angular material 2 button toggle by default selected

I'm just beginner in material but this should work. You can use ngModel with variable that can have two values "one", "two". Than you can observe changes using "yourFunction".

<md-button-toggle-group (ngModelChange)="yourFunction($event)" [ngModel]="selected">
 <md-button-toggle value="one">
  <span>one</span>
 </md-button-toggle>
 <md-button-toggle value="two">
  <span>second</span>
 </md-button-toggle>
</md-button-toggle-group>

You need to assign each button a value and then you can give the group an initial value (matching one of the buttons);

<md-button-toggle-group #group="mdButtonToggleGroup" value="button1">
    <md-button-toggle value="button1">
      <span>one</span>
    </md-button-toggle>
    <md-button-toggle value="button2">
      <span>second</span>
    </md-button-toggle>
  </md-button-toggle-group>