Helimagnetic Structure and Heavy-Fermion-Like Behavior in the Vicinity of the Quantum Critical Point in ${\mathrm{Mn}}_3\mathrm{P}$

Antiferromagnet ${\mathrm{Mn}}_3\mathrm{P}$ with Neel temperature $T_N=30\mathrm{K}$ is composed of Mn tetrahedrons and zigzag chains formed by three inequivalent Mn sites. Due to the nearly frustrated lattice with many short Mn-Mn bonds, competition of the exchange interactions is expected. We here investigate the magnetic structure and physical properties including pressure effect in single crystals of this material, and reveal a complex yet well-ordered helimagnetic structure. The itinerant character of this materials is strong, and the ordered state with small magnetic moments is easily suppressed under pressure, exhibiting a quantum critical point at $\sim 1.6\mathrm{GPa}$. The remarkable mass renormalization, even in the ordered state, and an incoherent-coherent crossover in the low-temperature region, characterize an unusual electronic state in ${\mathrm{Mn}}_3\mathrm{P}$, which is most likely effected by the underlying frustration effect.

Figure 1

(a) Crystal structure of noncentrosymmetric ${\mathrm{Mn}}_3\mathrm{P}$. Two unit cells are shown. Tetragonal structure of space group $I\overline{4}$ is composed of three Mn sites and one P site. The Mn1 and Mn2 sites form the tetrahedrons, while the Mn3 sites form the zigzag chain. (b) The helical magnetic structure of ${\mathrm{Mn}}_3\mathrm{P}$ was determined at 7 K and at ambient pressure. Three Mn sites are separated into six sites with different modulations of their magnetic moments. Nearly AF couplings between the magnetic moments almost lying in the $ab$ plane are seen at the Mn1a and Mn1b sites, respectively. The $c$-axis components are significant at the Mn2 and Mn3 sites.

Figure 2

Temperature dependence of (a) electrical resistivity, (b) $T$-divided specific heat ($C/T$), and (c) magnetic susceptibility at 0.1 T. All measurements detected two magnetic transitions: one at $T_{N1}=30\mathrm{K}$, the other at $T_{N2}=27.5\mathrm{K}$. The characteristic convex curve of $\rho$ above $T_{N1}$ is reminiscent of $f$-electron heavy fermion systems. (d) Magnetization curves at 2 K measured after field cooling.

Figure 3

(a) Temperature dependence of the magnetic Bragg intensities at (0.5, 2.5, $\delta$) with $\delta \sim 0.16$, measured at different pressures. At ambient pressure, the magnetic scattering appears below $T_{N1}$ and exhibits a small kink at $T_{N2}$ (indicated by arrows). The two transitions are poorly resolved under pressure, but the scattering is observed at the same wave vector. (b) Temperature dependence of the incommensurability $\delta$ of the magnetic wave vector (0.5, 0.5, $\delta$) at ambient pressure.

Figure 4

Variation of the magnetic-moment components $M_a$, $M_b$, $M_c$, and $M_{\text{total}}$, along the $c$ axis at six Mn sites, measured at 7 K under ambient pressure. $M_{\text{total}}$ shows a clear ellipticity of the helix at most Mn sites. $M_{\mathrm{ave}}$ denotes the average value at each Mn site. At the Mn1a and Mn1b sites, the magnetic moments almost lie in the $ab$ plane, but the moments are remarkably tilted at other sites. At the Mn3 sites, the squares and triangles indicate the two sublattices forming the zigzag chain. AF couplings between the sublattices appear in $M_c$ ($M_{a,b}$) at the Mn3a (Mn3b) sites. The Fullprof refinement was obtained as $R_F=11.3\%$.

Figure 5

(a) Electrical resistivity measured under pressure. The two transitions and the residual resistivity are simultaneously suppressed by applying pressure. (b) Resistivity behavior in the vicinity of the QCP. The residual resistivity ratio (RRR) is $\sim 58$. The characteristic convexity appears over a wide temperature range. Inset: the resistivity at low temperature deviates from FL behavior, and obeys a $T^{1.4}$ dependence. The $\rho$ vs $T^2$ plots at several pressures are shown in the Supplemental Material [16].

Figure 6

Pressure dependences of ${\rho }_0$ and $A$ coefficient, and pressure-temperature phase diagram of ${\mathrm{Mn}}_3\mathrm{P}$. In the vicinity of QCP, the NFL behavior is dominant. The $A$ value is already large in the ordered state and shows a small peak at the QCP.