We report $alpha$-Cu$_2$V$_2$O$_7$ to be an improper multiferroic with the simultaneous development of electric polarization and magnetization below $T_C$ = 35 K. The observed spontaneous polarization of magnitude 0.55 $mu$Ccm$^{-2}$ is highest among the copper based improper multiferroic materials. Our study demonstrates sizable amount of magneto-electric coupling below $T_C$ even with a low magnetic field. The theoretical calculations based on density functional theory (DFT) indicate magnetism in $alpha$-Cu$_2$V$_2$O$_7$ is a consequence of {em ferro-orbital} ordering driven by polar lattice distortion due to the unique pyramidal (CuO$_{5}$) environment of Cu. The spin orbit coupling (SOC) further stabilize orbital ordering and is crucial for magnetism. The calculations indicate that the origin of the giant ferroelectric polarization is primarily due to the symmetric exchange-striction mechanism and is corroborated by temperature dependent X-ray studies.
We investigate magnetoelectric coupling and low-energy magnetic excitations in multiferroic $alpha$-Cu$_2$V$_2$O$_7$ by detailed thermal expansion, magnetostriction, specific heat and magnetization measurements in magnetic fields up to 15~T and by high-field/high-frequency electron spin resonance studies. Our data show negative thermal expansion in the temperature range $leq 200$~K under study. Well-developed anomalies associated with the onset of multiferroic order (canted antiferromagnetism with a significant magnetic moment and ferroelectricity) imply pronounced coupling to the structure. We detect anomalous entropy changes in the temperature regime up to $sim 80$~K which significantly exceed the spin entropy. Failure of Gruneisen scaling further confirms that several dominant ordering phenomena are concomitantly driving the multiferroic order. By applying external magnetic fields, anomalies in the thermal expansion and in the magnetization are separated. Noteworthy, the data clearly imply the development of a canted magnetic moment at temperatures above the structural anomaly. Low-field magnetostriction supports the scenario of exchange-striction driven multiferroicity. We observe low-energy magnetic excitations well below the antiferromagnetic gap, i.e., a ferromagnetic-type resonance branch associated with the canted magnetic moment arising from Dzyaloshinsii-Moriya interactions. The anisotropy parameter $tilde{D}=1.6(1)$~meV indicates a sizeable ratio of DM- and isotropic magnetic exchange.
Critical phenomenon at the phase transition reveals the universal and long-distance properties of the criticality. We study the ferromagnetic criticality of the pyrochlore magnet Lu$_2$V$_2$O$_7$ at the ferromagnetic transition ${T_text{c}approx 70, text{K}}$ from the isotherms of magnetization $M(H)$ via an iteration process and the Kouvel-Fisher method. The critical exponents associated with the transition are determined as ${beta = 0.32(1)}$, ${gamma = 1.41(1)}$, and ${delta = 5.38}$. The validity of these critical exponents is further verified by scaling all the $M(H)$ data in the vicinity of $T_text{c}$ onto two universal curves in the plot of $M/|varepsilon|^beta$ versus $H/|varepsilon|^{beta+gamma}$, where ${varepsilon = T/T_text{c} -1}$. The obtained $beta$ and $gamma$ values show asymmetric behaviors on the ${T < T_text{c}}$ and the ${T > T_text{c}}$ sides, and are consistent with the predicted values of 3D Ising and cubic universality classes, respectively. This makes Lu$_2$V$_2$O$_7$ a rare example in which the critical behaviors associated with a ferromagnetic transition belong to different universality classes. We describe the observed criticality from the Ginzburg-Landau theory with the quartic cubic anisotropy that microscopically originates from the anti-symmetric Dzyaloshinskii-Moriya interaction as revealed by recent magnon thermal Hall effect and theoretical investigations.
We report the observation of a magnetic polarization of the O,$2p$-states in YMn$_2$O$_5$ through the use of soft X-ray resonant scattering at the oxygen $K$-edge. Remarkably, we find that the temperature dependence of the integrated intensity of this signal closely follows the macroscopic electric polarization, and hence is proportional to the ferroelectric order parameter. This is in contrast to the temperature dependence observed at the Mn,$L_3$-edge, which reflects the Mn magnetic order parameter. First principle calculations provide a microscopic understanding of these results and show that a spin-dependent hybridization of O,$2p$- and Mn, 3d-states results in a purely electronic contribution to the ferroelectric polarization, which can exist in the absence of lattice distortions.
We explore the field-temperature phase diagram of the XY pyrochlore antiferromagnet Er$_2$Ti$_2$O$_7$, by means of magnetization and neutron diffraction experiments. Depending on the field strength and direction relative to the high symmetry cubic directions $[001], [1bar{1}0]$ and $[111]$, the refined field induced magnetic structures are derived from the zero field $psi_2$ and $psi_3$ states of the $Gamma_5$ irreducible representation which describes the ground state of XY pyrochlore antiferromagnets. At low field, domain selection effects are systematically at play. In addition, for $[001]$, a phase transition is reported towards a $psi_3$ structure at a characteristic field $H_c^{001}=$ 43 mT. For $[1bar{1}0]$ and $[111]$, the spins are continuously tilted by the field from the $psi_2$ state, and no phase transition is found while domain selection gives rise to sharp anomalies in the field dependence of the Bragg peaks intensity. For $[1bar{1}0]$, these results are confirmed by high resolution inelastic neutron scattering experiments, which in addition allow us to determine the field dependence of the spin gap. This study agrees qualitatively with the scenario proposed theoretically by Maryasin {it et al.} [Phys. Rev. B {bf 93}, 100406(R) (2016)], yet the strength of the field induced anisotropies is significantly different from theory.
For a symmetry consistent theoretical description of the multiferroic phase of Ba$_2$CoGe$_2$O$_7$ a precise knowledge of its crystal structure is a prerequisite. In our previous synchrotron X-ray diffraction experiment on multiferroic Ba$_2$CoGe$_2$O$_7$ at room temperature we found forbidden reflections that favour the tetragonal-to-orthorhombic symmetry lowering of the titled compound. Here, we report the results of room-temperature single-crystal diffraction studies with both hot and cold neutrons to differentiate between the real symmetry lowering and multiple diffraction (the Renninger effect). A comparison of the experimental multiple diffraction patterns with simulated ones rules out the symmetry lowering. Thus, the structural model based on the tetragonal space group $Pbar{4}2_1m$ was selected to describe the Ba$_2$CoGe$_2$O$_7$ symmetry at room temperature. The precise structural parameters from neutron diffraction at 300K are presented and compared with the previous X-ray diffraction results.