Snubbing someone by being on your phone instead of paying attention to them is known as "Phubbing".
This article explains it, but I think it applies to more than just life partners.
[R]esearchers interviewed 145 people and found that 46% had been ‘phubbed’ by their partner – and that 37% felt depressed.
Study lead author Dr James A. Roberts said, ‘What we discovered was that when someone perceived that their partner phubbed them, this created conflict and led to lower levels of reported relationship satisfaction.
‘These lower levels of relationship satisfaction, in turn, led to lower levels of life satisfaction and, ultimately, higher levels of depression.’
Co-author Dr Meredith David said, ‘In everyday interactions with significant others, people often assume that momentary distractions by their cell phones are not a big deal.
‘However, our findings suggest that the more often a couple’s time spent together is interrupted by one individual attending to his/her cellphone, the less likely it is that the other individual is satisfied in the overall relationship.’