Observation of two ferromagnetic phases in ${\mathrm{Fe}}_3{\mathrm{Mo}}_3\mathrm{N}$

We report alloying-induced and field-induced ferromagnetism in the $\eta$-carbide-type compound ${\mathrm{Fe}}_3{\mathrm{Mo}}_3\mathrm{N}$, which shows a non-Fermi-liquid behavior in the vicinity of a ferromagnetic quantum critical point. Co substitution induces ferromagnetism in ${(\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x)$${}_3{\mathrm{Mo}}_3\mathrm{N}$ in the composition range $0.05\le x\le 0.60$. With increasing $x$, the magnetism varies from the Curie-Weiss-type paramagnetism with a maximum in the temperature dependence of the magnetic susceptibility to another paramagnetism without the maximum via a weak ferromagnetism. An itinerant electron metamagnetic transition is observed for low $x$ at a magnetic field of $\sim$14 T. The magnetic phase diagram, in which the alloying-induced and the field-induced ferromagnetic phases are separated, is different from conventional phase diagrams for weak ferromagnets. Taking account of the fact that a magnetic field induces a Fermi-liquid behavior, the quantum criticality for pure ${\mathrm{Fe}}_3{\mathrm{Mo}}_3\mathrm{N}$ appears to be dominated by the dispersive spin fluctuations observed in the alloying-induced ferromagnetic phase.

Figure 1

(a) Reciprocal susceptibility of ${(\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x)$${}_3{\mathrm{Mo}}_3\mathrm{N}$ for selected compositions. The data are offset and dashed lines represent their origins. (b) $x$ dependence of $T_{\mathrm{C}}$ and lattice constant. The dashed line serves as a visual guide.

Figure 2

Arrott plots corresponding to the low-field region for the composition range of $0.05\le x\le 0.70$. Dashed lines indicate the best linear fitting at low fields. For $0.20\le x\le 0.70$, the Arrott plots are linear over wide field regions. For $0.05\le x\le 0.15$, the Arrott plots are linear only at low fields but deviate progressively upwards at high fields; this phenomenon is often observed in the paramagnetic state far above $T_{\mathrm{C}}$, suggesting the coexistence of the doping-induced ferromagnetic and the paramagnetic fluctuations.

Figure 3

High-field magnetic isotherms measured at 4.2 K for selected samples with different compositions. Data are offset in increments of 0.25 ${\mu }_{\mathrm{B}}$/f.u. Dashed lines represent origins.

Figure 4

$dM/dH$ curves for $x=0.03$ at different temperatures. At $T=4.2$ K, a sharp peak was observed both in field-increasing and decreasing processes with a hysteresis. The inset shows magnetic isotherms obtained by integrating $dM/dH$. The data are offset in increments of 0.8 ${\mu }_{\mathrm{B}}$/f.u.

Figure 5

$dM/dH$ for several compositions in which magnetization shows a rapid increase at low fields and an anomaly at finite fields. With increasing $x$, the anomaly in $dM/dH$ is suppressed and the peak decreases to disappear at $x=0.125$. Both the field-increasing and decreasing processes are shown. No hysteresis was observed in these compositions, suggesting that the anomalies were due not to a first-order transition but a crossover.

Figure 6

Temperature dependence of critical and crossover fields of IEMTs for different compositions. Solid and open markers represent the first-order transition and the crossover fields, respectively. The former was estimated as the average of the transition fields in field-increasing and field-decreasing processes. Crosses represent CEPs of the first-order transition that were estimated as the field and the temperature at which the hysteresis width $\Delta H\to 0$. The dashed line serves as a visual guide. The critical point shifts downward in terms of field and temperature with increasing $x$, and zero temperature is reached at $x\simeq 0.05$, thus suggesting the existence of a QCEP.

Figure 7

$x$-$H$-$T$ phase diagram for ${(\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x)$${}_3{\mathrm{Mo}}_3\mathrm{N}$. Open and solid circles represent the CEP of the metamagnetic transition and $T_{\mathrm{C}}$, respectively. Dashed lines are guide for the eyes.

Figure 8

Arrott plots at high magnetic fields and at $T=4.2$ K. Dashed lines indicate the best linear fit for field-induced phases.

Figure 9

(a) $T_A$ vs $x$. (b) $T_0$ vs $x$. Open and solid circles represent the data for FIF and AIF, respectively.

Figure 10

Takahashi-Rhodes-Wohlfarth plot or Deguchi-Takahashi plot for parameters of AIF and FIF. Data for ${\mathrm{ZrZn}}_2$, ${\mathrm{Ni}}_3$Al, MnSi, and ${\mathrm{UGe}}_2$ are also plotted (Ref. [43]).