Instability of GaAs PHEMT during dc bias?

I am using a Agilent pHEMT (ATF34143) to be used as an amplifier at lower frequencies (1 MHz) and low temperatures (4 Kelvin). When I try to measure to dc characteristics of the transistor I see osciilations (fosc= 160 MHz) at the drain terminal. I use a bias tee (http://web.mac.com/gwj/Site/Bias_Tee.html) between the drain terminal and the supply voltage. Similar bias tee is used between gate and the gate supply.

When the oscillation begin to appear, I see an abrupt jump in the drain current. How can I eliminate these oscillations / make the circuit more stable?

Nothing to worry in the initial stages of design.
Design the matching circuit and re-check the same.

make sure you have good decoupling, especially to decouple the 160MHz one. the decoupling capacitor (for 160MHz you may need ~1000pF) shall be as close as possible to the transistor. also reduce the pcb trace length connected to the transistor, if they are not necessary. if you are using breadboard (dont know if thats possible at 4K) or other prototyping tech works only for low frequencies then getting oscillation is almost inevitable with this device. also dont aim for an enormous gain (>20dB) otherwise you will also likely to get oscillation. finally, use feedback to make it stable (of course you will lose noise performance which may not be good since you are working at 4K for, perhaps, noise purpose...).