HR people are not robot drones (even if that's not always apparent) and they appreciate a "thank you" same as anybody else. Nor are they solely devoted to the company bottom line or performance metrics as has been suggested, but take pride and satisfaction in a happy employee.
If you truly feel that level of gratitude towards this person, I don't see anything wrong, per se, with a small token of appreciation. A small potted plant and a handwritten thank-you note gets you a long way! Just be sure to keep it within a reasonable price-range ($5-$10).
Of course, it could be that the brown-shirts have taken over at your company and any sign of affection or gratitude between co-workers is equated with bribery or harassment and severely punished, in which case I can only say that I'm sorry and that you should restrict yourself to a company-approved "thank you" nod as you pass each other in the hallway.