Tutorial 4#
Antiferromagnetic square lattice#
We define a square lattice in the ab plane, with Cu+ ions with S=1 spin.
Define the lattice#
AFsq = spinw;
AFsq.genlattice('lat_const',[3 3 6],'angled',[90 90 90],'spgr',0)
AFsq.addatom('r',[0 0 0],'S', 1,'label','Cu1','color','b')
AFsq.table('atom')
plot(AFsq)
swplot.zoom(1.5)
ans =
1x4 table
matom idx S pos
_____ ___ _ ___________
'Cu1' 1 1 0 0 0
Couplings#
We create first neighbor couplings in the ab plane and plot the bonds. You can click on the different bonds to get the value of the corresponding matrix.
AFsq.gencoupling('maxDistance',5)
AFsq.table('bond',[])
AFsq.addmatrix('label','J1','value', 1,'color','red')
AFsq.addmatrix('label','J2','value',-0.1,'color','green')
AFsq.addcoupling('mat','J1','bond',1)
AFsq.addcoupling('mat','J2','bond',2)
plot(AFsq,'range',[2 2 0.5])
ans =
4x10 table
idx subidx dl dr length matom1 idx1 matom2 idx2 matrix
___ ______ _____________ _____________ ______ ______ ____ ______ ____ ______________
1 1 1 0 0 1 0 0 3 'Cu1' 1 'Cu1' 1 '' '' ''
1 2 0 1 0 0 1 0 3 'Cu1' 1 'Cu1' 1 '' '' ''
2 1 1 -1 0 1 -1 0 4.243 'Cu1' 1 'Cu1' 1 '' '' ''
2 2 1 1 0 1 1 0 4.243 'Cu1' 1 'Cu1' 1 '' '' ''
Magnetic structure#
For weak second neighbor ferromagnetic interaction the magnetic structure is Neel type, with the following parameters:
ordering wave vector k = (1/2 1/2 0)
spin are in arbitrary plane, lets point along the S = (1 0 0) direction
normal to the spin vectors n = (0 0 1)
magnetic supercell is 2x2x1
We use magnetic supercell, since the 2*k equal to a reciprocal lattice vector. In this case the spin wave code cannot use the incommensurate mode, thus we have to create a zero-k structure, that is a 2x2x1 magnetic supercell.Note that the spinw.genmagstr() automatically normalizes the spin vectors to the spin value of the magnetic atoms.
AFsq.genmagstr('mode','helical','k',[1/2 1/2 0],'n',[0 0 1], 'S',[1; 0; 0],'nExt',[1 1 1]);
disp('Magnetic structure:')
AFsq.table('mag')
AFsq.energy
plot(AFsq,'range',[2 2 1])
Magnetic structure:
ans =
1x8 table
num matom idx S realFhat imagFhat pos kvect
___ _____ ___ _ ___________ ___________ ___________ _________________
1 'Cu1' 1 1 1 0 0 0 1 0 0 0 0 0.5 0.5 0
Ground state energy: -2.200 meV/spin.
Spin wave spectrum#
We calculate the spin wave spectrum and correlation function along several linear q-scans in reciprocal space defined by the Qcorner corner points. The last number in the cell defines the number of steps in each linear scan.
Qcorner = {[0 0 0] [1/2 0 0] [1/2 1/2 0] [0 0 0] 200};
sqSpec = AFsq.spinwave(Qcorner, 'hermit', false);
sqSpec = sw_neutron(sqSpec);
sqSpec = sw_egrid(sqSpec,'Evect',linspace(0,6.5,500));
figure
sw_plotspec(sqSpec,'mode',3,'dashed',true,'dE',0.4,'qLabel',{'\Gamma' 'X' 'M' '\Gamma'})
caxis([0 4])
Warning: The two times the magnetic ordering wavevector 2*km = G, reciproc
lattice vector, use magnetic supercell to calculate spectrum!
Written by
Bjorn Fak & Sandor Toth
06-Jun-2014, 06-Feb-2017
Published with MATLAB® R2018b