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Path Integral Quantum Spin Dynamics

Lead Research Organisation: University of Leeds
Department Name: Physics and Astronomy

Abstract

Magnetic materials are particularly important for technological applications. They have been used for the last 50 years as the main source of computer data storage, facilitating the massive expansion in computing and the internet. Newer fields such as spintronics hope to use the magnetism alongside electronics to make new devices which combine the best of both worlds, for example magnetic tunnel junctions which are now being manufactured by all of the major global foundries for use as random access memories. New types of computing which mimic how the brain works have been suggested and magnetic materials look to play an important role in these. With quantum computing and superconducting computing developing at a rapid pace, scientists are considering how magnetic materials will be used devices.

It's vitally important that we understand how stable magnets are. Information is normally encoded by putting magnets into one of two opposite states. There is a probability that the magnet can change state and we lose information. Devices have to be carefully designed so that this is very unlikely. The main issue comes from heat, but quantum mechanics can also cause effects such as 'tunnelling', where the magnet can spontaneously change state. Quantum effects become more significant when devices are smaller, temperatures are lower, and in some types of magnets such as antiferromagnets. While the general principle is understood, we don't currently have the tools to simulate these effects for specific materials and devices to understand how they might impact the new applications for magnetic materials.

This research project is to build a new tool for modelling quantum effects in magnetic materials and to use it to study antiferromagnets which are a strong candidate for use in future memory devices. We will use a mathematical technique created by Richard Feynman called path integrals which allow quantum systems to be modelled by a larger set of classical systems. This allows us to include quantum effects on a very large scale with relatively low computational costs. This sort of modelling has proved very successful in molecular dynamics modelling but has not yet been applied to spin dynamics for modelling magnets. As well as developing the fundamental method we will create a software package so that researchers around the world can use the method in their efforts to predict material properties and interpret experiments. The project will enable quantitative modelling of magnetic materials beyond what is currently possible and drive future research.
 
Description Quantum corrections to spin thermodynamics can be included into classical models using a path integral approach. This allows inexpensive calculations of magnetic systems with a greater quantitative accuracy. Crucially we found that path integral spin dynamics has a fundamentally different structure from path integral molecular dynamics which means we cannot represent the low temperature behaviour by increased randomness in the system. Therefore path integral spin dynamics simulated with a classical spin model, where a single quantum spin is mapped to as single classical spin cannot produce quantitative results below a 'low temperature' limit.
Exploitation Route We expect the outcomes to inform future approaches to large scale simulations of spin systems. We ourselves have obtained further funding (Royal Society International Exchange Programme) to collaborate with researchers in Japan to identify ways to further develop this method. We have continued the work and have a new paper submitted for publication (https://arxiv.org/abs/2502.19113) which includes the exchange interaction and shows the first results for antiferromagnetic coupling where the new technique reproduces the quantum results which completely different from the classical result.
Sectors Digital/Communication/Information Technologies (including Software)

Electronics

 
Description International Exchanges 2023 Cost Share (JSPS)
Amount £11,780 (GBP)
Funding ID IEC\R3\233041 
Organisation The Royal Society 
Sector Charity/Non Profit
Country United Kingdom
Start 03/2024 
End 03/2026
 
Title Research Data supporting ''The importance of the interface for picosecond spin pumping in antiferromagnet-heavy metal heterostructures'' 
Description The data is relative to an optical pump-THz emission measurement in KCoF3-Pt(5 nm) and KNiF3-Pt(5 nm) as a function of temperature and magnetic field. tempKNiF3 and tempKCoF3 describe the temperature dependence of the THz emission measured at different fluences of the pump, in increasing order 0.026, 0.09, 0.28 mJ/cm3 (KCoF3) and 0.01, 0.09, 0.56 mJ/cm3 (KNiF3). suscepKNiF3 and suscepKCoF3 are SQUID measuremenst of the susceptibility of KNiF3 and KCoF3 as a function of temperature. polarizKNiF3 and polarizKCoF3 are time-traces of the emitted THz pulse measured when the sample is pumped by a linearly polarised pump along the [100], [010] and [001] plane. DirectionKCoF contains time-traces of the emitted THz pulse when KCoF3-Pt is pumped from the Pt side or the substrate side with the same fluenece of 1.7 mJ/cm2. Bdepend shows the amplitude of the THz emission in KCoF3 and KNiF3 as a function of magnetic field for the same pumping fluence of 1.7 mJ/cm2. 
Type Of Material Database/Collection of data 
Year Produced 2023 
Provided To Others? Yes  
URL https://www.repository.cam.ac.uk/handle/1810/348276
 
Title Quantum Spin Dynamics Model Based on a Path Integral Approach 
Description Implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2023 
Open Source License? Yes  
Impact None yet. 
URL https://github.com/stonerlab/PIQSD-SingleSpinBz
 
Title Sources for: Numerical Simulations of a Spin Dynamics Model Based on a Path Integral Approach 
Description This repository contains source code which implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2023 
Open Source License? Yes  
URL https://zenodo.org/record/7692092
 
Title Sources for: Numerical Simulations of a Spin Dynamics Model Based on a Path Integral Approach 
Description This repository contains source code which implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2023 
Open Source License? Yes  
URL https://zenodo.org/record/7688972
 
Title Sources for: Numerical Simulations of a Spin Dynamics Model Based on a Path Integral Approach 
Description This repository contains source code which implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2023 
Open Source License? Yes  
URL https://zenodo.org/record/7707957
 
Title Sources for: Numerical Simulations of a Spin Dynamics Model Based on a Path Integral Approach 
Description This repository contains source code which implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2023 
Open Source License? Yes  
URL https://zenodo.org/record/7688939
 
Title Sources for: Path integral spin dynamics for quantum paramagnets 
Description This repository contains source code which implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2024 
Open Source License? Yes  
URL https://zenodo.org/doi/10.5281/zenodo.11076773
 
Title Sources for: Path integral spin dynamics for quantum paramagnets 
Description This repository contains source code which implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2024 
Open Source License? Yes  
URL https://zenodo.org/doi/10.5281/zenodo.11073016
 
Title Sources for: Path integral spin dynamics for quantum paramagnets 
Description This repository contains source code which implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2024 
Open Source License? Yes  
URL https://zenodo.org/doi/10.5281/zenodo.11072984
 
Title Sources for: Path integral spin dynamics for quantum paramagnets 
Description This repository contains source code which implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2024 
Open Source License? Yes  
URL https://zenodo.org/doi/10.5281/zenodo.11098407
 
Title Sources for: Path integral spin dynamics for quantum paramagnets 
Description This repository contains source code which implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2024 
Open Source License? Yes  
URL https://zenodo.org/doi/10.5281/zenodo.12638435
 
Title Sources for: Path integral spin dynamics for quantum paramagnets 
Description This repository contains source code which implements a path integral approach to calculate the thermodynamics of quantum spin in a constant magnetic field along the z-direction. It contains functions for analytic solutions and a numerical approach based on atomistic spin dynamics. 
Type Of Technology Software 
Year Produced 2024 
Open Source License? Yes  
URL https://zenodo.org/doi/10.5281/zenodo.11072985