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Thermodynamic phase transitions in a frustrated magnetic metamaterial.

Anghinolfi L, Luetkens H, Perron J, Flokstra MG, Sendetskyi O, Suter A, Prokscha T, Derlet PM, Lee SL, Heyderman LJ - Nat Commun (2015)

Bottom Line: In equilibrium, thermodynamic phases appear with the associated phase transitions providing a characteristic signature of the underlying collective behaviour.Here we create a thermally active artificial kagome spin ice that is made up of a large array of dipolar interacting nanomagnets and undergoes phase transitions predicted by microscopic theory.This provides experimental evidence that a frustrated magnetic metamaterial can be engineered to admit thermodynamic phases.

View Article: PubMed Central - PubMed

Affiliation: Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland.

ABSTRACT
Materials with interacting magnetic degrees of freedom display a rich variety of magnetic behaviour that can lead to novel collective equilibrium and out-of-equilibrium phenomena. In equilibrium, thermodynamic phases appear with the associated phase transitions providing a characteristic signature of the underlying collective behaviour. Here we create a thermally active artificial kagome spin ice that is made up of a large array of dipolar interacting nanomagnets and undergoes phase transitions predicted by microscopic theory. We use low energy muon spectroscopy to probe the dynamic behaviour of the interacting nanomagnets and observe peaks in the muon relaxation rate that can be identified with the critical temperatures of the predicted phase transitions. This provides experimental evidence that a frustrated magnetic metamaterial can be engineered to admit thermodynamic phases.

No MeSH data available.


Related in: MedlinePlus

ZF-μSR relaxation rates and comparison with Monte Carlo simulations.For the weakly and strongly interacting artificial spin ice samples depicted in a, the relaxation rates are shown in b and c, respectively. The values of the transverse (λT, blue) and longitudinal (λL, red) relaxation rates were obtained by fitting a two-component relaxation function to the experimental muon spin polarization (the solid lines connecting the points in b and c are guides for the eye). The error bars represent the standard deviation of the fit parameters. For both samples, we can distinguish two main temperature regimes: at high temperatures the system is characterized by a single relaxation rate (fast fluctuation regime) and at low temperatures by two distinct rates. TFF marks the onset of the fast fluctuation regime where λT≈λL. For the strongly interacting sample (c), TFF is observed at a higher temperature than in the weakly interacting sample, indicating the slowing down of magnetic fluctuations due to the stronger magnetic correlations. Below TFF, additional temperature regimes, characterized by different slopes of λT and separated by peaks of λL at 145 and 35 K, can be distinguished. These peaks indicate critical fluctuations of the magnetic moments associated with the phase transitions between Ice I and Ice II at 145 K, and between Ice II and LRO at 35 K. The heat capacity computed from Monte Carlo simulations for both samples is shown in d and e (black curves). For the strongly interacting sample (e), the two peaks of the heat capacity occur at temperatures that match those of the phase transitions observed in the experiments. For the weakly interacting sample (d), the peaks in the heat capacity are shifted to lower temperatures, confirming that they are no longer experimentally accessible. The shading in b–e is a guide to the eye to identify the different phases. a.u., arbitrary unit; Int., interacting.
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f3: ZF-μSR relaxation rates and comparison with Monte Carlo simulations.For the weakly and strongly interacting artificial spin ice samples depicted in a, the relaxation rates are shown in b and c, respectively. The values of the transverse (λT, blue) and longitudinal (λL, red) relaxation rates were obtained by fitting a two-component relaxation function to the experimental muon spin polarization (the solid lines connecting the points in b and c are guides for the eye). The error bars represent the standard deviation of the fit parameters. For both samples, we can distinguish two main temperature regimes: at high temperatures the system is characterized by a single relaxation rate (fast fluctuation regime) and at low temperatures by two distinct rates. TFF marks the onset of the fast fluctuation regime where λT≈λL. For the strongly interacting sample (c), TFF is observed at a higher temperature than in the weakly interacting sample, indicating the slowing down of magnetic fluctuations due to the stronger magnetic correlations. Below TFF, additional temperature regimes, characterized by different slopes of λT and separated by peaks of λL at 145 and 35 K, can be distinguished. These peaks indicate critical fluctuations of the magnetic moments associated with the phase transitions between Ice I and Ice II at 145 K, and between Ice II and LRO at 35 K. The heat capacity computed from Monte Carlo simulations for both samples is shown in d and e (black curves). For the strongly interacting sample (e), the two peaks of the heat capacity occur at temperatures that match those of the phase transitions observed in the experiments. For the weakly interacting sample (d), the peaks in the heat capacity are shifted to lower temperatures, confirming that they are no longer experimentally accessible. The shading in b–e is a guide to the eye to identify the different phases. a.u., arbitrary unit; Int., interacting.

