It's  a  real  pleasure  to  have  a  visitor  or a  returning  visitor  to  Georgia  Tech. Professor Shaloo Rakheja from the  University  of  Illinois,  Urbana-Champaign.  Sure. Who  got  her  bachelor's  degree  in electrical  engineering  at  Indian  Institute  of  Technology. And  then  worked  for  a  few  years  before coming  here  to  Georgia  Tech  to  get  her  Masters  and PhD  in  electrical  and  computer  engineering with  our  very  own  Assad  Niamey,  sitting  right  there. And  then  did  a  postdoc  at  MIT  before  going  to  NYU  for a  few  years  and  then  joining University  of  Illinois  Electrical  and Computer  Engineering  in  2019, where  she  is  also  Director  for the  Center  for  Advanced  semiconductor  chips with  accelerated  performance, also  known  as  asap, which  is  an  NSF  funded  you  CRC. And  she  also  is  a  grantee  of  an  NSF  Career  Award. So  with  that,  I  will  turn  it  over  to  you.  All  right. I  hope  you  all  can  hear  me. So  it's  a  great  pleasure  to  be  back  here. I  remember  being  here  more  than  a  decade  ago. And  my  last  presentation  that  I  did  at  Georgia  Tech was  my  PhD  defense  presentation. Today  what  I  want  to  talk  about  is  my  perspective on  magnetic  materials  and more  specifically  antiferromagnetic. And  just  argue  that despite  a  lot  of the  challenges  associated  with  antiferromagnetic, these  are  still  amazing  materials  to  consider for  future  electronic  applications. And  before  I  get  started, I  want  to  thank  all  my  grand  sponsors  that  have  allowed me  to  do  this  research that  I'm  gonna  be  talking  about  today. Alright,  so  before  I  get  started, I  wanted  to  give  a  very  quick five-minute  overview  of  my  research. So  I  work  in  theoretical  modelling. So  a  lot  of  the  work  that  I  do  is  focused  on developing  new  simulation  methods  and  new  models for  a  number  of  unique  applications  such  as RF  Communication  and  low-power  memory  and  logic. Some  of  the  studies  that  I've  performed  recently include  doing  a  spin  charged  coupling  in  2D  materials, topological  materials, and  spin  transport  in  these  nanostructures. And  more  recently,  my  focus  has  been  on studying  electron  transport  in wide  band  gap  semiconductors. So  here  is  pretty  much  all of  the  materials  that  I've  been  working  on. So  35.3  nitrites,  I  have  done a  lot  of  work  in  photoconductive  switches, which  are  important  for  pulse  power  applications, as  well  as  high  electron  mobility  transistors, which  you  all  may  be  familiar  with. These  are  devices  that  are  used  for  RF  communication. Then  in  the  middle  of  the  slide, you  will  see  these antiferromagnetic  that  I  want  to  talk  about  today. And  more  specifically, the  antiferromagnetic  that  I  want  to talk  about  are  these  manganese  based  metals. Manganese  310,  manganese,  gallium  nitride. The  cool  thing  about  these  antiferromagnetic  metals  is that  they  have  some very  interesting  topological  properties. Also  very  uniquely,  this  is  a material  manganese  310  that  I'll talk  about  that  has a  very  weak  Ferro  magnetic  moment  as  well, which  gives  us  a  handle  as  an  external  user to  be  able  to  manipulate  the  order  parameter. Alright,  so  just  a  quick overview  of  my  work  in  electronic  devices  and  materials. So  the  work  that  I  do  allows  us  to  connect  technology, whether  it's  used  in  circuits  and  to  be  able  to  do  that, We  have  built  this  modelling  and simulation  framework  that  is  shown  over  here. So  at  the  middle  of  this  framework  we have  these  compact  device  models. These  are  called,  these  are basically  based  on  physics  equations, but  they  do  require experimental  data  such  as  S  parameters  IV, CV  in  order  to  be  validated  and  calibrated over  abroad  bias  and  temperature  range. Now,  these  compact  device  models  can  also  be validated  against  these  tickets  simulations. So  t  cat  stands  for  technology  computer  aided  design. So  generally  what  one  does  is  they  tried  to understand  how  electrons  are  moving  in  a  device. And  typical  methods  that  are used  are  Boltzmann  transport  equation, which  is  obviously  very  heavy  to  implement computationally  because  it requires  complex  Monte-Carlo  simulations. One  could  simplify  it  and  use deterministic  methods  like hydrodynamics  and  drift  diffusion. Now  speaking  of  Boltzmann  transport, I  have  a  postdoc  opening  in  my  group  to do  Boltzmann  transport  simulations for  gallium  nitride  and other  wide  band  gap  semiconductors. If  you're  interested,  please  let  me  know. But  eventually  our  hope  is  that with  the  sort  of  a  framework, we  get  to  the  circuit  level  simulations and  the  output  that  we're  getting  from  the  circuit. Simulations  can  allow  us  to fine  tune  the  choice  of  the  materials  as  well  as the  device  design  so  that  we  can  typically meet  the  specifications  of the  application  that  we're  interested  in. Now,  this  framework  that  I've  highlighted  over  here is  specifically  made  for  gallium  nitride, aluminum,  gallium  nitride  scandium nitrate  kind  of  devices. We  also  need  some  first  principles  calculations. I  don't  do  these  calculations  in  house. We  collaborate  with  a  lot  of external  people  who  are  great  at  density functional  theory  calculations  and electron  phonon  couplings  as  well. So  taking  gallium  nitride  as  an  example, we  have  been  working  with  Air  Force  in  order  to  implement a  better  and  more  scalable  method to  look  at  electron  transport  in  gallium  nitride. The  method  that  we  have  is  called  SKT, which  stands  for,  for  me,  kinetics  transport. And  I  hope  you  all  are  listening carefully  because  I  promised David  there  is  going  to  be  a  quiz  at  the  end  of  it. So  what  F  Katie  does, unlike  most  other  solvers that  you  all  may  be  familiar  with, examples  might  be  many  electrical  engineers use  synopsis  tools,  right? So  synopsis  and  Doris  is  an  example  of  a  t  cat  Solver. What  f  Katie  does  better  is  all  of  these  things. It  is  able  to  capture  the  physics  of  hot  carriers, which  is  very  important  for  high  frequency  applications. It  can  incorporate  full  band  structure of  the  devices  well. And  finally,  what  it  also  does  really  well  is  the  fact that  it  can  couple  Maxwell's  equations  to  transport. And  that  is  usually  not  very  easy with  the  commercial  solvers that  are  available  on  the  market. Today.  