Signatures of low-dimensional magnetism and short-range magnetic order in Co-based trirutiles

Features of low-dimensional magnetism resulting from a square-net arrangement of Co atoms in trirutile ${\mathrm{CoTa}}_2{\mathrm{O}}_6$ are studied in the present work by means of density functional theory and are compared with the experimental results of specific heat and neutron diffraction. The small total energy differences between the ferromagnetic (FM) and antiferromagnetic (AFM) configuration of ${\mathrm{CoTa}}_2{\mathrm{O}}_6$ shows that competing magnetic ground states exist, with the possibility of transition from FM to AFM phase at low temperature. Our calculation further suggests the semiconducting behavior for ${\mathrm{CoTa}}_2{\mathrm{O}}_6$ with a band gap of $\sim 0.41$ eV. The calculated magnetic anisotropy energy is $\sim 2.5$ meV with its easy axis along the [100] (in-plane) direction. Studying the evolution of magnetism in ${\mathrm{Co}}_{1-x}{\mathrm{Mg}}_x{\mathrm{Ta}}_2{\mathrm{O}}_6$ ($x=0$, 0.1, 0.3, 0.5, 0.7, and 1), it is found that the sharp AFM transition exhibited by ${\mathrm{CoTa}}_2{\mathrm{O}}_6$ at $T_N=6.2$ K in its heat capacity vanishes with Mg dilution, indicating the obvious effect of weakening the superexchange pathways of Co. The current specific heat study reveals the robust nature of $T_N$ for ${\mathrm{CoTa}}_2{\mathrm{O}}_6$ in applied magnetic fields. Clear indication of short-range magnetism is obtained from the magnetic entropy, however, diffuse components are absent in neutron diffraction data. At $T_N, {\mathrm{CoTa}}_2{\mathrm{O}}_6$ enters a long-range ordered magnetic state which can be described using a propagation vector, ($\frac{1}{4}\frac{1}{4}0$). Upon Mg dilution at $x\ge 0.1$, the long-range ordered magnetism is destroyed. The present results should motivate an investigation of magnetic excitations in this low-dimensional anisotropic magnet.

Figure 1

The crystal structure of ${\mathrm{CoTa}}_2{\mathrm{O}}_6$. (a) The Co atoms represented by blue spheres form ${\mathrm{CoO}}_6$ octahedra with the oxygen atoms (in red). (b) Shows a projection on to the $ab$ plane from which the square planar arrangement of Co can be seen. The figures were created using the xfplo version of FPLO [17].

Figure 2

(a) The specific heat of ${\mathrm{CoTa}}_2{\mathrm{O}}_6$ shows the magnetic phase transition at $T_N=6.2$ K. The peak at $T_N$ appears robust for 5 T and 7 T. As a lattice analog, the specific heat of ${\mathrm{MgTa}}_2{\mathrm{O}}_6$ is presented in red open circles. $d{C}_p/dT$ of $x=0.1$ is shown in the inset. (b) The plot of $C_p/T$ versus $T$ at 0 T for the different compositions of ${\mathrm{Co}}_{1-x}{\mathrm{Mg}}_x{\mathrm{Ta}}_2{\mathrm{O}}_6$. The sharp transition in the case of $x=0$ vanishes upon increasing $x$. The inset shows the specific heat of $x=0.5$ in 0 T and 7 T.

Figure 3

(a) The magnetic specific heat $C_m$ of ${\mathrm{CoTa}}_2{\mathrm{O}}_6$ (open circles). The red solid line is the specific heat of a square net of Ising spins while the blue line is a fit using a two-level Schottky term. The inset shows the $C_m$ along with a fit using Eq. (1). (b) Shows $C_m$ of $x=0.1$, 0.3, 0.5, and 0.7. The magnetic entropy, $S_m$, for ${\mathrm{Co}}_{1-x}{\mathrm{Mg}}_x{\mathrm{Ta}}_2{\mathrm{O}}_6 x$ = 0 to 0.7 are plotted in (c).

Figure 4

Raman scattering intensity of ${\mathrm{Co}}_{1-x}{\mathrm{Mg}}_x{\mathrm{Ta}}_2{\mathrm{O}}_6$ for (a) $x=0$, (b) $x=0.1$, 0.5, 0.7, and (c) $x=1.0$ at $T=300$ K. The thermal conductivity $\kappa \left(T\right)$ of the three compositions of ${\mathrm{Co}}_{1-x}{\mathrm{Mg}}_x{\mathrm{Ta}}_2{\mathrm{O}}_6$: $x=0$, 0.1, and 0.7. The phase transition at $T_N\approx 6$ K in the case of $x=0$ is shown enlarged in the inset.

Figure 5

Top: (a) The neutron powder diffraction pattern of ${\mathrm{CoTa}}_2{\mathrm{O}}_6$ at 295 K refined in the $P{4}_2/mnm$ space group. (b) Shows the pattern at 5 K where the magnetic peaks are shown magnified in the inset. ${\mathrm{\Gamma }}_2$ representation with a propagation vector $\left(\frac{1}{4}\frac{1}{4}0\right)$ accounts for the magnetic peaks. Nuclear Bragg peaks from the Al sample holder used for the experiment are accounted for in all cases. (c),(d) Shows the patterns for $x=0.1$ and 0.7, respectively, at 5 K. Bottom: A representation of a layer of Co magnetic moments in the $ab$ plane showing the $\left(++--\right)$ arrangement.

Figure 6

(a) Scalar-relativistic band structure within GGA for the FM state of ${\mathrm{CoTa}}_2{\mathrm{O}}_6$. Bands in black (red) indicate the spin-up (spin-down) channels. (b) Total (black) and partial DOS for Co (red), Ta (blue), apical-O (green), and planar-O (pink) of ${\mathrm{CoTa}}_2{\mathrm{O}}_6$ within GGA. (c) Orbital resolved DOS for Co-$3d$ states in ${\mathrm{CoTa}}_2{\mathrm{O}}_6$.