Цитирую доки:
between: operand 1 should be the column name, and operand 2 and 3 should be the starting and ending values of the range that the column is in. For example, ['between', 'id', 1, 10] will generate id BETWEEN 1 AND 10
https://github.com/yiisoft/yii2/blob/master/docs/g... 