X-ray resonant reflection from magnetic multilayers on the Web

MAG_sl: X-ray resonant specular reflection from magnetic multilayers

Introduction	Program Guide	Conditions of use	Access to MAG_sl	Retrieve results	Automation/fitting

Introduction

Fig.1 This page is a CGI interface to my program MAG_sl simulating x-ray resonant specular reflection from magnetic multilayers with the account for interface roughness or transition layers. In order to use this program please read first the paper by S.Stepanov and S.Sinha "X-ray resonant reflection from magnetic multilayers: Recursion matrix algorithm", Phys. Rev. B, v.61, No 22, p.15302-15311, (2000) on which it is based. In short, there is a resonant increase at the absorption edges of some rare-earth and transition elements in the electric multipole (e.g. quadrupole) part of x-ray scattering amplitude. In this case the scattering amplitude becomes a tensor with the orientation dependent on the orientation of the magnetic moment of respective atom. The x-ray scattering caused by those additional contributions is called "resonant magnetic scattering", although it is electric by nature. When all the magnetic moments are oriented in the same direction, one can probe the magnetization of the media (e.g. thin magnetic film or magnetic multilayer) with x-rays -- see Fig.1. The effect on x-ray scattering is the strongest when the magnetic field is applied along the direction of x-ray incidence (X-axis) and the incident x-rays are circularly polarized. In the other cases the effect may still exist but be less measurable. Again, please find more details in the paper and references therein.

The MAG_sl software makes use of the same recursive matrix algorithm (RMA) as other programs on this site: GID_sl, TER_sl, and TRDS_sl. Besides, all of these programs implement very similar input. Therefore, before learning MAG_sl it might be helpful to practice with a simpler software like TER_sl that simulates x-ray specular reflectivity from multilayers with no account for magnetic resonance effects.

Program Guide

This short guide provides some explanations on the MAG_sl data input and outlines the restrictions of this Web interface.

The MAG_sl program is executed on my office PC, that runs a Web server under Windows operating system. Since this PC is shared by all of the WEB users of my x-ray library, please, avoid overloading the server by running multiple tasks at the same time.

To obtain the results from MAG_sl you need to fill out the input form and click on the SUBMIT button. If your input is correct, the results will be presented as a figure and a link to respective downloadable ZIP file that contains all the data. Otherwise, a web page with respective error message will be returned.

In case the calculation succeeds, the downloadable ZIP file will contain the following ASCII files with the results of calculations:

MAGxxxxx.INP - input file for the program generated from the Web interface (substrate data, scan parameters, etc)
MAGxxxxx.PRF - another input file for the program generated from the Web interface (surface layer profile).
MAGxxxxx.TBL - the table of calculated parameters derived from INP and PRF files (dielectric susceptibilities, etc.). The TBL file also contains the explanation of data columns in the DAT file. Always check this file to ensure that your input was treated as you expected!
MAGxxxxx.DAT - the calculated data (the reflectivity curve, etc) in the x-y ASCII format.
MAGxxxxx.PLT - the GNUplot program batch file which can be used to generate plot from the DAT file.

The specification of substrate, x-rays, and scan parameters is pretty straightforward and perhaps does not require any comments.

The specification of surface layer profile is implemented with a simple script language. A typical syntax is:

; comments are allowed in any line, but should not contain special symbols like '"*?$!@%
period=15
 t=10 code=GaAs w0=0.8 sigma=2
 t=10 code=GaAs x=0.3 code2=AlAs x2=0.7 sigma=2
 t=10 code=SiGe rho=0.9 sigma=2
 t=10 x0=(5e-4,7e-6) tr=5
 t=10 w0=.5 tr=4
 t=10 w0=0.5
 t=10
;
 code=Fe t=35
 code=Gd t=50 F11=(-0.22,9.35) F1T=(0.37,9.65) mshare=1 mvector=(1 0 0)
 code=Gd t=50 F11=(-0.22,9.35) F1T=(0.37,9.65) mdensity=2.5 mvector=(1 0 0)
end period

Here:

