Switching power input and battery automatically with P-Channal MOSFET

I am going to design a circuit that uses a battery as a power source. And an adapter as the input power. So I need a circuit that switches the power source automatically from battery to input power. And I do not want to add a chip to do this because it will increase the cost of the board.

The simple circuit for that could be:
The shortcoming of this circuit is that it will consume some power by the diode D1 when the adapter plugs in.  In order to overcome this, a P-MOSFET is used to replace it.
The simulation showed it works well. I will test it later.

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