A vector bundle $E$ on a smooth projective variety $X$ is called Ulrich bundle if it is Arithmetically Cohen-Macaulay , i.e., $H^i(E(t)) = 0 $ for all $t \in Z$ and $0 < i < k$ and with Hilbert polynomial $cr\binom{t+k}{k}$ for some linear projection $X\to \mathbb P^k$

The following statement appeard in the survey paper of Beauville https://link.springer.com/article/10.1007%2Fs40879-017-0154-4

Let $E$ be an Ulrich bundle of rank $r$ on a non-singular projective variety $X$ why $E$ is slope semi-stable?