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Zero (ZF) and longitudinal field (LF) muon spin relaxation data of the {\itd}-metal alloy Ni$_{1-x}$V$_{x}$ are presented at several vanadiumconcentrations $x$ below and above the critical $x_c \approx 11$% wherelong-range ferromagnetic (FM) order is suppressed. The clear single precessionfrequency observed for Ni, as expected for a homogeneous FM, changes to ratherdamped oscillation with small V substitution at $x=4$%, confirming magneticinhomogeneities caused by the less magnetic V environments in the magnetic Nimatrix. Furthermore, local fields and spatial field distributions can beestimated to characterize different inhomogeneous regimes developing with $x$in the FM phase of Ni$_{1-x}$V$_{x}$. In the regime of $x=7-10$% a Kubo Toyabefunction well describes the low temperature ZF and LF asymmetry data supportinga static Gaussian field distribution. Closer to the quantum criticalconcentration a single scale static Kubo Toyabe function with one fielddistribution is not sufficient to describe the muon relaxation. These dataindicate that further changes in spatial distributions and dynamics areevolving as expected within the critical regime of a disordered quantumcritical point.

Probing the magnetic phases in the Ni-V alloy close to the disordered ferromagnetic quantum critical point with muSR