Illustrator - Thin Lines in Logo look pixelated when sized down

Hi there,

I'm having these issues with my logo that I'm exporting from Adobe Illustrator. It seems the thin lines are becoming distorted as the logo is used on a PC and in Word. I know the size and resultuion of these files are very high, how can I make the thin lines smooth at any size for my word and powerpoint documents?

Any help is appreicated thank you!