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Thermodynamic magnetic fluctuations in the 2D ferromagnet (CH3NH3)2CuCl4 near the transition temperature
Journal of Magnetism
and Magnetic
Materials
104-107
(1992) 775-776
North-Holland
Thermodynamic magnetic fluctuations in the 2D ferromagnet ( CH ,NH J ,CuCl, near the transition temperature L. Leylekian,
Y.M. Tsipenyuk
‘, M. Ocio and J. Hammann
Sewice de Physique de I’Etat condensP, C.E. Saclay, 91191, Gif-sur-Ywtte Cedex, France Thermodynamic magnetic fluctuations have been measured around the transition temperature T, = 8.77 K, in the Cu planes and perpendicular to the Cu planes. A sharp maximum of the noise power is detected at 9.5 K which corresponds roughly to the 2D to 3D space dimensionality crossover. Apart from low frequency instabilities in the Cu planes, noise power and out-of-phase susceptibility are rather well related by the fluctuation dissipation theorem. In the critical regime, a well defined I/f noise is observed.
In this paper, we report a study of the spontaneous magnetic fluctuations (measured in zero magnetic field) in the quasi-2D Heisenberg ferromagnet (CH, NH,),CuCI,. In the past years, the magnetic properties of these materials were extensively investigated [l] as well as their dimensionality crossovers near the transition temperature [2]. Recently, a preliminary investigation on their magnetic fluctuations at the transition temperature was published by one of us [3]. The present measurements were performed above and below the transition temperature T, (from our susceptibility measurements, T, = 8.76-8.78 K), and in the frequency range 0.01 Hz-10 kHz. We used a variable temperature cryogenic apparatus with dc SQUID magnetometry, already described in several reports on spin-glass studies [4]. The samples are long cylinders inserted concentrically in a third order cylindrical gradiametric pick-up coil. Two samples, approximately 5 mm diameter and 40 mm long were used. One had its axis along the cristallographic [llO] direction in the Cu planes (referred to as the I -c axis), the other was perpendicular to the Cu planes ( II-c axis). Details of the experimental procedure have been published extensively elsewhere [4,5]. As can be seen in fig. 1, the noise power exhibits an almost perfect l/f spectrum above T,, at 9.4 K (and at least up to about 9.6 K). This temperature range lies in the critical region E = 1 - T/T, ,< 0.2 [2], so the l/f character of critical fluctuations is clearly revealed experimentally. Below T,, (curves at 7.5 K) the system remains dissipative [1,2] but the l/f‘ character of fluctuations is progressively lost, mainly in the direction I -c where the upward curvature rather corresponds to a frequency log power behavior. This persistence of a large spectrum of relaxation times reveals the complexity and the disorder in the system at low temperature (defects, domain walls or possibly a very loose magnetic order). Near and below T,, strong instabili-
’ Institute for Physical Problems, 0312~8853/92/$05.00
0 1992
Moscow Elsevier
117334, USSR. Science
Publishers
7.5K
FREQUENCY
a
d
(Hz)
Fig. 1. RMS noise in units of dr,, Hz-‘/* at the input of the SQUID (@,, is the flux quantum: 2.07~ IO-’ G cm*). Curves a, b and c are measured with the axis of the gradiometer in the direction 1 -c (parallel to the Cu planes); d, e and f in the direction 11-c(perpendicular to the Cu planes).