We  have  demonstrated  that this  f  Katie  has  a  better  rate  of convergence  compared  to  all  of  the  commercial  solvers. And  our  paper  that  appeared  very recently  in  December  was  chosen  as  the  editor  spec, which  highlighted  some  of these  crucial  mathematical  details of  the  different  solvers. Our  hope  is  that  in  the  future, we  will  be  able  to  expand  the  functionality  of  f  k, d.  So  currently  what  f  Katie  does  very  well  is  look  at these  three-dimensional  electron  gases  in  a  structure. What  we  want  to  do  is  study  nanowires,  nano  sheets, and  even  scandium  based high  electron  mobility  transistors. So  if  people  don't know  aluminum  scandium  nitrate  as  a  ferroelectric. So  what  we  want  to  do  is  build  a  device  that  has a  gallium  nitride  channel  with aluminum  scandium  nitrate  sitting  on  top  of  it. And  the  applications,  of  course, RF  electronics  is  the  primary  focus of  many  of  the  things  that  I'm  looking  into. But  we  also  want  to  push  the  temperature. We  want  to  be  able  to  make sure  that  whatever  models  and  simulations  we  are building  are  equally  applicable at  high  temperature  as  they  are  at ultra  low  temperatures  for  some  of the  very  interesting  cryogenic  applications. Alright,  so  here's  a  few  examples  of the  devices  that  I've  been  looking at  also  apart  from  gallium  nitride. So  although  gallium  nitride  has  been the  main  focus  and  three-five  hams has  been  the  main  focus. Recently  we  have  a  very  small  SRC  funded  project to  do  2D  reconfigurable  devices. Have  a  collaborator  that  fabricates  these  devices, and  these  are  all  fabricated  in-house. This  is  a  hafnium  oxide  doped  with zirconium  ferroelectric  capacitor and  ferroelectric  tunnel  junction. So  we  basically  developed  models  for  some of  these  devices  that  are  validated  against  measurement. I  will  post  a  little  bit  about  our  models. So  what  is,  what  sets  our  models  apart from  everybody  else  in  the  literature  is  doing? There  are  four  key  things  that  we try  to  respect  in  our  models. The  first  is  self-consistency. What  that  means  is  you have  the  DC  operation  of  the  device, but  at  the  other  end,  you  also  have the  transient  operation  of  the  device. For  transient  operation,  it  is  important  to consider  all  of  the  capacitive  effects, displacement  current  that  would flow  through  the  device  terminals. So  what  we  do  is  we  try  to build  the  static  model  jointly  with this  dynamic  model  or  the  transient  model  so that  it  can  capture  all  of  the  relevant  physics. The  second  thing  that  we  do, which  has  been  a  pain  in the  industry  for  a  very  long  time, is  we  don't  have  models  that  are  applicable  to long  channel  devices  and short-channel  devices  simultaneously. So  we  are  able  to  capture  the  appropriate  physics. Then  one  unified  compact  framework. And  we  also  have  very  few  sets  of  parameters. So  for  any  model, we  need  to  train  the  model. We  need  to  know  what  the  parameters  in  the  models  are. And  to  train  that  model, we  have  to  do  this  multi-variable  optimization. So  the  bigger  the  space  of  the  parameters, the  more  complicated  this  process  gets. So  what  I  tried  to  ensure  is  that  the  models  that we're  building  has  very  few  parameters,  e.g. 40  parameters,  as  opposed  to  the  traditional  models  e.g. that  are  available  in  the  literature  in the  compact  model  council  would  have  200  parameters. So  it's  a  very  large  set  of parameters  that  people  have  to  deal  with. And  finally,  mathematical  robustness  is  quite  important. Mathematical  robustness  means  you have  these  analytic  equations. You  want  to  put  this  model into  a  circuit  simulator  because presumably  you're  trying  to build  some  electronic  circuit  with  it. The  moment  you  put  it  into  the  circuit  solver, what  the  circuit  solver  wants  is  that  your  models, all  the  currents  and  the  charges are  differentiable  to  the  nth  order. And  if  you  don't  have  that, then  the  circuit  simulator  will  complain  about  it. And  therefore,  your  circuit  friends  are  going to  come  to  you  and  say  your  model  is  crap, which  may  be  so, but  this  is  one  of  the  very  important  things  that  we've tried  to  ensure  in  our  models. So  with  this,  I  think  I'll  move  to  the  actual  real  part of  my  talk  on  Magnetics  and  spin  tropics. Spent  on  X  is  a  combination  of two  words,  spin  on  electronics. And  it  basically  aims  to utilize  the  spin  angular  momentum  of electrons  as  opposed  to  their  charge  in  order to  build  useful  electronic  devices. And  at  the  heart  of  any  spin  phonics  device or  a  circuit  is  a  ferromagnet, which  is  shown  over  here  and  it  contains  spins that  are  aligned  parallelly  with  each  other. What  one  could  do  is  assume  that a  thin  film  of  a  ferromagnet  behaves  like  a  giant  spin. And  we  usually  refer  to  it  as  a  macro  spin. And  the  idea  is  that, that  this  orientation  is  going  to encode  the  binary  states  of  0.1. And  we  need  some  method  in  order to  switch  the  state  of  the  magnet. So  presumably  one,  we'll  apply  some  external  signal toggle  the  state  and  apply a  reverse  signal  toggle  the  state  back. So  what  are  some  of  the  methods  that one  can  use  in  order  to  toggle  the  state. People  can  use  spin  torques, magnetic  fields,  combination  of these  where  the  electric  fields  and  voltages. The  idea  is  that  the  magnet is  sitting  in  one  of  its  energy  basins. So  you  can  think  that  this  orientation  corresponds  here. And  then  you  apply  the  signal and  the  orientation  then  kinda  like moves  on  the  face  space  and  gets  to the  other  equilibrium  basin. And  again,  this  is  a  very  simplified. The  real  picture  is  of  course,  way  more  complicated. Now  to  call  in  my  research  has  been to  understand  how  this  evolution  is  taking  place. And  generally  speaking,  you  would  end  up solving  this  first  order  differential  equation. This  is  known  as  the  Landau  Lifshitz  Gilbert  equation. What  it  does  is  it  tells you  this  is  my  M,  this  magnetization, and  this  is  how  its  varying  as  a  function  of  time  in response  to  all  of the  external  forces  that  you're  applying  to  the  system. One  of  the  forces  over  here  is this  torque  coming  from  the  spin  current,  e.g. that  you've  provided  to  the  system. So  generally  you  would  solve it  and  you  will  try  to  figure out  what  m  is  as  a  function  of  diamond, then  do  some  performance  estimates  and  so  on. Now,  the  biggest  application  of  ferromagnetic  has been  in  the  context  of  magnetic  memories. Can  anyone  give  me  an  