Research into geometrical frustration over the past two decades has revealed fundamentally new exotic behavior [1]. The magnetic interactions of the structure, coupled with the specific geometry causes frustration in the system, referred to as artificial spin ices. Several geometries exist, but for the purpose of this research, the kagome arrangement was used. In general, the geometry of these frustrated systems follows the ice rule, that being two interacting moments point in while two point out. The kagome however follows the modified ice rule of two moments pointing in while one points out or vice versa. These systems appear as 2D analogues to the 3D structure and it is the lattice configuration along with the specific frustration created that causes these exotic behaviors. Presented here are the magnetoresistances obtained for kagome magnetically frustrated systems in a single vertex and lattice format. Both geometries are compared in a magnetically connected format and a magnetically disconnected format in order to observe the exchange and dipolar energies. The structures were simulated with parameters for permalloy, using BORIS [2], and dimensions of 1µm long, 100nm wide and 10nm thick. The aim was to evaluate the magneto resistance, which was done assuming the current density aligns with the long axis and a basic resistor network. By comparing the simulated data for the connected and disconnected single vertex with the measurements taken previously for a lattice, a greater understanding of the effect of the disconnected versus connected structures can be achieved. Measurements of the kagome lattice showed that the disconnected lattice had a change in magnetoresistance that was 2~3 times greater than the connected lattice, experimentally. The simulations of the single vertex’s magnetoresistance differ by approximately an order of magnitude to those of the experiments. While the simulations are not for the full lattice, they shed some light on the experimental results obtained and the single vertex interactions that occur within the lattice. The simulation of the hybrid vertex appears to mirror that of the experimental data obtained for the hybrid lattice while the simulation of the connected vertex appears to differ somewhat from the experimental data obtained for the connected lattice. This highlights the implications of the experimental work in that the connected kagome has more complex interactions throughout the lattice while the magnetically disconnected hybrid is rather a simplified system. The subtle difference in the geometries of the connected and disconnected lattices aids in the explanation of the effects and interplay of both the spin structures and the current density. This work demonstrates the potential for using simulations to expose magnetic interactions in a lattice type structure and other interesting geometries, along with the enhanced magnetoresistance signals that were obtained.

**References:**

References: [1] Nisoli, C., Moessner, R., & Schiffer, P. (2013). Colloquium: Artificial spin ice: Designing and imaging magnetic frustration. Reviews of Modern Physics, 85(4), 1473. [2] Lepadatu, Serban. (2019). Boris Computational Spintronics User Manual.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/bc02a8200bfe4ba73c8d18a80397bf3d.jpg)
Figure 1. SEM images of an electrically connected but magnetically disconnected (hybrid) lattice (left). Also shown is the standard honeycomb lattice for comparison.

![](https://assets.underline.io/uploads/markdown_image/1/image/65475fb3f43153712262934a633adf6d.jpg)
Figure 2: Simulated single vertex and experimental lattice for the magnetically disconnected, electronically connected (hybrid) kagome plotted against the applied magnetic field. Data shown is the positive part of a full sweep of the magnetic field i.e. from a positive applied field through to the negative of the same applied field.

Micromagnetic simulations of artificial spin ice lattices and vertices

Single molecule magnetism (SMM) presents a novel avenue for the pursuit of a bottom up approach to the design of next generation magnets, their molecular origin of magnetism and sensitivity to their chemical environment allows SMMs to be designed and exploited at the molecular level1. Applications include proposals for SMMs to be used as qubits and components in spintronic devices2,3. Here we present the synthesis and magnetic properties of mononuclear Ln(III) complexes, where two Er(III) complexes exhibit SMM behavior and blocking temperatures of around 40K.4 We used a synthetic approach and ligand fine-tuning where the ligand field is favorable for the Er(III) compounds to exhibit SMM properties. Single crystal structure analysis was carried out to obtain structural information on all the presented complexes. The field dependence of the magnetization for both Er(III) compounds were measured at 2, 3 and 5 K; the magnetization curves did not saturate at high fields indicating the presence of significant magnetic anisotropy and/or low-lying excited states. In order to investigate the potential presence of slow relaxation of the magnetization caused by SMM behavior, ac magnetic susceptibility measurements were performed, in applied dc-fields from 0 to 3000 Oe, in attempts to suppress any quantum tunneling of the magnetization (QTM). For both compounds the in-phase and out-of-phase ac susceptibility show field-dependent signals; the optimum field was found to be 500 Oe and this was used for further ac measurements. In both cases, the ac measurements reveal temperature dependent in- and out-of-phase signals with clear maxima up to 3.5 K. The maxima of the frequency dependent out-of-phase susceptibility curves were used extract the relaxation time as a function of temperature.

**References:**

[1] B. M. Day, F.-S. Guo, R. A. Layfield, Acc. Chem. Res. 51,1880–1889 (2018). [2] M. Shiddiq et al., Nature 531, 348–351 (2016). [3] S. Thiele et al., Science 344, 1135–1138 (2014). [4] I.A. Kühne, et al., Dalton Trans 48, 15679 (2019)

**Images:**

 The Influence of Electron-Withdrawing Groups on the Relaxation Time of Field-Induced Er(III) Single Molecule Magnets.

*Session Co-Chair: Daria Gusakova, SPINtronique et Technologie des Composants*

*Session Co-Chair: Joo-Von Kim, Université Paris-Saclay*

These on-demand presentations are available to view at your leisure. 

AE: Micromagnetic Modelling

technical paper

INTERMAG 2021 Welcome Video



	
<figure class="video_container">
 <iframe src="https://screencast-o-matic.com/player/crflqFVnUpZ?v=6&ff=1&title=0&controls=1" width=640 height=360 frameborder="0" allowfullscreen="true"> </iframe>
</figure>

Want to buy a ticket? 

Register for INTERMAG 2021 here

[![](https://assets.underline.io/uploads/markdown_image/1/image/17ce76e7960db633258024eef8d6da7f.png)](https://intermag.org/register)

Got your ticket, but still can’t access the event?

Contact us and our team will look into it.

INTERMAG 2021

*Session Chair: Pan He, Fudan University*

These on-demand presentations are available to view at your leisure.

Solveig Felton

2

1

SHORT BIO

Presentations

Micromagnetic simulations of artificial spin ice lattices and vertices

The Influence of Electron-Withdrawing Groups on the Relaxation Time of Field-Induced Er(III) Single Molecule Magnets.

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES