Evolution of magnetic fluctuations through the Fe-induced paramagnetic to ferromagnetic transition in ${\mathrm{Cr}}_2\mathrm{B}$

In itinerant ferromagnets, the quenched disorder is predicted to dramatically affect the ferromagnetic to paramagnetic quantum phase transition driven by external control parameters at zero temperature. Here we report a study on Fe-doped ${\mathrm{Cr}}_2\mathrm{B}$, which, starting from the paramagnetic parent, orders ferromagnetically for Fe-doping concentrations $x$ larger than $x_{\mathrm{c}}=2.5\%$. In parent ${\mathrm{Cr}}_2\mathrm{B}, {}^{11}\mathrm{B}$ nuclear magnetic resonance data reveal the presence of both ferromagnetic and antiferromagnetic fluctuations. The latter are suppressed with Fe doping, before the ferromagnetic ones finally prevail for $x>x_{\mathrm{c}}$. Indications for non-Fermi-liquid behavior, usually associated with the proximity of a quantum critical point, were found for all samples, including undoped ${\mathrm{Cr}}_2\mathrm{B}$. The sharpness of the ferromagneticlike transition changes on moving away from $x_{\mathrm{c}}$, indicating significant changes in the nature of the magnetic transitions in the vicinity of the quantum critical point. Our data provide some constraints for understanding quantum phase transitions in itinerant ferromagnets in the limit of weak quenched disorder.

Figure 1

(a) The orthorhombic crystal structure of ${\mathrm{Cr}}_2\mathrm{B}$. (b) The local coordination of each boron site (green polyhedron) has eight nearest Cr atoms (large blue spheres) and two more B atoms (small green spheres) at apical positions.

Figure 2

(a) Comparison of the room-temperature ${}^{11}\mathrm{B}$ NMR spectra (gray shaded area) measured on polycrystalline Fe-doped ${\mathrm{Cr}}_2\mathrm{B}$ samples at various Fe-doping levels. Solid red lines are the powder line shape fits to a model that includes anisotropic shift and quadrupole effects up to the second order. A single ${}^{11}\mathrm{B}$ NMR component was sufficient in all cases. (b) Fe-doping dependence of the ${}^{11}\mathrm{B}$ NMR linewidth broadening parameter ${\delta }_{1/2}$ (solid circles, left scale) and of the quadrupole frequency ${\nu }_Q$ (open circles, right scale). The solid and dashed black lines are guides to the eye for the Fe-doping dependence of ${\delta }_{1/2}$ and ${\nu }_Q$, respectively.

Figure 3

Temperature dependencies of (a) the ${}^{11}\mathrm{B}$ central transition $(-1/2\leftrightarrow 1/2)$ peak, (b) the shift of the central transition peak $K$ and the spin-lattice relaxation rate $1/T_1$ divided by $T$ measured in parent undoped ${\mathrm{Cr}}_2\mathrm{B}$. The vertical and horizontal dashed lines in (a) and (c) mark room temperature values. The solid line in (b) is a fit with a Curie-Weiss dependence to a negative Curie-Weiss temperature of $T_{\text{CW}}=-12\left(3\right)$ K. The inset to (b) shows the temperature dependence of the Knight shift $K_{\mathrm{s}}$ on a log-log scale, obtained after subtracting the chemical shift $\sigma$ from $K$. Solid lines indicate the high-temperature slope of $K_{\mathrm{s}}\propto T^{-1}$ and the low-temperature slope of $K_{\mathrm{s}}\propto T^{-1/2}$.

Figure 4

(a) Temperature dependence of ferromagnetic resonance in 5% Fe-doped ${\mathrm{Cr}}_2\mathrm{B}$ (black circles) measured at $X\text{-band}$ (${}^{\mathrm{ESR}}\nu _{\mathrm{L}}=9.6$ GHz) frequencies. Solid red lines are fits of the spectra to the Dyson line shape. The dotted vertical line at 330 mT marks the resonance field of the $g=2$ electron paramagnetic resonance signal. (b) Comparison of ferromagnetic resonance spectra measured at 40 K for 5% (black circles), 4% (red triangles), and 3.5% (blue squares) Fe-doped ${\mathrm{Cr}}_2\mathrm{B}$, respectively. (c) Temperature dependence of the intensities of the ferromagnetic resonance spectra for 5% (black circles), 4% (red triangles), and 3.5% (blue squares) Fe-doped ${\mathrm{Cr}}_2\mathrm{B}$, respectively.

Figure 5

(a) The temperature evolution of the ${}^{11}\mathrm{B}$ NMR spectra for 5% Fe-doped ${\mathrm{Cr}}_2\mathrm{B}$. The solid red lines are fits to a model with quadrupole and anisotropic Knight-shift interactions. In the model we assumed temperature independent ${\nu }_{\mathrm{Q}}=461$ kHz and $\eta =0.08$. (b) The temperature dependencies of the isotropic (red circles, left scale) and anisotropic (blue squares, right scale) parts of the Knight shift. A fit of the ${}^{11}\mathrm{B}$ NMR shift $K\left(T\right)$ to Eq. (1) (solid red line) yields the chemical shift $\sigma =-270\left(8\right)$ ppm, $B=9.7\left(9\right)\times {10}^3$ ppm K and the ferromagnetic Curie-Weiss temperature $T_{\mathrm{CW}}=21\left(4\right)$ K. The dashed blue line is a guide to the eye. (c) Temperature dependence of the ${}^{11}\mathrm{B}$ NMR spin-lattice relaxation rate divided by temperature $1/T_{1}T$.

Figure 6

The temperature dependence of the ${}^{11}\mathrm{B}$ NMR Knight shift $K_{\mathrm{s}}=K-\sigma$ for 2% Fe-doped ${\mathrm{Cr}}_2\mathrm{B}$ (open circles). The Knight shifts are extracted directly from the shifts of the ${}^{11}\mathrm{B}$ NMR spectra $K$ obtained by subtraction of the chemical shift $\sigma =-253$ ppm. The solid red lines indicate that $K_{\mathrm{s}}\propto T^{-1}$ at high temperatures gradually changes to $K_{\mathrm{s}}\propto T^{-1/4}$ at low temperatures. Insets: Low-temperature ${}^{11}\mathrm{B}$ NMR spectra (gray shaded area) measured for 2% Fe-doped ${\mathrm{Cr}}_2\mathrm{B}$ ($T=5$ K) and 2.5% Fe-doped ${\mathrm{Cr}}_2\mathrm{B}$ ($T=15$ K). The solid red lines are line shape fits with $K=54$ ppm, ${\nu }_{\mathrm{Q}}=496$ kHz, and ${\delta }_{1/2}=155$ kHz (${\mathrm{Cr}}_2\mathrm{B}$ sample with 2% Fe doping) and $K=167$ ppm, ${\nu }_{\mathrm{Q}}=450$ kHz, and ${\delta }_{1/2}=243$ kHz (${\mathrm{Cr}}_2\mathrm{B}$ sample with 2.5% Fe doping).

Figure 7

Dependence of the NMR-determined Curie-Weiss temperature $T_{\mathrm{CW}}$ (open black circles) and magnetic ordering onset temperature $T_{\mathrm{c}}$ (solid blue circles) on the Fe-doping concentration of ${\mathrm{Cr}}_2\mathrm{B}$. The dotted black and the dashed blue lines are a guides to the eye. A transition is seen from a paramagnetic non-Fermi-liquid metal (NFL, yellow shading) with predominant antiferromagnetic correlations to a ferromagnetic metal (FM, blue shading) at the critical concentration $x_{\mathrm{c}}=2.5\%$.