example  of  a  company  that's  very successful  in  making  magnetic  spin  Torque  memories. Any  idea,  ever  spin, anyone  heard  of  it? So  every  spin  is  a  company  that is  actually  making  smoothies. Memories  are  a  number  of  other  companies, But  as  you  all  know, memory  industry  is  going  through  a  lot of  issues  right  now. So  I'm  not  sure  how  many  people  are actually  still  researching  this, at  least  for  this  quarter,  but that's  a  very  important  application. And  then  there  are  other  applications  as  well,  e.g. one  could  use  this  magnet  as  a  source  of  random  numbers. Because  if  you  look  at  this  equation, you  have  this  thermal  noise  term  over  here. So  it  could  be  argued  that  the  evolution  of the  magnetization  is  going  have some  sort  of  a  stochasticity  and  that  one  could  harness for  building  random  number  generators  and  so  on. Alright,  there  are  some  benefits  of  spin  draw  antics. First  is  that  these  elements  are  highly  scalable. They  could  also  be  more  energy  efficient compared  to  their  charge-based  counterparts. And  one  could  always  argue  that  well, even  if  fuel  power  down  the  device, the  magnet  is  going  to  be non-volatile  and  store  the  state. And  in  fact,  as  I  mentioned  before, memory  has  been the  biggest  killer  application  for  spin  tropics. And  here  are  some  examples  of  very  interesting  latest  and greatest  memories  coming  out  of universities  in  Japan  as  well  as  in  iMac. At  the  heart  of  all  of these  magnetic  memories  is this  element  or  two  terminal  device. And  this  is  popularly  called the  magnetic  tunnel  junction. It  has  two  electrodes  over  here that  are  made  out  of  a  ferromagnet. And  this  blue  layer  is a  ten  tunneling  barrier  like  magnesium  oxide. So  what  happens  in  this  empty  j  is  you  pass  the  current and  you  control  the  orientation  of  the  second  layer, which  is  called  the  free  layer. And  once  this  freely  or  changes, the  resistance  of  the  stack  would  also  change. The  resistance  could  be a  low  resistance  or  a  high  resistance depending  on  how  the  federal  magnetic  electrodes are  aligned  with  each  other. This  is  at  the  heart  of  all  of the  magnetic  memories  that  I  showed  earlier. But  interestingly,  this  element  could  also  be  used for  a  number  of diverse  applications  in  unconventional  computing. Random  number  generators  being a  very  important  application, but  we  can  also  use  it  as  a  microwave  oscillator, a  spin  wave  amateur  detector, memory  store, stochastic  oscillator  and  so  on  and  so  forth. So  this  is  a  very  powerful, diverse  element  that  one  could  use  now. And  all  of  these  devices  that  I've  talked  about, it's  all  about  Ferro  magnets. So  what  about  antiferromagnetic? Now,  antiferromagnetic represent  the  overwhelming  majority of  magnetically  ordered  materials. In  an  antiferromagnetic,  the  spins  are aligned  opposite  to  each  other. So  if  I  look  at  the  system  on  the  whole, there  is  no  magnetic  moment  over  here. So  in  his  1970  Nobel  lecture, lewis  Neil  said  that  these are  interesting  materials  but  useless. And  in  fact,  I  took  a  snapshot  of his  Nobel  lecture  and  let  me  read  from  this. Neil  says,  they  are  extremely interesting  from  the  theoretical  viewpoint, but  do  not  seem  to  have  any  applications. Now,  let  me  focus  on  the  positive  here  for  a  minute. Interesting  to  radically  interesting. So  what  is  interesting  about  this  antiferromagnetic? Well,  first  of  all, it  does  not  have  any  moment, so  it's  not  going  to  generate  these  dipolar  fields, which  also  means  that  an  antiferromagnetic  is going  to  be  immune  to  external  magnetic  fields. From  an  engineer's  perspective, what  that  means  is  you  could  take this  element  and  assuming you  could  bend  our  memory  out  of  it, you  could  basically  scale  it  down  and  stuck  it  very, very  close  to  each  other without  having  to  worry  about  crosstalk,  e.g. right?  The  other  thing  is  that  an  antiferromagnetic, the  dynamics  is  very  fast. In  Ferro  magnets. What  happens  is  we  have  to  worry  about a  nanosecond  for  any  interesting  dynamics  to  take  place. In  the  case  of  antiferromagnetic, the  precession  frequency  is  in  terahertz. One  could  at  least theoretically  argue  that  it  would  be  possible  to switch  this  antiferromagnetic  People  second  timescale to  radically  that  has  not been  demonstrated  experimentally  yet. And  even  theoretically  doing the  math  behind  it  seems  to  be  very  complicated. And  finally,  these  antiferromagnetic, because  of  the  way  there  moments  are  aligned, also  have  very  interesting  dynamics. They  can  switch,  they  can  have  oscillations, and  in  fact,  they  can  have  spikes, which  is  like  you  put  an  AC  current  and  the  Mac, the  moment  spikes,  and  so  on  and  so  forth. It  can  also  have  a  burst, which  means  that  it  can  have coupled  a  train  of  spikes,  e.g. so  there  are  some  interesting  features, but  obviously  there  are challenges  which  has  made  it  very  difficult  for  us thus  far  to  utilize these  antiferromagnetic  in any  useful  electronic  application. And  that  seems  to  be  the  status  as  of  today. So  what  are  the  difficulties? First  two  biggest  difficulties. There  is  no  moment  in  it. So  how  the  ****  are  you  supposed  to image  it  and  how  are  you  supposed to  flip  it  if  you're  trying  to change  the  orientation  and  you  want  to  do, one  could  say,  Well, why  don't  we  use  lasers  to  view  the  magnetic  patterns? Well,  as  an  engineer, what  we  want  to  do  is  we  want  to  use electrically  controllable  methods  in order  to  switch  the  antiferromagnetic and  after  it  has  been  switched, we  also  want  to  detect  the  switch  to  stay  at using  microelectronics  compatible  circuitry. That  second  problem  is  a  little  bit more  fundamental  even  today, people  are  still  arguing. How  does  the  magnet,  the  antiferromagnetic  switch. We  don't  understand  the  physics  fully. We  don't  understand  the  timescale. And  we  don't  understand  the  robustness  of the  switching  process  itself and  the  role  of  thermal  noise. In  fact,  everything  that  I  will  talk  about today  will  be  someone's  thermal  noise. And  it  will  also  be  under the  assumption  that  I  know  this  is  how the  magnet  is  switching  because  I  have  to  make a  framework  and  start  with  some  assumption. And  my  hope  is  that, that  the  models  I  start  building  from those  assumptions  have  some  experimental  proof. As  my  very  good  friend, Tony  law  says,  theory  is  not  real.  