Magnetic properties of single crystalline itinerant ferromagnet ${\mathrm{AlFe}}_2{\mathrm{B}}_2$

Single crystals of ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ have been grown using the self-flux growth method, and then we measured the structural properties, temperature- and field-dependent magnetization, and temperature-dependent electrical resistivity at ambient as well as high pressure. The Curie temperature of ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ is determined to be 274 K. The measured saturation magnetization and the effective moment for the paramagnetic Fe ion indicate the itinerant nature of the magnetism with a Rhode-Wohlfarth ratio $\frac{M_C}{M_{\text{sat}}}\approx 1.14$. Temperature-dependent resistivity measurements under hydrostatic pressure show that transition temperature $T_C$ is suppressed down to 255 K for $p=2.24$ GPa pressure with a suppression rate of $\sim -8.9$ K/GPa. The anisotropy fields and magnetocrystalline anisotropy constants are in reasonable agreement with density functional theory calculations.

Figure 1

(a) ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ unit cell. (b) The HAADF STEM image shows the uniform chemistry of the ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ crystal. The inset is a corresponding selected-area electron diffraction pattern. (c) High-resolution HAADF STEM image of ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ taken along the [101] zone axis along with a projection of a unit cell represented with Fe (red), Al (green), and B (yellow) spheres. The structural pattern of Al and FeB slab layers is also visible in the unit cell shown in (a). (d) EDS elemental mapping without taking into account of the B scattering effect, where green stripes are Al distributions and red stripes are Fe distributions.

Figure 2

(a) Powder XRD for ${\mathrm{AlFe}}_2{\mathrm{B}}_2$. I(Obs), I(Cal), and I(Bkg) stand for experimental powder diffraction, Rietveld refined, and instrumental background data. The green vertical lines represent the Bragg reflection peaks, and I(Obs-Cal) is the differential intensity between I(Obs) and I(Cal). The upper inset shows the crucible limited growth nature of ${\mathrm{AlFe}}_2{\mathrm{B}}_2$. The lower inset shows the pieces of as-grown platelike crystals. (b) Monochromatic XRD pattern from the plate surface of ${\mathrm{AlFe}}_2{\mathrm{B}}_2$. (c) Monochromatic XRD pattern from cut surface [001] collected using Bragg-Brentano geometry. The left inset shows the as-grown ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ crystal. The right inset is the photograph of the cut section of the crystal parallel to the (001) plane. The middle unidentified peak might be due to a differently oriented shard of cut ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ crystal. (d) Comparison of the monochromatic surface XRD patterns from (b) and (c) with a powder XRD pattern from (a) within an extended $2\theta$ range of ${60}^{\circ }$–${70}^{\circ }$ to illustrate the identification scheme of the crystallographic orientation.

Figure 3

(a) Temperature-dependent magnetization with a 0.01 T applied field along the [100] direction. (b) Field-dependent magnetization along principal directions at 2 K. [100] is the easy axis with the smallest saturating field, [010] is the intermediate axis with 1 T anisotropy, and [001] is the hardest axis with $\sim 5$ T anisotropy field. (c) Sucksmith-Thompson plot for $M\left(H\right)$ data along the [001] direction (and along [010] in the inset) to estimate the magnetocrystalline anisotropy constants. The red dash-dotted line is the linear fit to the hard axes isotherms at the high-field region ($>3$ T) whose $Y$ intercept is used to estimate the anisotropy constant $K$. (d) Arrott plot obtained with easy-axis isotherms within the temperature range of 265–285 K at a step of 1 K. The straight line through the origin is the tangent to the isotherm corresponding to the transition temperature.

Figure 4

Magnetocaloric effect in ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ obtained using $M\left(H\right)$ isotherms along [100]. (a) The change in entropy ($\mathrm{\Delta }S$) evaluation scheme at its highest value, (b) the change in entropy with 2 T and 3 T applied fields using easy-axis [100] isotherms. For the sake of comparison, the 2 ${\mathrm{T}}^{*}$ field data are taken from Ref. [9].

Figure 5

Generalized Arrott plot of ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ with magnetization data along the [100] direction within a temperature range of 250–290 K at a step of 1 K. $\beta =0.30\pm 0.04$ and $\gamma =1.180\pm 0.005$ were determined from the Kouvel-Fisher method. The two dash-dotted straight lines are drawn to visualize the intersection of the isotherms with the axes.

Figure 6

Determination of the critical exponents ($\beta$ and $\gamma$) using Kouvel-Fisher plots. See the text for details.

Figure 7

Determination of the critical exponent $\delta$ using Kouvel-Fisher plots using an $M\left(H\right)$ isotherm at $T_C$ to check the consistency of $\beta$ and $\gamma$ via Widom scaling. The data used for determining the exponent $\delta$ are highlighted with the red curve in the corresponding $M\left(H\right)$ isotherm. The data in the low-field region deviate slightly from the linear behavior in the logarithmic scale as shown in the inset. The range dependency of the value of $\delta$ is illustrated with different color tangents. The field range for the fitted data is indicated in the parentheses along with the value of $\delta$. See the text for details.

Figure 8

Normalized isotherms to check the validity of the scaling hypothesis. The isotherms in between 270–273 K are converged to a higher value ($T<T_C$) and the isotherms in between 275–280 K are converged to a lower $\mathrm{value}(T>T_C$). The inset shows the corresponding log-log plot clearly bifurcated in two branches in the low-field region.

Figure 9

Illustration of the consistency of the critical exponents $\beta$ and $\gamma$ used for the generalized Arrott plot (a) by reproducing the initial spontaneous magnetization $M_S$ and ${\chi }^{-1}\left(T\right)$ via the $Y$ and $X$ intercepts of the generalized Arrott plot. (b) Fitting of the extracted data (squares) from the generalized Arrott plot with corresponding power laws (red lines) in Eqs. (6) and (7).

Figure 10

Evolution of the single-crystal ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ resistivity with hydrostatic pressure up to 2.24 GPa. Pressure values at $T_C$ were estimated from linear interpolation between the $P_{300\mathrm{K}}$ and $P_{T\le 90\mathrm{K}}$ values (see the text). Current was applied along the crystallographic $a$ axis. The inset shows the evolution of the temperature derivative $d\rho /dT$ with hydrostatic pressure. The peak positions in the derivative were identified as transition temperature $T_C$. Examples of $T_C$ are indicated by arrows in the figure.

Figure 11

Temperature-pressure phase diagram of ${\mathrm{AlFe}}_2{\mathrm{B}}_2$ as determined from resistivity measurement. Pressure values were estimated as being described in Fig. 10 and in the text. Error bars indicate the room-temperature pressure $P_{300\mathrm{K}}$ and low-temperature pressure $P_{T\le 90\mathrm{K}}$. As shown in the figure, in the pressure region of 0–2.24 GPa the ferromagnetic transition temperature $T_C$ is suppressed upon increasing pressure, with a suppressing rate around $-8.9$ K/GPa.

Figure 12

The calculated density of states of ${\mathrm{AlFe}}_2{\mathrm{B}}_2$.