Spin Hall nano oscillators (SHNOs) have shown applications in unconventional
computing schemes and broadband frequency generation in the presence of applied
external magnetic field. However, under field-free conditions, the oscillation
characteristics of SHNOs display a significant dependence on the effective
field, which can be tuned by adjusting the constriction width, thereby
presenting an intriguing area of study. Here we study the effect of nano
constriction width on the magnetization dynamics in anisotropy assisted field
free SHNOs. In uniaxial anisotropy-based field-free SHNOs, either the
anisotropy field or the demagnetization field can dominate the magnetization
dynamics depending on the constriction width. Our findings reveal distinct
auto-oscillation characteristics in narrower constrictions with 20 nm and 30 nm
constriction width compared to their wider counterpart with 100 nm width. The
observed frequency shift variations with input current and constriction widths
stem from the inherent nonlinearity of the system. The interplay between the
B_demag and B_anis, coupled with changes in constriction width, yields rich
dynamics and offers control over frequency tunability, auto oscillation
amplitude, and threshold current. Notably, the spatial configuration of spin
wave wells within the constriction undergoes transformations in response to
changes in both constriction width and anisotropy. The findings highlight the
significant influence of competing fields at the constriction on the field-free
auto oscillations of SHNOs, with this impact intensifying as the constriction
width is varied.Comment: 25 pages, 11 figure