Strain-induced multiferroicity in Cr1/3NbS2

TL;DR

This work demonstrates strain-induced multiferroicity in Cr1/3NbS2 by revealing an in-plane polar vector that emerges when a nonpolar spin-spiral is subjected to shear strain. It introduces magnetoelectric birefringence (MEB), a reflection-based optical probe that unambiguously detects polar order via a trilinear coupling between polarization and magnetic field, enabling spatial imaging of the polar state. Temperature-dependent MEB shows the polar order onset coinciding with the helimagnetic transition at $T_c \approx 127$ K, identifying Cr1/3NbS2 as a type-II multiferroic. Strain engineering further tunes the polarization direction and magnitude, with uniform and nonuniform strain patterns producing distinct polarization textures, highlighting a general route to strain-induced multiferroicity in noncollinear magnets and providing a powerful tool for studying polar order in metals and 2D systems.

Abstract

Multiferroic materials, in which electric polarization and magnetic order coexist and couple, offer rich opportunities for both fundamental discovery and technology. However, multiferroicity remains rare due to conflicting electronic requirements for ferroelectricity and magnetism. One route to circumvent this challenge is to exploit the noncollinear ordering of spin cycloids, whose symmetry permits the emergence of polar order. In this work, we introduce another pathway to multiferroic order in which strain generates polarization in materials that host nonpolar spin spirals. To demonstrate this phenomenon, we chose the spin spiral in the well-studied helimagnet Cr1/3NbS2. To detect the induced polarization, we introduce the technique of magnetoelectric birefringence (MEB), an optical probe that enables spatially-resolved and unambiguous detection of polar order. By combining MEB imaging with strain engineering, we confirm the onset of a polar vector at the magnetic transition, establishing strained Cr1/3NbS2 as a type-II multiferroic.

Figures (4)

• Figure 1: Relationship between spin configuration and polarization. Schematic of (a) spin cycloid, which gives rise to a polarization $\bm{P}$, and (b) a spin helix, which does not. (c) The helimagnetic ground state of a layered system of spins with an easy-plane anisotropy, with FM in-plane exchange and a competition between FM and DMI out-of-plane exchange, found by atomistic simulations. (d) Same as (c), but including shear strain $u_{yz}$. Helical order along the $z$ axis is maintained, but there is an additional in-plane cycloidal structure, giving rise to a polarization. The direction of polarization is set by $u_{yz}$, and is therefore the same in each plane, yielding a net polarization along $\hat{x}$. Gray and orange arrows indicate spin and polarization direction, respectively.
• Figure 2: Experimental setup and observation of magnetoelectric birefringence. (a) Schematic of experimental setup to measure MEB with the light-scattering plane and the polar order parameter both along the $x$-axis of the laboratory coordinate system ($\alpha=\theta = 0$ deg). (b) MEB measured in the geometry of (a) as a function of incident angle $\beta$. (c) Same as (a), but with the light-scattering plane rotated by 90 deg and perpendicular to the polar order parameter ($\alpha = 90$ deg and $\theta=0$ deg). (d) MEB measured in the geometry of (c) as a function of incident angle $\beta$. All the curves in (b) and (d) are measured under a 20 Oe oscillating magnetic field and at 10 K.
• Figure 3: Temperature dependence of MEB. Temperature dependence of (a) MEB amplitude and (b) extracted direction $\theta$ of the polar order parameter. The dashed line indicates the transition temperature of the helical spin order in Cr1/3NbS2. Inset shows the MEB signal measured at 10 K.
• Figure 4: Strain control of the polar order parameter. Schematic of sample mounting configuration to induce (a) uniform shear strain (configuration A) and (b) a strain distribution (configuration B), where the sample is mounted on a silicon nitride substrate with a hole. (c,d) Spatial maps of polar order parameter directions for configurations A and B respectively. The arrows indicate the direction of the polar order parameter. (e,f) Histogram of the orientations of the polar order across the maps in (c,d), respectively. (g,h) MEB amplitude along the white dashed lines in (c,d). In the inset of panel (g) we show one representative MEB measurement taken in configuration A.