Experiments  are  real. So  hopefully  what  my  hope  is that  the  models  that  I'm  building  have a  very  strong  smoking  gun experimental  proof  that  this  is  what  is  going  to  happen. Alright,  so  in  my  research, what  we've  been  doing  is  trying  to  understand  can  we utilize  these  antiferromagnetic  as  shortstop  ours, as  the  main  element  in  spin  drawn  ICS  devices. If  so,  then  what  would  this  device  look  like? What  is  the  writing  mechanism? What  is  the  reading  mechanism? Then  finally,  what  would  be appropriate  methodologies  and  models in  order  to  estimate  the  performance, including  the  energy  dissipation  area, latency  of  the  device. I  have  a  number  of  review  articles. This  is,  by  the  way, a  blossoming  area  of  research. If  you're  interested,  this  is the  right  time  to  get  into  it because  everyone  is  super  excited about  the  vast  range  of  materials  that  are available  to  basically  understand  it. It's  just  huge.  So  I  have  a  number  of review  articles  if  you're  interested. I'm  happy  to  share  my  slides  and  you  can  take a  look  at  some  of  these  very  interesting  review  articles. Now,  there  are  some  spin  tronic  phenomena  that  are available  to  read  the  antiferromagnetic  state. First  as  magneto  resistance. What  does  this  do?  You  take  to antiferromagnetic  sandwich  them  and there  is  a  ten  or  tunneling  barrier  in  between. And  depending  on  the  orientation of  the  antiferromagnetic, you  might  get  a  low  resistance  and  high  resistance. Now  you  might  have  imagined  that  this is  only  theoretically  possible. It  has  not  been  experimentally  demonstrated  in pretty  much  all  of  the  antiferromagnetic  that we  know  off  it  has  not  accept. Last  month  the  paper  came  out  in  nature, which  demonstrated the  magneto  resistance  effect  in  manganese  tin, which  is  a  material  that  I  will  talk  about  today. So  that's  the  only  material  in  which this  has  been  experimentally  observed. Then  we  have  an  isotropic  magneto  resistance. These  are  all  resistive  measurements. What  these  measurements  are  doing  is  they  are  trying  to understand  how  does  magnetization the  resistance  of  the  stack. So  in  this  one,  essentially, this  resistance  depends  on the  orientation  of  the  Neil  order, which  is  the  antiferromagnetic  order and  the  direction  of  the  current. Now  this  one,  the  AMR, this  is  a  bulk  phenomenon. It  has  been  observed  experimentally, but  it  is  a  very  weak  effect. And  then  we  have  something  called  anomalous  Hall  Effect. How  many  of  you  are  familiar  with  Hall  effect? Anyone?  Okay?  Alright,  so  I'm  not  going  to  get  into, if  you're  not  familiar  with  Hall  effect, you  better  be  familiar  with  Hall  Effect. This  is  like  one  of  those basic  things  that  you  ought  to  know. So  anyway,  I'm  not  going  to  get  into  it, but  the  idea  here  is  simple. Norman  Hall  effect. What  you  end  up  doing  is  you  try  to  put a  magnetic  field  and  that  gives you  that  Hall  voltage  that  people  often  measure. In  the  case  of  magnetic  materials,  the  cool  thing  is, you  don't  have  to  apply any  magnetic  fields  and  you  get  this  whole  voltage. Now,  this  whole  effect, I  have  anomalous  oil  effects. So  what  is  anomalous  about  it? Well,  what  typically  happens  is  that  this  is an  odd  function  and therefore  are  not  expected  to  get  this. In  the  case  of  antiferromagnetic, it  should  cancel  out. But  interestingly,  in  manganese  tin, the  material  of  choice  today, this  phenomenon  has  been  experimentally  measured. It  occurs  in  this  material, so  it's  a  very  powerful  tool  to  look  at  M  and  three  SN. And  finally,  we  have  this  thing called  tunneling  and  isotropic  magneto  resistance, same  as  the  top  one. And  isotropic  magneto  resistance  is  just  that. The  structure  is  a  little  bit  complicated. The  effect  is  a  little  bit  stronger than  an  isotropic  magneto  resistance, but  typically,  this  last  one does  not  persist  to  room  temperature. There  are  some  challenges I  know  that  people  have  been  trying  to  do that  and  materials  like  IRM  and,  and  so  on. Then  on  the  writing  side. So  remember  my  goal  today  is  to  tell  you  how  to  write, how  to  read,  right? So  I've  talked,  told  you  how  we  can  read. There  are  four  effects. They  were  kinda  anomalous. Hall  Effect  is  the  only  one  that is  looking  promising  for  most  of  these  materials, writing  can  be  accomplished  with  spin  torque. Now  how  does  that  happen? Let's  go  back  to  my  favorite  device, that  tunnel  junction  to antiferromagnetic  within  MG  or  battery  or  in-between. Idea  is  while  you  pass  a  current  and  then  flip the  magnetization  of  the  second  electrode does  not  happen  in  reality, no  man  has  experimentally  demonstrated  it  yet. And  the  reason  for  this  is  that  in  order  for this  phenomenon  to  occur  in the  case  of  antiferromagnetic, you  need  commensurate  hetero  structures, you  need  perfect  epitaxy  and  you need  ballistic  transport  of  spins. So  that's  those  are  very challenging  to  achieve  in  experiments. The  second  one  is  a  nice  effect. This  is  a  bulk  effect. So  you  have  this  chunk  of an  antiferromagnetic  sitting  and  you  don't  need complex  multi-layer  structures  at this  effect  is  called  Edelstein  spin  orbit  torque. Complicated  name,  I  can't  seem  to  remember all  the  torques  that  are  now  available  in  the  literature. This  one  is  also  called  the inverse  when  galvanic  effect  in  case  you  want  to. Remember  that  the  idea  here  is  you  pass  current  and  that introduces  this  non-equilibrium  spin  polarization, which  basically  exchange  couples  to this  magnetization  and  flips  the  magnetization. This  one  requires  very  specific  kinds  of materials  and  crystals  once with  broken  inversion  symmetry, examples  in  which  this  has  been  experimentally demonstrated  is  m  into  AU  e.g. that's  been  done.  