ties develop at low frequencies in the Cu planes (direction I -cl, leading to a sharp increase of the noise below 0.3 Hz. As appears from the comparison with the out-of-phase susceptibility, this contribution cannot be related with the linear response of the system. Its origin is not clear for the time being. In the direct signal-time records, it corresponds to sudden random steps rather similar to the effect of some kind of avalanche events [7]. The power spectrum of magnetization S(w) can be derived from the data as developed in ref. [5]. Here, due to the anisotropy, S(w) is in fact a pondered average over all degrees of freedom. The result is given in fig. 2 as a function of temperature. In both directions the curves exhibit a sharp maximum centered at roughly 9.5 K, i.e. more than 0.5 K above T,. The presence of such a singularity was already mentioned in the preliminary work quoted above [3], even though
B.V. All rights
reserved
L. Leylekian et al. / Thermodynamic
776
the samples, as well as the experimental setup, were completely different [6]. There is a general agreement about the onset of a space dimensionality crossover from 2D to 3D in the temperature range where the singularity is observed [1,2]. Such a crossover would, indeed, correspond to a drastic decrease of the fluctuation amplitude when going from 2D to 3D, and thus to a maximum at the crossover temperature. The amplitudes of the maxima are similar in both directions showing that the fluctuations are still isotropic in this region. The observed isotropy is rather unexpected since, even if all authors do not agree on the spin dimensionality at the crossover, Heisenberg spins are ruled out [1,2]. After a minimum around 9 K, the power spectrum reaches a plateau below 8.7 K at all frequencies in the direction II-c, and at least above 3 Hz in the direction I -c. Below 3 Hz in the latter case, the low frequency instabilities result in a strong dispersion of the data, which show a maximum amplitude around 8 K. At the lowest frequencies they are so large as to almost hide the minimum at 9 K. Outside this range, the noise power I -c is larger than that 11-c by no more than a factor two. Measurements of the linear susceptibility x have been performed on the same samples in the range 0.17-17 Hz under ac fields of order 1 mOe. According to the fluctuation dissipation theorem, S(w) a T~“(w)/w. Fig. 3 displays Tx”(w)/w at 17 Hz as a function of T: such a presentation allows a direct comparison with the curves of S(w) given in fig. 2. There is a clear similitude between both kinds of results. Here also, the peak amplitudes at 9.5 K are
magneticfluctuations
in (CH., NH,3)2CuCl,
17 Hz * Hlc
-
TEMPERATURE
Fig. 3. Values of T~“(w)/w
H//c
(Kl
vs. T in both directions.
similar in both directions, while x; /x,; = 6 at the same temperature. Down to 0.17 Hz, the Tx”(w)/w curves versus T remain similar and their amplitude at the 9.5 K peak is proportional to l/f. To our knowledge the singularity of x” at 9.5 K was never seen before, probably for reasons of sensitivity. In summary, we have found for the spontaneous magnetization fluctuations in this quasi-2D Heisenberg ferromagnet: pure l/f noise in the critical regime; a sharp isotropic maximum in the crossover region from 2D to 3D behavior; large, very low frequency, instabilities below T, in the Cu planes.
References [l] For instance:
L.J. de Jongh, A.C. Botterman and A.R. Miedema, J. Appl. Phys. 40 (1969) 1363. M. A’in and J.
[2] [3] [4]
[5] [6]
6
7
8
TEMPERATURE
9
10 (K)
Fig. 2. Fluctuations power spectrum vs. T in both directions.
[7]
Hammann, A.I.P. Conf. Proc. 24 (1975) 309. J.P. Renard and A. Dupas, Phys. Lett. A 53 (1975) 141. L.J. De Jongh, Physica B 82 (1976) 247. Y.M. Tsipenyuk and V.P. Yanev, JETP Lett. 49 (1989) 42. P. RefrCgier, M. Ocio and H. Bouchiat, Europhys. Lett. 33 (1987) 503. M. Ocio, J. Hammann, P. RefrCgier and E. Vincent, Physica B 150 (1988) 353. P. RefrCgier and M. Ocio, Revue Phys. Appl. 22 (1987) 367. The samples of the present work have kindly been given to us by J.P. Renard, Lab. d’Electronique, Univ. Paris-Sud 91405 Orsay, France. Furthermore, we have measured a polycrystalline sample from the Institute for Physical Problems, Moscow, USSR, of the same origin as those used in ref. [3]. We always detected the same peak at 9.5 K. H.M. Jeager. C. Liu and S.R. Nagel, Phys. Rev. Lett. 62 (1989) 40.
