MULTIFERROICS

1. Introduction

Multiferroics are materials that combine two different ferroic ordering phenomena. Especially those showing simultaneous ordering of dipolar and magnetic degrees of freedom are remarkable, not only from an academic but also from a technological point of view. Due to the strong static and dynamic magnetoelectric effects characteristic of these multiferroics, they promise various applications, e.g., the current-free reading and writing in magnetic memory devices. When considering the conventional mechanisms of polar order, concomitant electrical and magnetic order in a single-phase material can be expected to be rare. Thus, in recent years, non-canonical mechanisms that can trigger polar order and multiferroicity have come into the focus of interest. Linear and non-linear dielectric spectroscopy are ideally suited to characterize the polar order and dipolar dynamics in multiferroics.

An overview of several classes of multiferroics investigated by us and others can be found in:

2. Examples:

a) Multiferroicity in an organic charge-transfer salt: Electric-dipole driven magnetism

We found the simultaneous occurrence of magnetic ordering and ferroelectricity in a two-dimensional organic charge-transfer salt, namely κ-(BEDT-TTF)₂Cu[N(CN)₂]Cl (κ-Cl), where BEDT-TTF stands for bis(ethylenedithio)-tetrathiafulvalene [7]. This represents the first example of multiferroicity within this interesting group of materials. In addition, it is one of the few examples of electronic ferroelectricity, where ferroelectric ordering is based only on electronic degrees of freedom. Moreover, and most interestingly, we found clear hints for a new mechanism of multiferroicity: In this material, ferroelectric ordering seems to break geometric spin frustration, thus triggering magnetic order. Therefore, here the ferroelectric order drives magnetic order, just the opposite case to what is observed in the famous multiferroics with helical spin order (e.g., TbMnO₃) where a spin-driven mechanism induces ferroelectricity.

Temperature dependence of the dielectric constant of κ-Cl, for various frequencies. The behaviour is typical for order-disorder type ferroelectricity, setting in below about 25 K. [from: P. Lunkenheimer et al., Multiferroicity in an organic charge-transfer salt that is suggestive of electric-dipole driven magnetism , Nature Mater. 11, 755 (2012).]

b) Skyrmions carrying electric polarization

As discovered in our group [Kézsmárki et al., Nat. Mater. 14, 1116 (2015)], GaV₄S₈, a member of the lacunar-spinel family, reveals the formation of a Néel-type SkL (see figure below). This material is the first bulk system hosting this type of skyrmions and only the second example of an insulating skyrmion system. It exhibits a complex magnetic phase diagram and undergoes a structural phase transition where orbital degeneracy is lifted. Moreover, GaV₄S₈ exhibits non-canonical ferroelectricity driven by orbital order and spin-driven excess polarization was detected in all magnetic phases of this material [10]. Overall, GaV₄S₈ has four different multiferroic phases!

Most importantly, we found that the Néel type skyrmions in GaV₄S₈, in addition to their uncommon topology, also are dressed with ferroelectric polarization with strong spatial modulation in the vicinity of the skyrmion cores (see figure below) [10]. This might enable the manipulation of magnetic skyrmions by electric fields and our findings represent a first important step in the development of skyrmion-based memory devices, employing the nondissipative electric-field control of magnetic vortices.

Spin texture of a Néel skyrmion (upper part) and associated polarization pattern (lower part). [after: E. Ruff, S. Widmann, P. Lunkenheimer, V. Tsurkan, S. Bordács, I. Kézsmárki, and A. Loidl, Multiferroicity and skyrmions carrying electric polarization in GaV4S8, Science Advances 1, e1500916 (2015).]

c) Magnetite

Magnetite is famous for being the first magnetic material known to mankind and for showing the Vervey transition, a metal-insulator transition of so far unknown origin, which is believed to be closely related to the occurrence of charge order. Moreover, indications for even another startling property of magnetite were found, namely the occurrence of ferroelectricity, which would make this material a multiferroic [see, e.g., Rado/Ferrari, Phys. Rev. B 12, 5166 (1975) and Miyamoto et al., Solid State Commun. 89, 51 (1994)]. Interestingly, for the generation of ferroelectricity in magnetite an exotic charge-order driven mechanism was shown to be applicable [see D.I. Khomskii, J. Mag. Mag. Mat. 306, 1 (2006)].

Temperature dependence of the dielectric constant of magnetite for various frequencies obtained with silver-paint (symbols) and sputtered gold contacts (lines). Comparing both data sets reveals electrode-dominated behaviour at high temperatures and an intrinsic nature of the results at low temperatures (T<40K). The frequency-dependent maxima at low temperatures show a behaviour, characteristic of relaxor ferroelectricity. [from: F. Schrettle, S. Krohns, P. Lunkenheimer, V.A.M. Brabers, and A. Loidl, Relaxor ferroelectricity and the freezing of short-range polar order in magnetite, Phys. Rev. B 83, 195109 (2011).]

However, a thorough characterization of the dielectric properties of magnetite is still missing and, thus, we have performed a detailed investigation of high-quality single-crystals using dielectric spectroscopy in a broad frequency and temperature range [5]. Indeed, we found convincing evidence for ferroelectric ordering in magnetite. However, quite unexpectedly our results reveal that the ferroelectricity of magnetite is not of simple canonic nature but shows the typical characteristics of so-called relaxor-ferroelectrics where the dipolar ordering is of short-range nature only (see figure above). Most importantly, our investigations lead to the surprising conclusion that the dipolar dynamics in magnetite, which in contrast to most other relaxor ferroelectrics is of electronic instead of ionic nature, slows down in a glasslike manner and finally becomes dominated by tunneling at low temperatures [5]. Thus, here we have electron dynamics reaching timescales as slow as 100s and exhibiting a glass transition at about 15 K. This new exotic ground state can be regarded as a new state of matter, a true "electron glass".

3. Some relevant publications from our group: