Material definitions used in Boris are available through a shared and user editable online materials database. This contains the most important material parameter values used for micromagnetic, charge and spin transport, and heat flow computations. Currently the database is small but the intention is to develop it over time as users send in entries to be added. For example these could include parameters used in publications, for materials under different growth conditions, interfaces, layer thicknesses, etc.

 

To obtain the latest material definitions in Boris, simply start the program and type the updatemdb console command. This will grab the material definitions in the table below and make them available for you to use.

 

To add a new computational mesh with given material parameters you can use the addmaterial command. The type of material will determine the type of computational mesh generated. For example the ferromagnetic type will generate a computational mesh with LLG/LLB solvers enabled. The conductor mesh type will generate a computational mesh with only the transport and heat solvers enabled, while the insulator mesh will only have the heat solver enabled (e.g. a substrate material).

 

Users can send in contributions using the requestmdbsync command after properly editing the entry (descriptions, DOI links references etc. – details in the manual). This command will place the entry in a holding database, and will be checked individually for validity before making it available in the publicly visible materials database.

 

Material parameters are listed below. Where applicable, these are given at room temperature where possible, unless otherwise specified. For definitions and descriptions hover mouse over the respective cell. Some parameter values have a DOI link enabled which gives the reference for it. You can sort the table by clicking on headers.

NameFormulaTypeContributorgrelαMs (kA/m)A (pJ/m)D (mJ/m2)J1 (mJ/m2)J2 (mJ/m2)K1 (kJ/m3)K2 (kJ/m3)ea1ea2Tc (K)μ (μB)σ (MS/m)amr (%)P(1)β(2)De(3) (m2/s)βD(4)θSHA(5)θiSHA(6)flST(7)λsf(8) (nm)λJ(9) (nm)λϕ(10) (nm)Gi (PS/m2)Gmix(11) (PS/m2)K (W/mK)ρ (kg/m3)C (J/kgK)
SiO2 SiO2 insulator N/A---------------------------1.42200730
Ni Ni ferromagnetic N/A1.10.0549080---50i1 + j0 + k0i0 + j1 + k06280.61420.440.010.0030.440-0232.35.7--1068908440
Py Ni80Fe20 ferromagnetic N/A10.02800130--00--87016.730.40.060.00160.40-06.51.61.9--46.48740430
Fe Fe ferromagnetic N/A10.0011710210--48-10i1 + j0 + k0i0 + j1 + k010442.22100.20.450.050.00290.450-09.52.24.4--79.57874450
Co_hcp Co ferromagnetic N/A1.10.0051440310--410140i0 + j0 + k1-13601.72171.90.420.0040.00410.420-0422.64.2--1228920420
MgO MgO insulator N/A---------------------------423580877
Si3N4 Si3N4 insulator N/A---------------------------853220680
Co/Pt Co ferromagnetic N/A1.30.160010-1.5--3800i0 + j0 + k1-13601.7251.90.420.0020.00120.42---4223.21 + i0.11.5 + i0.51228920420
Co90Fe10/Ru Co90Fe10 ferromagnetic N/A1.10.0071300150-103.70i1 + j0 + k0-13601.77410.340.0090.0010.34---131.72.11 + i0.11 + i0.31228800420
Pt Pt metal N/A-------------7---0.004-0.190.19-1.4----71.621452125.6
Ru Ru metal N/A-------------1.5---0.001-0.0060.006-4----11712060238
Ta Ta metal N/A-------------0.5---0.0002--0.15-0.15-1.9----57.516600140

 

(1) Current spin-polarisation defined as P = (n^{\uparrow} - n^{\downarrow}) / (n^{\uparrow} + n^{\downarrow}).

(2) Non-adiabaticity parameter used for Zhang-Li STT. In the limit of long domain wall widths this is approximated as \beta = \lambda _J^{2} / \lambda _{sf}^{2}.

(3) Electron diffusion constant, where the Einstein relation is D _e = \mu _e k _B T / e, with electron mobility linked to electrical conductivity by \sigma = n _{eff} e \mu _e. The effective density of states is given in terms of the Fermi energy as n _{eff} = g(E _F) k _B T = (3 n / 2 E _F) k _B T.

(4) Diffusion spin-polarisation defined as \beta _D = (l^{\uparrow} - l^{\downarrow}) / (l^{\uparrow} + l^{\downarrow}), where l^{\uparrow} and l^{\downarrow} are spin-dependent diffusion lengths. Values set to those of P if not known, but will not be correct in general.

(5) Spin-Hall angle. Can also be given in ferromagnetic layers, where it is used directly in the SOT added to the LLG/LLB equation, rather than in the spin transport solver. In this case it is an effective spin-Hall angle which depends on the exact multilayered stack composition, so it should refer specifically to a value used in a publication.

(6) Spin-Hall angle, but used for the inverse spin-Hall effect. Can be set to zero to disable the inverse spin-Hall effect in the spin transport solver, otherwise it should be the same as for the direct effect.

(7) Field-like SOT coefficient (ratio of field-like to damping-like SOT), used directly in the SOT added to the LLG/LLB equation, rather than in the spin transport solver. In this case the coefficient depends on the exact multilayered stack composition, so it should refer specifically to a value used in a publication.

(8) Spin-flip length, linked to the spin diffusion length by \lambda _{sdl} = \lambda _{sf} \sqrt{1 - P \beta _D}. This is also linked to the electron diffusion constant by \lambda _{sf} = \sqrt{\tau _{sf} D _e}.

(9) Exchange rotation length, linked to the exchange interaction energy between itinerant and localised electrons (s-d exchange interaction) by \lambda _J = \sqrt{\hbar D _e / J}. For these, values between J = 0.2 eV and J = 0.4 eV were assumed.

(10) Spin dephasing length, obtained as \lambda _{\phi} = \lambda _J \sqrt{l _{\perp} / l _L}. Here, l _{\perp} and l _L are the spin coherence and spin precession lengths respectively.

(11) Spin mixing conductance. The imaginary part is set to one 3rd of the real part if not known, as data in the literature on this is typically scarce.