Skyrmion robustness in non-centrosymmetric magnets with axial symmetry: The role of anisotropy and tilted magnetic fields

We investigate the stability of N\'eel skyrmions against tilted magnetic fields, in polar magnets with uniaxial anisotropy ranging from easy-plane to easy-axis type. We construct the corresponding phase diagrams and investigate the internal structure of skewed skyrmions with displaced cores. We find that moderate easy-plane anisotropy increases the stability range of N\'eel skyrmions for fields along the symmetry axis, while moderate easy-axis anisotropy enhances their robustness against tilted magnetic fields. We stress that the direction, along which the skyrmion cores are shifted, depends on the symmetry of the underlying crystal lattice. The cores of N\'eel skyrmions, realized in polar magnets with C$_{nv}$ symmetry, are displaced either along or opposite to the off-axis (in-plane) component of the magnetic field depending on the rotation sense of the magnetization, dictated by the sign of the Dzyaloshinskii constant. The core shift of antiskyrmions, present in chiral magnets with D$_{2d}$ symmetry, depends on the in-plane orientation of the magnetic field and can be parallel, anti-parallel, or perpendicular to it. We argue that the role of anisotropy in magnets with axially symmetric crystal structure is different from that in cubic helimagnets. Our results can be applied to address recent experiments on polar magnets with C$_{3v}$ symmetry, GaV$_4$S$_8$ and GaV$_4$Se$_8$

Asymmetric isolated skyrmions in polar magnets with easy-plane anisotropy

We introduce a new class of isolated magnetic skyrmions emerging within tilted ferromagnetic phases of polar magnets with easy-plane anisotropy. The asymmetric magnetic structure of these skyrmions is associated with an intricate pattern of the energy density, which exhibits positive and negative asymptotics with respect to the surrounding state with a ferromagnetic moment tilted away from the polar axis. Correspondingly, the skyrmion-skyrmion interaction has an anisotropic character and can be either attractive or repulsive depending on the relative orientation of the skyrmion pair. We investigate the stability of these novel asymmetric skyrmions against the elliptical cone state and follow their transformation into axisymmetric skyrmions, when the tilted ferromagnetic moment of the host phase is reduced. Our theory gives clear directions for experimental studies of isolated asymmetric skyrmions and their clusters embedded in tilted ferromagnetic phases

Experimental band structure of the nearly half-metallic CuCr2_2Se4_4: An optical and magneto-optical study

Diagonal and off-diagonal optical conductivity spectra have been determined form the measured reflectivity and magneto-optical Kerr effect (MOKE) over a broad range of photon energy in the itinerant ferromagnetic phase of CuCr$_2$Se$_4$ at various temperatures down to T=10 K. Besides the low-energy metallic contribution and the lower-lying charge transfer transition at $E$$\approx$2 eV, a sharp and distinct optical transition was observed in the mid-infrared region around $E$$=$0.5 eV with huge magneto-optical activity. This excitation is attributed to a parity allowed transition through the Se-Cr hybridization-induced gap in the majority spin channel. The large off-diagonal conductivity is explained by the high spin polarization in the vicinity of the Fermi level and the strong spin-orbit interaction for the related charge carriers. The results are discussed in connection with band structure calculations

Orbital-Order Driven Ferroelectricity and Dipolar Relaxation Dynamics in Multiferroic GaMo4_4S8_8

We present the results of broadband dielectric spectroscopy of GaMo$_4$S$_8$, a lacunar spinel system that recently was shown to exhibit non-canonical, orbitally-driven ferroelectricity. Our study reveals complex relaxation dynamics of this multiferroic material, both above and below its Jahn-Teller transition at T$_{\textrm{JT}}=47$ K. Above T$_{\textrm{JT}}$, two types of coupled dipolar-orbital dynamics seem to compete: relaxations within cluster-like regions with short-range polar order like in relaxor ferroelectrics and critical fluctuations of only weakly interacting dipoles, the latter resembling the typical dynamics of order-disorder type ferroelectrics. Below the Jahn-Teller transition, the onset of orbital order drives the system into long-range ferroelectric order and dipolar dynamics within the ferroelectric domains is observed. The coupled dipolar and orbital relaxation behavior of GaMo$_4$S$_8$ above the Jahn-Teller transition markedly differs from that of the skyrmion host GaV$_4$S$_8$, which seems to be linked to differences in the structural distortions of the two systems on the unit-cell level.Comment: 6 pages, 3 figures + Supplemental Material (2 pages, 2 figures