and Magnetic
Materials
104-107
(1992) 775-776
North-Holland
Thermodynamic magnetic fluctuations in the 2D ferromagnet ( CH ,NH J ,CuCl, near the transition temperature L. Leylekian,
Y.M. Tsipenyuk
‘, M. Ocio and J. Hammann
Sewice de Physique de I’Etat condensP, C.E. Saclay, 91191, Gif-sur-Ywtte Cedex, France Thermodynamic magnetic fluctuations have been measured around the transition temperature T, = 8.77 K, in the Cu planes and perpendicular to the Cu planes. A sharp maximum of the noise power is detected at 9.5 K which corresponds roughly to the 2D to 3D space dimensionality crossover. Apart from low frequency instabilities in the Cu planes, noise power and out-of-phase susceptibility are rather well related by the fluctuation dissipation theorem. In the critical regime, a well defined I/f noise is observed.
In this paper, we report a study of the spontaneous magnetic fluctuations (measured in zero magnetic field) in the quasi-2D Heisenberg ferromagnet (CH, NH,),CuCI,. In the past years, the magnetic properties of these materials were extensively investigated [l] as well as their dimensionality crossovers near the transition temperature [2]. Recently, a preliminary investigation on their magnetic fluctuations at the transition temperature was published by one of us [3]. The present measurements were performed above and below the transition temperature T, (from our susceptibility measurements, T, = 8.76-8.78 K), and in the frequency range 0.01 Hz-10 kHz. We used a variable temperature cryogenic apparatus with dc SQUID magnetometry, already described in several reports on spin-glass studies [4]. The samples are long cylinders inserted concentrically in a third order cylindrical gradiametric pick-up coil. Two samples, approximately 5 mm diameter and 40 mm long were used. One had its axis along the cristallographic [llO] direction in the Cu planes (referred to as the I -c axis), the other was perpendicular to the Cu planes ( II-c axis). Details of the experimental procedure have been published extensively elsewhere [4,5]. As can be seen in fig. 1, the noise power exhibits an almost perfect l/f spectrum above T,, at 9.4 K (and at least up to about 9.6 K). This temperature range lies in the critical region E = 1 - T/T, ,< 0.2 [2], so the l/f character of critical fluctuations is clearly revealed experimentally. Below T,, (curves at 7.5 K) the system remains dissipative [1,2] but the l/f‘ character of fluctuations is progressively lost, mainly in the direction I -c where the upward curvature rather corresponds to a frequency log power behavior. This persistence of a large spectrum of relaxation times reveals the complexity and the disorder in the system at low temperature (defects, domain walls or possibly a very loose magnetic order). Near and below T,, strong instabili-
’ Institute for Physical Problems, 0312~8853/92/$05.00
0 1992
Moscow Elsevier
117334, USSR. Science
Publishers
7.5K
FREQUENCY
a
d
(Hz)
Fig. 1. RMS noise in units of dr,, Hz-‘/* at the input of the SQUID (@,, is the flux quantum: 2.07~ IO-’ G cm*). Curves a, b and c are measured with the axis of the gradiometer in the direction 1 -c (parallel to the Cu planes); d, e and f in the direction 11-c(perpendicular to the Cu planes).
