with the SPAN instrument at HMI with 0.65 nm wavelength. The instrumental resolution was measured at 2 K. Decreasing the temperature the depolarization of the transmitted beam indicated that the sample was slightly ferromagnetic (TcE200 K) close to the frustration limit. This was not observed neither by neutron depolarization at smaller wavelength nor by small-angle
ARTICLE IN PRESS C. Pappas et al. / Physica B 397 (2007) 105–107
106
scattering [4]. It gradually lost the ferromagnetic order due to the onset of the freezing of the transverse components of the frustrated spins for To90 K. At 50 K the strongly irreversible RSG phase was reached. The sample was 4.9 mm thick and in a small magnetic field of about 2 A/cm. The intermediate scattering function and the form factor were determined by paramagnetic NSE techniques for 0.3 nm1oQo1.3 nm1 and 40 KoTo240 K. Fig. 1 shows the time evolution of the normalized intermediate scattering function sðQ; tÞ ¼ exp½ðgtÞn . sðQÞ
(1)
Stretched exponentials fitted to the data describe the time dependence quite well except for TX200 K, where the data are too small for decent values. The spin diffusive behaviour found in the ferromagnetic phase (200 K4T490 K) is still observed in the RSG phase (To60 K), which is a mixed phase of simultaneous ferromagnetic and spin glass order. At 40 K in the lower
a
1.0
104
40K 60K 80K 100K 120K 140K 160K 180K 200K 220K 240K
0.7 S(Q,tNSE)
40K 60K 80K 100K 120K 140K 160K 180K 200K 220K 240K
103
0.8 0.6 0.5 0.4 0.3 0.2 0.1
102 101 100 10-1 10-2 10-3 10-4 10-5 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Q / nm-1 0.1
1
Fig. 2. The inverse time constant g vs. the wave vector transfer Q. At To60 K the system is frozen. At T4100 K there is a change by a factor 104 w.r.t. low temperature. The lines are a guide to the eyes.
tNSE / ns
b
In Fig. 2, the observed inverse correlation time g is shown as a function of scattering vector Q. Obviously the sample seems to be ferromagnetic, when observed with long wavelength neutrons close to the frustration limit in a small field, and the same behaviour is found as for x ¼ 0.113 [3]. It appears that the mean inverse correlation time g has been increased by more than an order of magnitude in comparison with the ferromagnetic sample x ¼ 0.113 [3]. This fact is due to the smaller size of correlated spins in a mean domain size. Also the difference between the strongly irreversible RSG phase and the ferromagnetic phase has become larger by about a factor of 104, showing the influence of a large difference of ferromagnetic and spin glass phase and the effect of the spin freezing in the more dilute sample.
Q = 0.495 nm-1
0.9
0.0 0.01
3. Discussion
/ns-1
SðQ; tÞ ¼
mixed phase the spins are almost completely frozen within the time window observed in the experiment.
Q = 1.037 nm-1 1.0 0.8
S(Q,tNSE)
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.01
1
0.1 tNSE / ns
Fig. 1. The normalized intermediate scattering function S(Q,tNSE) of (Fe0.65Ni0.35)0.86Mn0.14 weakly depends on the scattering vector: (a) Q ¼ 0.495 nm1 and (b) Q ¼ 1.037 nm1. The lines result from fitting Eq. (1) to the data.
1.0 60K 80K 100K 120K 140K 160K 180K 200K
0.8 0.6 n
40 K 60 K 80 K 100K 120K 140K 160K 180K 200K 220K 240K
0.9
0.4 0.2 0.0 0.2
0.4
0.6
0.8
1.0 Q/
1.2
1.4
1.6
1.8
nm-1
Fig. 3. Dependence of the exponent n of the normalized intermediate scattering function S(Q,t) ¼ exp[(gt)n] on the wave vector transfer Q. The lines are a guide to the eyes.
ARTICLE IN PRESS C. Pappas et al. / Physica B 397 (2007) 105–107
The effects of the Q dependence is seen by the increase in g by a factor of 10 from the smallest scattering vector to the larger ones, i.e. from large spatial correlations to the smaller ones due the fall-off of the correlated regions. There are also contributions to the stretching exponent n of the function from 1 to smaller values, which however are affected by rather large errors (cf. Fig. 3). Altogether they show a Q dependence for the ferromagnetic phase and not the Q-independent behaviour which can be seen in classical glasses [5,6] or in the paramagnetic phase of ferromagnetic CdCr1.9In0.1S4 [7]. Thus, the behaviour is similar to the reentrant RSG of EuSrS studied by Shapiro et al. [8] and to the nearly percolating frustrated CdCr1.8In0.2S4 [9]. 4. Conclusion In summary the same behaviour of the spin dynamics was observed for the two Mn concentrations studied in the previous and the present experiment. Spin diffusion resulting in a Q dependence of S(Q,t) is present and appears to be inherent to a mixed RSG phase of FeNiMn. However, the present sample is so close to the frustration
107
point that the inverse correlation time g is increased unlike in the more ferromagnetic sample with x ¼ 0.113, by more than an order of magnitude.
Acknowledgment The allocation of beam time and the technical support by the staff of HMI are gratefully acknowledged.
References [1] [2] [3] [4] [5] [6] [7]
J. Hesse, Hyperfine Interact. 47 (1989) 357–378. V. Wagner, et al., BENSC Experimental Reports PHY 03-0223, 2003. V. Wagne, et al., Physica B 350 (2004) e1051–e1054. J. Klenke, Thesis ISSN 0177-316X, 1999, p. 71. F. Mezei, J. Appl. Phys. 53 (1982) 7654. C. Pappas, et al., Appl. Phys. A 74 (Suppl.) (2002) S907. M. Alba, C. Pappas, BENSC Experimental Reports PHY-03-0331, 2005, p. 55. [8] S.M. Shapiro, H. Maletta, F. Mezei, J. Appl. Phys. 57 (1985) 3485–3487. [9] S. Pouget, M. Alba, Physica B 267–268 (1999) 304–307.