# Extracted PowerPoint Skeleton

Source: `/Users/yimingzhang/My Drive (duseryiming@gmail.com)/Presentations/2026_IRM_summer_school/micromagnetics.pptx`
Slides: 49

## Slide 1: Micromagnetic Modeling
- Insert example micromagnetic modeling figure

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## Slide 2: So far we have covered….First principles theory + macroscopic experiments
- In theory:Fine-particle magnetismDomain states and their magnetic propertiesMagnetic mineralogyMaterial magnetic propertiesMagnetic anisotropy
- In the lab:Hystresis loop, backfield, FORC (VSM)NRM, TRM, IRM, ARM, etc (SQUID SRM)Temperature dependent remanence (MPMS measurements)X-T, AMS (Kappa bridge, MFK, magnon)

## Slide 3: So far we have covered….First principles theory + macroscopic experiments
- In the lab:X-T, AMS (Kappa bridge, MFK, magnon)Hystresis loop, backfield, FORC (VSM)NRM, TRM, IRM, ARM, etc (SQUID SRM)Temperature dependent remanence (MPMS measurements)

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## Slide 4: So far we have covered….First principles theory + macroscopic experiments
- In the lab:X-T, AMS (Kappa bridge, MFK, magnon)Hystresis loop, backfield, FORC (VSM)NRM, TRM, IRM, ARM, etc (SQUID SRM)Temperature dependent remanence (MPMS measurements)

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## Slide 5: So far we have covered….First principles theory + macroscopic experiments
- In the lab:X-T, AMS (Kappa bridge, MFK, magnon)Hystresis loop, backfield, FORC (VSM)NRM, TRM, IRM, ARM, etc (SQUID SRM)Temperature dependent remanence (MPMS measurements)

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## Slide 6: So far we have covered….First principles theory + macroscopic experiments
- In the lab:X-T, AMS (Kappa bridge, MFK, magnon)Hystresis loop, backfield, FORC (VSM)NRM, TRM, IRM, ARM, etc (SQUID SRM)Temperature dependent remanence (MPMS measurements)

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## Slide 7: Results interpretation and experimental design depends on micromagnetic understandingThis is a material science topic

## Slide 8: Computational material science
- Length scale
- e.g. the Verywey transition
- https://www.q-chem.com/explore/dft/cdft/
- Ti-Fe oxide phase diagram
- Micromagnetic modeling

Notes:
- Bai, F., Chang, L., Berndt, T. A., & Pei, Z. (2021). Micromagnetic calculations of the effect of magnetostatic interactions on isothermal remanent magnetization curves: Implications for magnetic mineral identification. Journal of Geophysical Research: Solid Earth, 126, e2021JB022335. https://doi. org/10.1029/2021JB022335Ge et al 2014 Geochem. Geophys. Geosyst., 15, 2021–2038, doi:10.1002/2014GC0052620 layers modeling a multilayer core-shellGe, K., Williams, W., Nagy, L., & Tauxe, L. (2021). Models of maghematization: Observational evidence in support of a magnetic unstable zone. Geochemistry, Geophysics, Geosystems, 22, e2020GC009504https://doi. org/10.1029/2020GC009504
- 2022 SSRM
- 5/11/2024
- 31

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## Slide 9: https://doi.org/10.1080/08927021003774287
- water-ice

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## Slide 10: An introduction to the atomistic modelCrystal and magnetic structure

## Slide 11: An introduction to the atomistic modelchemical energy model

## Slide 12: An introduction to the atomistic modelmagnetic energy model

## Slide 13: Simulation methodsmonte carlo

## Slide 14: Hemoilmenite example
- Chemical energy
- Magnetic energy
- Resultant lamellar magnetism

## Slide 15: Mesoscale Modelingprevious theory and modeling
- Butler, 1992

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## Slide 16: Mesoscale Modelingprevious theory and modeling
- Butler, 1992; Néel 1955

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## Slide 17: Natural magnetic grains in rocks
- 5 X
- 10 X
- Berkeley Hills volcanic rock
- Minnesota plagioclase in intrusive rock
- Metamorphosed anorthosite from Quebec
- 10 X

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## Slide 18: Natural magnetic grains in rocks
- Feinberg et al., 2006
- Zhang et al., 2021
- Bian et al., 2025

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## Slide 19: Natural magnetic grains in rocks
- Bian et al., 2025
- Wagner et al., 2021

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## Slide 20: Wyn Williams
- Karl Fabian
- Lesleis Nagy

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## Slide 21: Difference between materials research and rock magnetism research
- Materials researchRegular geometriesHomogeneous compositionVery short timescalesLandau-Lifshitz-Gilbert equationFinite difference modeling

