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Hexaferrites are a class of iron compounds which crystalize in a sandwich-like periodic stacking of iron-oxide layers containing different metal atoms. The simplest is the M-type with chemical formula AB12O19, where A = Ba, Pb ... and B = Fe, Ti ... Our recent measurements with frequency-dependent magnetic susceptibility technique on various substitutions within the M-type hexaferrite (Ba1−xPbxFe12−yAlyO19) has shown signatures of exotic phenomena which point toward a general relaxational mechanism in ferrimagnetic semiconductors. Moreover, it was shown that activation energies of relaxation dynamics increase by adding aluminum. Heat capacity measurements from room temperature down to liquid helium indicate that the whole temperature range can be fitted well by the Debye and Einstein contributions up to room temperature. The energy of the lowest Einstein mode came close to the energy of the Debye mode.

In this work we investigated the multiferroic nature of antiferromagnetic phases of the β-TeVO4 by dielectric spectroscopy and static polarization measurements in the presence of external magnetic field. We report the anisotropy of spontaneous polarization which follows formation of vector chiral ground state, and which is likely driven by the inverse Dzyaloshinskii-Moriya mechanism. Furthermore, influence of magnetic field on the ferroelectric properties of the domains are found. The possibility of control of the polar order in the vector chiral phase via manipulation of the spin-chiral energy landscape is discussed.

Hexaferrites are a class of iron compounds which crystalize in a sandwich-like periodic stacking of iron-oxide layers containing different metal atoms. The simplest is the M-type with chemical formula AB12O19, where A = Ba, Pb ... and B = Fe, Ti ... [1] Our recent research [2, 4] on various substitutions within the M-type hexaferrite has shown signatures of exotic phenomena which point toward a general relaxational mechanism in ferrimagnetic semiconductors. Frequency - dependent magnetic susceptibility (Fig. 1) and dc electric transport properties of three different compositions of hexaferrite Ba1−xPbxFe12−yAlyO19 show a correlation between activation energies which persists in the whole researched range of aluminum substitution x = 0 to 3.3. This result is discussed in the context of charged magnetic domain walls, the pinning of which is determined by charge carriers activated over the transport gap.

Dielectric characterization of multiferroics, using dielectric spectroscopy, answers the questions of electric dipole dynamics and their phase transitions. When probing the ordering of electric dipoles, dielectric spectroscopy may be somewhat restrictive in the sense that nonlinear effects are not readily recognized. Different methods are needed to obtain high-field properties of a particular phase in question. The Sawyer-Tower bridge is an experimental method that directly probes the static polarization of a sample [1]. In this work we will present a version of Sawyer-Tower bridge which we designed specifically to characterize of polarization of samples with low capacitances and in extreme conditions (low temperatures, high magnetic fields). We will demonstrate some of the physical quantities that can be extracted using this method as well as discuss issues we encountered during development. Finally, we will show preliminary polarization measurements on a one-dimensional quantum magnet β-TeVO4. [1] Stewart, M. ; Cain, M.G. Ferroelectric hysteresis measurement & analysis. InNPL Report CMMT(A) 152 ; National Physical Laboratory, University of Manchester: Manchester, UK, 1999

Unconventional orderings of spin may provide a way to form multiferroic phases. For instance, spiral magnetic orders can break the space inversion symmetry and create electric dipoles which is a prerequisite for ferroelectric ordering [1]. One such candidate system is the zig-zag spin chain β-TeVO4 which has a complex magnetic phase diagram at low temperatures. From the paramagnetic high-temperature phase, the system enters the antiferromagnetic incommensurate spin-density wave phase at TN1=4.65 K. Then, at TN2=3.28 K it forms the so-called spin stripes which establish as a second incommensurate spin-density wave is superimposed on top of the first one. Finally, the difference between their two wave vectors disappears at TN3=2.26 K and the system enters its ground state – the vector chiral phase. Interestingly, at this last phase transition the electric dipoles become allowed by crystal symmetry. [2, 3, 4] In this work we investigate the possibility of ferroelectricity in the spin-ordered phases of β-TeVO4 using dielectric spectroscopy and static polarization measurements in the presence of external magnetic field. We discuss the obtained nonlinear dielectric properties in the context of its magnetic phase diagram. [1] K. F. Wang, J. M. Liu, and Z. F. Ren, Adv. Phys 58, (2009), 321–448 [2] M. Pregelj, A. Zorko, O. Zaharko, H. Nojiri, H. Berger, L. C. Chapon, and D. Arcon, Nature Communications 6 (2015), 10.1038/ncomms8255. [3] M. Pregelj, O. Zaharko, M. Herak, M. Gomilsek, A. Zorko, L. C. Chapon, F. Bourdarot, H. Berger, and D. Arcon, Phys. Rev. B 94, 081114 (2016). [4] M. Pregelj, A. Zorko, M Gomišlek, M. Klanjšek, O. Zaharko, J. S White, H. Luetkens, F. Coomer, T. Ivek, D. Rivas-Góngora, H. Berger, D. Arčon, npj Quantum Materials 4, 22 (2019)

