Competing Ferri- and Antiferromagnetic Phases in Geometrically Frustrated ${\mathrm{LuFe}}_2{\mathbf{O}}_4$

We present a detailed study of magnetism in ${\mathrm{LuFe}}_2{\mathrm{O}}_4$, combining magnetization measurements with neutron and soft x-ray diffraction. The magnetic phase diagram in the vicinity of $T_N$ involves a metamagnetic transition separating an antiferro- and a ferrimagnetic phase. For both phases the spin structure is refined by neutron diffraction. Observed diffuse magnetic scattering far above $T_N$ is explained in terms of near degeneracy of the magnetic phases.

Figure 1

(a) $H$-$T$ phase diagram, which exhibits a PM, an AFM, and a fM phase, extracted from various $M(H)$ and $M(T)$ curves. The hysteretic region where either fM or AFM can be stabilized is hatched. Arrows across phase lines indicate for which measurement direction it is observed given the hysteresis. Spin structure in $C2/m$ cell [28] of the AFM (b) and fM phase (c). Gray arrows indicate bilayer net magnetization.

Figure 2

$T$ dependence of various properties, all measured on cooling. (a) Magnetization $M$, compared with another sample. Inset: Inverse susceptibility $H/M$ with Curie-Weiss fit (dashed blue line) from 450 to 750 K. (b) ac susceptibility measurement with different driving frequencies; the inset shows an enlarged area at $T_N$. (c) Integrated intensity of $(00\frac{3}{2})$ x-ray reflection at 706.4 eV (Fe $L_3$) and the $(\frac{1}{3}\frac{1}{3}0)$ neutron reflection, both in $H=0$. Inset: Energy scans across the Fe $L$ edges at $(00\frac{3}{2})$ with different incoming and outgoing polarization directions. (d) Integrated intensity for the $(\frac{1}{3}\frac{1}{3}\frac{3}{2})$ neutron reflection and $M(T)$, both in 2.5 T.

Figure 3

(a),(b) $M(H)$ curves. The measurement direction is indicated by arrows. Virgin curves are measured after cooling in $H=0$. (c),(d) Integrated intensity of different reflections in neutron diffraction (D23) vs $H$; compared with $M(H)$, in (c) only the intensity change to $I_0$ on structural reflections is illustrated.

Figure 4

(a) Neutron diffraction (N5) pattern at 220 K along the $(\frac{1}{3}\frac{1}{3}\ell )$ line in $H=2.5\mathrm{T}$ and in $H=0$. (b),(c) Integrated intensity for scans along $(\frac{1}{3}\frac{1}{3}\ell )$ in both magnetic phases corrected at 220 K as described in the text. The dashed line represents the result from the spin structures shown in Fig. 1 with the fitted domain population D1:D2:D3 and a Debye-Waller factor [28]. The gray area indicate the magnet dark angle and the red arrow a reflection affected by a second grain.

Figure 5

Reciprocal space map of the scattered intensity (logarithmic scale) in the $(hh\ell )$ plane by polarized neutrons in the spin flip channel (DNS) at different $T$.