Morphotropic Phase Boundaries in Ferromagnets: ${\mathrm{Tb}}_{1-x}{\mathrm{Dy}}_x{\mathrm{Fe}}_2$ Alloys

The structure and properties of the ferromagnet ${\mathrm{Tb}}_{1-x}{\mathrm{Dy}}_x{\mathrm{Fe}}_2$ are explored through the morphotropic phase boundary (MPB) separating ferroic phases of differing symmetry. Our synchrotron data support a first order structural transition, with a broadening MPB width at higher temperatures. The optimal point for magnetomechanical applications is not centered on the MPB but lies on the rhombohedral side, where the high striction of the rhombohedral majority phase combines with the softened anisotropy of the MPB. We compare our findings with single ion crystal field theory and with ferroelectric MPBs, where the controlling energies are different.

Figure 1

Phase diagram of ${\mathrm{Tb}}_{1-x}{\mathrm{Dy}}_x{\mathrm{Fe}}_2$ (TDF). The background shading shows the magnetic easy-axis direction calculated using anisotropy parameters from crystal field theory (see text). The easy axis reorients from $⟨111⟩$ for ${\mathrm{TbFe}}_2$ to $⟨001⟩$ for ${\mathrm{DyFe}}_2$. Overlayed is the morphotropic phase boundary determined from our synchrotron XRD (dotted lines) and magnetometry (solid line) measurements, as well as the easy axes reported previously from Mössbauer spectroscopy (open symbols) [11]. The cross in a circle indicates the optimal temperature ($40°\mathrm{C}$) for magnetomechanical device applications, as determined for TDF $x=0.73$ [12].

Figure 2

Contour plots showing the temperature dependence of the diffracted synchrotron x-ray intensity in the vicinity of the 440 Bragg reflection across a series of ${\mathrm{Tb}}_{1-x}{\mathrm{Dy}}_x{\mathrm{Fe}}_2$ compositions (a) $x=0.65$, (b) $x=0.70$, (c) $x=0.725$, (d) $x=0.75$, and (e) $x=0.78$. The solid white triangles in (a), (b), and (c) depict the sample magnetization $M$ in an applied field of $7.96\mathrm{kA}{\mathrm{m}}^{-1}$. Each $M(T)$ curve has its maximum highlighted by an arrow.

Figure 3

(a) Typical profile fits of ${\mathrm{Tb}}_{1-x}{\mathrm{Dy}}_x{\mathrm{Fe}}_2$ synchrotron XRD data. Here profiles for $x=0.70$ in the vicinity of the cubic 440 Bragg reflection are shown, at temperatures where two structures coexist: the left (right) panel reveals a 25% (75%) rhombohedral phase fraction from Gaussian peak fits. The outer peaks (red lines) correspond to the rhombohedral phase, the inner peak (green line) to the cubic fit. The blue lines underneath show the difference plots. (b) Temperature dependences across the MPB for $x=0.65$: (top panel) phase fractions from the fitted peak intensities; (middle panel) magnetization $M(T)$ measured in an applied field of $7.96\mathrm{kA}{\mathrm{m}}^{-1}$; (bottom panel) ordered atomic moment determined by neutron diffraction. Dashed lines are guides to the eye.

Figure 4

Theoretical behavior across the phase boundary using the single ion crystal field model (see text). Selected ${\mathrm{Tb}}_{1-x}{\mathrm{Dy}}_x{\mathrm{Fe}}_2$ compositions are shown. The calculated easy-axis directions are found to be of $⟨uuv⟩$ type; the solid lines (bottom panel) describe the angle of the easy axis from $⟨001⟩$. The dotted lines (top panel) show the calculated magnetization at $7.96\mathrm{kA}{\mathrm{m}}^{-1}$.