Mentions: We manufacture a thermally active artificial kagome spin ice system141516, with nanomagnets having spontaneous but collective macrospin reversals, by significantly reducing the size of the magnets compared with those found in conventional artificial spin ice. Our samples are therefore constructed from nanomagnets with a length, width and thickness of 63, 26 and 6 nm, ensuring thermally activated macrospin reversals at room temperature and below. To optimize the critical temperatures of the phase transitions, we modified the inter-magnet dipolar energy scale. Specifically, we considered two samples characterized by different nanomagnet separations, a (see Figs 1a,3a). The crossover from the high-temperature paramagnetic phase to the lower temperature spin ice manifold was addressed with a weakly interacting sample designed with magnets far apart (a=400 nm), resulting in relatively low critical temperatures in the sub 10 K range. A second strongly interacting sample was designed with much more closely packed nanomagnets (a=170 nm, shown in Fig. 1a), resulting in higher (sub 150 K) critical temperatures, which allowed us to observe phase transitions within the spin ice manifold. The magnetic metamaterials are manufactured over unprecedented areas. They are made up of nine 5 × 5 mm2 arrays separated from each other by 10 μm, with each array corresponding to 109 nanomagnets. This ensures the high degeneracy of states, and therefore thermodynamics, characteristic of bulk systems.


Thermodynamic phase transitions in a frustrated magnetic metamaterial.

Anghinolfi L, Luetkens H, Perron J, Flokstra MG, Sendetskyi O, Suter A, Prokscha T, Derlet PM, Lee SL, Heyderman LJ - Nat Commun (2015)

ZF-μSR relaxation rates and comparison with Monte Carlo simulations.For the weakly and strongly interacting artificial spin ice samples depicted in a, the relaxation rates are shown in b and c, respectively. The values of the transverse (λT, blue) and longitudinal (λL, red) relaxation rates were obtained by fitting a two-component relaxation function to the experimental muon spin polarization (the solid lines connecting the points in b and c are guides for the eye). The error bars represent the standard deviation of the fit parameters. For both samples, we can distinguish two main temperature regimes: at high temperatures the system is characterized by a single relaxation rate (fast fluctuation regime) and at low temperatures by two distinct rates. TFF marks the onset of the fast fluctuation regime where λT≈λL. For the strongly interacting sample (c), TFF is observed at a higher temperature than in the weakly interacting sample, indicating the slowing down of magnetic fluctuations due to the stronger magnetic correlations. Below TFF, additional temperature regimes, characterized by different slopes of λT and separated by peaks of λL at 145 and 35 K, can be distinguished. These peaks indicate critical fluctuations of the magnetic moments associated with the phase transitions between Ice I and Ice II at 145 K, and between Ice II and LRO at 35 K. The heat capacity computed from Monte Carlo simulations for both samples is shown in d and e (black curves). For the strongly interacting sample (e), the two peaks of the heat capacity occur at temperatures that match those of the phase transitions observed in the experiments. For the weakly interacting sample (d), the peaks in the heat capacity are shifted to lower temperatures, confirming that they are no longer experimentally accessible. The shading in b–e is a guide to the eye to identify the different phases. a.u., arbitrary unit; Int., interacting.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4595626&req=5

