High-field magnetization and magnetic phase diagrams for three symmetry axes in single-crystal ${\mathrm{CeAl}}_2$

We measured high-field magnetization, up to 56 T, in ${\mathrm{CeAl}}_2$ crystallized in ${\mathrm{MgCu}}_2$-type cubic structure, using a pulse magnet. We observed the conventional metamagnetic transition from antiferromagnetism to field-induced ferromagnetism near 5 T. Magnetic phase diagrams were determined for the $\langle 100\rangle , \langle 110\rangle$, and $\langle 111\rangle$ axes using high quality single crystals, as identified by the detection of the de Haas-van Alphen oscillation. As reported in previous research with polycrystalline samples for mapping the magnetic phase diagram of ${\mathrm{CeAl}}_2$, two phase boundaries were observed within the antiferromagnetic phase. This structure of the magnetic phase diagram is similar to that of centrosymmetric skyrmion system such as ${\mathrm{GdRu}}_2{\mathrm{Si}}_2$, in which the Ruderman–Kittel–Kasuya–Yosida interaction plays an important role. Our measurements using single crystals revealed that phase boundaries within the antiferromagnetic phase varied depending on magnetic field direction. For magnetization along $\langle 100\rangle$, a weak, broad shoulder was observed that reached to approximately 15 K, far higher than the 4 K Néel temperature. This single-crystal study resolves the detailed magnetic phase diagrams to three symmetry axes. Mapping the orientation-dependent magnetic phase diagrams supports the magnetic structure determination for each phase and each symmetry axis. The newly mapped orientation-dependent magnetic phase diagrams provide insights that clarify underlying magnetic correlation and plausible skyrmion phase in heavy fermion compound ${\mathrm{CeAl}}_2$.

Figure 1

Magnetizations for $H\left|\right|\langle 111\rangle , \langle 110\rangle$, and $\langle 100\rangle$ for magnetic field strengths up to 56 T.

Figure 2

(a) Magnetization for $\langle 111\rangle$ in the temperature range 1.3–4.2 K with induction setup. (b) First derivative of magnetization with respect to magnetic field strength in the temperature range 1.3–4.2 K. The black dashed lines are visual guides only.

Figure 3

Magnetic phase diagram for $H\left|\right|\langle 111\rangle$. $H_1$ (green open circle) and $H_2$ (blue open circle) represent the lower and higher magnetic fields at the magnetic phase transitions within AF phase, respectively. $H_3$ (red open circle) shows the magnetic field of boundary between AF and FIF phases. The skyrmion phase is expected to be in the phase between $H_1$ and $H_2$.

Figure 4

(a) Magnetization for $\langle 110\rangle$ in the temperature range 1.3–4.2 K with induction setup. (b) First derivative of magnetization with respect to magnetic field strength in the temperature range 1.3–4.2 K. The black dashed lines are visual guides only. There are offsets for visibility.

Figure 5

Magnetic phase diagram for $H\left|\right|\langle 110\rangle$. $H_1$ (green open circle) and $H_2$ (blue open circle) represent the lower and higher magnetic fields at the magnetic phase transitions within AF phase, respectively. $H_3$ (red open circle) shows the magnetic field of boundary between AF and FIF phases. The skyrmion phase is expected to be in the phase between $H_1$ and $H_2$.

Figure 6

(a) Magnetization for $\langle 100\rangle$ in the temperature range 1.4–20 K with induction setup. (b) First derivative of magnetization with respect to magnetic field strength in the temperature range 1.4–20 K. The black dashed lines are visual guides only. There are offsets for visibility.

Figure 7

Magnetic phase diagram for $H\left|\right|\langle 100\rangle$. (Inset) Phase diagram for higher temperatures. $H_1$ (green open circle) and $H_2$ (blue open circle) represent the lower and higher magnetic fields at the magnetic phase transitions within AF phase, respectively. $H_3$ (red open circle) shows the magnetic field of boundary between AF and FIF phases. The skyrmion phase is expected to be in the phase between $H_1$ and $H_2$. $H_4$ (gold open circle) means the magnetic field that the novel anomaly emerges after $H_1, H_2$, and $H_3$ merge.

Figure 8

(a) Magnetization with the sublinear part subtracted for $H\left|\right|\langle 111\rangle , \langle 110\rangle$, and $\langle 100\rangle$ for the magnetic field strengths up to 56 T. (b) Fast Fourier transform (FFT) spectrum in the magnetic field strength of 10–20 T for $H\left|\right|\langle 111\rangle$. Inset: Temperature dependence of de Haas-van Alphen oscillation amplitude for the estimation of the $\alpha$-branch effective mass. (c) FFT spectra for the magnetic field strength of 45–55 T for $H\left|\right|\langle 111\rangle$