This paper demonstrates the anisotropic response of quantum critical fluctuations with respect to the direction of the magnetic field $B$ in Ni-doped CeCoIn$_5$ by measuring the magnetization $M$ and specific heat $C$. The results show that $M/B$ at $B=0.1 {rm T}$ for both the tetragonal $c$ and $a$ directions exhibits $T^{-eta}$ dependencies, and that $C/T$ at $B=0$ follows a $-ln T$ function, which are the characteristics of non-Fermi-liquid (NFL) behaviors. For $B,||,c$, both the $M/Bpropto T^{-eta}$ and $C/T propto -ln T$ dependencies change into nearly temperature-constant behaviors by increasing $B$, indicating a crossover from the NFL state to the Fermi-liquid state. For $B,||,a$, however, the NFL behavior in $C/T$ persists up to $B=7 {rm T}$, whereas $M/B$ exhibits temperature-independent behavior for $Bge 1 {rm T}$. These contrasting characteristics in $M/B$ and $C/T$ reflect the anisotropic nature of quantum critical fluctuations; the $c$-axis spin component significantly contributes to the quantum critical fluctuations. We compare this anisotropic behavior of the spin fluctuations to superconducting properties in pure CeCoIn$_5$, especially to the anisotropy in the upper critical field and the Ising-like characteristics in the spin resonance excitation, and suggest a close relationship between them.
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