LLG-铁磁学

LLGequationreportYangqiHuang2020/3/3ReportinferromagneticsTwoexpressionsofLLGequation2𝑑𝑚𝑑𝑡=−𝛾𝑚×𝐻+𝛼𝑚×𝑑𝑚𝑑𝑡𝑑𝑚𝑑𝑡=−𝛾1+𝛼2𝑚×𝐻−𝛼𝛾1+𝛼2𝑚×𝑚×𝐻Theoriginalequation:Field-liketermDamping-liketerm𝑑𝑚𝑑𝑡=𝑇𝑜𝑟𝑞𝑢𝑒MagneticfieldSTT(SOT)Damping𝑑𝑚𝑑𝑡=−𝛾𝑚×𝐻+𝛼𝑚×𝑑𝑚𝑑𝑡+𝑇𝑠𝑡𝑡M=MsmbaPrecision?Transformationofthetwoexpression3𝑑𝑚𝑑𝑡=−𝛾𝑚×𝐻+𝛼𝑚×𝑑𝑚𝑑𝑡𝑚×𝑑𝑚𝑑𝑡=−𝛾𝑚×𝑚×𝐻+𝛼𝑚×𝑚×𝑑𝑚𝑑𝑡𝛼𝑚×𝑚×𝑑𝑚𝑑𝑡=𝛼𝑚∙𝑑𝑚𝑑𝑡𝑚−𝑚∙𝑚𝑑𝑚𝑑𝑡=−𝛼𝑑𝑚𝑑𝑡𝑚×𝑑𝑚𝑑𝑡=−𝛾𝑚×𝑚×𝐻−𝛼𝑑𝑚𝑑𝑡𝑑𝑚𝑑𝑡=−𝛾𝑚×𝐻+𝛼−𝛾𝑚×𝑚×𝐻−𝛼𝑑𝑚𝑑𝑡⇒𝑑𝑚𝑑𝑡=−𝛾1+𝛼2𝑚×𝐻−𝛼𝛾1+𝛼2𝑚×𝑚×𝐻Theeffectivefield4𝑑𝑚𝑑𝑡=−𝛾1+𝛼2𝑚×𝐻−𝛼𝛾1+𝛼2𝑚×𝑚×𝐻Exchangeenergy:𝐸𝑒𝑥=𝐴𝑖𝑗𝑚𝑖∙(𝑚𝑖−𝑚𝑗)∆𝑖𝑗2Anisotropyenergy:𝐸𝑘𝑉=𝐾1sin2𝜃Zeemanenergy:𝐸𝑧=−𝜇0𝑀∙𝐻𝐸𝑥𝑡𝑣𝑑𝑉Demagnetizationenergy:𝐸𝑑=−12𝑀∙𝐻𝑑𝑑𝑉𝑚𝑎𝑔𝑛𝑒𝑡𝜕𝐸𝑡𝑜𝑡𝜕𝑚=𝑚×𝐻𝑒𝑓𝑓𝐸𝑡𝑜𝑡=𝐸𝑒𝑥+𝐸𝑘+𝐸𝑧+𝐸𝑑𝐻𝑒𝑓𝑓=𝐻𝑒𝑥+𝐻𝑘+𝐻𝐸𝑥𝑡+𝐻𝑑Spintransfertorque5Slonczewskiterm𝑇𝑠𝑡𝑡=−𝛾0ℏ𝜇0𝑀𝑠21𝑑𝐽𝑒𝑔𝜃𝑚×𝑚×𝑚𝑝𝑑:𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠;𝐽:𝑐𝑢𝑟𝑟𝑒𝑛𝑡𝑑𝑒𝑛𝑠𝑖𝑡𝑦;𝑔𝜃:𝑒𝑓𝑓𝑒𝑐𝑖𝑒𝑛𝑐𝑒𝑑𝑚𝑑𝑡=−𝛾𝑚×𝐻+𝛼𝑚×𝑑𝑚𝑑𝑡+𝑇𝑠𝑡𝑡𝑑𝑚𝑑𝑡=−𝛾1+𝛼2𝑚×𝐻−𝛼𝛾1+𝛼2𝑚×𝑚×𝐻−𝛾0ℏ𝜇0𝑀𝑠21𝑑𝐽𝑒𝑔𝜃𝑚×𝑚×𝑚𝑝𝐻𝑒𝑓𝑓=𝐻𝑒𝑥+𝐻𝑘+𝐻𝐸𝑥𝑡+𝐻𝑑⇒𝐼𝑛𝑚𝑎𝑐𝑟𝑜𝑠𝑖𝑚𝑢𝑙𝑎𝑡𝑖𝑜𝑛:𝐻𝑒𝑓𝑓=𝐻𝑢+𝐻𝑒𝑥𝑡Quantummechanism(veryshortranged)Effectiveuniaxialanisotropy𝐻𝑢=𝐻𝑘+𝐻𝑑Spintransfertorque6⟹𝑑𝑚𝑑𝑡=−𝛾1+𝛼2𝑚×𝐻−𝛼𝛾1+𝛼2(𝐻𝑢+𝐻𝑒𝑥𝑡)𝑚×𝑚×𝑧+−𝛾0ℏ𝜇0𝑀𝑠21𝑑𝐽𝑒𝑔𝜃𝑚×𝑚×𝑧−Set𝐻𝑒𝑓𝑓=𝐻𝑢+𝐻𝑒𝑥𝑡=(𝐻𝑢+𝐻𝑒𝑥𝑡)𝑧+,𝑚𝑝=𝑧−𝑑𝑚𝑑𝑡=−𝛾1+𝛼2𝑚×𝐻−𝛼𝛾1+𝛼2𝑚×𝑚×𝐻−𝛾0ℏ𝜇0𝑀𝑠21𝑑𝐽𝑒𝑔𝜃𝑚×𝑚×𝑚𝑝Effectivedamping(−𝛼𝛾1+𝛼2𝐻𝑢+𝐻𝑒𝑥𝑡+𝛾