# Neutron Diffraction and $\mu$SR Studies of Two Polymorphs of Nickel Niobate (NiNb$_2$O$_6$)

## TL;DR

This study characterizes the magnetic structures and phase transitions of two polymorphs of NiNb$_2$O$_6$ using neutron diffraction and $bc$SR, revealing differences in transition temperatures, critical exponents, and magnetic ordering.

## Contribution

It provides the first detailed magnetic structure of the $eta$-NiNb$_2$O$_6$ polymorph and compares it with the known columbite form, highlighting differences in magnetic ordering and critical behavior.

## Key findings

- $eta$-NiNb$_2$O$_6$ has a higher transition temperature ($T_N \,\sim\, 15$ K) than columbite ($T_N = 5.7$ K).
- Critical exponents indicate reduced dimensionality, more pronounced in columbite.
- Magnetic structure involves antiferromagnetically-coupled chains aligned along specific axes.

## Abstract

Neutron diffraction and muon spin relaxation ($\mu$SR) studies are presented for the newly characterized polymorph of NiNb$_2$O$_6$ ($\beta$-NiNb$_2$O$_6$) with space group P4$_2$/n and $\mu$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$_6$. $\mu$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 $\mu$SR measurements also allowed us to estimate the critical exponent of the order parameter $\beta$ for each polymorph. We found $\beta =$ 0.25(3) and 0.16(2) for the $\beta$ and columbite polymorphs respectively. The single crystal neutron scattering data gives a value for the critical exponent $\beta =$~0.28(3) for $\beta$-NiNb$_2$O$_6$, in agreement with the $\mu$SR value. While both systems have $\beta$ 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 $\beta$-polymorph are likely much larger.