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CrystalFieldMagnetisation.cpp
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CrystalFieldMagnetisation.cpp
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#include "MantidCurveFitting/Functions/CrystalFieldMagnetisation.h"
#include "MantidCurveFitting/Functions/CrystalFieldPeaksBase.h"
#include "MantidCurveFitting/Functions/CrystalElectricField.h"
#include "MantidCurveFitting/FortranDefs.h"
#include "MantidAPI/FunctionFactory.h"
#include "MantidAPI/FunctionValues.h"
#include "MantidAPI/FunctionDomain.h"
#include "MantidAPI/FunctionDomain1D.h"
#include "MantidAPI/IFunction1D.h"
#include "MantidAPI/Jacobian.h"
#include "MantidKernel/Exception.h"
#include "MantidKernel/PhysicalConstants.h"
#include <cmath>
#include <boost/algorithm/string/predicate.hpp>
namespace Mantid {
namespace CurveFitting {
namespace Functions {
namespace {
// Does the actual calculation of the magnetisation
void calculate(double *out, const double *xValues, const size_t nData,
const ComplexFortranMatrix &ham, const int nre,
const DoubleFortranVector Hmag, const double T,
const double convfact, const bool iscgs) {
const double beta = 1 / (PhysicalConstants::BoltzmannConstant * T);
// x-data is the applied field magnitude. We need to recalculate
// the Zeeman term and diagonalise the Hamiltonian at each x-point.
int nlevels = ham.len1();
for (size_t iH = 0; iH < nData; iH++) {
DoubleFortranVector en;
ComplexFortranMatrix ev;
DoubleFortranVector H = Hmag;
H *= xValues[iH];
if (iscgs) {
H *= 0.0001; // Converts from Gauss to Tesla.
}
calculateZeemanEigensystem(en, ev, ham, nre, H);
// Calculates the diagonal of the magnetic moment operator <wf|mu|wf>
DoubleFortranVector moment;
calculateMagneticMoment(ev, Hmag, nre, moment);
double Z = 0.;
double M = 0.;
for (auto iE = 1; iE <= nlevels; iE++) {
double expfact = exp(-beta * en(iE));
Z += expfact;
M += moment(iE) * expfact;
}
out[iH] = convfact * M / Z;
}
}
// Calculate powder average - Mpowder = (Mx + My + Mz)/3
void calculate_powder(double *out, const double *xValues, const size_t nData,
const ComplexFortranMatrix &ham, const int nre,
const double T, const double convfact, const bool cgs) {
for (size_t j = 0; j < nData; j++) {
out[j] = 0.;
}
// Loop over the x, y, z directions
DoubleFortranVector Hmag(1, 3);
std::vector<double> tmp(nData, 0.);
for (int i = 1; i <= 3; i++) {
Hmag.zero();
Hmag(i) = 1.;
calculate(&tmp[0], xValues, nData, ham, nre, Hmag, T, convfact, cgs);
for (size_t j = 0; j < nData; j++) {
out[j] += tmp[j];
}
}
for (size_t j = 0; j < nData; j++) {
out[j] /= 3.;
}
}
}
DECLARE_FUNCTION(CrystalFieldMagnetisation)
CrystalFieldMagnetisation::CrystalFieldMagnetisation()
: CrystalFieldPeaksBase(), API::IFunction1D(), m_nre(0),
m_setDirect(false) {
declareAttribute("Hdir", Attribute(std::vector<double>{0., 0., 1.}));
declareAttribute("Temperature", Attribute(1.0));
declareAttribute("Unit", Attribute("bohr")); // others = "SI", "cgs"
declareAttribute("powder", Attribute(false));
declareAttribute("ScaleFactor", Attribute(1.0)); // Only for multi-site use
}
// Sets the base crystal field Hamiltonian matrix
void CrystalFieldMagnetisation::setHamiltonian(const ComplexFortranMatrix &ham,
const int nre) {
m_setDirect = true;
m_ham = ham;
m_nre = nre;
}
void CrystalFieldMagnetisation::function1D(double *out, const double *xValues,
const size_t nData) const {
// Get the field direction
auto Hdir = getAttribute("Hdir").asVector();
if (Hdir.size() != 3) {
throw std::invalid_argument("Hdir must be a three-element vector.");
}
auto T = getAttribute("Temperature").asDouble();
auto powder = getAttribute("powder").asBool();
double Hnorm =
sqrt(Hdir[0] * Hdir[0] + Hdir[1] * Hdir[1] + Hdir[2] * Hdir[2]);
DoubleFortranVector H(1, 3);
if (fabs(Hnorm) > 1.e-6) {
for (auto i = 0; i < 3; i++) {
H(i + 1) = Hdir[i] / Hnorm;
}
}
auto unit = getAttribute("Unit").asString();
const double NAMUB = 5.5849397; // N_A*mu_B - J/T/mol
// Converts to different units - SI is in J/T/mol or Am^2/mol.
// cgs is in erg/Gauss/mol (emu/mol). The value of uB in erg/G is 1000x in J/T
// NB. Atomic ("bohr") units gives magnetisation in uB/ion, but other units
// give the molar magnetisation.
double convfact = boost::iequals(unit, "SI")
? NAMUB
: (boost::iequals(unit, "cgs") ? NAMUB * 1000. : 1.);
const bool iscgs = boost::iequals(unit, "cgs");
if (!m_setDirect) {
// Because this method is const, we can't change the stored en / wf
// Use temporary variables instead.
DoubleFortranVector en;
ComplexFortranMatrix wf;
ComplexFortranMatrix ham;
ComplexFortranMatrix hz;
int nre = 0;
calculateEigenSystem(en, wf, ham, hz, nre);
ham += hz;
if (powder) {
calculate_powder(out, xValues, nData, ham, nre, T, convfact, iscgs);
} else {
calculate(out, xValues, nData, ham, nre, H, T, convfact, iscgs);
}
} else {
// Use stored values
if (powder) {
calculate_powder(out, xValues, nData, m_ham, m_nre, T, convfact, iscgs);
} else {
calculate(out, xValues, nData, m_ham, m_nre, H, T, convfact, iscgs);
}
}
auto fact = getAttribute("ScaleFactor").asDouble();
if (fact != 1.0) {
for (size_t i = 0; i < nData; i++) {
out[i] *= fact;
}
}
}
} // namespace Functions
} // namespace CurveFitting
} // namespace Mantid