Herein,
we construct three-dimensional (3D) Fe3O4 epitaxial
nanowires at a 10 nm length scale on a 3D MgO nanotemplate
using an original nanofabrication technique that mainly comprises
nanoimprint lithography and inclined thin-film deposition. Despite
the high density of inevitable nanoscale defects, the ultrasmall Fe3O4 nanowires exhibit a prominent Verwey transition
at about 112 K with a maximum relative change in resistance of 9.5,
which is 6 times larger than that of the thin-film configuration.
Numerous measurements on a large number of Fe3O4 nanowires grown concurrently on the same 3D MgO nanotemplate reveal
a dramatic difference in their electrical transport property with
the presence/absence of the Verwey transition. A comparative study
of Fe3O4 wires of increasing volume and a thin
film reveals that a profound change in the Verwey transition is observed
only for wires with a volume on the order of 10 nm3. Moreover,
a significant decrease in the sharpness of the resistance jump and
the transition temperature of the Verwey response is noticed with
an increasing volume of Fe3O4. This indicates
the potency of the 3D nanofabrication technique in controlling nanoscale
defects, which is further reconfirmed through magnetoresistance measurement.
A feature of the magnetoresistance curve identifies the antiphase
boundaries as a major source of defects. The occurrence of the smallest
magnetoresistance in the ultrasmall nanowire with the highest Verwey
transition temperature and resistance change ratio proves that 3D
isotropic spatial confinement into a length scale comparable to the
average spacing between two antiphase boundaries enables the favorable
control over nanoscale defects. A simple statistical model satisfactorily
illustrates the dependence of electrical transport properties on the
volume of Fe3O4 from the macroscale down to
the nanoscale. Finally, an ultrasmall nanowire with a low defect concentration
allows the estimation of the true coherence length of the fundamental
quasiparticle, the trimeron, responsible for the Verwey transition.