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chizz contains the molar static magnetic susceptibility. This is not the full 3x3 susceptibility tensor χ_m, but its component along the applied magnetic field direction zL χ_m,zz. The values are in SI units (m 3 mol -1 ). To convert chizz from SI units to CGS units (cm 3 mol -1 ), use

Populations are computed for all energy levels assuming thermal Boltzmann equilibrium and are included in the calculation of the magnetic moment and the magnetic susceptibility. Populations are computed for all energy levels assuming thermal Boltzmann equilibrium and are included in the calculation of the magnetic moment and the magnetic susceptibility.

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Curry more magnic

Calculates magnetometry data: magnetic moment, static magnetic susceptibility.

curry(Sys,Exp); curry(Sys,Exp,Opt); muz = curry(. ); [muz,chizz] = curry(. ); [. ] = curry(. );

See also the user guide on how to use curry .

curry calculates the magnetic moment and the molar static magnetic susceptibility for given fields and temperatures.

There are up to two standard output arguments (here standard refer to empty Opt.Output ). If no output argument is requested, curry plots the calculated curves.

muz contains the values of the longitudinal magnetic moment, i.e. along the direction of the applied magnetic field (zL), for the fields and temperatures requested.

The units are either Bohr magnetons μ_B if the value is understood as single-molecule magnetic moment μ_z, or N_Aμ_B if the value is understood as molar magnetic moment μ_m,z. N_A is the Avogadro constant. For example, muz = 0.53 means the single-molecule magnetic moment μ_z is 0.53 μ_B and the molar magnetic moment μ_m,z is 0.53 N_Aμ_B. To convert the molar magnetic moment to SI units (J T -1 mol -1 ), use

muz_SI = muz*avogadro*bmagn; % unit conversion from NA*muB to J T^-1 mol^-1

chizz contains the molar static magnetic susceptibility. This is not the full 3x3 susceptibility tensor χ_m, but its component along the applied magnetic field direction zL χ_m,zz. The values are in SI units (m 3 mol -1 ). To convert chizz from SI units to CGS units (cm 3 mol -1 ), use

chizz_cgs = chizz_SI/(4*pi*1e-6); % unit conversion from SI to CGS units

If Opt.Output is given the number of outputs depend on Opt.Output (see Output).

There are three inputs to the function, the last one is optional.

Sys is a spin system structure containing the spin quantum numbers and the spin Hamiltonian parameters. In addition to the parameters used by all EasySpin functions, TIP can be introduced.

Temerature-independent paramagnetism added to the magnetic susceptibility. EasySpin understand TIP to be in SI units.

TIP_cgs = 7e-4; % TIP in cm^3 mol^-1 TIP_SI = (4*pi*1e-6) * TIP_cgs; % TIP in SI units Sys.TIP = TIP_SI;

Exp contains experimental parameters such as the magnetic field range and temperature. Compared to EasySpin's EPR simulation functions, curry needs only very few parameters.

This gives the temperature, or list of temperatures, for which magnetization data should be calculated, in kelvin. For example, Exp.Temperature = 298 corresponds to room temperature, and Exp.Temperature = 4:300 specifies a temperature range. If an array of values is given, data are calculated for each temperature in the array.

Populations are computed for all energy levels assuming thermal (Boltzmann) equilibrium and are included in the calculation of the magnetic moment and the magnetic susceptibility.

Temperature has to be provided.

Field gives the magnetic field strength, in mT, for which magnetization data should be calculated. If an array of values is given, data are calculated for each field value in the array.

If Field is missing, EasySpin assumes that no field is applied.

Magnetic moment is often measured as a function of field and for a few temperatures, while molar static magnetic susceptibility is measured as function of temperature for a few fields. This can be done also in simulations:

Temperature or list of Temperatures, for which magnetic susceptibility should be calculated, in Kelvin.

Magnetic field strength, in mT, for which magnetic susceptibility should be calculated. If an array of values is given, data are calculated for each field value in the array.

Magnetic field strength, in mT, for which magnetic moment should be calculated. If an array of values is given, data are calculated for each field value in the array.

curry calculates magnetic susceptibility as numeric derivative of the magnetic moment at the given field value. However, the experimental data is often obtained by measuring the magnetization at a given field value and divide it by the field strength. For sufficiently small field strength this correspond to the derivative at zero field. In cases the field strength is not small experimental results might be better reproduced by:

m4chi = curry(Sys,Exp,Opt); % magnetic moment at the field used in the experiment % divide magnetic moment by magnetic field and unit conversion chisim_cgs = m4chi*avogadro*bmagn*1e2./repmat(Exp.Field(:),1,numel(Exp.Temperature)); chisim_si = (4*pi*1e-6) *chisim_cgs ; % convert to SI units

curry not only supports powder samples, but also single crystals. The following fields are needed for single-crystal calculations:

An Nx3 or Nx2 array that specifies single-crystal orientations for which the magnetic moment and the susceptibility should be computed. Each row of CrystalOrientation contains the three Euler rotation angles that transform the crystal frame (C) to the lab frame (L). If only two Euler angles are given, the third is set to zero. If CrystalOrientation is empty or not specified, the full powder is computed.

Exp.CrystalOrientation = [0 0 0]; % single crystal, crystal z axis aligned with B0 Exp.CrystalOrientation = [0 pi/2 0]; % single crystal, crystal z axis perpendicular to B0 Exp.CrystalOrientation = [0 0 0; 0 pi/2 0]; % two crystals Exp.CrystalOrientation = []; % powder

Specifies the symmetry of the crystal. You can give either the number of the space group (between 1 and 230), the symbol of the space group (such as 'P212121' or 'Ia-3d' ), or the symbol for the point subgroup of the space group (in either Schönflies or Hermann-Mauguin notation, such as 'D2h' or 'mmm' ).

Exp.CrystalSymmetry = 11; % space group number (between 1 and 230) Exp.CrystalSymmetry = 'P21/c'; % space group symbol Exp.CrystalSymmetry = 'C2h'; % point group, Schönflies notation Exp.CrystalSymmetry = '2/m'; % point group, Hermann-Mauguin notation

When CrystalSymmetry is given, all symmetry-related sites in the crystal are generated and included in the calculation. If CrystalSymmetry is not given, space group 1 (P1, point group C1, one site per unit cell) is assumed.

The three Euler angles, in radians, for the transformation of the crystal frame to the molecular frame. Use this field when specifying a crystal containing spin systems that are tilted with respect to the crystal frame. E.g. Param.MolFrame=[0,pi/4,0] tilts the x and z axis of the spin system's molecular frame (xM, zM), relative to the crystal frame (xC,yC,zC).

The structure Opt collects computational parameters. Opt need not be specified, in which case default values for all fields are used. The field names and their possible values are as follows.

String to specify the output curry should provide in the given order. Keywords should be seperated by blanks. The following keywords are allowed:

If Opt.Output is given the number of outputs depend on Opt.Output (see Output).

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