Magnetization dynamics and frustration in the multiferroic double perovskite ${\mathrm{Lu}}_2{\mathrm{MnCoO}}_6$

We investigate the magnetic ordering and the magnetization dynamics (from kHz to THz time scales) of the double perovskite ${\mathrm{Lu}}_2{\mathrm{MnCoO}}_6$ using elastic neutron diffraction, muon spin relaxation, and micro-Hall magnetization measurements. This compound is known to be a type II multiferroic with the interesting feature that a ferromagneticlike magnetization hysteresis loop couples to an equally hysteretic electric polarization in the bulk of the material despite a zero-field magnetic ordering of the type $\uparrow \uparrow \downarrow \downarrow$ along Co-Mn spin chains. Here we explore the unusual dynamics of this compound and find extremely strong fluctuations, consistent with the axial next-nearest-neighbor Ising (ANNNI) model for frustrated spin chains. We identify three temperature scales in ${\mathrm{Lu}}_2{\mathrm{MnCoO}}_6$ corresponding to the onset of highly fluctuating long-range order below $T_N=50\pm 3$ K identified from neutron scattering, the onset of magnetic and electric hysteresis, with change in kHz magnetic and electric dynamics below a 30 K temperature scale, and partial freezing of $\sim \mathrm{MHz}$ spin fluctuations in the muon spin relaxation data below $12\pm 3$ K. Our results provide a framework for understanding the multiferroic behavior of this compound and its hysteresis and dynamics.

Figure 1

Elastic neutron scattering data for $T=1.6$ and 75 K. $\lambda =4.217$ Å. The lines show Gaussian fits to the peaks. The ticks underneath the data indicate the symmetry-allowed nuclear (top row) and magnetic (bottom row) Bragg positions. The $\left\{110\right\}$ and $\left\{002\right\}$ peaks are also labeled on the graph. The broad peak labeled as ICAFM (incommensurate antiferromagnetism) contains contributions from multiple magnetic peaks. Table 1 lists the magnetic Bragg peaks corresponding to the bottom row of tick marks.

Figure 2

The temperature dependence of the integrated intensity of the neutron diffraction peak, shown in Fig. 1, near $70.{70}^{\circ }$ [ICAFM (a)] and the temperature dependence of the intensity of the elastic scattering at $68.{82}^{\circ }$ (b). The integrated intensity of the $70.{70}^{\circ }$ peak was determined from fits to a broad Gaussian line shape. The dashed lines are guides to the eye, which have been drawn with $T_{\mathrm{N}}=50$ K.

Figure 3

Zero field ${\mu }^{+}\mathrm{SR}$ spectra showing the asymmetry in muon detection rates as a function of time, plotted here for temperatures of $T=$ 1.5, 30, and 50 K.

Figure 4

Temperature dependences of the ${\mu }^{+}\mathrm{SR}$ asymmetry $A(t=0)$, and the quantities $\lambda , \mathrm{\Lambda }$, and $A_{\mathrm{bg}}$ extracted from fits to the $\mu \mathrm{SR}$ spectra, as described in the text.

Figure 5

(a) Single crystal cluster positioned on a Hall sensor with $10\times 10\mu {\mathrm{m}}^2$ active area (blue square). The crystal cluster is extracted from a polycrystal shown in the inset. (b) Zoomed-in picture showing the sample morphology. (c) Sample's stray field measured by the Hall sensor $\langle B_{\mathrm{z}}\rangle$ for $T$ between 7.5 and 20 K for $H_{\parallel }$ sensor plane (predominantly $H\parallel c$) and (d) for $H_{\perp }$ sensor plane (predominantly $H\perp c$). (e) Hysteresis loop at $T=0.3$ K for $H_{\parallel }$. (f) Coercive magnetic field $B_c$ vs temperature $T$ for $H_{\perp }$ the sensor plane, showing a peak that is labeled $T_f$.

Figure 6

$T$ dependence of different measured properties of ${\mathrm{Lu}}_2{\mathrm{MnCoO}}_6$, showing three temperature scales: $T_N, T_H$, and $T_f$. (a) shows $M\left(T\right)$ after zero-field cooling (ZFC) and field cooling (FC) in ${\mu }_{0}H=0.1$ T, as well as $\mathrm{\Delta }P=P({\mu }_{0}H=0T)-P({\mu }_{0}H=15T)$ [9]. (b) ac magnetic susceptibility at 10 Hz, 100 Hz, and 1 kHz, (c) dielectric constant ${\epsilon }_r$ measured for $H\left|\right|E$ with a static ${\mu }_{0}H$ of 0 and 14 T and a small oscillating $H$ at 10 kHz, (d) $T$ dependence of the ICAFM peak at $70.{70}^{\circ }$ in the neutron scattering for ${\mu }_{0}H=0$, (e) $T$ dependence of $A(t=0)$ and $A_{bg}$ from $\mu \mathrm{SR}$ measurements, as described in the text, and (f) $T$ dependence of the coercive magnetic field $B_c$ for $H_{\perp }$ from micro-Hall measurements.