Ferromagnetism in ${\text{Co}}_7{\left({\text{TeO}}_3\right)}_4{\text{Br}}_6$: A byproduct of complex antiferromagnetic order and single-ion anisotropy

Pronounced anisotropy of magnetic properties and complex magnetic order of a new oxi-halide compound ${\text{Co}}_7{\left({\text{TeO}}_3\right)}_4{\text{Br}}_6$ has been investigated by powder and single-crystal neutron-diffraction, magnetization, and ac susceptibility techniques. Anisotropy of susceptibility extends far into the paramagnetic temperature range. A principal source of anisotropy are anisotropic properties of the involved octahedrally coordinated single ${\text{Co}}^{2+}$ ions, as confirmed by angular-overlap-model calculations presented in this work. Incommensurate antiferromagnetic order sets in at $T_N=34\text{K}$. The propagation vector is strongly temperature dependent reaching ${\mathbf{k}}_1=\left[0.9458\left(6\right),0,0.6026\left(5\right)\right]$ at 30 K. A transition to a ferrimagnetic structure with ${\mathbf{k}}_2=0$ takes place at $T_C=27\text{K}$. The magnetically ordered phase is characterized by very unusual anisotropy as well: while $M\text{−}H$ scans along the $b$ axis reveal spectacularly rectangular but otherwise standard ferromagnetic hysteresis loops, $M\text{−}H$ studies along other two principal axes are perfectly reversible, revealing very sharp spin-flop (or spin-flip) transitions, such as in a standard antiferromagnet (or metamagnet). Altogether, the observed magnetic phenomenology is interpreted as an evidence of competing magnetic interactions permeating the system, in particular of the single-ion anisotropy energy and the exchange interactions. Different coordinations of the ${\text{Co}}^{2+}$ ions involved in the low-symmetry $C2/c$ structure of ${\text{Co}}_7{\left({\text{TeO}}_3\right)}_4{\text{Br}}_6$ render the exchange-interaction network very complex by itself. Temperature-dependent changes in the magnetic structure, together with an abrupt emergence of a ferromagnetic component, are ascribed to continual spin reorientations described by a multicomponent, but yet unknown, spin Hamiltonian.

Figure 1

(Color online) Observed (dots), calculated (red solid line), and difference (green curve at bottom of the panels) neutron powder-diffraction patterns (DMC instrument, $\lambda =2.453\text{Å}$) of ${\text{Co}}_7{\left({\text{TeO}}_3\right)}_4{\text{Br}}_6$ at 45 K (top) and 30–35 K (bottom). Intensities are normalized to the same monitor.

Figure 2

(Color online) Temperature dependence of the ICM magnetic vector components refined from the DMC data, $\lambda =2.453\text{Å}$.

Figure 3

(Color online) Difference neutron powder diffraction $T-45\text{K}$ of ${\text{Co}}_7{\left({\text{TeO}}_3\right)}_4{\text{Br}}_6$ with $T$ in the range of 25–32 K (DMC instrument, $\lambda =4.2\text{Å}$). Patterns are linearly shifted along the $y$ axis and only the most relevant $2\theta$ region is selected. The inset on the right-hand side, correlated in temperatures with the main panel, shows the sequence of the magnetic transitions schematically.

Figure 4

(Color online) Observed 5–45 K magnetic difference pattern calculated $\left(\lambda =2.453\text{Å}\right)$ and difference patterns of ${\text{Co}}_7{\left({\text{TeO}}_3\right)}_4{\text{Br}}_6$ denoted by crosses, red solid, and green dotted lines, respectively. Inset: the choice of the $XYZ=a^{\ast }bc$ orthogonal system and morphology of the single crystal used.

Figure 5

(Color online) The $ac$ projection of the low-temperature (5 K) magnetic structure of ${\text{Co}}_7{\left({\text{TeO}}_3\right)}_4{\text{Br}}_6$. The four crystallographic sets of ${\text{Co}}^{2+}$ ions are shown by violet—Co(1), red—Co(2), green—Co(3), and orange—Co(4). The Co(21) and Co(32) ions, as well as Co(22) and Co(32), superimpose on this projection. The pairs $\text{Co}\left(ij\right)/\text{Co}\left(ij+1\right)$ have opposite $M_x$ and $M_z$ magnetic components but the same $M_y$ component. The sign of $M_y$ is shown near the symbol of each ion. Spatial orientations of local magnetic moments are illustrated by three-dimensional vectors.

Figure 6

(Color online) Main panel: temperature dependence of real component of ac susceptibility (3 Oe, 430 Hz) for measuring field oriented along three principal axes. dc susceptibility in small applied field (100 Oe) provides almost identical result. Black curve represents the Curie plot for free $S=3/2$, $\text{g}=2.5$, ions (Curie constant $C=20.5\text{emu}\text{K}/\text{mol}$) Inset top: product ${\chi }_{\text{dc}}T$ vs temperature. Inset bottom: susceptibility inverse ${\chi }_{\text{dc}}^{-1}$ vs temperature.

Figure 7

(Color online) Temperature dependence of out-of-phase (imaginary) component of ac susceptibility for three principal axes. Above the transition range there is overlap of the data points for all three measurement directions. The data for ${\chi }^{\prime }$ (Fig. 6) and ${\chi }^{″}$ were taken within the same experimental runs. Inset: zoomed transition temperature range. Residual signal in measurement along $c$ axis (green symbols) is ascribed to imperfect sample alignment and/or nonvanishing cross-talk between the in-phase and out-of-phase components in the phase-sensitive detection.

Figure 8

(Color online) Calculated products $\chi T$ for each of the four $\text{Co}\left(i\right)$ octahedra employing full single-ion Hamiltonian and AOM. Calculated results for real single crystal as a whole is shown at bottom (plot at left). Results corrected for weak ferromagnetic interactions ($\lambda =2$, see text) is also shown, (plot at bottom right), to be compared with the experimental results for $\chi T$, Fig. 6.

Figure 9

(Color online) The alignment of $g^2$ tensor (violet ellipsoid) and the ligands (oxygen in red, bromine in green) of four different Co set in the $XYZ=a^{\ast }bc$ orthogonal coordinate system.

Figure 10

(Color online) Magnetization (per one Co ion) vs field characteristics for $c$-axis direction in a broad temperature range. $M\left(h\right)$ curves reveal almost switching but perfectly reversible behavior of magnetization in magnetically ordered phase.

Figure 11

(Color online) Magnetization (per one Co ion) vs field curves for $a^{\ast }$ direction at three characteristic temperatures. Spin-flop transitions are marked with arrows.

Figure 12

(Color online) Temperature dependence of spin-flip field $H_{\text{SF}}^c$, high-field saturation magnetization $M_{\text{sat}}$, and the slope in $MH$ curve at high fields ${\chi }_{\text{HF}}$, all for magnetic field applied along $c$ axis.

Figure 13

(Color online) Main panel: magnetic hysteresis loops for the $b$-axis direction at different temperatures. Magnetization is scaled to one Co ion. Inset: virgin hysteresis curve at 2 K. At higher temperatures there is a more abrupt magnetization transition to quasisaturation by the application of magnetic field of the order of 100 Oe or less.

Figure 14

Temperature dependence of the coercive field for $b$-axis field direction. Solid line is guide for the eye only.