Spin reorientation and magnetoelastic properties of ferromagnetic $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ systems with a morphotropic phase boundary

The spin reorientation (SR) and magnetoelastic properties of pseudobinary ferromagnetic $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ ($0\le x\le 1.0$) systems involving a morphotropic phase boundary (MPB) were studied by high-resolution synchrotron x-ray diffraction (XRD), magnetization, and magnetostriction measurements. The easy magnetization direction of the Laves phase lies along the $\langle 111\rangle$ axis with $x<0.65$, whereas it lies along the $\langle 100\rangle$ axis for $x>0.65$ below Curie temperature ($T_{\mathrm{C}}$). The temperature-dependent magnetization curves showed SR; this can be explained by a two-sublattice model. Based on the synchrotron (XRD) and magnetization measurements, the SR phase diagram for a MPB composition of $\mathrm{T}{\mathrm{b}}_{0.35}\mathrm{N}{\mathrm{d}}_{0.65}\mathrm{C}{\mathrm{o}}_2$ was obtained. Contrary to previously reported ferromagnetic systems involving MPB, the MPB composition of $\mathrm{T}{\mathrm{b}}_{0.35}\mathrm{N}{\mathrm{d}}_{0.65}\mathrm{C}{\mathrm{o}}_2$ exhibits a low saturation magnetization ($M_{\mathrm{S}}$), indicating a compensation of the Tb and Nd magnetic moments at MPB. The anisotropic magnetostriction (${\lambda }_{\mathrm{S}}$) first decreased until $x=0.8$ and then continuously increased in the negative direction with further increase of Nd concentration. The decrease in magnetostriction can be attributed to the decrease of spontaneous magnetostriction ${\lambda }_{111}$ and increase of ${\lambda }_{100}$ with opposite sign to ${\lambda }_{111}$. This paper indicates an anomalous type of MPB in the ferromagnetic $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ system and provides an active way to design novel functional materials with exotic properties.

Figure 1

Synchrotron XRD patterns (typical 222, 440, and 800 peaks) of $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ for $x=0$, 0.5, 0.65, 0.7, and 1.0 with a wavelength of 0.11725 Å at (a) 300 K and (b) 90 K.

Figure 2

Composition dependence of magnetostriction coefficients ${\lambda }_{111}$ and ${\lambda }_{100}$ for $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$. The yellow shaded area corresponds to MPB.

Figure 3

ZFC and FC temperature dependence of magnetization (M-T) curves of the $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ system ($x=0$, 0.3, 0.5, 0.6, 0.65, 0.7, 0.8, and 1.0) measured under an applied magnetic field of 500 Oe.

Figure 4

SR diagram of $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ with cubic, rhombohedral, tetragonal, and orthorhombic crystal symmetries. Blue balls, red stars, and purple triangles denote the $T_{\mathrm{C}}$ points, synchrotron XRD data, and $T_{\mathrm{SR}}$, respectively, while the blue dotted line shows the phase boundary between rhombohedral and tetragonal phases. Regions I, II, and III are deduced from the analysis of the results of synchrotron XRD data, and region IV is expected from the temperature dependence of magnetization. The inset on the right-hand side shows a schematic description of the SR process in R phase, T phase, and O phase and at MPB.

Figure 5

Magnetic measurements. (a) The magnetization vs magnetic field (M-H) hysteresis loops for $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ at 90 K under an applied magnetic field of 0.8 and 12 kOe. Zoom hysteresis loops are shown in the insets. (b) Composition dependence of saturation magnetization ($M_{\mathrm{S}}$), coercive fields ($H_{\mathrm{C}}$), and magnetic anisotropy constant ($K_1$). The yellow shaded area in Fig. 5 corresponds to the critical composition of MPB.

Figure 6

Magnetostrictive measurements. (a) Magnetostriction (${\lambda }_{\mathrm{S}}$) for polycrystalline $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ alloys at 90 K under an applied magnetic field of 10 kOe. (b) Composition dependence of the ratio ${\lambda }_{\mathrm{S}}/K_1$ for the $\mathrm{T}{\mathrm{b}}_{1-x}\mathrm{N}{\mathrm{d}}_x\mathrm{C}{\mathrm{o}}_2$ system.