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Insights into the evolution from ferromagnetism to antiferromagnetism: A doping-dependent study of

NaCrGe 2 O 6 and NaCrSi 2 O 6 are isostructural compounds exhibiting diﬀerent magnetic ground state. NaCrGe 2 O 6 adopts a ferromagnetic ground state with Tc =6 K, whereas NaCrSi 2 O 6 orders antiferromagnetically below T N =3.4 K. Although it has been proposed that the intriguing magnetic behavior in Cr-based pyroxenes involves competition between antiferromagnetic direct exchange and ferromagnetic super-exchange 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 on 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 NaCrSi x Ge 2 − x 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 NaCrGe 2 O 6 and NaCrSi 2 O 6 indicate that replacing Ge with Si has profound eﬀect to the intrachain coupling, whereas it has neglectable eﬀect to the interchain couplings. We compare our results, which indicate NaCrGe 2 O 6 is magnetic quasi-1D and NaCrSi 2 O 6 is 3D, with LiCr(Si,Ge) 2 O 6 where LiCrSi 2 O 6 is proposed to be magnetic quasi-1D and LiCrGe 2 O 6 is 3D, and discuss the diﬀerent behavior 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.