Magnetic Refinements

Topas v5 will perform magnetic refinements. There are various options for handling the magnetic symmetry which are explored in a tutorial: Magnetic Tutorial.

Two common pitfalls are comparing moments between different pieces of software (there are several different conventions in use) and scaling moments appropriately when the magnetic cell size is different to the nuclear. Scaling is discussed in the tutorial. There are notes on moment conventions on Branton's IUCr commission website (IUCr commission website). I've reproduced the June 2012 version of these below, though they may change.

One way of checking refinements (to make sure no symmetry bugs) is to write everything out in p1 using a command like:

p1_fractional_to_file aac-0-xyzs.txt
in_str_format

and then checking the refinement in P1 (1.1). This is probably a sensible thing to do in early days of magnetic topas. You can also put the line below into an input file which will check Fmag in space group in use against P1 (1.1) with a tolerance of 1.0e-9 (it will slow the refinement a little):

test_mag 1.0e-9

Topas Coordinate System

The topas coordinate system is in Bohr Magneton/Angstrom units, with x||a, y||b and z||c. This is the reduced lattice coordinate system, where the magnetic metric tensor (M) is the same metric used for interatomic distances (G).

The refined moments can be displayed in alternate systems using macros as shown in the following:

site Fe2_1  x 0.00000 y 0.75000 z 0.00000 occ Fe+2 1  beq 1 mlx 0.00000 mly 0.00000 mlz @ 0.26118`
MM_CrystalAxis_Display( 0.00033`, 0.00000, 3.08356`)
MM_Cartesian_Display(-0.96490`, 0.00000`, 2.92859`)

In this example it's a monoclinic cell with a 18.254469 b 5.689239 c 11.428258 be 108.24182 and moments along c. These are 3.084 BM from the crystalaxis display which is equivalent to (0.9649^2 + 0^2 + 2.92859^2)^0.5 from the Cartesian.

There are also macros available which let you refine in other coordinate systems. For example, the macro MM_Cartesian_Refine(@, 0, @, 0, @, 0) corresponds to the coordinate system below.

Let X correspond to cross product.

Reciprocal lattice is:

a* = b X c
b* = c X a
c* = a X b

In MM_Cartesian_Refine, the lattice is in Cartesian coordinates, ie.

ax i
bx i + by j
cx i + cy j + cx k

where i, j, k are unit Cartesian vectors, Or,

i || a
j || a X (a X b) = a X c*
k || a X b = c*

Crystal coordinate systems for defining components of magnetic moments

[N.B. This is a frozen summary. Go to IUCr commission website for up to date information.]

(1) Bohr Magneton/Angstrom units, with x||a, y||b and z||c This is the reduced lattice coordinate system, where the magnetic metric tensor (M) is the same metric used for interatomic distances (G).

(2) Bohr Magneton units, with x||a, y||b and z||c This is the crystal-axis coordinate system, where components of the moment are defined by their projections along the lattice basis vectors. If we define L = {{a,0,0},{0,b,0},{0,0,c}}, then the magnetic metric tensor is M = L^(-1).G.L^(-1), which is unitless.

(3) Bohr Magneton units, with x||a, y||b* and z||(a x b*) This is an orthonormal coordinate system defined by a and b*. The magnetic metric tensor is the identity matrix.

(4) Bohr Magneton units, with x||a, y||(c* x a) and z||c* This is an orthonormal coordinate system defined by a and c*. The magnetic metric tensor is the identity matrix.

(5) Bohr Magneton units for the magnitude, plus two spherical-coordinate angles measured relative to the X and Z axes of system (4). φ runs from 0 to 2π in the XY plane, and θ runs from 0 to π relative to Z.

Usage

FULLPROF: Systems (2) and (5) can both be used for refinements. The implementation of system (5) requires that the a and c axes be orthogonal, excluding triclinic cases.

JANA: System (1) is used internally; but systems (2) and (5) can both be used for refinements.

GSAS: Systems (4) is used for refinements; but systems (1) and (3) can be displayed as output.

TOPAS: The parameters of system (1) are explicitly defined (in an unreleased version), though built-in macros for systems (2) and (4) are available for refinements. 