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Magnetization study on the field-induced quantum critical point in YbRh_2Si_2

We study the field-induced quantum critical point (QCP) in YbRh$_2$Si$_2$ by low-temperature magnetization, $M(T)$, and magnetic Grüneisen ratio, $Γ_{\rm mag}$, measurements and compare the results with previous thermal expansion, $β(T)$, and critical Grüneisen ratio, $Γ^{cr}(T)$, data on YbRh$_2$(Si$_{0.95}$Ge$_{0.05}$)$_2$. In the latter case, a slightly negative chemical pressure has been used to tune the system towards its zero-field QCP. The magnetization derivative $-dM/dT$ is far more singular than thermal expansion, reflecting a strongly temperature dependent pressure derivative of the field at constant entropy, $(dH/dP)_S=V_mβ/(dM/dT)$ ($V_m$: molar volume), which saturates at $(0.15\pm 0.04)$ T/GPa for $T\to 0$. The line $T^\star(H)$, previously observed in Hall- and thermodynamic measurements, separates regimes in $T$-$H$ phase space of stronger $(ε>1$) and weaker $(ε<1$) divergent $Γ_{\rm mag}(T)\propto T^{-ε}$.