Intermediate matrices in the positive definite ordering.

Question

Let $$ M= \left[ {\begin{array}{cc} a & b \\ b & c \\ \end{array} } \right],$$ be a positive definite matrix such that $M \succeq xI_d$, for some $x > 0$. Here '$\succeq$' means the usual order on positive definite matrix. Now, let $x'$ be a number such that $a>x'>x$. Can we find conditions on $x'$ such that $$ \left[ {\begin{array}{cc} a & b \\ b & c \\ \end{array} } \right] \succeq \left[ {\begin{array}{cc} x' & 0 \\ 0 & x \\ \end{array} } \right]?$$