Quantum multiferroics
Multiferroics are materials with coupled magnetic and ferroelectric order. The underlying microscopic mechanism is rooted in relativistic spin-orbit intearactions. For obvious reasons, multiferroics are of great industrial significance. We, however, are more interested in fundamental aspects. Which exotic phases of quantum magnetic materials have electrical polarization? What can we learn about the magnetic system and magnetic quantum phase transitions by studying dielectric properties? Is it possible that dielectric degrees of freedom play an active role in quantum phase transitions and collective excitations?
Dielectric relaxation via quantum-critical magnons
![Enlarged view: False-color plot of the real (top) and imaginary (bottom) parts of the dielectric susceptibility of Cs2Cu2Mo3O12 as a function of magnetic field and temperature [2].](/highlights/quantum-multiferroics/_jcr_content/par/textimage_692861044_/image.imageformat.lightbox.1890985521.png)
The material Cs2Cu2Mo3O12 is is a quantum multiferroic that is very similar to Rb2Cu2Mo3O12 descrived in the next example. What makes the Cs-compound special tough, is that, in addition to the singular behavior of dielectrioc susceptibility at the magnetic phase transition [1] seen in the Rb-system, it shows a new type of magnetism-related dielectric anomaly. Well below the magnetic phase boundary, but also in the high-field non-magnetic regime this anomaly is a relaxation peak in the imaginary part of dielectric susceptibility. We have demonstrated that it is due to Debye relaxation of some dipolar defrees of freedom, which is mediated by the magnetic soft mode of the field-induced magnon BEC [2]. Thanks to that mechanism the temperature of the anomaly dips to zero at the magnetic saturation transition, where the magnon gap closes.
[1] D. Flavián, P. A. Volkov, S. Hayashida, K. Yu. Povarov, S. Gvasaliya, P. Chandra, A. Zheludev, Dielectric relaxation in the quantum multiferroics Rb2Cu2Mo3O12 and Cs2Cu2Mo3O12, external page Phys. Rev. B 110, 174433 (2024).
[2] D. Flavián, Pavel A. Volkov, S. Hayashida, K. Yu. Povarov, S. Gvasaliya, Premala Chandra, and A. Zheludev, Dielectric Relaxation by Quantum Critical Magnons, external page Phys. Rev. Lett. 130, 216501 (2023).
Multiferroic quantum criticality
The frustrated ferro-antiferromagnet Rb2Cu2Mo3O12 is a qantum paramagnet. In the absence of an external field, it doesn't order magnetically at any temperature. It becomes ordered in applied magnetic fields and has a very interesting H-T phase diagram [1]. It turns out that the magnetically ordered phases are also ferroelectric, and that electrical polarization is linearly coupled to the magnetic order parameter that is the staggered magnetization.
In strong applied fields magnetic order is again destroyed, in a quantum phase transition described in terms of a Bose-Einstein condensation (BEC) of magnons. Since electrical polarization is the primary order parameter, all magnetic critical exponents can be directly measured in the dielectric channel. This enabled us, for the first time, to measure the scaling of critical susceptibility at a BEC quantum critical point [2].
[1] S. Hayashida, D. Blosser, K. Yu. Povarov, Z. Yan, S. Gvasaliya, A. N. Ponomaryov, S. A. Zvyagin, and A. Zheludev, external page Phys. Rev. B 100, 134427 (2019).
[2] S. Hayashida, L. Huberich, D. Flavián, Z. Yan, K. Yu. Povarov, S. Gvasaliya, A. Zheludev, Critical dielectric susceptibility at a magnetic BEC quantum critical point, external page Phys. Rev. Research 3, 033053 (2021)
Multiferroic phases of linarite
![Enlarged view: Pyroelectric current measurements of electrical polarization in linarite [3].](/highlights/quantum-multiferroics/_jcr_content/par/textimage_516494836/image.imageformat.lightbox.890272704.png)
Magnetization is an axial vector, but electrical polarization a polar one. Out of symmetry considerations, the two can only couple if there is another axial vector in the system. Very often such is the vector of pseudochirality in a helimagnetic structure. The frustrated quasi-one-dimensional material PbCuSO4(OH)2 (linarite) has a very complicated phase diagram in applied magnetic fields. Some of these phases are ferroelectric, while others fail to satisfy the above-mentioned symmetry requirements. By measuring the direction of electrical polarization in this compound we are able to deduce the spin arrangements in the multiferroic incommensurate phases [1].
[1] K. Yu. Povarov, Y. Feng and A. Zheludev, external page Phys. Rev. B94, 214409 (2016).
Improper ferroelectricity at a magnetic quantum phase transition
![Enlarged view: Dielectric anomalies measured isothermally at different magnetic field in quantum multiferroic Sul-Cu<sub>2</sub>Cl<sub>4 </sub>[2].](/highlights/quantum-multiferroics/_jcr_content/par/textimage_1659340314/image.imageformat.lightbox.230810604.png)
Sul-Cu2Cl4 is a peculiar quasi-one-dimensional "spin tube" system. The ground state is non magnetic, but an external magnetic field induces long-range helimagnetic order, following a Bose-Einstein condensation (BEC) of magnons quantum phase transition. Due to peculiarities of the crystal structure the incommensurate helimagnetic phase supports a ferroelectric polarization. Despite initial reports by another group (who too used our samples) [1], this is an improper ferroelectric, meaning that electrical polarization is not the primary order parameter [2]. It is not critical at the transition, but nontheless shows a very strong anomaly at the transition point, which can be very precisely measured. In this way, through dielectric experiments we are able to obtain a very accurate measurement of the BEC crossover exponent. In addition we study the highly non-linear dielectric response within the ordered phase.
[1] F. Schrettle, S. Krohns, P. Lunkenheimer, A. Loidl, E. Wulf, T. Yankova and A. Zheludev, external page Phys. Rev. B 87, 121105(R) (2013).
[2] K. Yu. Povarov, A. Reichert, E. Wulf and A. Zheludev, external page Phys. Rev. B 92, 140410(R) (2015).