Long-range magnetic order in quasi-one-dimensional chromium-based $(S=\frac{3}{2})$ pyroxenes $(\mathrm{Li},\mathrm{Na})\mathrm{Cr}{(\mathrm{Si},\mathrm{Ge})}_2{\mathrm{O}}_6$

Quasi-one-dimensional Cr-based $(d^3,S=\frac{3}{2})$ pyroxenes $(\mathrm{Li},\mathrm{Na})\mathrm{Cr}{(\mathrm{Si},\mathrm{Ge})}_2{\mathrm{O}}_6$ reach long-range magnetic order at low temperatures. At substitution of small size cations ${\mathrm{Li}}^{1+}$ and ${\mathrm{Si}}^{4+}$ for large size cations ${\mathrm{Na}}^{1+}$ and ${\mathrm{Ge}}^{4+}$ the competition between antiferromagnetic and ferromagnetic exchange interactions strengthens so that antiferromagnetic long-range order in $\mathrm{Li}\mathrm{Cr}{\mathrm{Si}}_2{\mathrm{O}}_6$ $(T_N=11\mathrm{K})$, $\mathrm{Li}\mathrm{Cr}{\mathrm{Ge}}_2{\mathrm{O}}_6$ $(T_N=3.7\mathrm{K})$, and $\mathrm{Na}\mathrm{Cr}{\mathrm{Si}}_2{\mathrm{O}}_6$ $(T_N=3\mathrm{K})$ changes for ferromagnetic long-range order in $\mathrm{Na}\mathrm{Cr}{\mathrm{Ge}}_2{\mathrm{O}}_6$ $(T_C=6\mathrm{K})$. This tendency is tentatively attributed to diminishing direct overlap of Cr $t_{2g}$ orbitals responsible for antiferromagnetic exchange interaction against background of ferromagnetic $\mathrm{Cr}-\mathrm{O}-\mathrm{Cr}$ superexchange interaction.

Figure 1

The temperature dependences of magnetic susceptibility of $\mathrm{Li}\mathrm{Cr}{\mathrm{Si}}_2{\mathrm{O}}_6$ (a), $\mathrm{Li}\mathrm{Cr}{\mathrm{Ge}}_2{\mathrm{O}}_6$ (b), $\mathrm{Na}\mathrm{Cr}{\mathrm{Si}}_2{\mathrm{O}}_6$ (c), and reduced magnetization in $\mathrm{Na}\mathrm{Cr}{\mathrm{Ge}}_2{\mathrm{O}}_6$ (d). $H=0.1\mathrm{T}$.

Figure 2

The field dependences of magnetization at various temperatures in $\mathrm{Li}\mathrm{Cr}{\mathrm{Si}}_2{\mathrm{O}}_6$ (a), $\mathrm{Li}\mathrm{Cr}{\mathrm{Ge}}_2{\mathrm{O}}_6$ (b), $\mathrm{Na}\mathrm{Cr}{\mathrm{Si}}_2{\mathrm{O}}_6$ (c), $\mathrm{Na}\mathrm{Cr}{\mathrm{Ge}}_2{\mathrm{O}}_6$ (d).

Figure 3

The temperature dependences of specific heat in $\mathrm{Li}\mathrm{Cr}{\mathrm{Si}}_2{\mathrm{O}}_6$ (a), $\mathrm{Li}\mathrm{Cr}{\mathrm{Ge}}_2{\mathrm{O}}_6$ (b), $\mathrm{Na}\mathrm{Cr}{\mathrm{Si}}_2{\mathrm{O}}_6$ (c), $\mathrm{Na}\mathrm{Cr}{\mathrm{Ge}}_2{\mathrm{O}}_6$ (d). The insets show magnetic specific heat $C_{\mathrm{magn}}$ in Cr-based pyroxenes.

Figure 4

The temperature dependences of magnetic entropy in $\mathrm{Li}\mathrm{Cr}{\mathrm{Si}}_2{\mathrm{O}}_6$ (a), $\mathrm{Li}\mathrm{Cr}{\mathrm{Ge}}_2{\mathrm{O}}_6$ (b), $\mathrm{Na}\mathrm{Cr}{\mathrm{Si}}_2{\mathrm{O}}_6$ (c), $\mathrm{Na}\mathrm{Cr}{\mathrm{Ge}}_2{\mathrm{O}}_6$ (d).