arXiv2017
Neutron diffraction and muon spin relaxation ($μ$SR) studies are presented for the newly characterized polymorph of NiNb$_2$O$_6$ ($β$-NiNb$_2$O$_6$) with space group P4$_2$/n and $μ$SR data only for the previously known columbite structure polymorph with space group Pbcn. The magnetic structure of the P4$_2$/n form was determined from neutron diffraction using both powder and single crystal data. Powder neutron diffraction determined an ordering wave vector $\vec{k}$ = ($\frac{1}{2},\frac{1}{2},\frac{1}{2}$). Single crystal data confirmed the same $\vec{k}$-vector and showed that the correct magnetic structure consists of antiferromagnetically-coupled chains running along the a or b-axes in adjacent Ni$^{2+}$ layers perpendicular to the c-axis, which is consistent with the expected exchange interaction hierarchy in this system. The refined magnetic structure is compared with the known magnetic structures of the closely related tri-rutile phases, NiSb$_2$O$_6$ and NiTa$_2$O$_6$. $μ$SR data finds a transition temperature of $T_N \sim$ 15 K for this system, while the columbite polymorph exhibits a lower $T_N =$ 5.7(3) K. Our $μ$SR measurements also allowed us to estimate the critical exponent of the order parameter $β$ for each polymorph. We found $β=$ 0.25(3) and 0.16(2) for the $β$ and columbite polymorphs respectively. The single crystal neutron scattering data gives a value for the critical exponent $β=$~0.28(3) for $β$-NiNb$_2$O$_6$, in agreement with the $μ$SR value. While both systems have $β$ values less than 0.3, which is indicative of reduced dimensionality, this effect appears to be much stronger for the columbite system. In other words, although both systems appear to well-described by $S = 1$ spin chains, the interchain interactions in the $β$-polymorph are likely much larger.