0ℏ𝜇0𝑀𝑠21𝑑𝐽𝑒𝑔𝜃)𝑚×𝑚×𝑧+When𝛼𝑒𝑓𝑓=0,thesystembecomeunstable(Jc0)𝐽𝑐0=𝛼𝛾𝜇0𝑀𝑠2𝑑𝑒𝐻𝑢+𝐻𝑒𝑥𝑡(1+𝛼2)𝛾0ℏ𝑔𝜃To-DMIandRashbaeffect7DMHamiltonian:𝐻𝐷𝑀𝐼=−𝐷𝑖𝑗∙(𝑆𝑖×𝑆𝑗)Innumericalcalculation,theenergydensityofDMIcanbewrittenas:𝜀𝐷𝑀=𝐷(𝑚𝑧𝜕𝑚𝑥𝜕𝑥−𝑚𝑥𝜕𝑚𝑧𝜕𝑥+𝑚𝑧𝜕𝑚𝑦𝜕𝑦−𝑚𝑦𝜕𝑚𝑧𝜕𝑦Rashbaeffectivefield:𝐻𝑐𝑑=2𝛼𝑅𝑚ℏ𝑒𝑀𝑠𝑃𝐽𝑒(𝑧×𝑗𝑒)RashbaHamiltonian:𝐻𝑅=𝛼𝑅(𝑝×𝑧)∙𝜎𝛼𝑅:Rashbacoefficient;𝜎:Paulimatrix𝑑𝑚𝑑𝑡=−𝛾𝑚×(𝐻+𝐻𝑐𝑑)+𝛼𝑚×𝑑𝑚𝑑𝑡Rashbaeffect8TheHamiltonianofasingleferromagnetic2DEGsandwichedbetweentwodissimilarmaterials𝐻=𝑝22𝑚+𝛼𝑅ℏ𝑝×𝑧∙𝜎−𝐽𝑠𝑑𝜎∙𝑀KineticenergyRashbahamiltonianExchangeenergyOne-electroneigenenergyandwavefunction𝐸𝑘±=ℏ2𝑘22𝑚±𝛼𝑅𝒌×𝒛−𝐽𝑠𝑑𝑴Ψ𝑘±=12𝐴±𝑒𝑖𝛾𝑘1exp(𝑖𝒌∙𝒓)Aistheareaofthefilm,𝛾𝑘=(𝛼𝑅𝑘𝑥+𝐽𝑠𝑑𝑠𝑖𝑛𝜃)/(𝛼𝑅𝑘𝑦−𝐽𝑠𝑑𝑐𝑜𝑠𝜃)Rashbaeffect9Boltzmanequationofthetwobands,𝑒𝐸𝑥−𝜕𝑓0𝜎𝜕𝑘𝑥=𝑑2𝑘′𝑊𝑘𝑘′𝜎𝜎′(𝑓𝑘𝜎−𝑓𝑘′𝜎′)𝜎′ScatteringpropertyWhen𝐸𝐹≫𝐽𝑠𝑑≫𝛼𝑅𝑘𝐹,𝑊𝑘𝑘′𝜎𝜎′=𝜋𝑛𝑖𝑉2/ℏ𝜏:𝑟𝑒𝑙𝑎𝑥𝑎𝑡𝑖𝑜𝑛𝑡𝑖𝑚𝑒𝑓𝑘±=𝑓0±−𝑒𝐸𝑥𝜏(−𝜕𝑓0±𝜕𝑘𝑥)Rashbaeffect10Thespindensity:Thespincurrent:Thespintorque:Rashbaeffectivefield:𝐻𝑐𝑑=2𝛼𝑅𝑚ℏ𝑒𝑀𝑠𝑃𝐽𝑒(𝑧×𝑗𝑒)IntroductionofOOMMF•郑晨天•OOMMF简介•各个模块的功能介绍•仿真步骤介绍•OOMMF扩展程序介绍•OOMMF数据分析方法介绍11Micromagneticsimulation•张志仲•微磁仿真数值方法原理介绍•微磁仿真中数值精度对仿真结果的影响•一些实际微磁仿真的工作（DW，Skx）12Macrosimulation•高天琦•Macrosimulation的基本思想、方法简介•Macrosimulation的仿真工具及算法•一些实例13SOT•覃小婉•自旋轨道矩简介•自旋轨道矩器件简介•自旋轨道矩在神经网络中仿真应用14