Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Neutron Diffraction and $\mu$SR Studies of Two Polymorphs of Nickel
  Niobate (NiNb$_2$O$_6$)   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.

14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas