NON-CANONICAL FERROELECTRICITY

1. Introduction

Ferroelectricity, the parallel ordering of electrical dipoles below a phase transition temperature in specific materials, is a fascinating physical phenomenon and has a long history of investigation in our group [1-3]. It also plays an important role in many areas of modern technology (e.g., non-volatile data storage). In conventional ferroelectrics, this polar order is caused by the displacement of ions or the ordering of permanent dipolar moments, arising at a structural phase transition. However, in recent years non-canonical ferroelectricity mechanisms have come into the focus of interest, especially as they often favour the generation of multiferroic states. Generally, the investigation by dielectric spectroscopy of the dipole fluctuations occurring in most ferroelectrics, can help achieving a thorough understanding of the microscopic mechanisms governing this ordering phenomenon. As discussed below, in recent years we have concentrated on orbital-order-driven, spin-driven, and charge-order-driven ferroelectricity, often also leading to multiferroic states. Moreover, antiferroelectrics, which are only rarely investigated by dielectric spectroscopy, have also come into the focus of our interest [21].

Here are some overview articles from us on various classes of ferroelectrics:

2. Dielectric properties of ferroelectrics

Ferroelectrics reveal specific signatures in their frequency- and temperature-dependent dielectric properties which allows for their classification according to the microscopic mechanisms generating the ferroelectric polarization. Moreover, in order-disorder and relaxor ferroelectrics, information on the dipolar dynamics can be obtained. They can be roughly divided into three classes:

1.	Displacive ferroelectrics, where the dipoles are generated below the ferroelectric transition. They show negligible frequency dependence in the dielectric frequency range.
2.	Order-disorder ferroelectrics, where the dipoles already exist above the transition. Their characteristic dynamics then can be investigated by dielectric spectroscopy.
3.	Relaxor ferroelectrics with a smeared-out diffusive phase transition, ascribed to nanoscale, clusterlike polar ordering. Their dielectric spectra reveal strong relaxation behaviour.

The figure below shows the behaviour of the dielectric constant, characteristic of these three material classes.

(a) - (c) Schematic plots of the dielectric constant ε'(T) of materials belonging to the three classes of ferroelectrics as typically detected by dielectric spectroscopy. The different lines represent ε'(T) at different frequencies. The peaks mark the transition into the ferroelectric state (not well defined for relaxors). Frames (d) - (f) show ε'(T) of three multiferroics (LiCuVO4 [6], κ-(BEDT-TTF)2Cu[N(CN)2]Cl [10] and Fe3O4 [8], respectively), representing corresponding experimental examples. [from: S. Krohns and P. Lunkenheimer, Ferroelectric polarization in multiferroics, Phys. Sci. Rev. 4, 20190015 (2019).]

3. Examples

a) Orbital-order driven ferroelectricity

Orbital order and ferroelectricity are usually decoupled. However, in few materials orbitally-driven ferroelectricity was found to arise upon their Jahn-Teller transitions: Here ferroelectricity is triggered by the orientational ordering of orbitals, dumbbell-shaped clouds of electrons around an atom (see figure below). We investigated orbitally-driven ferroelectricity in several lacunar spinels [9,12,13,17,23,24]. For example, in GaV₄S₈, by combining THz and MHz-GHz spectroscopy, for the first time we succeeded in measuring the coupled orbital and dipolar fluctuations expected in this new type of ferroelectrics (see figure below) [12]. We found highly non-canonical behaviour of the detected dynamics, which helps unravelling the nature of orbital-order driven ferroelectricity and the intriguing entanglement between the polar and orbital dynamics.

Temperature-dependent dielectric loss of an orbital-order driven ferroelectric at frequencies 0.5 - 2.5 THz [12]. There is a dramatic change at the simultaneous orbital and ferroelectric phase transition at 44 K. There, the orbitals of the vanadium atoms (shown in red) order, the V4 tetrahedra in the crystalline structure become elongated, and ferroelectric polarization arises. This is accompanied by an astonishing slowing down of the relaxation time, characterizing the orbital and dipolar fluctuations, by about five orders of magnitude (see inset). [from: Z. Wang, E. Ruff, M. Schmidt, V. Tsurkan, I. Kézsmárki, P. Lunkenheimer, and A. Loidl, Polar dynamics at the Jahn-Teller transition in ferroelectric GaV4S8, Phys. Rev. Lett. 115, 207601 (2015).]

b) Spin-driven ferroelectricity

"Spin-driven" means that the polar order is triggered by the ordering of the spins, e.g., in a ferromagnetic phase. In addition to orbital-order driven ferroelectricity, several lacunar-spinel systems mentioned above also exhibit spin-driven polar order [9,13]. This we investigated in detail in GaV₄S₈ [9]. We found that all its magnetic phases (ferromagnetic, cycloidal and skyrmion lattice) reveal spin-driven excess polarization (see figure below) indicating polar order.

Spin-driven excess polarization at the magnetic transitions in GaV4S8 [9]. The polarization reveals a steplike increase at the transitions from the cycloidal to the skyrmion phase and from the skyrmion to the ferromagnetic phase. [from: 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).]

Another example are the spin-driven polar states in LiCuVO₄, where we found evidence for a vector-chiral state with ferroelectric polarization [18]. In vector-chiral phases, predicted long ago, the twist direction (clock- or counter clock-wise) between neighboring spins is ordered, while the angles between adjacent spins are disordered. Our findings represent the long-sought experimental proof for this kind of phase. It is the spin twist in the vector-chiral phase of LiCuVO₄ that induces ferroelectricity.

c) Charge-order driven ferroelectricity

In a variety of materials, charge ordering can also induce ferroelectricity [van den Brink and Khomskii, J. Phys.: Condens. Matter 20, 434217 (2008)] as schematically indicated in the figure below. It shows a 1D chain with complete charge order (CO). If CO is accompanied by dimerization, a net polarization appears.

Schematic representation of CO without dimerization, not leading to polar order (a), and of CO accompanied by dimerization, generating a net polarization (b). The arrows indicate the individual dipolar moments, which do not compensate for case (b). [from: P. Lunkenheimer and A. Loidl, Dielectric spectroscopy on organic charge-transfer salts, J. Phys.: Condens. Matter 7, 373001 (2015).]

Charge order is found in several transition-metal compounds, with the Verwey transition in magnetite being the most prominent example [8], but it is also often observed in low-dimensional organic compounds. We have investigated this phenomenon in various organic charge-transfer salts [10,11,16,25]. For example, we found the simultaneous occurrence of magnetic ordering and ferroelectricity in κ-(BEDT-TTF)₂Cu[N(CN)₂]Cl (κ-Cl), where BEDT-TTF stands for bis(ethylenedithio)-tetrathiafulvalene [10]. This is one of the few examples where ferroelectric ordering is based only on electronic degrees of freedom. Interestingly, in this material ferroelectric ordering seems to break geometric spin frustration, thus triggering magnetic order and making the material multiferroic. Therefore, here the ferroelectric order drives magnetic order, which is just the opposite to the spin-driven ferroelectricity found in many multiferroics.

For κ-Cl, the existence of CO is quite controversial. We thus have investigated a related system with well-established CO, κ-(BEDT-TTF)₂Hg(SCN)₂Cl (short: κ-Hg). Indeed, we found CO-driven electronic ferroelectricity in κ-Hg, too [16], corroborating the validity of the new multiferroicity mechanism proposed by us for κ-Cl [10].

4. Some relevant publications from our group