Abstract
Artificial Spin Ice (ASI), consisting of a two dimensional array of nanoscale magnetic elements, provides a fascinating opportunity to observe the physics of out-of-equilibrium systems. Initial studies concentrated on the static, frozen state, whilst more recent studies have accessed the out-of-equilibrium dynamic, fluctuating state. This opens up exciting possibilities such as the observation of systems exploring their energy landscape through monopole quasiparticle creation, potentially leading to ASI magnetricity, and to directly observe unconventional phase transitions. In this work we have measured and analysed the magnetic relaxation of thermally active ASI systems by means of SQUID magnetometry. We have investigated the effect of the interaction strength on the magnetization dynamics at different temperatures in the range where the nanomagnets are thermally active. We have observed that they follow an Arrhenius-type Néel-Brown behaviour. An unexpected negative correlation of the average blocking temperature with the interaction strength is also observed, which is supported by Monte Carlo simulations. The magnetization relaxation measurements show faster relaxation for more strongly coupled nanoelements with similar dimensions. The analysis of the stretching exponents obtained from the measurements suggest 1-D chain-like magnetization dynamics. This indicates that the nature of the interactions between nanoelements lowers the dimensionality of the ASI from 2-D to 1-D. Finally, we present a way to quantify the effective interaction energy of a square ASI system, and compare it to the interaction energy computed with micromagnetic simulations.
Highlights
Artificial Spin Ice (ASI) systems are patterns of interacting ferromagnetic nanoelements whose particular geometry forces the ground state of the system to be magnetically frustrated, as not all the pairwise magnetic dipolar interactions between elements can be satisfied simultaneously[1,2,3]
These systems include thermal annealing processes taking place during fabrication[20], and systems where the anisotropy barrier of the nanomagnets has been tuned to be in a thermally accessible regime by judicious choice of a magnetic material with a lowered Curie temperature (TC)[21,22] and by carefully heating the sample above its blocking temperature (TB)[23]. These reports were shortly followed by studies of thermally fluctuating ASIs which have been imaged via PEEM24–27 and TXM28,29 in real time in a variety of geometries, and recently via magnetic force microscopy (MFM) imaging of the intermediate thermally stable states after a temperature quenching process[30]
The lower bound is given by the temperature at which the magnetization starts to increase in the Zero field cooling (ZFC), and the upper bound by the average TB
Summary
Artificial Spin Ice (ASI) systems are patterns of interacting ferromagnetic nanoelements whose particular geometry forces the ground state of the system to be magnetically frustrated, as not all the pairwise magnetic dipolar interactions between elements can be satisfied simultaneously[1,2,3]. These systems include thermal annealing processes taking place during fabrication[20], and systems where the anisotropy barrier of the nanomagnets has been tuned to be in a thermally accessible regime by judicious choice of a magnetic material with a lowered Curie temperature (TC)[21,22] and by carefully heating the sample above its blocking temperature (TB)[23] These reports were shortly followed by studies of thermally fluctuating ASIs which have been imaged via PEEM24–27 and TXM28,29 in real time in a variety of geometries, and recently via MFM imaging of the intermediate thermally stable states after a temperature quenching process[30]. The present work provides a systematic study of the effect of frustration in the dimensionality of artificial spin-ice systems with different geometries, and opens the door to the design and analysis of desired exotic states and emergent behaviours[40]
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