Incommensurate Magnetism Near Quantum Criticality in CeNiAsO

We report the discovery of incommensurate magnetism near quantum criticality in CeNiAsO through neutron scattering and zero field muon spin rotation. For $T<T_{N1}=8.7(3)\mathrm{K}$, a second order phase transition yields an incommensurate spin density with a wave vector $\mathbf{k}=\mathbf{(}0.44(4),0,0\mathbf{)}$. For $T<T_{N2}=7.6(3)\mathrm{K}$, we find coplanar commensurate order with a moment of $0.37(5){\mu }_B$, reduced to 30% of the saturation moment of the $|\pm \frac{1}{2}⟩$ Kramers doublet ground state, which we establish through inelastic neutron scattering. Muon spin rotation in ${\mathrm{CeNiAs}}_{1-x}{\mathrm{P}}_x\mathrm{O}$ shows the commensurate order only exists for $x\le 0.1$ so we infer the transition at $x_c=0.4(1)$ is between an incommensurate longitudinal spin density wave and a paramagnetic Fermi liquid.

Figure 1

(a) Crystallographic structure of CeNiAsO, and spin structure for $T_{N2}<T<T_{N1}$ (b) and $T<T_{N2}$ (c). Blue stars indicate the single crystallographic muon site. Two equivalent muon sites above and below oxygen become inequivalent within the magnetically ordered state. (d) Temperature-doping phase diagram. Red, blue, and green symbols are from specific heat, $\mu \mathrm{SR}$, and neutron data, respectively. Brown dots are from Luo et al. [13]. We assign open (closed) symbols to the higher (lower) $T$ transition. The inset to (d) shows the $q_z=0$ small Fermi surface excluding $4f$ electrons. The arrow shows the magnetic wave vector, which connects extended areas of the Fermi surface. The dashed lines are guides to the eye.

Figure 2

Temperature dependence of (a) the longitudinal ($m_a$) and (b) the transverse moments ($m_c$ for high $T$ and $m_b$ for low $T$ phase). Black dots were extracted from Rietveld fits to neutron diffraction data. The 2 and 8 K data points were averaged over two chopper settings. Blue diamonds were inferred from $\mu \mathrm{SR}$ fits. The solid lines are guides to the eye. (c) Temperature dependence of the averaged static field. (d) Specific heat $C_p/T$ in zero field and for ${\mu }_{0}H=14\mathrm{T}$. The upturn in $C_p/T$ at 14 T is due to the nuclear spin contributions as indicated by the solid red line.

Figure 3

(a),(b) Zero-field longitudinal configuration $\mu \mathrm{SR}$ spectra at $T=7$ and 0.05 K. The colored lines were calculated for the magnetic structures of Fig. 1. (c),(d) Diffraction patterns collected at $T=2\mathrm{K}$ and 8 K on NOMAD, after subtracting $T=15\mathrm{K}$ data as a measure of nuclear diffraction. Red and blue lines correspond to the spin configurations in Fig. 1. The gray dashed lines in (c) mark the nuclear Bragg positions, where thermal expansions give rise to a peak-derivative anomaly. In (d) the horizontal green bar at $Q=1.1{\AA }^{-1}$ indicates the instrument resolution of $0.04{\AA }^{-1}$ as detailed in the inset.

Figure 4

Normalized inelastic spectrum with incident energy $E_i=100\mathrm{meV}$ (black dots) for (a) CeNiAsO and (b) the nonmagnetic reference LaNiAsO. (c) The $T=7\mathrm{K}$ difference spectrum: $\tilde{I}(Q,E)=I_{\mathrm{Ce}}-r{I}_{\mathrm{La}}$ where $r={\sigma }_{\mathrm{CeNiAsO}}/{\sigma }_{\mathrm{LaNiAsO}}$. (d),(e) Momentum-integrated scattering at $T=7\mathrm{K}$ and 200 K inferred from the method in Refs. [38, 39, 40]. The horizontal black bar indicates energy resolution. The inset in (d) shows a magnetic excitation at 2 meV in the ordered state with $E_i=50\mathrm{meV}$ (brown dots). The cyan and red solid lines were calculated for the crystal field model described in the text.