And  finally, the  nice  effect  that  seems  to  work  is the  spin  Hall  effect,  spin  or  PyTorch. So  you  pass  a  current through  this  green  layer  on  the  top. I'm  not  sure  if  it's  ten  invisible as  green  layer  from  the  back. But  I  have  this  green  layer. You  pass  a  current  that basically  exerts  its  been  torque  on this  bottom  antiferromagnetic  and  flips the  magnetization  of  the  antiferromagnetic. Now  the  third  effect  that  seems  to  work  very  well, whether  your  magnetic  material  is an  insulator  or  whether  it  is  metals. So  we  want  to  talk  about  how  to utilize  that  in  the  case  of  metals. So  pop  quiz  time. What  are  the  two  methods  that  we  will  use  to describe  M13  assigned  for  reading  and  writing. So  I'll  just  remind  everyone  for  reading. We're  going  to  be  doing  the  anomalous Hall  effect  for  writing. We're  gonna  be  doing  that  last  one. Alright,  so  there  are  a  number  of antiferromagnetic  materials  that  I've  been  looking  into. So  we  have  these  insulators, nickel  oxide  and  manganese  fluoride. These  are  the  poster  children  of  antiferromagnetic. So  whenever  we  think  of  antiferromagnetic, those  are  the  materials  and  they're  pretty  good. The  Carrey  matt  nons  charge  less  spin  waves  basically, but  I'm  not  going  to  talk  about  that. And  then  there  is  chromium. Chromium  is  a  nice  material. It's  a  magneto  electric  material. Not  going  to  talk  about  that. I'm  going  to  talk  about  not  even  see  U,  M, and  S,  but  I  wanted  to  highlight  this  material  here. This  material  is  a  metal. Now,  this  was  the  first  material  in which  are  electrically  controlled switching  of  the  antiferromagnetic  order was  demonstrated  at  the  time  when  I  was  still  a  student. It  was  a  science  paper and  everyone  was  super  happy  about  it. But  later  on  it  was  found that  the  signals  that  they  measured were  not  related  to the  switching  of  the  antiferromagnetic  order, but  rather  to  joule  heating  and atomic  motion  related  to  electro  migration. Nonetheless,  the  set  the  stage  for  what  we  could  expect an  anti  ferromagnet  and  generated  a  lot  of excitement  in  the  field  about  eight  years  ago. Now  there's  a  lot  of  interests  in  manganese, tin  and  M13  IR. The  cool  thing  over  here, which  I'm  going  to  talk  about  is  if  you  look at  this  material  here, I  have  made  some  atoms and  then  there  are  those  arrows  on  the  atoms. Those  are  the  moments  that  are  in  that  atom. The  cool  thing  is  that  this  is a  non  collinear  anti  ferromagnet. What  does  non-colinear  mean? It  means  that  it's  a  co-planar  system. Coplanar  means  all  the  spins  are  in  that  same  plane. So  the  blue  planes  is  where  the  spins  are  contained. And  then  it  does  non-colinear  because the  spins  are  not  in  a  straight  line. They  are  pointing  at hundred  and  20  degrees  with  respect  to  each  other. These  are  also  called  negative  Pi  reality  materials. And  the  sky  reality  breaks the  time  reversal  symmetry  here. So  it  gives  us  some  very  unique  transport  signatures that  are  not  possible  in  any  other  material. Now  that  I've  wasted  half  of my  lecture  time  to  talk  about  the  background. I  want  to  jump  right  into  it. What  is  so  unique  about  this? So  this  is  a  unit  cell  of  M13  ascended. It's  basically  hexagonal. And  it  consists  of  this  ABAB stacking  sequence  of  the  zeros  01  plane. In  the  plane  we  have  a  gummy  lattice  of  manganese  atoms. And  it  has  a  very  weak  in  plane,  an  isotropy. If  you're  not  familiar  with  anisotropy, isotropy  just  means  the  preference of  the  system  to  lie  along  a  certain  direction. Now  and  then  three  SN  is  unique  because  you  could stabilize  this  phase  only  when  manganese  is  in  excess. So  you  won't  need  something  like  M  and  3.0  to  S n.  So  some  of those  manganese  atoms  are  going  to  replace  the  tin  atoms. And  if  you  didn't  have  that  access, you  would  get  contaminated  with  M  and  n, which  is  not  an  antiferromagnetic. Also  at  the  new  temperature  is  410  Kelvin, which  means  that  if  you  were  to heat  it  above  this  temperature, it  would  not  be  a  magnetically  ordered  material. And  this  basically  has this  one-twenty  decree  spin  structure, which  is  what  I'm  referring  to  as  a  negative  guy  reality. There  are  other  kinds of  structures  that  are  enabled  at  low  temperature, but  I  don't  think  anyone  fully understands  what's  happening  below 50  Kelvin  or  what's  happening even  in  this  helix  antiferromagnetic  phase. I'm  not  going  to  focus  on  these  two  phases, but  I'm  going  to  focus  on this  triangular  antiferromagnetic  phase. So  m  and  three  SN  is  unique. It's  a  while  semi-metal. So  it  has  these  awhile  nodes, but  that  does  not  important from  an  engineer's  perspective. What  is  important  from  an  engineer's  perspective is  this  fundamental  crystal  structure. And  the  way  the  moments, the  spin  is  arranged  in  this  plane, it  gives  mm3sn,  very  large  magneto  transport  signatures. That's  what  we  want  as  engineers, we  want  to  be  able  to  measure  this  electrically. And  even  though  you  look  over  here, it  has  a  very  weak  magnetic  woman. So  it's  pretty  much antiferromagnetic  except  for a  very  weak  Ferro  magnetic  moment, which  makes  this  material  very,  very  special. And  it  has  some  other  unique  properties  as  well  and has  a  very  nice  anomalous  Hall  effect. So  the  first  point  here  allows  me  to  detect  it, measure  it,  and  the  last  point  over here  allows  me  to  control  it. So  I  have  a  method  for  electrical  control, and  I  have  a  method  for  electrical  detection. That  is  what  I  want  as  an  engineer. No  other  material  that  I  know  of  from the  antiferromagnetic  family  satisfies these  criteria  as  well  as  M13  SN  does. Now,  this  notion  that  I  want  to  try that  electrical  control  of magnetic  order  is  at  the  heart  of  spin  drownings  devices. That's  what  I  wanted  to  get  across. And  there  has  been  tremendous  progress  in  elementary  SN. I  only  started  working  in  this  material about  two  years  ago  and they  weren't  a  whole  lot  of  papers  available, but  suddenly  in  2021, a  lot  of  nature  papers  started  coming  out. So  this  is  a  seminal  paper, one  of  the  first  papers  that  short  something  very  unique. They  said,  Okay,  let's  put  platinum under  M  and  three SN  pass  electric  current  through  platinum. Somehow  they  were  able  to  see  that this  m  and  three  SN  antiferromagnetic  order started  having  a  chiral  spin  rotation. And  how  did  they  measure  it? Anomalous  Hall  effect. They  measured  anomalous  Hall  signal  and  saw  very clearly  that  this  was  undergoing  oscillation. So  at  the  time  we  were  building models  that  this  was  one  of  the  papers  that  we referred  to  for  validating  some of  the  work  that  we  were  doing  at  the  time. And  in  fact,  just  a  month  ago, a  new  paper  has  come  out  in  nature, which  shows  that  one  code to  build  these  tunnel  junctions. So  you  have  to  antiferromagnetic electrodes  with  MgO  in-between. Depending  on  the  relative  orientation of  the  two  antiferromagnetic  electrodes, you  could  measure  a  magneto  resistance  about  2%. You  might  think  it's  so  small. Well  it's  better  than  zero. Previously  we  had  nothing. Now  we  have  to  present, so  hopefully  we  will  get  better  and  better. As  time  goes  by.  