Magnetic properties of the $\left({\mathrm{Mo}}_{2/3}{R}_{1/3}\right){}_2\mathrm{AlC} (R=\mathrm{Ho},\mathrm{Dy}) i\text{−}\mathrm{MAX}$ phases studied by x-ray magnetic circular dichroism and neutron diffraction

We report on the magnetic properties of single crystals of Ho- and Dy-based ${\left({\mathrm{Mo}}_{2/3}{R}_{1/3}\right)}_2\mathrm{AlC} i\text{−}\mathrm{MAX}$ phases. In these nanolamellar compounds, where planes of $R$ and Mo arranged in a skewed triangular lattice are separated by planes of Al and C, geometrical frustration and magnetic exchange interactions lead to complex magnetic properties. Temperature-dependent bulk magnetization, specific heat, and resistivity measurements reveal two magnetic phase transitions in Dy $i\text{−}\mathrm{MAX}$ (15 and 12 K) and only one in Ho $i\text{−}\mathrm{MAX}$ (8.5 K). Strong magnetic anisotropy and metamagnetic transitions with a step at $\frac{1}{3}$ of saturation moment along the crystal $a$ axis are observed in field-dependent bulk magnetization curves. X-ray magnetic circular dichroism measurements unveil induced moments on Mo and Al, and a quantitative estimation of the orbital and spin moments of Mo based on magneto-optical sum rules suggests an unusual interaction between the $R 4f$ and the Mo $4d$ magnetic moments. Magnetic structures are derived from neutron diffraction measurements, revealing a zero-field incommensurate amplitude modulated order in both compounds, followed by an antiferromagnetic equal-moments structure at lower temperature for Dy $i\text{−}\mathrm{MAX}$. The bulk magnetization $\frac{1}{3}$ step is found to be linked to the flip of one $R$ moment out of three within the planes. Detailed phase diagrams for Ho and Dy $i\text{−}\mathrm{MAX}$ are derived from these measurements.

Figure 1

Cross-section of the monoclinic crystal structure of ${\left({\mathrm{Mo}}_{2/3}{R}_{1/3}\right)}_2\mathrm{AlC}$ as seen from the $a$ axis (right) and top view of its constituent layers seen from the out-of-plane c* axis (left).

Figure 2

Bulk magnetization of (a) Dy $i\text{−}\mathrm{MAX}$ and (b) Ho $i\text{−}\mathrm{MAX}$ single crystals, measured as a function of $T$ with a small magnetic field (${\mu }_{0}H=0.1\mathrm{T}$ for Dy $i\text{−}\mathrm{MAX}$ and ${\mu }_{0}H=0.01\mathrm{T}$ for Ho $i\text{−}\mathrm{MAX}$) applied along the $a, b$, and c* crystal axes, from 2 to 300 K. (c)–(e) Areas of the magnetic transitions of interest for both compounds, along the three field directions.

Figure 3

Isothermal bulk magnetization curves of a Dy $i\text{−}\mathrm{MAX}$ single crystal, measured as a function of applied magnetic field, with $H$ aligned along the $a$ (top), $b$, and c* (bottom) crystal axes. The insets show the magnetization curves at $T=2\mathrm{K}$ with increasing and decreasing field up to ${\mu }_{0}H=7\mathrm{T}$, and all other curves were measured with increasing field only. The arrows differentiate between increasing and decreasing field at the position of the hysteresis. The inset features the net moments determined from neutron diffraction at 2 K.

Figure 4

Dy $i\text{−}\mathrm{MAX}$ element-specific x-ray magnetic circular dichroism (XMCD) intensity vs $H$ measured at the Al $K$ edge, Dy $M_5$ edge (top, at $T=4.3\mathrm{K}$) and Mo/Dy $L_3$ edge (bottom, at $T=2.7\mathrm{K}$). The inset at the bottom shows the Dy $L_3$-edge XMCD intensity up to ${\mu }_{0}H=17\mathrm{T}$. The divergence between the Al $K$ edge and Dy $M_5$ right after the first transition can be ascribed to measurement artifacts.

