  The crystallographic, magnetic and thermal properties of BiMn2PO6 and
BiZn2PO6 were investigated by x-ray diffraction, magnetic susceptibility \chi,
heat capacity Cp, and 31P NMR measurements as well as by density-functional
band-theory calculations. Both compounds show a strong monotonic lattice
softening on cooling, where the Debye temperature decreases by a factor of two
from \Theta_D=650K at T=300K to \Theta_D=300K at T=2K. The \chi(T) data for
BiMn2PO6 above 150K follow a Curie-Weiss law with a Curie constant consistent
with a S=5/2 with g=2 and an antiferromagnetic (AFM) Weiss temperature
\theta_CW= -78K. The \chi data indicate long-range AFM ordering below TN=30K,
confirmed by a sharp lambda-type peak in Cp(T) at 28.8K. The band-theory
calculations indicate that BiMn2PO6 is an AFM compound with dominant
interactions J1/kB= 6.7K and J3/kB= 5.6K along the legs and rungs of a two-leg
spin-ladder, respectively. In addition to the long-range AFM ordering at
TN=30K, a second transition at 10 K is observed from the \chi and NMR
measurements but is not evident in the Cp data. The Cp data at low T suggest a
significant contribution from AFM spin waves moving in three dimensions and the
absence of a spin-wave gap. A detailed analysis of the NMR spectra indicates
commensurate magnetic order between 10K and 30K and a possible incommensurate
modulation and/or spin canting below 10K. The commensurate order is consistent
with microscopic simulations that yield a collinear Neel-type AFM spin
arrangement both within and between the ladders, despite the presence of
multiple weak interactions frustrating this magnetic structure. Frustration for
AFM ordering and 1D spatial anisotropy of the 3D spin interactions are
manifested in the frustration ratio f=|{\theta}CW|/TN=2.6, indicating a
suppression of TN from 68K in the absence of these effects to 30K in BiMn2PO6.
