Is it possible to find an example of an $\mathbb{R}$-Cartier divisor $D$ on an irreducible variety $X$ that is non-trivial, nef, effective and numerically rigid?

By "numerically rigid" I mean that if $E$ is another $\mathbb{R}$-Cartier effective divisor such that $E$ is numerically equivalent to $D$ then $D=E$.

For curves this clearly cannot be the case, since an effective non-trivial divisor is always ample.