It  gets  worse. Yeah.  It  gets  worse  at  room  temperature. This  is  low  temperature. Yeah.  Why  did  this  happen? And  m  and  three  SN  and  not  in nickel  oxide  or  any  other  antiferromagnetic. It's  because  of  that  week federal  magnetic  moment  that  I  talked  about. It's  VQ,  but  it's  finite and  that  is  what  is  important  for  us  to  control  it. In  fact,  in  M  and  PT, people  have  demonstrated  about  100  per  cent  DMR, but  I'm  not  interested  in  MPT. I'm  interested  in  M13  ascend. So  I'm  not  going  to  talk  about  that  anyway. So  what  I  want  to  do  today  is  just  talk  about some  of  the  models  that  my  group  has been  developing  to  understand. I  pass  current. Then  how  does  the  spin  structure  of  M13  SN  change? And  by  change,  I  want  to specifically  look  at  oscillations  of  this. And  what  we  do  is  we  want  to  focus  on  the  right  bought, how  much  current  is  required? What  is  the  frequency  of  this  oscillation? But  we  will  spend just  a  little  bit  of  time  to  look  at  readout. And  then  I  hope  that  the  models that  we  have  can  allow  me  to  understand the  relationship  between  the  frequency  of oscillation  and  the  input  spin  current. Now  for  people,  I  said  when  I  started  this  lecture,  okay, that  antiviral  magnets  have  terahertz  frequency. So  obviously,  when  we  start  working,  we  thought, okay,  I'm  entry  essentially have  some  terahertz  oscillations. And  it  turns  out  that  this  material  is  so unique  that  only  and  only  in  this  material, you  could  actually  tune that  frequency  down  to  the  gigahertz  range, something  that's  not  possible with  other  antiferromagnetic  materials. So  my  next  few  slides, I  was  told  this  will  be  a  broad  audience  of  students. I  tried  to  cut  down  the  math, but  these  will  be  a  little  bit  still  a  little  bit  dense. But  let's  see  what  I'm  doing  here. We  have  this  platinum, we  have  this  amine  trigger  Sam, I  pass  current  gets  polarized  and  B basically  affects  the  orientation  of  m  entry  assign. What  I'm  expecting  is  that  those  spins  that  I  showed, the  triangles  that  I  showed  earlier, they  are  oriented  in  this  x,  y  plane. The  way  I  have  set  up  my  device  here. Exactly  the  same  as the  experimental  setup  that I  showed  on  the  previous  slide. Again,  the  goal  is  to  ensure  that  whatever  I'm  doing, I  can  readily  validated,  right? So  that's  what  I  did.  So  how  do  I  start  here? Well,  the  general  processes  this, whenever  we  start  thinking  about  dynamics, step  one  is  to  write  down  the  free  energy  of  the  system. Free  energy  is  the  energy  that  it  would  have  in the  ground  state  when  it  does  not  being  perturbed. So  we  have  exchange  coupling. If  anyone  remembers  from high  school  physics  spins  this  opposite  dot-product, that  is  the  exchange. Then  we  have  anisotropy. Isotropy  is  the  preference  of the  magnet  to  lie  along  a  certain  direction. And  in-between. And  I'm  three  ascent, we  have  this  unique  dorm  or  BMI. Anyone  knows  what  DMI  stands  for? I  wouldn't  know  when  I  was  a  student. Dmi  stands  for  Xian  lotion  SKY  Warrior  interactions. So  this  is  an  interaction  that says  spins  are  going  to  be like  that  candidate  from  each  other. And  we  know  an  m  and  three  S.  And  we saw  that  spins  are  non-colinear. They  were  not  anti-parallel  fully. They  were  in  a  120  degree  spin  structure. So  that  is  that,  that  is  step  one. How  my  students  start. Step-2  is  when  you've  got  that  energy, put  it  inside  your  equation  of  motion. Now  for  antiferromagnetic, this  is  where  all  the  debate  comes. The  equation  of  motion  that  I'm  going  to  use  is the  same  equation  that  we  used  for  Ferro  magnets, that  Landau  Lifshitz  Gilbert  equation. So  a  lot  of  researchers  are  still arguing  that  equation  should not  be  valid  for  antiferromagnetic. Or  sometimes  they  argue  that  it  should  be, it  should  be  fine  to  be  used  for  antiferromagnetic, except  that  you  have  to  change  some  terms in  it  to  basically  be commensurate  with  the  notion  of  antiferromagnetic. But  again,  I  will  start  from  this  assumption  assuming that  it's  exactly  the  same  as  federal  magnets, but  the  key  differences. Now,  I  have  to  solve  this  for three  spends  in  inventory  essence  spin  one  is  like  this, then  we  have  one-twenty  another  123  spins. And  that  has  to  be  done  self-consistently. So  I  don't  usually  like  doing  that. So  what  my  students  did was  a  very  smart  thing.  They  said. Instead  of  solving  for  m1,  m2,  and  m3, why  don't  we  solve  this  equation for  some  effective  vectors. Effective  vectors  are  just  some  algebraic  combination of  m1,  m2,  and  m3. So  the  first  one  is  small  m, which  basically  is  the  average  magnetization. And  then  we  have  some  other  staggered  or  the  parameters. But  anyway,  when  we  start  with  this, what  we  also  do  is  we  look  at how  these  vectors  are  oriented. So  if  I  look  at  the  bottom  figure  here, what  I  see  is  that  N1  and  N2  make  this  90  degree  angle. And  there  is  the  small  in-plane, an  isotropy  or  small  week  Ferro  magnetic  moment  m. This  is  what  allows  me  to  control  this  whole  dynamic. And  what  I  also  want  you  to appreciate  us  the  spin  orientation. It's  120  degree,  but  not  quite  so, not  quite  so  it  seems  to  be  one-twenty, but  it  has  a  slight  deviation. And  only  one  of  the  moments  is  along  It's  easy  access. The  other  two  are  not. Those  are  subtle  things  that  will,  you  know, that  we  have  to  remember  when  we're  modeling  all  of  this. So  before  we  did  anything, before  we  even  solve  any  equations  with  time, the  first  thing  is  to  figure  out what  the  ground  state  of  the  system  is. Interestingly,  when  we  solve  for  ground-state, we  get  six  ground  states. These  are  six  minimum  energy  states of  M  and  three  SN  at  any  given  time. It  could  be  here  or  here,  or  here. One  of  these  states, the  6-fold  an  isotropy  is  very  important. The  energy  difference  between  this  and this  and  all  the  other,  it's  small. And  it's  that  smallness  of the  energy  difference  that  allows me  to  very  efficiently  control  this  material. Alright,  and  remember  that the  magnetic  