Magnetic properties of the quasi two-dimensional centered honeycomb antiferromagnet ${\mathrm{GdInO}}_3$

The crystal structure and magnetic property of the single crystalline hexagonal rare-earth indium oxides ${\mathrm{GdInO}}_3$ have been studied by combing experiments and model calculations. The two inequivalent ${\mathrm{Gd}}^{3+}$ ions form the centered honeycomb lattice, which consists of honeycomb and triangular sublattices. The dc magnetic susceptibility and specific heat measurements suggest two antiferromagnetic phase transitions at $T_{\text{N1}}=2.3\mathrm{K}$ and $T_{\text{N2}}=1.02\mathrm{K}$. An inflection point is observed in the isothermal magnetization curve, which can be an indication of an up-up-down phase with a 1/3 magnetization plateau, further supported by our theoretical calculation. We also observe a large magnetic entropy change originated from the magnetic frustration in ${\mathrm{GdInO}}_3$. By considering a classical spin Hamiltonian, we establish the ground state phase diagram, which suggests that ${\mathrm{GdInO}}_3$ has a weak easy-axis anisotropy and is close to the equilateral triangular-lattice system. The theoretical ground-state phase diagram may be used as a reference in NMR, ESR, or $\mu \mathrm{SR}$ experiments in future.

Figure 1

(a) Observed (circles) and calculated (solid lines) XRD patterns at room temperature. The vertical bars in each panel mark the positions of nuclear Bragg reflections of ${\mathrm{GdInO}}_3$. The lower curves represent the difference between observed and calculated patterns. The inset shows the as-grown boule of ${\mathrm{GdInO}}_3$ single crystal. (b) The XRD pattern of as-grown single crystal along the [001] orientation. The inset shows the corresponding Laue photograph.

Figure 2

(a) Crystal structure ($P{6}_{3}cm$) with one unit cell of ${\mathrm{GdInO}}_3$. (b) Crystal structure with one unit cell of ${\mathrm{GdInO}}_3$ along the [010] projection; the curved dotted line represents the arclike alignment of two inequivalent atomic sites of Gd ions. The three planar oxygen ions (O3, O4, O4) are also labeled. (c) Two inequivalent atomic sites of Gd ions form the stuffed honeycomb lattice along the [001] projection. $J_1$ is the nearest neighbor (NN) spin coupling constant between Gd1 and Gd2; $J_2$ is the NN spin coupling constant between Gd2. The sublattice labels A and B represent Gd2 and C represents Gd1.

Figure 3

(a) Temperature-dependent magnetization for $\mathbf{H}\parallel c$ and H $\perp$ c of ${\mathrm{GdInO}}_3$ with ZFC process under 200 Oe. The inset shows an expansion of the magnetization over the temperature range 0 K to 16 K where magnetic transition $T_{\text{N1}}$ appears. (b) Inverse magnetic susceptibility ${\chi }^{-1}$ deduced from the ZFC magnetization. The dashed and dash-dotted lines are fit to the data with a CW law as described in the text.

Figure 4

(a) Isothermal magnetization curves for $\mathbf{H}\parallel c$ and H $\perp c$ obtained at 1.8 K. A very tiny loop of magnetization curve for $\mathbf{H}\parallel c$ is shown in the inset. (b) Isothermal magnetization curves for $\mathbf{H}\parallel c$ obtained at 1.8 K (black curves) and its first derivative $\mathrm{d}M/\mathrm{d}H$ (purple curves). The upper dotted line represents the saturation magnetic moment; the lower dotted line indicates the transitions close to 1/3 of $M_s$.

Figure 5

(a) Specific heat $C_p$ (solid circles) as a function of temperature in zero field and the Debye and Einstein terms for the lattice heat capacity fit (dash dot lines); the inset show the $C_p\left(T\right)$ curves of ${\mathrm{GdInO}}_3$ and ${\mathrm{EuInO}}_3$ in the low temperature range from 0.35 K to 30 K. (b) $C_p\left(T\right)/T$ curves of ${\mathrm{GdInO}}_3$ in the low temperature range from 0.35 K to 30 K. The two black arrows indicate the two successive magnetic phase transitions $T_{\text{N1}}$ and $T_{\text{N2}}$. The inset shows the full magnetic ions ${\mathrm{Gd}}^{3+}$ contribution to the entropy, as indicated by the blue dotted line positioned at R ln(8).

Figure 6

Isothermal magnetization curves obtained in the temperature range from 2 K to 50 K and under magnetic fields 0 to 9 T.

Figure 7

Temperature variation of magnetic entropy change $-\mathrm{\Delta }{S}_{\text{M}}$ for ${\mathrm{GdInO}}_3$ calculated from the magnetization data. The inset shows RC as a function of magnetic field.

Figure 8

(a) Ground state spin configurations at the selected points (triangles) in the $D>0$ region and (b) the ground state phase diagram in zero field. The states shown in (a) represent the parameter points indicated by triangles in panel (b). Phase 1 is (Phases 3 and 7 are) collinear in the $ab$ plane (along $c$). Other phases are noncollinear and coplanar; Phase 2 is (Phases 4–6 are) in the $ab$ plane (the plane including the $c$ axis). The 1–2, 3–4, 4–5, 6–7 transitions are second-order induced by softening of a magnon mode. The 3–7, 4–6, and 5–6 transitions are bridged by a high-symmetry line $J_1=J_2$. The 1–7, 2–5, and 2–6 transitions are bridged by another high-symmetry line $D=0$. The 4–5 boundary is evaluated numerically.

Figure 9

Magnetization processes for $\mathbf{h}\parallel c$ for $J_1<J_2$ with (a) $D/J_2=0.05$ (small easy-axis) and (b) $D/J_2=-0.05$ (small easy-plane). See the text for explanations about the schematic spin configurations.

Figure 10

Magnetization processes for $\mathbf{h}\parallel c$ for $J_1>J_2$ with (a) $D/J_2=0.05$ (small easy axis) and (b) $D/J_2=-0.05$ (small easy plane). See the text for explanations about the schematic spin configurations.

Figure 11

(a) Parameter regimes for realizing two distinct types of the (in)stability of the UUD-$C$ state (see the text). The triangles indicate the parameter set presented in Fig. 10 and panels (b) and (c) in this figure. (b) Low-field magnetization processes for $\mathbf{h}\parallel c$ for $(D/J_2,J_1/J_2)=(-0.15,1.9)$ and (c) the same for $(D/J_2,J_1/J_2)=(-0.30,1.9)$. See Fig. 10 for the spin state indices.

Figure 12

Magnetization processes for $\mathbf{h}\parallel a$ (or any direction of $\mathbf{h}\perp c$) for $J_1>J_2$ with (a) $D/J_2=0.05$ (small easy-axis) and $J_1<J_2$, (b) $D/J_2=-0.05$ (small easy-plane) and $J_1<J_2$, (c) $D/J_2=0.05$ and $J_1>J_2$, and (d) $D/J_2=-0.05$ and $J_1>J_2$. See the text for explanations about the schematic spin configurations.