";" and "!" are the comment symbols. The lines starting with these symbols are ignored and when those symbols are present somewhere in the middle of the line, everything to the right of them is ignored too.
"period=" and "end period" mark the beginning and the end of a periodic group of layers. The maximum of two enclosed periods is allowed.
"t=10" is the layer thickness in Angstroms. NOTE: this is the only mandatory parameter of layer (i.e. it cannot be skipped). The other parameters, when not specified, are assigned reasonable default values -- either zero (e.g. the rms roughness height) or the same as in the substrate (e.g. the material code).
"code=" is a code of material in the X0h database. Use this code for automatic calculation of layers x0 (chi₀). For the reference of available codes see the substrate code menu or the box at the right side of the surface layers input field. Please, be advised that the codes are case sensitive (while the script keywords are not).
Alternatively you can specify the code as a valid chemical formula and provide the material density ("rho=").
If no code is specified, the substrate code is used by default.
"x=", "code2=", "x2=", "code3=" are the parameters to specify composite materials and solid solutions. For example, a structure like Ga_0.3Al_0.7As can be specified as: "code=GaAs x=0.3 code2=AlAs", or even shorter: "x=0.3 code2=AlAs" (provided that the substrate is GaAs). You can also specify "x2=0.7", but this is redundant, because the program automatically takes care of the sum of all "xN" being equal to one (e.g. the input like "x2=0.8" in the above example would cause an error message).
Maximum of 4 codes are allowed per layer and all of them must correspond to existing records in the X0h database.
"x0=" is the layer x-ray susceptibility chi₀. This parameter, when specified, replaces the data given by the X0h database.
NOTE-1: x0 comes from the dynamical diffraction theory. It is related with the parameters delta and eta often used for reflectivity as: x0=2*(delta+i*eta).
NOTE-2: When you specify the x0 parameter it is normally converted into: x0 = (-|x0r|, |x0i|). This is because the x-ray server programs use the exp(ikr) representation of plane waves for which one normally expects x0r < 0. However, this does not cover some absorption edges in the soft x-ray region where apparently x0r may change its sign. To disable the default transformation, you can use the edge=1 flag in combination with the "x0=..." input. In this case the x0r data for this layer is used as entered.
"w0=" is a Debye-Waller-like factor for x0. It may be used to correct the x0 value provided by the X0H database:
```
                   x0=w0*x0
```
By default, this factor is equal to one. Unlike usual Debye-Waller factor, w0 can be greater than one, because it is simply one more way to specify x0.
"sigma=" and "tr=" are the rms roughness and the transition layer thickness at the upper layer interface, respectively, expressed in Angstroms. You are not allowed to specify non-zero values for both of these parameters for the same layer and the values should not exceed the layer thickness. The calculations with "sigma" are much faster. However, at sigma > ~5A they become inaccurate (the Nevot and Croce method becomes inapplicable) and "tr"should be used instead (tr=2*sigma).
"mshare=" and "mdensity=" are the share of magnetic atoms (e.g. the number in the [0.:1.] range), and their density in atoms/cm^3, respectively. Only one of the two can be specified at the same time.
"mvector=(x,y,z)" is parameter defining the orientation of magnetic moments in the layer. The x,y,z coordinates are chosen as follows: x along beam on the surface; z along the internal normal to the surface, y perpendicular to the above two.
"F10=", "F11=", "F1T=", are the resonant scattering amplitudes renormalized with the (3*lambda)/(8*pi*r0) modifier (r0 is the classical electron radius):
See Eq.(17)-(21) in the paper for more details. For some of the magnetic resonances those amplitudes can be found in the Ph. D. thesis by M.D.Hamrick (see Ref.[41] in the paper). Unfortunately I am not aware of any comprehensive tables for those amplitudes. One may consider determining them experimentally.

Below is a practical example -- a profile for 15-period Gd/Fe multilayer with 50 Angstroms of resonantly reflecting Gd and 35 Angstroms of non-resonant Fe in each period. The magnetic momenta of all Gd atoms are assumed to be aligned along the direction of incident beam (x-axis):

period=15
 code=Gd t=50 F11=(-0.22,9.35) F1T=(0.37,9.65) mshare=1 mvector=(1 0 0)
 code=Fe t=35
end period

For the rest of parameters you are suggested to follow the common sense. To ensure that your input was correct, please verify respective listing file -- a file with the ".TBL" extension in the ZIPped archive referred from the MAG_sl results screen.

Access to MAG_sl

To simplify understanding the MAG_sl you can start with several templates listed below. They correspond to Figures 3 to 5 of the paper respectively. All the templates link to the same program and provide the same functionality. They differ by preloaded data to demonstrate some possible applications of MAG_sl.
Besides, when submitting the MAG_sl task, it is possible to check the progress watching option. The progress watching is obviously more comfortable, but it might not work with some old Web browsers. Also, it is a bit slower because of putting an additional load on the network and launching each 5 seconds a monitoring program on my computer. Welcome to try both of the ways and choose the most convenient for your needs.

New of December-2012: POST-Method Templates

GET-Method Templates
This is an older, but better tested method. Generally it works very well except for
known problems with the IE browser & some firewalls when the structure description
exceeds 2K bytes (with some firewalls the restriction may be even 1K bytes).

Retrieve results

Here is a tool to retrieve the results of finished jobs if you know the job ID. Some possible uses of this tool are:

You started a job with the progress watch option; the server returned the job ID and began reporting the progress. However, you found that the calculations would take too long. Then, you may break the connection and retrieve the data later on with this tool. If the calculations are not finished, the tool will resume the watch process.
The data are accidentally deleted from your client computer and you want another copy of them. In this case you should be aware that results are usually stored on the server for about one day after respective job is finished.