Magnetic phase diagram of CeAu${}_2$Ge${}_2$: High magnetic anisotropy due to crystal electric field

CeAu${}_2$Ge${}_2$ single crystals (with tetragonal ThCr${}_2$Si${}_2$ structure) have been grown in Au-Ge flux (AGF) as well as in Sn flux (SF). X-ray powder diffraction and EDX measurements indicate that in the latter case, Sn atoms from the flux are incorporated in the samples, leading to a decrease of the lattice constants by $\approx$0.3% compared to AGF samples. For both types of samples, a strong anisotropy of the magnetization $M$ for the magnetic field $\mathbf{B}$ parallel and perpendicular to the $c$ direction is observed with $M_{\left|\right|}/M_{\perp }\approx 6\text{--}7$ in low fields just above 10 K. This anisotropy is preserved to high fields and temperatures and can be quantitatively explained by crystal electric field effects. Antiferromagnetic ordering sets in around 10 K as previously found for polycrystalline samples. From the magnetization data of our single crystals we obtain the phase diagrams for the AGF and SF samples. The magnetic properties depend strongly on the flux employed. While the AGF samples exhibit a complex behavior indicative of several magnetic transitions, the SF samples adopt a simpler antiferromagnetic structure with a single spin-flop transition. This effect of a more ordered state induced by disorder in form of Sn impurities is qualitatively explained within the anisotropic next-nearest neighbor Ising (ANNNI) model, which assumes ferromagnetic and antiferromagnetic interactions in agreement with the magnetic structure previously inferred from neutron-scattering experiments on polycrystalline CeAu${}_2$Ge${}_2$ by Loidl et al. [Phys. Rev. B 46, 9341 (1992)].

Figure 1

Left: x-ray powder diffraction patterns of several samples of CeAu${}_2$Ge${}_2$ grown in Au-Ge or Sn flux (denoted by AGF and SF, respectively). The crosses mark the calculated peak heights and positions. The arrow in the top panel indicates Au inclusions. Right: (103), (112), and (004) peaks on an expanded horizontal scale. The vertical line illustrates the systematic shift of the center peak between AGF and SF samples.

Figure 2

Electron microscopy pictures: on the left, sample VF474 AGF, and on the right, sample VF467 SF (see text for details).

Figure 3

Left: magnetization $M$ vs temperature $T$ of AGF and SF CeAu${}_2$Ge${}_2$ with the magnetic field $B=0.1$ T aligned either parallel or perpendicular to the $c$ axis. The arrows in the upper frame mark additional anomalies in the magnetization curves (see main text). Right: magnetization $M$ vs external magnetic field $B$ at $T=2.6$ K of AGF and SF CeAu${}_2$Ge${}_2$.

Figure 4

Comparison of measured and calculated magnetization of AGF CeAu${}_2$Ge${}_2$. For details, see text. Left: measured and calculated data for $T=2.6$ K. The solid line is the calculated magnetization with the crystal-field parameters from Ref. 10, the dashed lines indicate the magnetization for the pure $|\pm \frac{5}{2}\rangle$ and $|\mp \frac{3}{2}\rangle$ states. Right: calculated and measured data for $T=10$ and 20 K. For clarity, only the data taken with increasing field are shown.

Figure 5

Left: magnetization $M$ of SF (red circles) and AGF (blue triangles) grown CeAu${}_2$Ge${}_2$ compared to the calculated data in fields up to 15 T with the magnetic field $B$ aligned parallel and perpendicular to the $c$ axis. Right: magnetization $M$ of SF (red circles) and AGF (blue triangles) grown CeAu${}_2$Ge${}_2$ compared to the calculated data (solid black line) in fields up to 60 T with the magnetic field $B$ aligned perpendicular to the $c$ axis. The solid lines below 12 T indicate the low-field VSM data.

Figure 6

Inverse dc susceptibility $\chi -{\chi }_0$ vs temperature of CeAu${}_2$Ge${}_2$ in an external field $B=100$ mT aligned $\mathbf{B}\parallel \mathbf{c}$ (left) and $\mathbf{B}\perp \mathbf{c}$ (right). The solid red lines are calculated susceptibilities on the basis of the neutron scattering data of Loidl et al.[10] For the determination of ${\chi }_0$, see text. For clarity, the data are shifted by $100\mathrm{mole}/\mathrm{emu}$ each.

Figure 7

Left: magnetization $M$ vs temperature $T$ in different magnetic fields $\mathbf{B}\parallel \mathbf{c}$. Right: $M$ vs external magnetic field $\mathbf{B}\parallel \mathbf{c}$ at different temperatures $T$.

Figure 8

Magnetic susceptibility $\chi =dM/dB$ of CeAu${}_2$Ge${}_2$ vs field $\mathbf{B}\parallel \mathbf{c}$ at $1.6$, $2.6$, 5, $7,$ and 10 K.

Figure 9

$B$-$T$ phase diagram of AGF (left) and SF (right) CeAu${}_2$Ge${}_2$ with the magnetic field aligned parallel to the $c$ axis.