moment  that  I'm getting  in  this  system  is  very,  very  small. So  we  had  this  framework, but  we  were  still  not  happy  with  it. We  said,  well,  the  equations  are  looking  very  bad. So  what  can  we  do  to  simplify  them,  right? That's,  that's  the  whole  point. We  want  to  come  up  with  analytic  models. So  what  we  did  was  something  unique. We  said,  well,  we  know  that we  had  three  effective  vectors, m,  N1,  and  N2. So  why  don't  we  represent  N1 and  N2  in  terms  of  some  azimuthal  angle. We  know  that  even  when  I'm  trying  to  switch  the  system, N1  and  N2  want  to  remain  in  the  plane. They  don't  want  to  go  out. So  I  can  just  define  them  in  terms  of  phi. Phi  is  our  azimuthal  angle  that  I  measured  from  x  axis. So  N1  and  N2  are  still  perpendicular. You  can  quickly  do  the  dot-product  here and  you  can  determine  that  they  are perpendicular  to  each  other. So  now  we  start  with  LLC. Simplify  it  into  three  equations. One  for  small  m,  one  for  N1,  one  for  N2. Not  happy  with  it. We  further  simplify  it  in  terms  of  phi. That's  what  we  do.  And  that's when  interesting  things  start  happening. When  we  write  down  the  equation  of  motion  in  terms  of this  phi  angle  of  this  new  order, we  get  the  second-order  equation  of  motion. What  is  interesting  about this  equation  of  motion,  everything  looks  fine. Phi  double  dot,  phi  dot, phi  dot  is  the  angular  velocity. So  in  measurement  of  anomalous  Hall  signal, that  is  what  you're  going  to  be  measuring  this  guy. So  this  guy  needs  to  vary  with  time. If  phi  dot  varies  with  time, you  can  determine  and an  AC  signal  associated  with  this  process. What  is  unique  over  here  is  this  sinusoid  six  phi  term. So  it's  a  non-linear  equation, very  hard  to  solve  analytically  actually. But  the  thing  is  that  this  pre-factor in  the  case  of  m  and  three  as  N  is  very  small, it's  only  ten  to  the  negative  four. To  be  very,  very  honest. We  did  not  derive  this  equation  religiously  because  what, when  my  students  started  working  on  it, he  didn't  get  the  science  X5  term. He  did  not.  In  order  to  get  to  that  science  expired  term, you  had  to  do  some  perturbation  theory  and  he  was  like, I'm  not  doing  it,  it's  too  much  work. And  that  seemed  to  be  fine for  the  time  being  because  it's  so  small. Right.  So  why  bother  with  it? And  I'll  tell  you  why  bother  with  it. Then  after  we  wrote  the  paper,  paper  is  out. I  wasn't  happy  with  it. But  whatever,  we  go  back  and  we  were  like, Okay,  let's  heuristically  argue that  there  is  a  sign  six  fighter. Let's  argue,  let's  change  the  equation. Let's  change  the  equation  and  then  see  what  happens. So  after  we  change  the  equation, we  wanted  to  determine  this  prefactor,  but  we'll  see. So  this  equation  of  motion, if  you  remember  from  early  physics  days, is  exactly  the  same  equation  as that  of  a  simple  gravity  pendulum. It's  exactly  the  same. So  here  in  this  example, this  pendulum  is  being  driven  by a  damping  of  Beta  and  a  torque  of  gamma. And  this  has  inertial  motion. So  what  did  we  learn? We  learned  that the  antiferromagnetic  M13  ASN  has  similarities  with classical  motion  of  massive  bodies that  are  driven  by  Newton's  kinetic  equation. That's  what  we  learned  and  we  can  solve  it. In  fact,  when  we  have  inertia,  the  system  accumulates. Energy,  can  switch  very  fast. So  that's  what  we  learned  from  this  process. In  fact,  as  I  said, why  is  all  of  this  important? This  is  important  because the  smallness  of  the  term  allows me  to  have  a  dynamic  at  very,  very  small  currents, making  this  material  highly  energy efficient  for  spin  tronic  applications, if  you  look  at  other  materials, they  require  orders  of  magnitude more  current,  not  inventory  asset. Finally,  because  of  the  smallness of  this  term,  but  sadly, we  could  not  derive  religiously, but  we  argued  theoretically  and  validated it  against  fall  numerical  simulations. It  also  shows  that  the  dynamics  can be  tuned  from  gigahertz  to  terahertz. So  in  the  last  few  minutes, I'll  just  show  you  what  we  did. We  simulated  the  terahertz  dynamics. So  what  we  do  is  we  apply  a  very large  current  and  we  get  dynamics  at  6.5  terahertz. So  this  is  how  the  three  moments  M1,  M2, and  M3  are  oscillating on  the  phase-space  and  it's  rather  fast. Then  I  do  something  unique. I  reduce  the  current  to  about  ten  to  the  five. It's  very  small,  four  orders  of  magnitude  smaller. Well,  the  system  oscillate. Yes.  And  that's  what  we  demonstrate  it. I  apologize,  this  is  very  crappy. It's  so  slow  that  my  computer  has  difficulty  processing. This  oscillation  is  actually happening  at  half  a  gigahertz. That  tunability  is  not  afforded  in the  case  of  any  other  antiferromagnetic  material. And  I  know  I'm  running  short  on  time. How  much,  how  many  minutes  do  I  have?  Three  or  4  min. So  what  do  I  want  to  talk  about? Yeah,  maybe  i'll,  I'll  talk  a  little  bit  about  this. The  low  frequency  oscillations. We  want  these  low  frequency  oscillations. Why?  Because  these  are  more  energy  efficient. I  don't  know  of any  microelectronics  circuit  that  could detect  signals  that  terahertz  frequency. So  this  would  be  a  little  bit  more  appropriate  in the  case  of  building  practical  electronic  devices. Because  otherwise  we  have  to  put  so  much current  that  we  would  burn  the  system  down. So  we  actually  did  a  lot  more  simulations. Not  very  interesting,  but  we  showed  that the  frequency  goes  as  low  as  about  0.2  ghz. And  then  as  you  are  increasing,  the  current  increases. If  you  look  at  this  first  one,  that's  what  I  said. And  antiferromagnetic  shows  spiking  behavior. Here  it  shows  better,  it's  less  spiky. And  then  as  the  current  increases, it  gets  better  and  better. And  the  critical  current  and  our  cases, 1.7  into  ten  to  the  five  ampere  per  centimeter. Really  small  amount  of  current  compared  to anything  else  that  we've  seen  so  far. Now,  how  do  we  prove  what  we've  done  is  correct? So  this  would  be  my  last  closing  slide. And  then  I'll  have  one  more  thank  yous  laid  in  a  minute. So  how  do  we  prove  what  we  did  was  right? So  what  we  did  was  we  said,  Okay, let's  run  our  full  blown  LLT  simulation and  estimate  the  frequency as  a  function  of  the  spin  current. So  these  dots  are  taken  from  simulations. And  the  dashed  line  over  here  