Phase transitions in single-crystalline magnetoelectric LiCoPO${}_4$

Specific heat, magnetic torque, and magnetization studies of LiCoPO${}_4$ olivine are presented. They show that a unique set of physical properties of LiCoPO${}_4$ leads to the appearance of features characteristic of two-dimensional Ising systems near the Néel temperature $T_N$ = $21.6$ K and to the appearance of an uncommon effect of the influence of a magnetic field on the magnetocrystalline anisotropy. The latter effect manifests itself as a first-order transition, discovered at $\sim$9 K, induced by a magnetic field of 8 T. The physical nature of this transition was explained, and a model describing experimental dependences satisfactorily was proposed.

Figure 1

Orthorhombic (Pnma) olivine structure of LiCoPO${}_4$. Three unit cells ($a$ = 10.20 Å, $b$ = 5.92 Å, and $c$ = 4.70 Å) stacked along the $b$ axis are presented. Starting from the lowest one, they show, respectively, oxygen coordinations of Co (octahedral), Li (octahedral), and P (tetrahedral) ions, examples of strong Co–O–Co and weak Co–O–P–O–Co superexchange couplings, and the antiferromagnetic ordering of magnetic moments of the Co ions.

Figure 2

Specific heat of LiCoPO${}_4$. (a) Temperature dependence of the total specific heat in zero magnetic field $B$. Inset shows the $\lambda$ anomaly near the Néel temperature $T_N$. The parameters $p=1.31\times {10}^{-4}$ J/(mole K${}^4$) and $q=-1.06\times {10}^{-8}$ J/ (mole K${}^6$) determine the lattice contribution. (b) Magnetic contribution to the specific heat $C_m$ as a function of temperature, measured on heating, in $B$ parallel to the $b$ axis. Curves for different $B$ values are shifted along the $C_m$ axis by the values given in parentheses. Inset shows the dependence of $T_N$ on $B$ (experimental points and fitted parabola). The solid lines present logarithmic dependences fitted to the experimental data near $T_N$. (c) $C_m-Q^{\pm }$ vs $\ln \left(\tau \right)$, $\tau =|T-T_N|/T_N$. Solid lines are linear approximations valid for $\sim e^{-5}<\tau <\sim e^{-0.6}$ above and below $T_N$.

Figure 3

Magnetic contribution to the specific heat of LiCoPO${}_4$, $C_m$, measured on heating and on cooling. Curves for different magnetic field values are shifted along the $C_m$ axis by the values given in parentheses. (a) Lack of hysteresis around $T_N$. (b) Thermal hysteresis near $T=9$ K for $B=9$ T.

Figure 4

Field-induced first-order phase transition. Curves in panels (a) and (b) are shifted along the $y$ axes by the values given in parentheses. (a) Magnetic specific heat vs temperature. For $B⩾8$ T, the anomaly at $\sim$9 K is visible. Vertical blue and red arrows indicate the temperatures at which torque was measured. Solid lines present the calculated magnon contributions. The insets show experimental (circles) and fitted theoretical (solid lines) dependences of two parameters appearing in Eq. (3), $a_1$ [in J/(mole K${}^{1/2}$)] and $a_2$ (in K), on $B$. (b) Magnetic torque for $\mathbf{B}$ rotating within the b-c plane ($\theta$ is counted from the $b$ axis). Curves plotted with full and open symbols were measured for $\mathbf{B}$ rotating in opposite directions. Dependences calculated within the proposed model (solid lines) are superimposed on the experimental curves. (c) Outline of the proposed two-sublattice model of the magnetic structure. (d) Superimposed magnetic torque dependences measured at $T=9$ and 12 K. The oblique arrows indicate directions along which the torque maximum moves with increasing $B$ at $T=9$ and 12 K.

Figure 5

Magnetization of LiCoPO${}_4$ along the $b$ axis, measured in the magnetic field applied along the $b$ axis. (a) Magnetization in $B=9$ T (and its derivative with respect to $T$) as a function of temperature. (b) Magnetizations at $T=9$ and 10 K (and their derivatives with respect to $B$) as a function of the magnetic field. Solid line superimposed on the experimental dependence for 9 K was calculated within the two-sublattice model proposed.

Figure 6

Molecular field approximation for a standard ferromagnet. Red curve presents the Brillouin function. Straight solid line presents the case of zero external field. The dash-dot and dashed lines show, respectively, the cases of the external field applied along and against the molecular field.

Figure 7

Coordinate system and the symbols used.