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Thermally induced magnetic relaxation in square artificial spin ice

View Article: PubMed Central - PubMed

ABSTRACT

The properties of natural and artificial assemblies of interacting elements, ranging from Quarks to Galaxies, are at the heart of Physics. The collective response and dynamics of such assemblies are dictated by the intrinsic dynamical properties of the building blocks, the nature of their interactions and topological constraints. Here we report on the relaxation dynamics of the magnetization of artificial assemblies of mesoscopic spins. In our model nano-magnetic system - square artificial spin ice – we are able to control the geometrical arrangement and interaction strength between the magnetically interacting building blocks by means of nano-lithography. Using time resolved magnetometry we show that the relaxation process can be described using the Kohlrausch law and that the extracted temperature dependent relaxation times of the assemblies follow the Vogel-Fulcher law. The results provide insight into the relaxation dynamics of mesoscopic nano-magnetic model systems, with adjustable energy and time scales, and demonstrates that these can serve as an ideal playground for the studies of collective dynamics and relaxations.

No MeSH data available.


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Temperature and time dependence of the magnetic relaxation.Color maps of the magnetization as a function of time and temperature for (a) the d = 420 nm and (b) the d = 380 nm array. In both color maps a strong connection between the time and temperature is observed as stripe like features. This implies that a given magnetization value can be found using several combinations of time and temperature. The contour density along the gray lines for t = 300 s corresponds to the relaxation rates shown in Fig. 3d. The maps further highlight the effect of the observation time on the temperature shift of the maximum for the relaxation rate, as indicated by the crosses for the case of t = 3 s and t = 300 s.
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f4: Temperature and time dependence of the magnetic relaxation.Color maps of the magnetization as a function of time and temperature for (a) the d = 420 nm and (b) the d = 380 nm array. In both color maps a strong connection between the time and temperature is observed as stripe like features. This implies that a given magnetization value can be found using several combinations of time and temperature. The contour density along the gray lines for t = 300 s corresponds to the relaxation rates shown in Fig. 3d. The maps further highlight the effect of the observation time on the temperature shift of the maximum for the relaxation rate, as indicated by the crosses for the case of t = 3 s and t = 300 s.

Mentions: The behavior in Fig. 3a,b illustrates the interdependence of the remanent magnetization on time and temperature. This is further elucidated in Fig. 4 were the magnetization is plotted as a function of temperature and time in a color map. It can be seen that the magnetization changes in a stripe like fashion, where a given value of the magnetization is not unique, but can be achieved through different combinations of time and temperature. The contour lines in the figure have constant magnetization and are separated by the same magnetization step. This implies that the time and temperature dependence of the relaxation rate S is reflected in the density of contour lines, where a low density means a low relaxation rate. An alternative way of looking at the data presented in Fig. 3d is to look at contour line density along the gray lines at t = 300 s in Fig. 4. If the observation time is changed from 300 s to a shorter observation time of 3 s, represented by the gray lines at t = 3 s, the temperature of the maximum relaxation rate, increases by roughly 20 K. This accords with the shift of the M vs. T curves for different observation times in Figs 2c and 3c.


Thermally induced magnetic relaxation in square artificial spin ice
Temperature and time dependence of the magnetic relaxation.Color maps of the magnetization as a function of time and temperature for (a) the d = 420 nm and (b) the d = 380 nm array. In both color maps a strong connection between the time and temperature is observed as stripe like features. This implies that a given magnetization value can be found using several combinations of time and temperature. The contour density along the gray lines for t = 300 s corresponds to the relaxation rates shown in Fig. 3d. The maps further highlight the effect of the observation time on the temperature shift of the maximum for the relaxation rate, as indicated by the crosses for the case of t = 3 s and t = 300 s.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5121627&req=5

f4: Temperature and time dependence of the magnetic relaxation.Color maps of the magnetization as a function of time and temperature for (a) the d = 420 nm and (b) the d = 380 nm array. In both color maps a strong connection between the time and temperature is observed as stripe like features. This implies that a given magnetization value can be found using several combinations of time and temperature. The contour density along the gray lines for t = 300 s corresponds to the relaxation rates shown in Fig. 3d. The maps further highlight the effect of the observation time on the temperature shift of the maximum for the relaxation rate, as indicated by the crosses for the case of t = 3 s and t = 300 s.
Mentions: The behavior in Fig. 3a,b illustrates the interdependence of the remanent magnetization on time and temperature. This is further elucidated in Fig. 4 were the magnetization is plotted as a function of temperature and time in a color map. It can be seen that the magnetization changes in a stripe like fashion, where a given value of the magnetization is not unique, but can be achieved through different combinations of time and temperature. The contour lines in the figure have constant magnetization and are separated by the same magnetization step. This implies that the time and temperature dependence of the relaxation rate S is reflected in the density of contour lines, where a low density means a low relaxation rate. An alternative way of looking at the data presented in Fig. 3d is to look at contour line density along the gray lines at t = 300 s in Fig. 4. If the observation time is changed from 300 s to a shorter observation time of 3 s, represented by the gray lines at t = 3 s, the temperature of the maximum relaxation rate, increases by roughly 20 K. This accords with the shift of the M vs. T curves for different observation times in Figs 2c and 3c.

View Article: PubMed Central - PubMed

ABSTRACT

The properties of natural and artificial assemblies of interacting elements, ranging from Quarks to Galaxies, are at the heart of Physics. The collective response and dynamics of such assemblies are dictated by the intrinsic dynamical properties of the building blocks, the nature of their interactions and topological constraints. Here we report on the relaxation dynamics of the magnetization of artificial assemblies of mesoscopic spins. In our model nano-magnetic system - square artificial spin ice – we are able to control the geometrical arrangement and interaction strength between the magnetically interacting building blocks by means of nano-lithography. Using time resolved magnetometry we show that the relaxation process can be described using the Kohlrausch law and that the extracted temperature dependent relaxation times of the assemblies follow the Vogel-Fulcher law. The results provide insight into the relaxation dynamics of mesoscopic nano-magnetic model systems, with adjustable energy and time scales, and demonstrates that these can serve as an ideal playground for the studies of collective dynamics and relaxations.

No MeSH data available.


Related in: MedlinePlus