Sounds like you are upset with them.

"HM told me that the HR will contact me for the next step, so I will just contact the HR this time, right?"

What's the logic behind it?

 

"It has been a week since the phone interview with the YY (HM).  "

Sounds like you are upset with them.  If that's not your intention, you need to change the tone.  Why don't just say, I talked with YY about a xyz position last week.