Materials in which magnetic orderings induce ferroelectricity are promising candidates for magnetoelectric effect (ME). On one hand, it provides an opportunity to explore fundamental interactions between charges, spin, orbital and lattice degrees of freedom. On the other hand, ME enables new directions for development of novel devices. Although bulk, non-composite magnetoelectric materials seem to be rare and elusive, one promising way to achieve the ME effect is through spiral magnetic orders which can allow the existence of electric dipoles by breaking the space inversion symmetry [1]. The quasi-one-dimensional quantum magnet β-TeVO 4 is a zig-zag spin chain system with anisotropic interactions between spins and a spiral ordered ground state [2, 3]. Its phase diagram is complex: firstly, at T N1 =4.65 K the system paramagnetic phase gives way to an incommensurate spin-density wave in which spins are collinear. Then, below T N2 =3.28 K a spin stripe phase is observed [3, 4]. This phase develops as a superposition of two spin density waves with a small difference in modulation and orthogonal direction of spin. Finally, at T N3 =2.28 K the difference between wave vectors disappears and the vector chiral ground state is established [5]. Most interestingly, at T N3 there are tantalizing indications of emergent electric dipoles, the nature and mechanism of which are still not resolved. In this work we present the dielectric response of β-TeVO 4 single crystal samples in the static limit at low temperatures and in the presence of external magnetic field. The currently available magnetic phase diagram will be discussed in the context of dielectric properties, and of low-temperature magnetic ordering as a potentially multiferroic phase. [1] K. F. Wang, J. M. Liu, and Z. F. Ren, Adv. Phys 58, 321–448 (2009). [2] Y. Savina, O. Bludov, V. Pashchenko, S. L. Gnatchenko, P. Lemmens, and H. Berger, Phys. Rev. B 84, 104447 (2011). [3] M. Pregelj, A. Zorko, O. Zaharko, H. Nojiri, H. Berger, L. C. Chapon, and D. Arcon, Nature Communications 6 (2015), 10.1038/ncomms8255. [4] Y. O. Savina, O. M. Bludov, V. A. Pashchenko, S. L. Gnatchenko, P. Lemmens, and H. Berger, Low Temperature Physics 41, 283 (2015). [5] M. Pregelj, O. Zaharko, M. Herak, M. Gomilsek, A. Zorko, L. C. Chapon, F. Bourdarot, H. Berger, and D. Arcon, Phys. Rev. B 94, 081114 (2016).

We study the antiferomagnetic ground state of low-dimensional SeCuO3 by combining torque magnetometry with simple phenomenological approach to magnetic anisotropy and Density Functional Theory (DFT) calculations. Combining measured torque data with phenomenological approach allows us to choose between several symmetry allowed shapes of magnetic anisotropy energy (MAE) and to determine spin orientation in zero and finite magnetic field. Results obtained in magnetic fields larger than spin-flop field indicate that spin reorientation is more complicated than usual spin flop found in collinear antiferromagnet. The microscopic origin of MAE in SeCuO3 was also investigated theoretically, based on DFT+U calculations including spin-orbit coupling on an antiferromagnetic model. It was evidenced inequivalent copper sites impact differently the magnetic anisotropy of this system, leading to a change of the easy magnetization axis. This work is fully supported by the HrZZ grant UIP-2014-09-9775 and by the COGITO project "Theoretical and experimental study of magnetic and multiferroic materials".

We report on magnetic field induced spin reorientation in antiferromagnetically (AFM) ordered state of low-dimensional magnet SeCuO3 observed by torque magnetometry experiment. Monoclinic SeCuO3 was reported to be quasi-isolated linear spin tetramer system Cu2-Cu1-Cu1-Cu2 where strong Cu1-Cu1 interaction leads to spin singlet formation. Below TN=8K AFM long-range order (LRO) sets in. The question arises whether spin singlet persists in LRO state or is broken allowing Cu1 spins to participate in the LRO state. We performed extensive torque magnetometry measurements in AFM state of SeCuO3. We employ simple phenomenological model using symmetry allowed magnetocrystalline anisotropy energy (MAE) to simulate spin reorientation and measured torque. This approach can quantitatively describe our data only under assumption of partial spin reorientation. Based on these results, we propose a model of magnetic order in H=0 and in H>HSF. The microscopic origin of MAE in SeCuO3 was also investigated using DFT+U calculations including spin-orbit coupling on an AFM model. It was evidenced inequivalent Cu sites impact differently the magnetic anisotropy of this system. Our results suggest that Cu1 singlets persist even in AFM LRO state, and only Cu2 spins reorient in finite magnetic field. This work is fully supported by the Croatian Science Foundation (grant UIP-2014-09-9775) and by the COGITO project Theoretical and experimental study of magnetic and multiferroic materials.

In antiferromagnets orientation of spin axis (spins) in zero magnetic field and "difficulty" of rotating this axis in any other direction in finite magnetic field can be described by magnetocrystalline anisotropy energy which has to obey the point group symmetry operations for a specific crystal. Even then several different energy shapes are possible leaving ambiguous possibilities for the direction of spins in AFM state. Experimentally, this anisotropy can be probed by magnetic torque measurements in finite magnetic field which allows the unambiguous determination of the AFM ground state for a specific system. In this work we will present in detail our torque magnetometry experiment on SeCuO3 at low temperatures which enabled us to probe the symmetry of the AFM state in this system.

Magnetic lattice in monoclinic SeCuO3 is comprised of isolated quantum spin tetramers. Weak intertetramer interaction results in long-range antiferromagnetic (AFM) order at below TN=8K. However, exact magnetic structure of this phase is still unresolved. While several experimental techniques such as neutron diffraction and NMR are successful in determining magnetic structure, magnetic field induced spin reorientation is rarely studied due to highly time-consuming experiments. We present alternative method which combines torque magnetometry with simple phenomenological approach to magnetic anisotropy. Using this approach we determine the orientation of spin axis in AFM state of SeCuO3 with respect to crystal axes in zero magnetic field and also symmetry of AFM state by studying spin reorientation in finite magnetic field.