Magnetic properties of ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_2\mathrm{Al}{\mathrm{B}}_2$ and the impact of substitution on the magnetocaloric effect

In this work, we investigate the magnetic structures of ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_2\mathrm{Al}{\mathrm{B}}_2$ solid-solution quaternaries in the $x=0$ to 1 range using x-ray and neutron diffraction, magnetization measurements, and mean-field theory calculations. While ${\mathrm{Fe}}_2\mathrm{Al}{\mathrm{B}}_2$ and ${\mathrm{Mn}}_2\mathrm{Al}{\mathrm{B}}_2$ are known to be ferromagnetic (FM) and antiferromagnetic (AFM), respectively, herein we focused on the magnetic structure of their solid solutions, which is not well understood. The FM ground state of ${\mathrm{Fe}}_2\mathrm{Al}{\mathrm{B}}_2$ becomes a canted AFM at $x\approx 0.2$, with a monotonically diminishing FM component until $x\approx 0.5$. The FM transition temperature ($T_{\mathrm{C}}$) decreases linearly with increasing $x$. These changes in magnetic moments and structures are reflected in anomalous expansions of the lattice parameters, indicating a magnetoelastic coupling. Lastly, the magnetocaloric properties of the solid solutions were explored. For $x=0.2$ the isothermal entropy change is smaller by 30% than it is for ${\mathrm{Fe}}_2\mathrm{Al}{\mathrm{B}}_2$, while the relative cooling power is larger by 6%, due to broadening of the temperature range of the transition.

Figure 1

(a) The chemical unit cell of $M_2\mathrm{Al}{\mathrm{B}}_2$, (b) FM structure of ${\mathrm{Fe}}_2\mathrm{Al}{\mathrm{B}}_2$ [8], (c) AFM structure of ${\mathrm{Mn}}_2\mathrm{Al}{\mathrm{B}}_2$ [21], and (d) sublattice structure of simplified mean-field model of $M_2\mathrm{Al}{\mathrm{B}}_2$.

Figure 2

Observed XRD patterns (symbols) and the corresponding Rietveld refinement (solid lines) for different ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_2\mathrm{Al}{\mathrm{B}}_2$ powders with various $x$ values. Reflections are labeled by their Miller indices; impurity reflections are marked by * for $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ and # for ${\left({\mathrm{Fe}}_{1-y}{\mathrm{Mn}}_y\right)}_4{\mathrm{Al}}_{13}$. The patterns for $x=0.5$ and 0.75 were measured on a natural B sample. All patterns shown here were obtained using a Rigaku diffractometer.

Figure 3

Refined LPs and unit-cell volumes of ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_2\mathrm{Al}{\mathrm{B}}_2$ powders at RT as function of $x$ obtained from XRD (black symbols) and NPD (red symbols). (a), (b), and (c) show the $a, b$, and $c$ LPs, respectively, and (d) unit-cell volume. Circles indicate measurements performed on natural B samples; squares indicate those performed on ${}^{11}\mathrm{B}$ samples. Samples measured with NPD are plotted using the refined $x$. The discrepancies between the NPD and XRD measurements of the same samples originate from systematic errors which are discussed in Sec. 4c.

Figure 4

ZFC magnetization for (a) $x\le 0.5$, and (b) $x>0.5$. Measurements for $x=0.3$, 0.5, and 0.75 were performed on natural B samples. Error bars are smaller than linewidths. Note: $\mathrm{emu}/\left(\mathrm{g}\mathrm{Oe}\right)=4\pi \times {10}^{-3}{\mathrm{m}}^3/\mathrm{kg}$.

Figure 5

Derivatives of the ZFC magnetization for (a) $x\le 0.5$ and (b) $x>0.5$. Inset in (a) shows a zoomed-in view of the low-temperature regions. Measurements for $x=0.3$, 0.5, and 0.75 were performed on natural B samples. Note: $\mathrm{emu}/\left(\mathrm{g}\mathrm{Oe}\right)=4\pi \times {10}^{-3}{\mathrm{m}}^3/\mathrm{kg}$.

Figure 6

(a) Field-dependent average magnetic moment of ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_2\mathrm{Al}{\mathrm{B}}_2$ at 2 K as function of $x$. (b) Isothermal magnetic entropy change for a field change of 0–20 kOe as function of the relative temperature. Measurements for $x=0.3$, 0.5, and 0.75 were performed on natural B samples. The standard errors are smaller than the symbol size. Note: ${\mu }_0\mathrm{Oe}={10}^{-4}\mathrm{T}$.

Figure 7

(a) Observed NPD pattern of ${\mathrm{Fe}}_2\mathrm{Al}{\mathrm{B}}_2$ powders (symbols) at 350 K, the corresponding Rietveld refinement (solid line), and their difference (blue bottom solid line). Inset zooms in on the FM reflection at 8 K. (b) Observed NPD (symbols) of ${\left({\mathrm{Fe}}_{0.8}{\mathrm{Mn}}_{0.2}\right)}_2\mathrm{Al}{\mathrm{B}}_2$ at different temperatures and the corresponding Rietveld refinements (solid line). Reflections are marked using their Miller indices and fractional Miller indices (for AFM reflections). Reflections marked by “?” correspond to unidentified impurity phases. The measurements were performed using the BT-1 diffractometer. The error bars are smaller than the symbol size.

Figure 8

Temperature evolution of $a$ and $c$ LPs (left $y$ axis) and $b$ (right $y$ axis) of (a) ${\mathrm{Fe}}_2\mathrm{Al}{\mathrm{B}}_2$ and (b) ${\left({\mathrm{Fe}}_{0.5}{\mathrm{Mn}}_{0.5}\right)}_2\mathrm{Al}{\mathrm{B}}_2$ samples determined from NPD patterns.

Figure 9

(a) Temperature evolution of observed total ordered magnetic moment (symbols) in ${\left({\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x\right)}_2\mathrm{Al}{\mathrm{B}}_2$. (b) Observed (symbols) and calculated (solid lines) critical temperature of FM (black) and AFM (red) components as function of $x$. Different regions in the phase diagram are labeled by magnetic phases present in them.

Figure 10

Observed ordered magnetic moments at base temperature as function of $x$. Solid lines are fits of Eq. (5).