ties develop at low frequencies in the Cu planes (direction I -cl, leading to a sharp increase of the noise below 0.3 Hz. As appears from the comparison with the out-of-phase susceptibility, this contribution cannot be related with the linear response of the system. Its origin is not clear for the time being. In the direct signal-time records, it corresponds to sudden random steps rather similar to the effect of some kind of avalanche events [7]. The power spectrum of magnetization S(w) can be derived from the data as developed in ref. [5]. Here, due to the anisotropy, S(w) is in fact a pondered average over all degrees of freedom. The result is given in fig. 2 as a function of temperature. In both directions the curves exhibit a sharp maximum centered at roughly 9.5 K, i.e. more than 0.5 K above T,. The presence of such a singularity was already mentioned in the preliminary work quoted above [3], even though
B.V. All rights
reserved
L. Leylekian et al. / Thermodynamic
776
the samples, as well as the experimental setup, were completely different [6]. There is a general agreement about the onset of a space dimensionality crossover from 2D to 3D in the temperature range where the singularity is observed [1,2]. Such a crossover would, indeed, correspond to a drastic decrease of the fluctuation amplitude when going from 2D to 3D, and thus to a maximum at the crossover temperature. The amplitudes of the maxima are similar in both directions showing that the fluctuations are still isotropic in this region. The observed isotropy is rather unexpected since, even if all authors do not agree on the spin dimensionality at the crossover, Heisenberg spins are ruled out [1,2]. After a minimum around 9 K, the power spectrum reaches a plateau below 8.7 K at all frequencies in the direction II-c, and at least above 3 Hz in the direction I -c. Below 3 Hz in the latter case, the low frequency instabilities result in a strong dispersion of the data, which show a maximum amplitude around 8 K. At the lowest frequencies they are so large as to almost hide the minimum at 9 K. Outside this range, the noise power I -c is larger than that 11-c by no more than a factor two. Measurements of the linear susceptibility x have been performed on the same samples in the range 0.17-17 Hz under ac fields of order 1 mOe. According to the fluctuation dissipation theorem, S(w) a T~“(w)/w. Fig. 3 displays Tx”(w)/w at 17 Hz as a function of T: such a presentation allows a direct comparison with the curves of S(w) given in fig. 2. There is a clear similitude between both kinds of results. Here also, the peak amplitudes at 9.5 K are
magneticfluctuations
in (CH., NH,3)2CuCl,
17 Hz * Hlc
-
TEMPERATURE
Fig. 3. Values of T~“(w)/w
H//c
(Kl
vs. T in both directions.
similar in both directions, while x; /x,; = 6 at the same temperature. Down to 0.17 Hz, the Tx”(w)/w curves versus T remain similar and their amplitude at the 9.5 K peak is proportional to l/f. To our knowledge the singularity of x” at 9.5 K was never seen before, probably for reasons of sensitivity. In summary, we have found for the spontaneous magnetization fluctuations in this quasi-2D Heisenberg ferromagnet: pure l/f noise in the critical regime; a sharp isotropic maximum in the crossover region from 2D to 3D behavior; large, very low frequency, instabilities below T, in the Cu planes.
References [l] For instance:
L.J. de Jongh, A.C. Botterman and A.R. Miedema, J. Appl. Phys. 40 (1969) 1363. M. A’in and J.
[2] [3] [4]
[5] [6]
6
7
8
TEMPERATURE
9
10 (K)
Fig. 2. Fluctuations power spectrum vs. T in both directions.
[7]
Hammann, A.I.P. Conf. Proc. 24 (1975) 309. J.P. Renard and A. Dupas, Phys. Lett. A 53 (1975) 141. L.J. De Jongh, Physica B 82 (1976) 247. Y.M. Tsipenyuk and V.P. Yanev, JETP Lett. 49 (1989) 42. P. RefrCgier, M. Ocio and H. Bouchiat, Europhys. Lett. 33 (1987) 503. M. Ocio, J. Hammann, P. RefrCgier and E. Vincent, Physica B 150 (1988) 353. P. RefrCgier and M. Ocio, Revue Phys. Appl. 22 (1987) 367. The samples of the present work have kindly been given to us by J.P. Renard, Lab. d’Electronique, Univ. Paris-Sud 91405 Orsay, France. Furthermore, we have measured a polycrystalline sample from the Institute for Physical Problems, Moscow, USSR, of the same origin as those used in ref. [3]. We always detected the same peak at 9.5 K. H.M. Jeager. C. Liu and S.R. Nagel, Phys. Rev. Lett. 62 (1989) 40.