Figure 5

Magnetic field–temperature phase diagrams derived from all measurements conducted on Dy $i\text{−}\mathrm{MAX}$, with the field applied (a) along the $a$ axis and (b) a combination of axes $b$ and c* (filled symbols for $b$ and empty symbols for c*). The purpose of the dotted lines is to delineate roughly the various areas of the phase diagram, and they should not be taken as the genuine boundaries.

Figure 6

Isothermal bulk magnetization curves of a Ho $i\text{−}\mathrm{MAX}$ single crystal, measured as a function of applied magnetic field, with $H$ aligned along the $a$ (top), $b$, and c* (bottom) crystal axes. The magnetization curves at $T=2\mathrm{K}$ were measured with increasing and decreasing field, while the curves at other temperatures were measured with increasing field only. The net moments determined from neutron diffraction at 2 K are also plotted.

Figure 7

Magnetic field–temperature phase diagrams derived from all measurements conducted on Ho $i\text{−}\mathrm{MAX}$, with the field applied (a) along the $a$ axis and (b) a combination of axes $b$ and c* (filled symbols for $b$ and empty symbols for c*). The phase labeled I corresponds to the zero-field magnetic order.

Figure 8

(a) Transport measurements on Ho and Dy $i\text{−}\mathrm{MAX}$ single crystals, as a function of temperature, with (b) the region of the magnetic transitions. Heat capacity as a function of temperature for (c) Dy $i\text{−}\mathrm{MAX}$ and (d) Ho $i\text{−}\mathrm{MAX}$, with and without applied magnetic field. The insets show the full temperature range.

Figure 9

Normalized $L_{3,2}$-edge x-ray absorption near-edge structure (XANES; left axis) and x-ray magnetic circular dichroism (XMCD; right axis, same scale as XANES) spectra measured at $T=2.7\mathrm{K}$ on Dy $i\text{−}\mathrm{MAX}$ (top) and Ho $i\text{−}\mathrm{MAX}$ (bottom), with a magnetic field applied close to the $a$ axis.

Figure 10

X-ray magnetic circular dichroism (XMCD) spectra at the $L_2$ edges of (a) Dy and (b) Ho, with applied fields allowing us to reach the first metamagnetic step as well as saturation. The spectrum at the first step is multiplied by a factor of 3 for comparison purposes. X-ray absorption near-edge structure (XANES)/XMCD at (c) the $K$ edge of Al and (d) $L_{3,2}$ edges of Mo, on Ho and Dy $i\text{−}\mathrm{MAX}$, at saturation field. For all measurements, the field is applied close to the $a$ axis.

Figure 11

Ho $i\text{−}\mathrm{MAX}$ element-specific x-ray magnetic circular dichroism (XMCD) intensity vs $H$ measured at the Al $K$ edge, Ho $M_5$ edge (top, at $T=4.3\mathrm{K}$), and Mo/Ho $L_3$ edge (bottom, at $T=2.7\mathrm{K}$). The inset at the bottom shows the Ho $L_3$-edge XMCD intensity up to ${\mu }_{0}H=17\mathrm{T}$.

Figure 12

Dy $i\text{−}\mathrm{MAX}$ magnetic structures determined from neutron scattering measurements conducted with $H$ applied along the $a$ axis. The incommensurate phase ($T=12.5\mathrm{K}$ and ${\mu }_{0}H=0\mathrm{T}$) is followed by the structures at $T=2.4\mathrm{K}$ with applied fields of 0, 2.5, and 6 T ($T=2.4\mathrm{K}$), corresponding to the ground state, first metamagnetic step, and at saturation. The depiction on the left corresponds to the magnetic unit cell for commensurate phases, and the one on the right pictures a rare-earth (RE) plane as seen from the out-of-plane c* direction. For clarity, only Dy atoms are shown.

Figure 13

Ho $i\text{−}\mathrm{MAX}$ magnetic structures determined from neutron scattering measurements conducted with $H$ applied along the $a$ axis. Measurements were done at $T=2.4\mathrm{K}$ with applied fields of 0, 1, and 4 T ($T=2.4\mathrm{K}$), corresponding to the ground state, metamagnetic step, and at saturation. The depiction on the left corresponds to the magnetic unit cell for commensurate phases. The one on the right pictures two consecutive rare-earth (RE) planes as seen from the out-of-plane c* direction. For clarity, only Ho atoms are shown.