Short Summary Report

A digital archeological investigation was conducted on previously measured THz data in magnetic fields. Hidden features demonstrating non-trivial selection rules were discovered in the presence of a magnetic field, which are thickness-dependent. The g-factors for some of the excitations demonstrate different observed values depending on the polarization of incident THz radiation, contradicting our expectations of light-matter interaction.

Evaluate initialization cell and __then evaluate__ `.slides` cell below

.slides

Thank your for your attention!

Introduction

Talk about a material structure

.slide

## THz spectroscopy of $Fe_2 Mo_3 O_8$ in magnetic fields

<u>K. V. Vasin</u> <sup>1,2</sup>, A. R. Nurmukhametov <sup>1</sup>,  A. Strinic <sup>2</sup>, L. Prodan <sup>2</sup>, V. Tsurkan <sup>2,3</sup>, I. Kézsmárki <sup>2</sup>, M. V. Eremin <sup>1</sup>, and J. Deisenhofer <sup>2</sup> 

<br/><br/>

- Institute of Physics, Kazan (Volga region) Federal University, 420008, Kremlevskaya 18
- Institute of Physics, Augsburg University, 86159, Universitätsstraße 1
- Institute of Applied Physics, MD-2028 Chisinau, Republic of Moldova

<br/>
  
*krikus.ms@gmail.com*

---

## Crystal and magnetic structure

<Row>
 <CrystalStructure/>
 <div style="text-align:left">
    

  - $Fe_2 Mo_3 O_8$
  - Hexagonal structure (polar) $P6_{3mc}$ group
  - Collinear AFM ordering below $60K$
  - __II type multiferroic material__

  <br/><br/>

  Single crystals were grown by the chemical transport reaction method @ Augsburg University <!-- .element: class="fragment" data-fragment-index="1" -->

  <br/>


  
  $Fe^{2+} (3d^6)$ <!-- .element: class="fragment" data-fragment-index="2" -->
  
  - A-site  <!-- .element: class="fragment" data-fragment-index="2" --> $FeO_4$ <!-- .element: class="fragment" data-fragment-index="2" -->
  - B-site <!-- .element: class="fragment" data-fragment-index="2" --> $FeO_6$ <!-- .element: class="fragment" data-fragment-index="2" -->
 
 </div> 
</Row>

Crystal data

Load preconstructed CIF

CrystalStructure = Graphics3D[NotebookStore["tuberculosis-b03"], ImageSize->{400,500}];

Experimental data

Plot THz data using

thzData = NotebookStore["myopic-fbc"]; DropHalf[list_List] := Drop[list, -Length[list]/2 // Ceiling]

THzPlot[OptionsPattern[]] := With[{
  data = KeyValueMap[With[{field = #1, plot = #2},
          Drop[Drop[
          {#[[1]], #[[2]] + field 100} &/@ DropHalf[Drop[plot // First, 2][[All,4;;5]]]
          , 200], -200]
        ]&, thzData[[OptionValue["Part"]]][OptionValue["Key"]] // KeySort]
},
  If[OptionValue["ZeroField"],
    ListLinePlot[data // First, 
  
      PlotStyle->Table[Blend[OptionValue["Gradient"], i], {i,0.,0.,1./8}],
      AxesLabel->{"wavenumber (cm^{-1})", "absorption"},
      PlotRange->OptionValue["PlotRange"],
      ImageSize->OptionValue["ImageSize"]
    ]
  ,
    ListLinePlot[data, 
  
      PlotStyle->Table[Blend[OptionValue["Gradient"], i], {i,0.,1.,1./8}],
      AxesLabel->{"wavenumber (cm^{-1})", "absorption"},
      Epilog->{Table[Style[Text[StringTemplate["``T"][i], {50, 50 + 100 i}], FontSize->14], {i, 0, 7}], MetaMarker[OptionValue["Marker"]]},
      PlotRange->OptionValue["PlotRange"],
      ImageSize->OptionValue["ImageSize"]
    ]  
  ]
]

Options[THzPlot] = {"Part"->1, "Key"->1.6`, "Gradient"->{Blue // Lighter, Red}, "PlotRange"->{{30, 120}, {0,830}}, "ImageSize"->{330, 450}, "ZeroField"->False, "Marker"->Null};

