Weak ferrimagnetism and multiple magnetization reversal in $\alpha$-Cr${}_3$(PO${}_4$)${}_2$

The chromium(II) orthophosphate $\alpha$-Cr${}_3$(PO${}_4$)${}_2$ is a weak ferrimagnet with the Curie temperature $T_C$ $=$ 29 K confirmed by a $\lambda$-type peak in specific heat. Dominant antiferromagnetic interactions in this system are characterized by the Weiss temperature $\Theta$ $=$ 96 K, indicating an intermediate frustration ratio $|$$\Theta$$|$/$T_C$ ∼ 3. In its magnetically ordered states $\alpha$-Cr${}_3$(PO${}_4$)${}_2$ exhibits a remarkable sequence of temperature-induced magnetization reversals sensitive to the protocol of measurements, i.e., either field-cooled or zero-field-cooled regimes. The reduction of the effective magnetic moment 4.5 $\mu$${}_{\mathrm{B}}$/Cr${}^{2+}$, as compared to the spin-only moment 4.9 $\mu$${}_{\mathrm{B}}$/Cr${}^{2+}$, cannot be ascribed to the occurrence of the low-spin state in any crystallographic site of the Jahn-Teller active 3$d^4$ Cr${}^{2+}$ ions. X-ray absorption spectra at the $K$ edge indicate divalent chromium and unravel the high-spin state of these ions at the $L_{2,3}$ edges. Weak ferrimagnetism and multiple magnetization reversal phenomena seen in this compound could be ascribed to incomplete cancellation and distortion of partial spontaneous magnetization functions of Cr${}^{2+}$ in its six crystallographically inequivalent positions.

Figure 1

Structural features of $\alpha$-Cr${}_3$(PO${}_4$)${}_2$. (a) Close-packed arrangement of tubes from phosphate tetrahedra and Cr${}^{2+}$ ions. (b) Helical arrangement of the six independent Cr${}^{2+}$ ions within a tube (right) and the same tube section with coordination polyhedra [CrO${}_{\mathrm{n}}$] (left). The phosphate groups PO${}_4$ are represented by the light-yellow tetrahedra.

Figure 2

The Cr $K$-edge x-ray absorption spectra in various chromium compounds taken at $T$ $=$ 300 K.

Figure 3

The “linear” dependence of the $K$-edge energy on the oxidation state of chromium. The size of symbols corresponds roughly to the error bars.

Figure 4

The Cr $L_{2,3}$ edges x-ray absorption spectra in $\alpha$-Cr${}_3$(PO${}_4$)${}_2$ and Cr${}_2$O${}_3$ taken at $T$ $=$ 300 K. The $C{T}_{1–3}$ spectral features are ascribed tentatively to the charge transfer transitions.

Figure 5

The temperature dependence of the specific heat $C_p$ in $\alpha$-Cr${}_3$(PO${}_4$)${}_2$. Inset : $C_p$/$T$ vs $T^2$ curves taken at $B$ $=$ 0 and $B$ $=$ 9 T.

Figure 6

The temperature dependence of magnetic susceptibility in $\alpha$-Cr${}_3$(PO${}_4$)${}_2$ taken at rising temperature at $B$ $=$ 0.1 T after cooling in zero field. Inset: Enlarged portions of $\chi$($T$) curves taken with rising temperature after cooling at $B$ $=$ 0 (ZFC regime) and $B$ $=$ 0.1 T (FC regime).

Figure 7

The inverse magnetic susceptibility in $\alpha$-Cr${}_3$(PO${}_4$)${}_2$. The product ($\chi$ – $\chi$${}_0$)·($T$ – $\Theta$) indicates increasing relevance of ferromagnetic interactions when approaching the critical temperature $T_C$ $=$ 29 K from above.

Figure 8

The field dependences of magnetization in $\alpha$-Cr${}_3$(PO${}_4$)${}_2$ taken at selected temperatures both below and above the critical temperature $T_C$ $=$ 29 K (1–25 K, 2–27 K, 3–29 K, 4–50 K). The inset represents the magnetization loop taken at 2 K.

Figure 9

The field dependence of magnetization in $\alpha$-Cr${}_3$(PO${}_4$)${}_2$ taken at $T$ $=$ 2 K. The solid lines are the extrapolations of the linear segments of the $M$($B$) curve at $B$ < $B_1$ and $B$ > $B_2$. The horizontal line denotes value of saturation magnetization $M_{\mathrm{sat}}$ for $g$ factor $g$ $=$ 1.98 $\mu$${}_{\mathrm{B}}$ [19]].