## Phd LPTM : Cergy-Pontoise, France

### Spin transport in magnetic thin films materials by Monte Carlo simulations.

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In the past decade, spin transport have caught the attention of many researchers [1,2,3,4,5,6,7]. The spin resistivity ρ, has been shown to depend on magnetic ordering stability. At low temperatures T, scattering of itinerant electrons is due to spin-waves. However, at high temperatures, ρ is proportional to the spin-spin correlations so that its behavior is complicated around the magnetic transition temperature. The purpose of my PhD consists to investigate spin transport mechanisms by Monte Carlo simulations in a context of spintronic emergence, where a precise comprehension of scattering mechanisms is requiered in the elaboration of new nanotechnology devices.

The model developed allow an unified procedure to study spin scattering and resistivity for different solids and in a large range of temperature. In case of ferromagnetic semiconductor materials [8,10], we highlighted different parts of magnetic resistivity behavior in function of temperature, figure 1.A.

**Figure-1 : A. ***Resistivity ρ in arbitrary units versus temperature T, for different magnetic fields B: 0 (black circles), 0.25 (empty circles), 0.5(black triangles), 0.75 (empty triangles).*

- At low temperature T<5, the resistivity increase with decreasing T. The origin of this behavior comes from itinerant spins freezing due to their interactions with a well ordered lattice.
- Below the critical temperature 5<T<10, the solid consists in a large cluster of parallel spins with some isolated antiparallel sites wish play the role of center of diffusion. In that temperature range, the resistance decreases with increasing T.
- At Tc~10, the resistivity exhibits a peak. This behavior come from the coupling between itinerant spins and fluctuation of the lattice spins. We found that the resistivity peak is a consequence of the lattice percolation which drive itinerant spins to localize in large parallel lattice spin clusters (low energy area) figure 1.B.

**Figure-1 : B. ***3D visualisation of itinerant spin localisation (blue arrow) in the lattice (red arrow) near the temperature transition.*

This qualitative results was corroborated by an approach based on the Boltzmann equation considering lattice spin clusters as centers of diffusion [11].

The model also allow comparison between simulations and experimental data. We chose an antiferromagnetic semiconductor MnTe which exhibits a high Néel temperature T~300K. We found a good agreement between simulations and experiments [13].

An other part of this work consisted in study frustrated antiferromagnetic materials [9]. In case of an Ising model, the spin resistivity versus temperature exhibits a discontinuity at the temperature transition Tn (a first order transition [12]): an upward jump or a downward fall, depending on which degenerate state the system comes from, figure 2.A.

**Figure-2 : A. ***Resistivity function of T for first (white points) and second degenerate (black points) states. The insets show the two degenerate states with the red planes underlining the ferromagnetic plane in a unit cell.*

**Figure-2 : B.*** Energy landscape at T=1 in a cubic box of dimension 2ax2ax2a (with a the lattice parameter) for the first and second degenerate states. The energy scale is indicated on the figure in abitrary units.*

In the case of degenerate state 1, figure 2.A, inset 1, electrons travel along ferromagnetic planes (low energy planes) parallel to the applied electrical field, figure 2.B1. In that case, ρ is low below Tn and exhibits an upward jump at Tn, figure 2.A. In case of degenerate state 2, figure 2.A, inset 2, electrons are slowed down by perpendicular ferromagnetic planes (energy barriers) and propagate across high energy planes 2.B2, leading to a downward fall at Tn.

Finally, electron diffusivity strongly depends on lattice-electron interaction length, that determine how many parallel and antiparallel lattice spins interacting with a given electron, figure.3.

**Figure-3 : ***Different physical quantities versus D1 (interaction length) in lattice unit a in the case of the first and second degenerate states. From top to bottom: resistivity, velocity, difference of the number of spin up and down located within the interaction length, energy of an itinerant spin. In each plot the circles correspond to T=Tn-dT, and the diamonds to T=Tn+dT.*

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