.slide

## Unpublished low-frequency excitations data
Absorption spectrum in THz range __measured below $T_N = 60K$__

<Row>
  <div>
    <div class="p-4" >$E^{\omega}||\mathbf{a}~~H^{\omega}||\mathbf{c}$</div>
    <THzPlot Part={2} Key={0.7000000000000001} ZeroField={True} PlotRange={ {{30,135}, {0,150}} } ImageSize={350} Gradient={ {RGBColor[0.368417, 0.506779, 0.709798], RGBColor[0.880722, 0.611041, 0.142051]} }/>
    
  </div>
  <div>
    <div class="p-4" >$E^{\omega}||\mathbf{c}~~H^{\omega}||\mathbf{a}$</div>
    <THzPlot Part={3} Key={0.7000000000000001} ZeroField={True} PlotRange={ {{30,135}, {0,150}} } ImageSize={350} Gradient={ {RGBColor[0.528488, 0.470624, 0.701351], RGBColor[0.560181, 0.691569, 0.194885]} }/>
  </div>
  <div>
    <div class="p-4" >$E^{\omega}||\mathbf{a}~~H^{\omega}||\mathbf{b}$</div>
    <THzPlot Part={1} Key={0.7000000000000001} ZeroField={True} PlotRange={ {{30,135}, {0,150}} } ImageSize={350} Gradient={ {RGBColor[0.363898, 0.618501, 0.782349], RGBColor[0.922526, 0.385626, 0.209179]} }/>
  </div>
</Row>


__Ana Strinic, Benjamin Csizi and Co @ Augsburg University (Germany)__

Field dependency

Append data

__Layout__

.slide

# Field dependency
The measurements were taken inside a cryostat @ 4K 

<Row>
  <div>
    <div class="p-4" >$E^{\omega}||\mathbf{a}~~H^{\omega}||\mathbf{c}$</div>
    <THzPlot Part={2} Key={0.7000000000000001} Gradient={ {RGBColor[0.368417, 0.506779, 0.709798], RGBColor[0.880722, 0.611041, 0.142051]} } Marker={"marked-full-1"}/>

<b class="pt-2">g=2.0, g=2.38</b> <!-- .element: class="fragment" data-fragment-index="1" -->
    
  </div>
  <div>
    <div class="p-4" >$E^{\omega}||\mathbf{c}~~H^{\omega}||\mathbf{a}$</div>
    <THzPlot Part={3} Key={0.7000000000000001} Gradient={ {RGBColor[0.528488, 0.470624, 0.701351], RGBColor[0.560181, 0.691569, 0.194885]} } Marker={"marked-full-2"}/>

<b class="pt-2">g=2.0, g=2.46</b> <!-- .element: class="fragment" data-fragment-index="1" -->
      
  </div>
  <div>
    <div class="p-4" >$E^{\omega}||\mathbf{a}~~H^{\omega}||\mathbf{b}$</div>
    <THzPlot Part={1} Key={0.7000000000000001} Gradient={ {RGBColor[0.363898, 0.618501, 0.782349], RGBColor[0.922526, 0.385626, 0.209179]} } Marker={"marked-full-3"}/>

<b class="pt-2">g=2.7, g=3.4</b> <!-- .element: class="fragment" data-fragment-index="1" -->
      
  </div>
</Row>


<SlideEventListener Id={"fd-simple"}/>
<LinesPlacer Event={"fd-simple"} Fragment={1}/>

LinesPlacer[OptionsPattern[]] := With[{win = CurrentWindow[], event = OptionValue["Event"], fragment = StringTemplate["fragment-``"][OptionValue["Fragment"]]},
  EventHandler[event, {fragment -> Function[Null,
    FrontSubmit[{Red, Line[{{89, 0}, {89 - 1.96 0.4688280 8, 100 8}}], Line[{{112.5, 0}, {112.5 - 2.38 0.4688280 8, 100 8}}]}, MetaMarker["marked-full-1"], "Window"->win];
    FrontSubmit[{Red, Line[{{89, 0}, {89 - 2 0.4688280 8, 100 8}}], Line[{{112.5, 0}, {112.5 - 2.46 0.4688280 8, 100 8}}]}, MetaMarker["marked-full-2"], "Window"->win];
    FrontSubmit[{Red, Line[{{89, 0}, {89 - 2.7 0.4688280 8, 100 8}}], Line[{{112.5, 0}, {112.5 - 3.4 0.4688280 8, 100 8}}]}, MetaMarker["marked-full-3"], "Window"->win];
  ]}];
  ""
];

