Phase Diagram of the BCC S=1/2 Heisenberg Antiferromagnet with First and Second Neighbor Exchange

We use linked-cluster series expansions, both at T=0 and high temperature, to analyse the phase structure of the spin-$\text{half}$ Heisenberg antiferromagnet with competing first and second-neighbor interactions on the 3-dimensional body-centred-cubic lattice. At zero temperature we find a first-order quantum phase transition at $J_2\mathrm{/}{J}_1\simeq 0.705\pm 0.005$ between AF${}_1$ (Ne'el) and AF${}_2$ ordered phases. The high temperature series yield quite accurate estimates of the bounding critical line for the AF${}_1$ phase, and an apparent critical line for the AF${}_2$ phase, with a bicritical point at $J_1/J_2\simeq 0.71$,$kT/J_1\simeq 0.34$. The possibility that this latter transition is first-order cannot be excluded.