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## Slide 22: Difference between materials research and rock magnetism research
- Rock magnetism researchIrregular geometriesHomogeneous/heterogeneous compositionLarge range of timescalesLocal energy minima (LEM)Finite element modeling
- Nikolaisen et al., 2020

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## Slide 23: FEM micromagnetic modeling
- Represent realistic grain geometry with small tetrahedron meshEach tetrahedron represents a small chunk of atoms
- Approximate micromagnetic behaviors Anisotropy energyExchange energyDemagnetizing energyExternal field energy (Zeeman energy)
- Hamiltonian physics is a way of describing motion and stability using energy, and in micromagnetics it helps us understand how tiny magnetic moments choose their directions by balancing different energy costs and rewards.

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## Slide 24: Magnetocrystalline: Cubic
- The Magnetic Energy Components
- Micromagnetic Theory
- []
- [010]
- [001]
- [100]
- []
- , are the direction cosines of the magnetization vectorand are the (temperature –dependent)crystalline anisotropy constants
- Slide from Wyn Williams

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## Slide 25: Magnetocrystalline:cubic
- The Magnetic Energy Components
- Micromagnetic Theory
- []
- [010]
- [001]
- [100]
- []
- Slide from Wyn Williams

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## Slide 26: Exchange
- The Magnetic Energy Components
- Micromagnetic Theory
- is the (temperature –dependent)Exchange constant
- Slide from Wyn Williams

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## Slide 27: External Field (Zeeman energy)
- The Magnetic Energy Components
- Micromagnetic Theory
- is the (temperature –dependent)saturation (intrinsic) magnetization
- No field
- Slide from Wyn Williams

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## Slide 28: Demagnetizing energy (Stray field)
- The Magnetic Energy Components
- Micromagnetic Theory
- is the magnetic scalar potential and must be defined in all space.
- =
- an be calculated in many different ways:Define non-magnetic mesh to infinity.Thin non-magnetic mesh, spatially ‘transformed’ to infinity.Integration of free space on to the boundary of the magnetic region. ⟹ Boundary Element Method
- Slide from Wyn Williams

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## Slide 29: Demagnetizing energy (Stay field)
- The Magnetic Energy Components
- Micromagnetic Theory
- is the magnetic scalar potential and must be defined in all space.
- =
- = -
- Slide from Wyn Williams

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## Slide 30: Demagnetizing energy (Stay field)
- The Magnetic Energy Components
- Micromagnetic Theory
- is the magnetic scalar potential
- =
- Slide from Wyn Williams

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## Slide 31: Micromagnetic Modeling
- Single particles or assemblages
- Variable compositionOxidation: core-shell
- Realistic natural particle morphologiesfocused ion beam nanotomographyMagnetic particle in obsidian
- Ge et al 2014
- Bai et al 2021
- Lascu et al. 2018
- SimulateHysteresisRemanence curvesFORC diagramsRelaxation times
- 31

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## Slide 32: Micromagnetic application
- Show uniformly magnetized 30nm cubeShow 80nm cube with vortex edgesShow 80nm cube with vortex along diagonal

## Slide 33: Micromagnetic application
- Show temperature dependence of A and KShow x-T simulation for Kappabridge Touch on the possibility of simulating AMS

## Slide 34: Micromagnetic application
- Show simulation of hysteresis

## Slide 35: Micromagnetic application
- Show energy comparison between vortex and uniform stateShow energy comparison between two opposite vortex statesIntroduce NEB

## Slide 36: Micromagnetic application
- From NEB energy barrier to relaxation time and VRM acquisition, linking back to Arrhenius equation and the relaxation graph in the first principles theory

## Slide 37: Micromagnetic application
- Progress on continuous time Markov chain application in micromagnetic modeling

## Slide 38: MERRILL – hands on
- Example 5a….f

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## Slide 39: MERRILL – hands on
- Example 5a….f

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## Slide 40: MERRILL – hands on
- Example 5a….f

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## Slide 41: MERRILL – hands on
- Example 5a….f

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## Slide 42: MERRILL – hands on
- Example 5a….f

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## Slide 43: MERRILL – hands on
- Example 5a….f

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## Slide 44: MERRILL – hands on
- Field along ~ 1, 0, 0
- Field along ~ 1, 1, 1

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## Slide 45: Micromagnetic modeling on an MD grain

## Slide 46: MD grain modeling
- natural oxidized titanomagnetite (Krása et al., 2005)
- Pokhil and Moskowitz, 1997; Hurbert and Schäfer, 1998
- Imaging surface charges withMagnetic Force Microscopy
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- 13x13 m

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## Slide 47: Slide 47

## Slide 48: Slide 48

## Slide 49: Slide 49