Competition Between Multiferroic and Magnetic Soliton Lattice States in DyFeO$_3$

TL;DR

This study investigates the competition between an incommensurate Dy-domain-wall soliton lattice and a uniform ferroelectric state in DyFeO3. It combines high-resolution neutron diffraction, Monte-Carlo modeling of a $1D$ Ising-domain-wall system, and a free-energy framework with Lifshitz-type coupling to Fe and Dy moments under external fields. At zero field, Dy domain walls form a periodic soliton lattice with long-range interactions mediated by Fe magnons; applying a magnetic field along the c-axis suppresses the IC order and stabilizes a commensurate, ferroelectric state, while in-plane fields polarize Dy moments and drive a field-induced ferromagnetic state. The results show that an applied electric field can further manipulate the soliton lattice, leading to dimerization when both E and H fields are present, and they map a phase diagram with IC, FE1, and FE2 states, informing electric control of magnetism in multiferroics.

Abstract

Simultaneous breaking of time reversal and inversion symmetries in multiferroics couples ferroelectricity to magnetism and is a source of unusual physical phenomena that can be used in next-generation electronic devices. A notable example is DyFeO$_3$, which under applied magnetic fields exhibits a giant linear magnetoelectric response and a large spontaneous electric polarization induced by coexisting orders of Fe and Dy spins. Here, we use high-resolution neutron diffraction to show that at zero field DyFeO$_3$ hosts an incommensurate magnetic soliton lattice formed by spatially ordered Dy domain walls with an average domain size of 231(8) Å. The long-ranged interaction between the domain walls is mediated by magnons propagating through the Fe subsystem and is analogous to the Yukawa force in particle physics. An applied magnetic field destroys the long-ranged incommensurate order, unlocks the linear magnetoelectric response and stabilizes the ferroelectric state. The magnetic domain walls are electrically charged and the soliton array dimerizes when both electric and magnetic fields are applied. Numerical simulations with experimental parameters suggest, that the generic competition between the ferroelectric and incommensurate states can be effectively controlled by an applied electric field.

Figures (4)

• Figure 1: Formation of magnetic soliton lattice in DyFeO$_3$ (a,b) Crystal structure of DyFeO$_3$. Blue, red and black balls represent Dy, Fe and O ions, respectively. Green arrows in panel (b) demonstrate the ordering pattern of Dy moments in the $ab$-layer at zero field. (c) Neutron diffraction data measured along the $(0,0,l)$ direction at $T = 1.7$ and 3.5 K. The intensity is shown on a logarithmic scale. Red lines show the fitting results with the Monte-Carlo model as described in the main text. The absorption correction was included in the calculated curve. (d) Schematic field-temperature phase diagram of DyFeO$_3$wang2016simultaneous for $B \| c$. The blue and grey area correspond to $\Gamma_1$ and $\Gamma_4$ magnetic orders of the Fe subsystem, and the disordered state within the Dy subsystem. The violet area corresponds to the IC Dy order. The application of a magnetic field causes a spin reorientation of Fe moments, $\Gamma_1\rightarrow\Gamma_4$ and stabilizes a short-range commensurate Dy order (red area). (e) Visualization of the Ising axis directions of Dy$^{3+}$ moments. The axes lie within the $ab$-plane at $\pm29^{\circ}$ to the $b$-axis. (f,g) Temperature dependence of intensity (f) and IC parameter $\delta$ of the Dy order. (h) Sketch of the incommensurate magnetic structure of the Dy subsystem. Dy moments form an AFM structure with a domain size $L = \frac{c}{2\delta}$.
• Figure 2: Field-induced ferromagnetic state. (a) Field dependence of the neutron intensity measured along $(0,0,l)$ at $T = 1.7$ K with the magnetic field applied along the $b$-axis (easy axis of magnetization). The intensity is shown on a logarithmic scale. (b,c) Field dependence of the $\delta$ parameter (b) and peak intensity (c) obtained with the magnetic field ramped up (blue) and down (red). Yellow line in panel (c) demonstrates bulk magnetization from Ref. zhao2014ground measured at $T = 2$ K.
• Figure 3: Field-induced suppression of the soliton lattice and domain wall distribution. (a) Field dependence of the neutron intensity measured along $(0,0,l)$ at $T = 1.7$ K. The intensity is shown on a logarithmic scale with the magnetic field applied along the $c$-axis. (b-d) Representative scans along the $(0,0,l)$ direction taken at 3 T (b), 2 T (c) and 0.2 T (d) (dots represent the measured signal). The green lines are the absorption corrected fits to the data using the Monte Carlo model with the intensity shown on a logarithmic scale (Sec. xx of SM SM). (e) Mode, mean and full width half maximum (FWHM) of the pair distribution function (PDF) fitted for different fields. (f) Representative PDF extracted from our model of the data shown in panels (b-d).
• Figure 4: Origin of the incommensurate order and the phase diagram of DyFeO$_3$ (a) Three phases obtained by numerical minimization of the free energy density in applied electric and magnetic fields: the IC state (blue), the uniform ferroelectric state, FE$_1$ with $\sigma = 1$ and $0 < \phi < 90^{\circ}$ (grey), and the uniform ferroelectric state FE$_2$ (red) with Dy spins in the $\Gamma_5$-state and $\phi = 0$ ($\Gamma_4$ symmetry). (b) Magnetic field dependence of the electric polarization from Ref. tokunaga2008magnetic and calculated by our theory. (c-h) Coordinate dependence of the angle $\phi$ describing the direction of the Néel vector in the IC state (c,f), the sign change of the Dy order parameter $\sigma$ (d,g) and the electric polarization (e,h). Data are calculated for $H_0 = E_0 = 0$ (c-e) and $H_0 = 1.5$ T, $E_0 = 35$kV$\cdot$cm$^{-1}$ (f-h). The dashed line in the panels (c,f) show the average value of $\phi$. Distances are measured in units of the lattice constant $c$.