Figure 1

Antiferromagnetic ${\mathrm{Fe}}^{3+}$ clusters with projections of $⟨111⟩$-oriented spins viewed in (001) cross sections of PFN at different scales.Reuse & Permissions

Figure 2

Magnetic moment $m$ vs $T$ of PFN(001) obtained on ZFC/FH (curve 1), on FC (curve 2) with ${\mu }_{0}H=0.1\mathrm{T}$, and on ZFH as TRM (curve 3) (inset: low-$T$ data magnified) (left-hand ordinate). Magnetoelectric moment $m_{\mathrm{ME}}^{\prime }$ vs $T$ obtained with $E_{\mathrm{ac}}=12.5\mathrm{kV}/\mathrm{m}$ on ZFC/FH in ${\mu }_0{H}_{\mathrm{dc}}=0.2\mathrm{T}$ and $E_{\mathrm{dc}}=0$ (curve 4, open circles) or $50\mathrm{kV}/\mathrm{m}$ (curve 5, solid squares) (right-hand ordinate). $T_N$ and the dominance of the AF, SAF, and CG “phases” are indicated.Reuse & Permissions

Figure 3

(a) ac susceptibility ${\chi }^{\prime }$ vs $T$ measured with ${\mu }_0{H}_{\mathrm{ac}}=0.4\mathrm{mT}$ at frequencies $f=0.01$, 0.031, 0.1, 0.316, 1, 3.16, 10, 31.6, 100, 316, and 1000 Hz. (b) $f$ dependence of the peak temperature ($T_m$) of ${\chi }^{\prime }$ ($T$) taken from (a), plotted as $\ln (f/\mathrm{Hz})$ vs $T_m$, and fitted by a critical power law (solid line). (c) $\Delta m=m_{\mathrm{wait}}^{\mathrm{ZFC}}-m_{\mathrm{ref}}^{\mathrm{ZFC}}$ vs $T$ obtained on FH in ${\mu }_{0}H=0.1\mathrm{T}$ after ZFC from $T=200$ to 4.5 K and waiting for $\Delta t={10}^4$ and 0 s, respectively, at $T_w=7\mathrm{K}$. (d) de Almeida–Thouless phase boundary approximated by $T_{\max }(H)$ (see arrow in Fig. 2, inset) vs $({\mu }_{0}H{)}^{2/3}$ after ZFC to 4.5 K. (e) Relaxation of $M_R/H$ vs $t$ at $T=5\mathrm{K}$ after FC in ${\mu }_0{H}_{\mathrm{dc}}=0.01$, 1, and 5 T, best-fitted to stretched exponentials, Eq. (4). (f) ME moment, $m_{\mathrm{ME}}^{\prime }$ vs $T$, obtained with $E_{\mathrm{ac}}=25\mathrm{kV}/\mathrm{m}$ after FC from $T=160$ to 4.5 K on FH in ${\mu }_0{H}_{\mathrm{dc}}=+2$ (upper curve), 0 (middle curve), and $-2\mathrm{T}$ (lower curve), and $E_{\mathrm{dc}}=0$ (solid curve) and $100\mathrm{kV}/\mathrm{m}$ (open symbols).Reuse & Permissions