Monday, January 30, 2017

The challenge of multiferroism in organic Mott insulators

A theoretical picture of the Mott insulating phase of organic charge transfer salts [such as (BEDT-TTF)2X] is that they can be described by a single-band Hubbard model on an anisotropic triangular lattice at half filling. The spin excitations can then be described by the corresponding Heisenberg model. In these models, each lattice site corresponds to a single anti-bonding orbital on a pair (dimer) of BEDT-TTF molecules. Thus the internal structure of the dimer and the corresponding two-band Hubbard model at three-quarters filling is "integrated out" leaving a one-band picture.

However, there are some dielectric relaxation experiments that can be interpreted as inconsistent with the picture above.
The key question is whether there is charge order within the dimer, in particular, does it have a net dipole moment?
A 2010 theory paper by Hotta proposed this and an effective Hamiltonian for the Mott insulating phase where the spin on the dimer and the dipoles are coupled together. She suggested that a spin liquid phase could be driven by the dipoles, rather than spin frustration.
This picture also leads to the possibility of a multiferroic phase: coexisting ferromagnetic and ferroelectric phases.

There are two helpful recent reviews, presenting alternative views of the experiments.

Dielectric spectroscopy on organic charge-transfer salts
P Lunkenheimer and A Loidl

Ferroelectricity in molecular solids: a review of electrodynamic properties 
S Tomić and M Dressel

The figure below shows experimental measurements from this paper. (The authors of the first review above and Hotta are co-authors.) The figure shows the temperature dependence of the real part of the dielectric constant at different frequencies. Note how it becomes very large at low frequencies (almost static) near about 25 K, which coincidentally is the temperature at which this organic charge transfer salt becomes antiferromagnetic (with weak ferromagnetism due to spin canting).

The above dielectric behaviour is similar to what one sees at a ferroelectric transition.

However, one should be cautious about this interpretation for multiple reasons. These are tricky experiments.

Dielectric dispersion spectroscopy is a bulk probe, not a microscopic one. One is not measuring the electric dipole moment of a single unit cell but rather the electric polarisation of a bulk crystal that has surfaces and contains defects, and impurities. For example, charge accumulation on the sample surface can enhance the measured dielectric constant and lead to significant frequency dependence, even when the actual material has no intrinsic frequency dependence (This is known as Maxwell-Wagner polarisation or the space-charge effect).

There are reports of significant sample dependence; the dielectric constant can vary by up to two orders of magnitude!

The origin of the dependence of the results on the direction of the electric field is not clear (at least to me). One usually finds the largest effects when the electric field is parallel to the least conducting direction (i.e. perpendicular the layers) in the crystal.

The magnitude of the electric dipole moment that one deduces from the magnitude of the dielectric constant (by fitting the temperature dependence to a Curie form, as in the dashed line in the figure above) is an order of magnitude larger than the moment on single dimers that is deduced from infrared (IR) measurements. This last discrepancy is emphasized by the authors of the second review above.

(IR measures the vibrational frequencies of the BEDT-TTF molecules; spectral shifts are correlated with the charge density on the molecule. Splitting of spectral lines corresponds to the presence of charge order, as discussed here.)

If one does accept that charge order occurs, further questions that arise include:

How do we know that the charge order is occurring within the dimers not between dimers?

Are these dielectric properties necessary or relevant for the insulating, superconducting, and magnetic properties (antiferromagnetism or spin liquid) or is it just a second-order effect (causality or correlation)?

What is the relevant effective Hamiltonian in the Mott insulating phase?

How is this similar and different to multiferroic behaviour in inorganic materials?

What role does spin-orbit coupling [and specifically the Dzyaloshinskii-Moriya interaction] play?

What experimental signatures could be considered a "smoking gun" for the presence of electric dipoles on single dimers?

How does one understand the different experiments which probe the system on very different time scales?

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