Spin wave spectrum of the distorted kagome KCu3As2O7(OD)3

This is the calculation used to estimate the spin exchange parameters in KCu3As2O7(OD)3: [1] G. J. Nilsen, et al., PRB 89, 140412 (2014). This section defines the positions of the magnetic moments using the space group operators and the spin Hamiltonian.

Define the lattice
Magnetic ground
Optimised ground state
Spin wave dispersion
Test dispersion on commensurate cell
Powder averaged spectrum

Define the lattice

J   = -2;
Jp  = -1;
Jab = 0.75;
Ja  = -J/.66 - Jab;
Jip = 0.01;

hK = spinw;
hK.genlattice('lat_const',[10.2 5.94 7.81],'angled',[90 117.7 90],'spgr','C 2/m')

hK.addatom('r',[0   0   0],'S',1/2,'label','MCu2','color','b')
hK.addatom('r',[1/4 1/4 0],'S',1/2,'label','MCu2','color','k')

hK.gencoupling

hK.addmatrix('label','J-',  'color','r',   'value',J)
hK.addmatrix('label','J''','color','g',   'value',Jp)
hK.addmatrix('label','Ja', 'color','b',   'value',Ja)
hK.addmatrix('label','Jab','color','cyan','value',Jab)
hK.addmatrix('label','Jip','color','gray','value',Jip)

hK.addcoupling('mat','J-','bond',1)
hK.addcoupling('mat','J''','bond',2)
hK.addcoupling('mat','Ja','bond',3)
hK.addcoupling('mat','Jab','bond',5)
hK.addcoupling('mat','Jip','bond',10)

hK.plot('range',[2 2 0.3],'bondMode','line','bondLineWidth0',2,...
    'cellMode','none','atomLegend',false,'baseShift',[4 -3 0]')
swplot.zoom(1.4)

Magnetic ground

Approximate ground magnetic ground state with a single k-vector: S_i = 2*pi*k*r_i. The magnetic unit cell is defined using the rotating coordinate system.

hK.genmagstr('mode','helical','n',[0 0 1],'S',[1 0 0]','k',[0.77 0 0.115],'next',[1 1 1]);
hK.plot('range',[2 2 0.3],'bondMode','line','bondLineWidth0',2,...
    'cellMode','inside','atomLegend',false,'baseShift',[4 -3 0]')
swplot.zoom(1.4)

hK.energy

Ground state energy: -0.783 meV/spin.

Optimised ground state

To determine the exact ordering wave vector, the magnetic structure is optimised using non-linear optimisation algorithm and assuming planar magnetic structure. From the optimal ordering wave vector the exact spin directions are created.

optpar.func = @gm_planar;
optpar.nRun = 5;
optpar.xmin = [    zeros(1,6), 0.5 0 0.0, 0 0];
optpar.xmax = [2*pi*ones(1,6), 1.0 0 0.5, 0 0];

hK.genmagstr('mode','random','nExt',[1 1 1])
magoptOut = hK.optmagstr(optpar);

kOpt = hK.mag_str.k;
hK.genmagstr('mode','helical','n',[0 0 1],'S',[1 0 0]','k',kOpt','next',[1 1 1]);

hK.plot('range',[2 2 0.3],'bondMode','line','bondLineWidth0',2,...
    'cellMode','inside','atomLegend',false,'baseShift',[4 -3 0]')
swplot.zoom(1.4)

hK.energy

Ground state energy: -0.783 meV/spin.

Spin wave dispersion

We calculate the spin wave dispersion and spin-spin correlation function S(Q,omega) and plot S^perp that gives the neutron scattering cross section.

hkSpec = hK.spinwave({[0 0 0] [1 0 0] 500},'hermit',false);
hkSpec = sw_neutron(hkSpec);
hkSpec = sw_egrid(hkSpec,'Evect',linspace(0,5,500),'imagChk',false);

figure
sw_plotspec(hkSpec,'mode','pretty','linestyle','-');
caxis([0 20])

Test dispersion on commensurate cell

We recalculate the dispersion on a superlattice, that should give the same S(Q,omega), but it is much slower. We choose the superlattice, that approximates the propagation vector within 0.05 rlu by giving this number to the 'nExt' option in spinw.genmagstr() instead of the vector with three integers. We create the magnetic superlattice and then define the k-vector as zero. In this case the spinw.spinwave function will be run in commensurate mode. Carefull, this code will create a magnetic supercell with 270 atoms.

hK.genmagstr('mode','helical','next',0.05) hK.mag_str.k = [0 0 0]';

hkSpec = hK.spinwave({[0 0 0] [1 0 0] 50},'Hermit',false); hK.fileid(0) hkSpec = sw_neutron(hkSpec,'pol',false); hkSpec = sw_egrid(hkSpec,'Evect',linspace(0,5,500),'imagChk',false);

figure sw_plotspec(hkSpec,'mode','color','axlim',[0 20],'dE',0.3);

Powder averaged spectrum

We calculate the powder spectrum on the smaller unit cell between Q = 0 - 3 Angstrom^-1.

hK.genmagstr('mode','helical','n',[0 0 1],'S',[1 0 0]','k',kOpt','next',[1 1 1]);
powSpec = hK.powspec(linspace(0,3,80),'nrand',500,'Evect',linspace(0,5,500));

figure;
sw_plotspec(powSpec,'dE',0.01,'axlim',[0 0.05])

Written by
Goran Nilsen and Sandor Toth
27-Jun-2014, 06-Feb-2017

Tutorial 18