is  also  simulation. But  it  is  the  simulation  of the  pendulum  equation  that  I showed  you  that  seemed  to  match. But  then  you  could  say,  Wow, you're  matching  one  theory  with  another  theory. Whereas  reality,  okay. I'll  show  you  where  reality  is. This  is  the  paper  that  I  keep  coming  back  to. This  is  the  2021  nature  paper. This  came  out  sadly  after  we  wrote  our  paper, so  we  could  not  cite  it. They  did  something  similar  in  their  experiments. They  calculate  the  frequency  of  oscillation  as a  function  of  the  input  current  that  they  are  applying. And  we  see  exactly, we  account  for  the  changes  in the  thickness  and  other  materials  specific  parameters. We  saw  that  the  court  the  exact  same  results as  we  got  in  our  models  and  simulations, which  gives  us  a  lot  more  confidence  in  the  things that  we  have  been  doing  and  in  the  interest  of  time. Let  me  just  go  to  my  computer. My  computer,  so  it's  not  going to  I  will  tell  you  what  I  was  going  to  say  it. So  my  computer  is  when  I  was  a  student, it  came  back.  It  came  back. What  I  want  to  very  quickly  do  with  this  last  slide. So  there  has  been, let's  see  if  it'll  show  up, but  we  will  wait  for  it  to  show  up. What  I  wanted  to  say  was  that  the, I've  talked  about  this  rich  set  of  dynamics, oscillations  and  MN  three  ascend. So  there  is  a  lot  of  interests  very recently  in  doing  neuromorphic  computing. That's  not  an  area  I  work  in, but  a  lot  of  other  researchers  are  now saying  that  one  could  use  these antiferromagnetic  and  use  their  spiking  nature  to mimic  the  action  potentials  of  biological  neurons. That's  one  very  active  area  of  research. And  I've  written  some,  mentioned some  papers  that  have  looked  into the  action  potential  behavior  of  antiferromagnetic. And  then  they're  also  claiming that  one  could  do  some  sort of  analog  computing  or building  some  logic  gates  with  it  using spiky  inputs  rather  than  DC  signals, as  would  be  normally  the  case. Alright,  so  with  that,  I'm  done. So  my  group  is  very interested  in  working  on  m.  And  three  are  saying, we're  looking  into  new  textures and  effects  of  thermal  noise  and  heating. And  how  does  one  cup  of one  oscillator  with  another  oscillator. So  those  are  some  of  the  interesting  research  topics. And  I  will  remind  folks, if  you're  interested  in  a  postdoc  position, please  let  me  know. I  am  getting  a  little  desperate, so  sorry  for  soliciting  here, but  I  thought  I  would  use the  platform  to  just  remind  everyone  knows  that. And  I  want  to  thank  my  students  who  did  the  work, and  my  collaborators  and  our  funding  agencies, and  thank  you  all  for  being here.  Questions. Thank  you.  Very  practical  question. So  you  have  one  of  these  configuration that  you  study  where  you  have a  sensory  dielectric  between these  two  antiserum  ferromagnetic  materials. How  important  is  the  thickness  of  this  material? And  you  mentioned  that  it's  important  to  have high-quality  interfaces  like epitaxial  growth,  to  have  any. For  collinear  one  I  see. Yeah. Claim  that  the  quality is  not  important  because  the  reason  for this  TMR  is  not  what  happens  in  ferromagnetic, where  you  have  spin polarized  currents  transferring  torque. The  reason  that  this  happens  in M13  assent  is  because  of  time-reversal, symmetry  breaking  and  bearing  phase  and  so  on. So  the  whole  physics  is  different. There  are  some  theoretical  calculations  that  also showed  that  an  amine  three  S  and the  quality  is  not  important, just  need  ten  enough, maybe  to  3  nm  fine  and  good  enough. Yeah,  but  no  other  material has  been  has  shown  this  at  all. So  I  have  to  read  that  paper  more  carefully. But  that's  the  claim. Get  my  stepson.  Thank  you  for  the  talk. I  have  a  I  think  maybe  a  really  simple  question, but  the  last  couple  of  slides  you  showed  on  your  graph  of the  frequency  versus  the  plotted  pendulum  equation that  there's  a  threshold  current. And  I  was  just  curious  about  the  where  does  that  arise? Is  that  a  quantum  transition  or  is  it  something  more? Yeah,  so  usually  a  thresholding  behavior  is  very  common in  magnetic  materials  because  you  have these  six  equivalent  basins  of  anodyne. I'm  in  three  essence  that  the  magnet is  lying  in  one  of  the  energy  basis. So  we  always  start  from  ground  state,  okay? And  then  what  we  want  to  do is  apply  a  stimulus  and  then  give  it enough  energy  so  it  can  overcome that  energy  barrier  and  flip  to  the  other  side. In  any  magnetic  material, that  amount  of  current  that  is  required  to  cause this  transition  is  proportional to  the  anisotropy  of  the  system. In  the  case  of  M13, ascending  isotropy  is  so  small, That's  the  argument  I  made.  It's  very  small. So  the  amount  of  current  is  orders  of  magnitude smaller  than  any  other  known  antiferromagnetic  materials. But  it's  really  to  just  classically, it's  just  taking  it  over that  energy  barrier.  That's  what  it's  doing. There  is  no  quantum  transitions  and  my  simulations, I  don't  understand  quantum. So  sorry.  One  more  question  from  anybody. Alright. So  very  interesting  talk. So  is  there  any  idea about  the  energy  barrier  between  these  states? Is  it  that,  that  energy  barrier  is  pretty  low  or  it's about  100  joule  per  meter cube  is  very  small,  it's  very  small. Then  if  someone  argues  for  ferromagnet,  they  can  say, we  can  make  a  very  low  energy  barrier  magnet  and then  the  current  density  for  switching would  be  very  low,  Correct? Um,  so  the  advantage  that you  consider  here  are  these  new  features  like  you  can, you  can  tune  the oscillation  frequency  and  stuff  like  that. So  you  cannot,  yeah, I  think  biomarkers  are  very  solid  so I  can't  replace  them  unfortunately, but  the  benefit  is  bursting, spiking  new  kinds  of  dynamics. So  hopefully,  we'll  find  some  potential  use. And  in  fact,  we  can  increase  the current  and  increase  the  frequency. So  the  microwave  signal  generation  should  be  good. But  the  signal  is  every  measure, like  at  least  people  measure  is  very  weak. Again,  about  100  microvolt, if  you're  lucky,  it's  very  small. So  the  argument  here  is  not, this  is  gonna  be  magnets that  we  can  switch  it  more  easily, just  marked  for  new  new  new  functionality,  correct? Correct. Alright. Well,  I  think  we're  at  the  top  of  the  hour, so  we'll  thank  our  speaker  one  more  time. Thank  you.