Insights into the evolution from ferromagnetism to antiferromagnetism: A doping-dependent study of ${\mathrm{NaCrSi}}_x{\mathrm{Ge}}_{2-x}{\mathrm{O}}_6(0\le x\le 2)$

${\mathrm{NaCrGe}}_2{\mathrm{O}}_6$ and ${\mathrm{NaCrSi}}_2{\mathrm{O}}_6$ are isostructural compounds exhibiting different magnetic ground states. ${\mathrm{NaCrGe}}_2{\mathrm{O}}_6$ adopts a ferromagnetic ground state with $Tc=6\mathrm{K}$, whereas ${\mathrm{NaCrSi}}_2{\mathrm{O}}_6$ orders antiferromagnetically below $T_N=3.4\mathrm{K}$. Although it has been proposed that the intriguing magnetic behavior in Cr-based pyroxenes involves competition between antiferromagnetic direct exchange and ferromagnetic superexchange interactions, a delicate balance that is sensitive to Cr-Cr distance and local distortion, no spectroscopy study has been done to determine the microscopic interactions in these compounds. To delve deeper into the evolution from ferromagnetism to antiferromagnetism, we performed a doping-dependent study to investigate how the substitution of Ge by Si affects the magnetic properties of ${\mathrm{NaCrSi}}_x{\mathrm{Ge}}_{2-x}{\mathrm{O}}_6$ ($x=0$, 0.5, 1, 1.5, 2). Neutron diffraction and magnetization measurements show that replacing larger Ge with smaller Si simultaneously suppresses the ferromagnetic order. The lattice constants and the unit-cell volume contract, i.e., chemical pressure effect, and the Cr-Cr distance within the chain gradually decreases with increasing Si doping. High-resolution inelastic neutron-scattering studies of the spin waves of ${\mathrm{NaCrGe}}_2{\mathrm{O}}_6$ and ${\mathrm{NaCrSi}}_2{\mathrm{O}}_6$ indicate that replacing Ge with Si has profound effect on the intrachain coupling, whereas it has negligible effect on the interchain couplings. We compare our results, which indicate ${\mathrm{NaCrGe}}_2{\mathrm{O}}_6$ is magnetic quasi-one-dimensional (1D) and ${\mathrm{NaCrSi}}_2{\mathrm{O}}_6$ is three-dimensional (3D), with $\mathrm{LiCr}{(\mathrm{Si},\mathrm{Ge})}_2{\mathrm{O}}_6$, where ${\mathrm{LiCrSi}}_2{\mathrm{O}}_6$ is proposed to be magnetic quasi-1D and ${\mathrm{LiCrGe}}_2{\mathrm{O}}_6$ is 3D, and discuss the different behaviors in magnetic dimensionality crossover in the context of how substituting Ge with Si fine-tunes the relative ratio between the intrachain and interchain couplings that defines the magnetic dimensionality in these materials.

Figure 1

Schematic view of the ${\mathrm{NaCrSi}}_2{\mathrm{O}}_6$ magnetic structure. Two chains made of ${\mathrm{CrO}}_6$ octahedra (cyan) and their coupling via ${\mathrm{SiO}}_4$ tetrahedra (pink) are illustrated. Only the ${\mathrm{Cr}}^{3+}$ (red balls) magnetic ions are shown for clarity. The intrachain (J1) and interchain (J2 and J3) magnetic exchange interactions are labeled.

Figure 2

(a) The field dependence of magnetization measured at 2 K and (b) temperature dependence of magnetic susceptibility measure with $H=1000$ Oe for ${\mathrm{NaCrSi}}_x{\mathrm{Ge}}_{2-x}{\mathrm{O}}_6$. The low-temperature region of the inverse susceptibility is enlarged in the inset.

Figure 3

Neutron powder diffraction pattern of ${\mathrm{NaCrSi}}_x{\mathrm{Ge}}_{2-x}{\mathrm{O}}_6$ between ${10}^{\circ }\le 2\theta \le {45}^{\circ }$ measured at 1.5 and 10 K: (a) $\mathit{x}$ = 0, (b) $\mathit{x}$ = 0.5, (c) $\mathit{x}$ = 1, and (d) $\mathit{x}$ = 2.

Figure 4

Order parameter of ${\mathrm{NaCrSi}}_x{\mathrm{Ge}}_{2-x}{\mathrm{O}}_6$: temperature dependence of the integrated intensity of (1 1 0) magnetic peak for $x=0$, 0.5, and 2.

Figure 5

(a) Low-energy magnet excitation spectrum of ${\mathrm{NaCrGe}}_2{\mathrm{O}}_6$ measured using the SEQUOIA instrument at 1.8 K. Simulated scattering intensity including (b) $J_1=–0.45 \pm$ 0.01 meV; (c) $J_1=–0.43 \pm$ 0.01 meV and $J_2=–0.03 \pm$ 0.005 meV; (d) $J_1=–0.41 \pm$ 0.01 meV, $J_2=–0.03 \pm$ 0.005 meV, and $J_3=–0.02 \pm$ 0.005 meV in Eq. (1).

Figure 6

(a) Low-energy magnet excitation spectrum of ${\mathrm{NaCrSi}}_2{\mathrm{O}}_6$ measured using the SEQUOIA instrument at 1.8 K. The dashed lines denote the $Q$ values corresponding to (1 1 0), (0 0 1), and (0 2 0) magnetic peaks. Simulated scattering intensity including (b) $J_1$ = 0.12 $\pm$ 0.02 meV and $J_2$ = 0.05 $\pm$ 0.01 meV; (c) $J_1$ = 0.09 $\pm$ 0.02 meV, $J_2$ = 0.03 $\pm$ 0.01 meV, and J3 = $–0.02 \pm$ 0.01 meV in Eq. (1).

Figure 7

Intensity vs energy transfer integrated between $Q=0$ and 2 ${\AA }^{-1}$ for $T=1.8$ and 10 K indicate the $\sim 2.6$ meV and $\sim 0.5$ meV magnetic excitation observed in (a) ${\mathrm{NaCrGe}}_2{\mathrm{O}}_6$ and (b) ${\mathrm{NaCrSi}}_2{\mathrm{O}}_6$, respectively.

Figure 8

Doping dependence of $D_{\text{Cr-Cr}}$ for ${\mathrm{NaCrSi}}_x{\mathrm{Ge}}_{2-x}{\mathrm{O}}_6$ from this study and ${\mathrm{LiCrSi}}_x{\mathrm{Ge}}_{2-x}{\mathrm{O}}_6$ from Ref. [10]. The magnetic ground state and the magnetic dimensionality of the end compounds are labeled.