MatButtonToggle component doesn’t implement ControlValueAccessor therefore you can’t use ngModel on it. ngDefaultControl was introduced for other purposes.
MatButtonToggle is supposed to be a part of mat-button-toggle-group. But if you want to use it as a standalone component and bind model to it here is some example of how you can do it:
<mat-button-toggle
[checked]="myFlagForButtonToggle"
(change)="myFlagForButtonToggle = $event.source.checked">
Toggle me!
</mat-button-toggle>
Plunker Example