(tutorial07)= # Tutorial 7 ## k=0 Kagome antiferromagnet We create a lattice with space group "P -3" where all first neighbor bonds are symmetry equivalent and add a magnetic Cr+ with S=1 spin. ### Define the lattice ```matlab AFkagome = spinw; AFkagome.genlattice('lat_const',[6 6 10],'angled',[90 90 120],'spgr','P -3') AFkagome.addatom('r',[1/2 0 0],'S', 1,'label','MCu1','color','r') plot(AFkagome,'range',[2 2 1]) ``` ```{image} /_static/img/tutorials/tutorial07/tutorial7_02.png :alt: ``` ### Create bonds Generate the list of bonds and lists them. ```matlab AFkagome.gencoupling('maxDistance',7) disp('Bonds:') AFkagome.table('bond',[]) ``` ```text Bonds: ans = 21x10 table idx subidx dl dr length matom1 idx1 matom2 idx2 matrix ___ ______ ______________ ____________________ ______ ______ ____ ______ ____ ______________ 1 1 0 1 0 0 0.5 0 3 'MCu1' 3 'MCu1' 1 '' '' '' 1 2 0 -1 0 -0.5 -0.5 0 3 'MCu1' 1 'MCu1' 2 '' '' '' 1 3 0 0 0 0.5 0 0 3 'MCu1' 2 'MCu1' 3 '' '' '' 1 4 0 0 0 0 -0.5 0 3 'MCu1' 3 'MCu1' 1 '' '' '' 1 5 1 0 0 0.5 0.5 0 3 'MCu1' 1 'MCu1' 2 '' '' '' 1 6 -1 0 0 -0.5 0 0 3 'MCu1' 2 'MCu1' 3 '' '' '' 2 1 1 -1 0 0.5 -0.5 0 5.196 'MCu1' 1 'MCu1' 2 '' '' '' 2 2 0 1 0 0.5 1 0 5.196 'MCu1' 2 'MCu1' 3 '' '' '' 2 3 -1 0 0 -1 -0.5 0 5.196 'MCu1' 3 'MCu1' 1 '' '' '' 2 4 0 0 0 -0.5 0.5 0 5.196 'MCu1' 1 'MCu1' 2 '' '' '' 2 5 -1 -1 0 -0.5 -1 0 5.196 'MCu1' 2 'MCu1' 3 '' '' '' 2 6 1 1 0 1 0.5 0 5.196 'MCu1' 3 'MCu1' 1 '' '' '' 3 1 0 1 0 0 1 0 6 'MCu1' 1 'MCu1' 1 '' '' '' 3 2 -1 -1 0 -1 -1 0 6 'MCu1' 2 'MCu1' 2 '' '' '' 3 3 1 0 0 1 0 0 6 'MCu1' 3 'MCu1' 3 '' '' '' 4 1 0 1 0 0 1 0 6 'MCu1' 2 'MCu1' 2 '' '' '' 4 2 -1 -1 0 -1 -1 0 6 'MCu1' 3 'MCu1' 3 '' '' '' 4 3 1 0 0 1 0 0 6 'MCu1' 1 'MCu1' 1 '' '' '' 5 1 0 1 0 0 1 0 6 'MCu1' 3 'MCu1' 3 '' '' '' 5 2 -1 -1 0 -1 -1 0 6 'MCu1' 1 'MCu1' 1 '' '' '' 5 3 1 0 0 1 0 0 6 'MCu1' 2 'MCu1' 2 '' '' '' ``` ### Hamiltonian We create AFM first neighbor interaction and weak 2nd neighbor AFM exchange. ```matlab AFkagome.addmatrix('label','J1','value',1.00,'color','r') AFkagome.addmatrix('label','J2','value',0.11,'color','g') AFkagome.addcoupling('mat','J1','bond',1) AFkagome.addcoupling('mat','J2','bond',2) plot(AFkagome,'range',[3 3 1]) ``` ```{image} /_static/img/tutorials/tutorial07/tutorial7_03.png :alt: ``` ### Generate magnetic structure We create a k = (0 0 0) magnetic structure, with the three spin directions in the unit cell (120 degree between neighbors). The spin vector components are given in the coordinate system of the lattice vectors (abc). ```matlab S0 = [1 -2 1; 2 -1 -1; 0 0 0]; AFkagome.genmagstr('mode','direct','k',[0 0 0],'n',[0 0 1],'unit','lu','S',S0); disp('Magnetic structure:') AFkagome.table('mag') AFkagome.energy plot(AFkagome,'range',[3 3 1]) ``` ```text Magnetic structure: ans = 3x7 table num matom idx S realFhat pos kvect ___ ______ ___ _ __________________________ _________________ ___________ 1 'MCu1' 1 1 0 1 0 0.5 0 0 0 0 0 2 'MCu1' 2 1 -0.866 -0.5 0 0 0.5 0 0 0 0 3 'MCu1' 3 1 0.866 -0.5 0 0.5 0.5 0 0 0 0 Ground state energy: -1.110 meV/spin. ``` ```{image} /_static/img/tutorials/tutorial07/tutorial7_04.png :alt: ``` ### Calculate spin wave dispersion ```matlab afkSpec = AFkagome.spinwave({[-1/2 0 0] [0 0 0] [1/2 1/2 0] 100},'hermit',false); figure sw_plotspec(afkSpec,'mode',1,'axLim',[0 3],'colorbar',false,'colormap',[0 0 0],'dashed',true) ``` ```{image} /_static/img/tutorials/tutorial07/tutorial7_05.png :alt: ``` ### Powder spectrum ```matlab afkPow = AFkagome.powspec(linspace(0,2.5,150),'Evect',linspace(0,3,250),... 'nRand',1e3,'hermit',false,'imagChk',false); figure sw_plotspec(afkPow,'axLim',[0 0.2]) ``` ```{image} /_static/img/tutorials/tutorial07/tutorial7_06.png :alt: ``` ```text Written by Bjorn Fak & Sandor Toth 06-Jun-2014, 06-Feb-2016 ``` Published with MATLAB® R2018b