f3: ZF-μSR relaxation rates and comparison with Monte Carlo simulations.For the weakly and strongly interacting artificial spin ice samples depicted in a, the relaxation rates are shown in b and c, respectively. The values of the transverse (λT, blue) and longitudinal (λL, red) relaxation rates were obtained by fitting a two-component relaxation function to the experimental muon spin polarization (the solid lines connecting the points in b and c are guides for the eye). The error bars represent the standard deviation of the fit parameters. For both samples, we can distinguish two main temperature regimes: at high temperatures the system is characterized by a single relaxation rate (fast fluctuation regime) and at low temperatures by two distinct rates. TFF marks the onset of the fast fluctuation regime where λT≈λL. For the strongly interacting sample (c), TFF is observed at a higher temperature than in the weakly interacting sample, indicating the slowing down of magnetic fluctuations due to the stronger magnetic correlations. Below TFF, additional temperature regimes, characterized by different slopes of λT and separated by peaks of λL at 145 and 35 K, can be distinguished. These peaks indicate critical fluctuations of the magnetic moments associated with the phase transitions between Ice I and Ice II at 145 K, and between Ice II and LRO at 35 K. The heat capacity computed from Monte Carlo simulations for both samples is shown in d and e (black curves). For the strongly interacting sample (e), the two peaks of the heat capacity occur at temperatures that match those of the phase transitions observed in the experiments. For the weakly interacting sample (d), the peaks in the heat capacity are shifted to lower temperatures, confirming that they are no longer experimentally accessible. The shading in b–e is a guide to the eye to identify the different phases. a.u., arbitrary unit; Int., interacting.
Mentions: We manufacture a thermally active artificial kagome spin ice system141516, with nanomagnets having spontaneous but collective macrospin reversals, by significantly reducing the size of the magnets compared with those found in conventional artificial spin ice. Our samples are therefore constructed from nanomagnets with a length, width and thickness of 63, 26 and 6 nm, ensuring thermally activated macrospin reversals at room temperature and below. To optimize the critical temperatures of the phase transitions, we modified the inter-magnet dipolar energy scale. Specifically, we considered two samples characterized by different nanomagnet separations, a (see Figs 1a,3a). The crossover from the high-temperature paramagnetic phase to the lower temperature spin ice manifold was addressed with a weakly interacting sample designed with magnets far apart (a=400 nm), resulting in relatively low critical temperatures in the sub 10 K range. A second strongly interacting sample was designed with much more closely packed nanomagnets (a=170 nm, shown in Fig. 1a), resulting in higher (sub 150 K) critical temperatures, which allowed us to observe phase transitions within the spin ice manifold. The magnetic metamaterials are manufactured over unprecedented areas. They are made up of nine 5 × 5 mm2 arrays separated from each other by 10 μm, with each array corresponding to 109 nanomagnets. This ensures the high degeneracy of states, and therefore thermodynamics, characteristic of bulk systems.

Bottom Line: In equilibrium, thermodynamic phases appear with the associated phase transitions providing a characteristic signature of the underlying collective behaviour.Here we create a thermally active artificial kagome spin ice that is made up of a large array of dipolar interacting nanomagnets and undergoes phase transitions predicted by microscopic theory.This provides experimental evidence that a frustrated magnetic metamaterial can be engineered to admit thermodynamic phases.

View Article: PubMed Central - PubMed

Affiliation: Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland.

ABSTRACT
Materials with interacting magnetic degrees of freedom display a rich variety of magnetic behaviour that can lead to novel collective equilibrium and out-of-equilibrium phenomena. In equilibrium, thermodynamic phases appear with the associated phase transitions providing a characteristic signature of the underlying collective behaviour. Here we create a thermally active artificial kagome spin ice that is made up of a large array of dipolar interacting nanomagnets and undergoes phase transitions predicted by microscopic theory. We use low energy muon spectroscopy to probe the dynamic behaviour of the interacting nanomagnets and observe peaks in the muon relaxation rate that can be identified with the critical temperatures of the predicted phase transitions. This provides experimental evidence that a frustrated magnetic metamaterial can be engineered to admit thermodynamic phases.

No MeSH data available.


Related in: MedlinePlus