No Arabic abstract
We present magnetodielectric measurements in single crystals of the cubic spin-1/2 compound Cu$_2$OSeO$_3$. A magnetic field-induced electric polarization ($vec{P}$) and a finite magnetocapacitance (MC) is observed at the onset of the magnetically ordered state ($T_c = 59$ K). Both $vec{P}$ and MC are explored in considerable detail as a function of temperature (T), applied field $vec{H}_a$, and relative field orientations with respect to the crystallographic axes. The magnetodielectric data show a number of anomalies which signal magnetic phase transitions, and allow to map out the phase diagram of the system in the $H_a$-T plane. Below the 3up-1down collinear ferrimagnetic phase, we find two additional magnetic phases. We demonstrate that these are related to the field-driven evolution of a long-period helical phase, which is stabilized by the chiral Dzyalozinskii-Moriya term $D vec{M} cdot(bs{ abla}timesvec{M})$ that is present in this non-centrosymmetric compound. We also present a phenomenological Landau-Ginzburg theory for the ME$_H$ effect, which is in excellent agreement with experimental data, and shows three novel features: (i) the polarization $vec{P}$ has a uniform as well as a long-wavelength spatial component that is given by the pitch of the magnetic helices, (ii) the uniform component of $vec{P}$ points along the vector $(H^yH^z, H^zH^x, H^xH^y)$, and (iii) its strength is proportional to $eta_parallel^2-eta_perp^2/2$, where $eta_parallel$ is the longitudinal and $eta_perp$ is the transverse (and spiraling) component of the magnetic ordering. Hence, the field dependence of P provides a clear signature of the evolution of a conical helix under a magnetic field. A similar phenomenological theory is discussed for the MC.
We have investigated the magnetoelectric coupling in the lone pair containing piezoelectric ferrimagnet Cu2OSeO3. Significant magnetocapacitance develops in the magnetically ordered state (TC = 60 K). We find critical behavior near TC and a divergence near the metamagnetic transition at 500 Oe. High-resolution X-ray and neutron powder diffraction measurements show that Cu2OSeO3 is metrically cubic down to 10 K but that the ferrimagnetic ordering reduces the symmetry to rhombohedral R3. The metric cubic lattice dimensions exclude a magnetoelectric coupling mechanism involving spontaneous lattice strain, and this is unique among magnetoelectric and multiferroic materials.
The chiral helimagnet Cr1/3NbS2 has been investigated by magnetic, transport and thermal properties measurements on single crystals and by first principles electronic structure calculations. From the measured field and temperature dependence of the magnetization for fields applied perpendicular to the c axis, the magnetic phase diagram has been constructed in the vicinity of the phase transitions. A transition from a paramagnetic to a magnetically ordered phase occurs near 120 K. With increasing magnetic field and at temperatures below 120 K, this material undergoes transitions from a helimagnetic to a soliton-lattice phase near 900 Oe, and then to a ferromagnetic phase near 1300 Oe. The transitions are found to strongly affect the electrical transport. The resistivity decreases sharply upon cooling near 120 K, and the spin reorientation from the helimagnetic ground state to the commensurate ferromagnetic state is evident in the magnetoresistance. At high fields a large magnetoresistance (55 % at 140 kOe) is observed near the magnetic transition temperature. Heat capacity and electronic structure calculations show the density of states at the Fermi level is low in the magnetically ordered state. Effects of spin fluctuations are likely important in understanding the behavior of Cr1/3NbS2 near and above the magnetic ordering transitions.
A detailed zero and transverse field (ZF&TF) muon spin rotation (muSR) investigation of magnetism and the magneto-electric coupling in Cu2OSeO3 is reported. An internal magnetic field B_int(T=0) = 85.37(25) mT was found, in agreement with a ferrimagnetic state below Tc = 57.0(1) K. The temperature dependence of the magnetic order parameter is well described by the relation B_int = B(0)(1-(T/Tc)^2)^b with an effective exponent b = 0.39(1) which is close to the critical exponent B ~ 1/3 for a three dimensional (3D) magnetic system. Just above Tc the muon relaxation rate follows the power low lambda (T)propto (T/Tc - 1)^omega with omega = 1.06(9), which is characteristic for 3D ferromagnets. Measurements of B_int(T) with and without an applied electrostatic field E = 1.66 x 10^5 V/m suggest a possible electric field effect of magnitude Delta Bv = Bv(0 V)-Bv(500 V) = - 0.4(4) mT.
Dielectric properties were investigated under various magnitudes and directions of magnetic field (H) for a chiral magnetic insulator Cu2OSeO3. We found that the skyrmion crystal induces electric polarization (P) along either in-plane or out-of-plane direction of the spin vortices depending on the applied H-direction. The observed H-dependence of P in ferrimagnetic, helimagnetic, and skyrmion crystal state can be consistently described by the d-p hybridization model, highlighting an important role of relativistic spin-orbit interaction in the magnetoelectric coupling in Cu2OSeO3. Our analysis suggests that each skyrmion particle can locally carry electric dipole or quadrupole, which implies that the dynamics of skyrmions are controllable by the external electric field.
Strongly correlated materials with multiple order parameters provide unique insights into the fundamental interactions in condensed matter systems and present opportunities for innovative technological applications. A class of antiferromagnetic honeycomb lattices compounds, A4B2O9 (A = Co, Fe, Mn; B = Nb, Ta), have been explored owing to the occurrence of linear magnetoelectricity. We observe a highly nonlinear magnetoelectric effect on single crystals of Co4Ta2O9 (CTO), distinctive from the linear behavior in the isostructural Co4Nb2O9. Ferroelectricity emerges primarily along the [110] direction under magnetic fields, with the onset of antiferromagnetic order at TN = 20.5 K. For in-plane magnetic field, a spin-flop occurs at HC ~ 0.3 T, above which the ferroelectric polarization gradually becomes negative and reaches a broad minimum. Upon increasing magnetic field further, the polarization crosses zero and increases continuously to ~60 uC/m2 at 9 T. In contrast, the polarization for a magnetic field perpendicular to the hexagonal plane increases monotonously and reaches ~80 uC/m2 at 9 T. This observation of a strongly nonlinear magnetoelectricity suggests that two types of inequivalent Co2+ sublattices generate magnetic field-dependent ferroelectric polarization with opposite signs. These results motivate fundamental and applied research on the intriguing magnetoelectric characteristics of these honeycomb lattice materials.