Field-induced metamagnetic transitions and two-dimensional excitations in ludwigite ${\mathbf{Co}}_{\mathbf{4}.\mathbf{76}}{\mathbf{Al}}_{\mathbf{1}.\mathbf{24}}{\left({\mathbf{O}}_{\mathbf{2}}{\mathbf{BO}}_{\mathbf{3}}\right)}_{\mathbf{2}}$

This paper presents an extensive study of the structural, magnetic, and thermodynamic properties of the heterometallic ludwigite ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$. This material orders ferrimagnetically at 57 K. Despite the fact that, in ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$, one quarter of the Co ions of the parent compound ${\mathrm{Co}}_3{\mathrm{O}}_2{\mathrm{BO}}_3$ is replaced by nonmagnetic ${\mathrm{Al}}^{3+}$ ions, the $T_C$ of the former (57 K) is larger than that of the latter (42 K). We obtain the phase diagram of ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$ in an external magnetic field. We find a line of second-order phase transitions where the system presents a metamagnetic transition (from 57 to 25 K). This line ends at a tricritical point at 25 K and 4.3 T, below which the transition to the paramagnetic phase is first order (from 25 to 3 K). In the magnetic phase at low temperatures specific heat measurements in zero and finite magnetic fields show that the low-energy excitations are magnetic (magnons) and elastic (phonons) excitations with two-dimensional character. These measurements also reveal the magnetocaloric properties of this material.

Figure 1

On the left, a schematic structure of the unit cell of the ludwigites projected along the $c$ axis is shown. The oxygen polyhedra centered on the metal ions are shown. The numbers indicate nonequivalent crystallographic metallic sites given in Table 2. Boron ions (green spheres) have trigonal coordination. The projections of the layers formed by sites 1, 2, and 3 are emphasized in green. On the right is shown a different view of the plane formed by metal at sites 1, 2, and 3. Here we can see that there is a triangular coordination for metal site 2. These figures were generated by the vesta 3.1.1 software [25].

Figure 2

Magnetization versus temperature for ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$ under an applied magnetic field of 100 Oe in both regimes: field-cooled [(FC): closed symbol] and zero-field-cooled [(ZFC): open symbol]. The inset shows the real part $\left({\chi }^{\prime }\right)$ of the ac magnetic susceptibility of ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$ as functions of temperature for 100 Hz, 1, and 10 kHz close to the region of the peak.

Figure 3

${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$ magnetization versus applied magnetic-field curves at 4.5, 10, 25, and 100 K. The inset shows the derivative of the curves.

Figure 4

${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$ magnetization versus temperature under an applied field of 1000 Oe in both regimes: field cooled (FC: closed symbol) and zero-field cooled (ZFC: open symbol) for oriented crystals. The inset shows the hysteresis loops for oriented crystals at 4.5 K.

Figure 5

${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$ specific heat plotted as $C/T$ versus $T$ for applied magnetic fields of 0, 3, 5, and 9 T. The inset: Low-temperature specific heat versus temperature for 0 and 9 T. The lines through the data are fittings to a power-law $C=a{T}^2$ (see the text).

Figure 6

Entropy as a function of temperature obtained from the specific heat curves for ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$ at applied fields of 0, 3, 5, and 9 T. The inset: Isothermal magnetic entropy change $[-\mathrm{\Delta }S=S(H=0)-S(H\ne 0\left)\right]$ of ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$ as a function of temperature for magnetic-field changes up to 9 T.

Figure 7

The phase diagram of ${\mathrm{Co}}_{4.76}{\mathrm{Al}}_{1.24}{\left({\mathrm{O}}_2{\mathrm{BO}}_3\right)}_2$. The phase boundaries were determined as follows: The white circle is the transition temperature obtained from the magnetic susceptibility $\chi \left(T\right)$ and magnetization $M\left(T\right)$. The green squares are from specific heat $C(T,H)$, and the purple triangles are from $\partial M/\partial H$. Three phases are defined as follows: paramagnetic (PM), FIM, and spin flop. A tricritical point separating the lines of second- and first-order transitions appears at $\left(H_t=4.2\mathrm{T},T_t=25\mathrm{K}\right)$, indicated by a blue diamond symbol. The spin-flop phases are in fact metastable phases where FIM and PM phases coexist.