Magnetocrystalline phase diagram of Tb: A triple line

Single crystalline terbium was examined employing both uniaxial and hydrostatic pressure. A temperature vs pressure phase diagram was compiled in both cases and, a three-dimensional magnetic phase diagram temperature vs crystalline lattice parameters was established employing a linear approximation. A triple line was obtained which separates paramagnetic, ferromagnetic, and helical antiferromagnetic phases. The temperature range where the helical antiferromagnetic phase exists is a nonlinear function of the strain. The complex magnetic states observed for Tb are interrelated with its band structure and Fermi surface shape.

Figure 1

Set of temperature dependencies of the mutual inductance, proportional to magnetic susceptibility $\chi \left(T\right)$, under uniaxial compression along the $c$ axis. Curves shifted vertically for clarity, onsets omitted. Pressures from top to bottom: 0, 120, 240, 360, 470, 590, 710, 830, 940, and $1060\text{bar}$. The arrows mark $T_N$, the magnetic ordering temperature, and $T_1$, the temperature when the sample converts to the ferromagnetic phase, dashed curves are guides to eye. Abbreviations: PM, paramagnetic; HAFM, helical antiferromagnetic; and FM, simple ferromagnetic phases.

Figure 2

Set of temperature dependencies of the resistivity measured in the basal plane under hydrostatic pressure. Curves shifted vertically for clarity. Pressures from bottom to top: 0, 4, 7.5, and $12\mathrm{kbar}$. Arrows mark $T_N$, the magnetic ordering temperature, and $T_1$, the temperature when the sample converts to the ferromagnetic phase. Abbreviations: PM, paramagnetic; HAFM, helical antiferromagnetic; and FM, simple ferromagnetic phases.

Figure 3

Tb magnetic phase diagrams under uniaxial tension and compression (a) and hydrostatic pressure (b) note the different pressure scales. Squares, Néel temperature $T_N$, under tension when open and under compression when solid. Circles, temperature of conversion to the ferromagnetic phase $T_1$, under tension when open and under compression when solid. Abbreviations: PM, paramagnetic; HAFM, helical antiferromagnetic; FM, simple ferromagnetic phases. Vertical dotted line: arrows mark the range where helical ordering occurs, equal for (a) and (b) plots. Vertical dashed line marks magnetic triple points [suggestion for the plot (b)].

Figure 4

Crystallomagnetic phase diagram for Tb. Solid circle, Tb under ambient pressure and Néel temperature. Straight arrows indicate the dependence of the lattice parameters on uniaxial and hydrostatic compression. Open circles correspond to magnetic triple points under uniaxial and hydrostatic compression, respectively. Dashed lines show the lines where the $c∕a$ ratio is constant as a reference (ratios indicated on the lines); the bold dashed line is a triple line, defined by two triple points, that separates the ranges of ferromagnetic (FM), and helical antiferromagnetic (HAFM) ordering. Insets: the two feasible shapes of the Fermi surface (double zone presentation), presumably separated by the triple line.

Figure 5

(Color online) 3D crystallomagnetic phase diagram for Tb viewed along the triple line (see text). Its projection on the $c\text{−}a$ plane is shown in Fig. 4. Solid circle, Tb under ambient pressure and Néel temperature, open circles correspond to the magnetic triple points under uniaxial and hydrostatic compression, respectively. Dashed lines mark the projections on the horizontal plane, bold dashed line marks the projection of the triple line. Abbreviations: PM, paramagnetic; HAFM, helical antiferromagnetic; FM, simple ferromagnetic phases.