Thickness dependency of AB-cut

Resample the data in order to match number of points

reSampler[min_,max_,step_:0.1][data_List] := With[{i = Interpolation[data, InterpolationOrder->1]},
  Table[{x,  i[x]}, {x, min, max, step}]
]

Extract the given key from an array of data

getTHz[key_, scale_:1] := KeyValueMap[With[{field = #1, plot = #2},
          Drop[Drop[
          {#[[1]], scale #[[2]] + field 100} &/@ DropHalf[Drop[plot // First, 2][[All,4;;5]]]
          , 200], -200]
        ]&, thzData[[1]][key] // KeySort];

A slider to control

ThicknessSlider[OptionsPattern[]] := With[{ev = OptionValue["Event"]},
  EventHandler[InputRange[0.1, 1, 0.3, 1, "Label"->"Thickness (mm)"], Function[value,
    EventFire[ev, "Change", Round[value / 0.3 + 1]];
  ]]
]

Dynamic plot

THzDynamic[OptionsPattern[]] := 
  With[{
    colors = Table[Blend[OptionValue["Gradient"], i], {i,0.,1.,1./8}],
    keys = {0.1`,0.4`,0.7000000000000001`,1.6`},
    ev = OptionValue["Event"]
  },

  LeakyModule[{lines = reSampler[35, 130] /@ getTHz[1.6`]},
    EventHandler[ev, {"Change" -> Function[part,
      If[part == 1,
        lines = reSampler[35, 130] /@ getTHz[keys[[part]], 0.5]
      ,
        lines = reSampler[35, 130] /@ getTHz[keys[[part]]]
      ];
    ]}];
    
    Graphics[Table[With[{i = i},
        {colors[[i]], Line[lines[[i]] // Offload]}
      ], {i, 1, Length[lines]}], 
      Axes->True,
      AxesLabel->{"wavenumber (cm^{-1})", "absorption"},
      Epilog->{Table[Style[Text[StringTemplate["``T"][i], {50, 50 + 100 i}], FontSize->14], {i, 0, 7}], MetaMarker[OptionValue["Marker"]]},
      PlotRange->OptionValue["PlotRange"],
      ImageSize->OptionValue["ImageSize"],
      TransitionDuration->300,
      TransitionType->"Linear"
    ]  
  ]
]

Options[THzDynamic] = {"Gradient"->{Blue // Lighter, Red}, "PlotRange"->{{30, 120}, {0,830}}, "ImageSize"->{450, 450}, "Marker"->Null, "Event"->Null};

G-factor fitter

A live g-factor plot with control buttons

Now dynamic g-factor

GFactor[OptionsPattern[]] := With[{marker = OptionValue["Marker"], win = CurrentWindow[], view = OptionValue["View"]}, 

    EventHandler[InputButton["+"], Function[Null,
      EventFire[view, ToString[placeLine[marker, win], StandardForm]];
    ]]
] 

GFactorView[OptionsPattern[]] := With[{ev = OptionValue["Event"]},LeakyModule[{field = " "},
  EventHandler[ev, Function[data,
    field = data;
  ]];
  EditorView[field // Offload] // CreateFrontEndObject
]]

A function to append a line to a plot

placeLine[marker_String, win_, pos_:{{50,100}, {80,700}}] := LeakyModule[{line = pos},
  FrontSubmit[{
    PointSize[0.04], Red, 
    EventHandler[Point[pos // First], {"drag" -> Function[xy, line = {xy, line[[2]]}]}],
    EventHandler[Point[pos // Last ], {"drag" -> Function[xy, line = {line[[1]], xy}]}],
    Green, Line[line // Offload]
  }, MetaMarker[marker], "Window"->win];

  TextView[With[{p = line}, With[{diff = p[[2]] - p[[1]]},
  (diff[[1]]/( diff[[2]] / 100) ) / 0.4688280 
]] // Offload, "Label"->"g-factor"]
]

__Layout__

.slide

# Thickness dependency
Let us have a look at __ab__-cuts only, where EM wave propagates along the __c__-axis.

<Row>
  <THzDynamic Event={"thz-dyn"} Marker={"marked-dyn"}/>
  <div class="sm-controls text-left pt-4">

    <ThicknessSlider Event={"thz-dyn"}/>

    <GFactor Marker={"marked-dyn"} View={"view-g"}/>
    <GFactorView Event={"view-g"}/>
    
  </div>
</Row>