Polar Dynamics at the Jahn-Teller Transition in Ferroelectric GaV4S8

We present a dielectric spectroscopy study of the polar dynamics linked to the orbitally driven ferroelectric transition in the skyrmion host GaV4S8. By combining THz and MHz-GHz spectroscopy techniques, we succeed in detecting the relaxational dynamics arising from coupled orbital and polar fluctuations in this material and traced its temperature dependence in the paraelectric as well as in the ferroelectric phase. The relaxation time significantly increases when approaching the critical temperature from both sides of the transition. It is natural to assume that these polar fluctuations map the orbital dynamics at the Jahn-Teller transition. Due to the first-order character of the orbital-ordering transition, the relaxation time shows an enormous jump of about five orders of magnitude at the polar and structural phase transition.Comment: 5 pages, 4 figure

New type of ellipsometry in infrared spectroscopy: The double-reference method

We have developed a conceptually new type of ellipsometry which allows the determination of the complex refractive index by simultaneously measuring the unpolarized normal-incidence reflectivity relative to the vacuum and to another reference media. From these two quantities the complex optical response can be directly obtained without Kramers-Kronig transformation. Due to its transparency and large refractive index over a broad range of the spectrum, from the far-infrared to the soft ultraviolet region, diamond can be ideally used as a second reference. The experimental arrangement is rather simple compared to other ellipsometric techniques.Comment: submitted to Appl. Phys. Let

Magnetic field control of cycloidal domains and electric polarization in multiferroic BiFeO3_3

The magnetic field induced rearrangement of the cycloidal spin structure in ferroelectric mono-domain single crystals of the room-temperature multiferroic BiFeO$_3$ is studied using small-angle neutron scattering (SANS). The cycloid propagation vectors are observed to rotate when magnetic fields applied perpendicular to the rhombohedral (polar) axis exceed a pinning threshold value of $\sim$5\,T. In light of these experimental results, a phenomenological model is proposed that captures the rearrangement of the cycloidal domains, and we revisit the microscopic origin of the magnetoelectric effect. A new coupling between the magnetic anisotropy and the polarization is proposed that explains the recently discovered magnetoelectric polarization to the rhombohedral axis

Magnetic-field-induced transition in BaVS3

The metal-insulator transition (MIT) of BaVS3 is suppressed under pressure and above the critical pressure of p~2GPa the metallic phase is stabilized. We present the results of detailed magnetoresistivity measurements carried out at pressures near the critical value, in magnetic fields up to B=12T. We found that slightly below the critical pressure the structural tetramerization -- which drives the MIT -- is combined with the onset of magnetic correlations. If the zero-field transition temperature is suppressed to a sufficiently low value (T_MI<15K), the system can be driven into the metallic state by application of magnetic field. The main effect is not the reduction of T_MI with increasing B, but rather the broadening of the transition due to the applied magnetic field. We tentatively ascribe this phenomenon to the influence on the magnetic structure coupled to the bond-order of the tetramers.Comment: 5 pages, 5 figure

Polar and magnetic order in GaV4Se8

In the present work, we provide results from specific heat, magnetic susceptibility, dielectric constant, ac conductivity, and electrical polarization measurements performed on the lacunar spinel GaV4Se8. With decreasing temperature, we observe a transition from the paraelectric and paramagnetic cubic state into a polar, probably ferroelectric state at 42 K followed by magnetic ordering at 18 K. The polar transition is likely driven by the Jahn-Teller effect due to the degeneracy of the V4 cluster orbitals. The excess polarization arising in the magnetic phase indicates considerable magnetoelectric coupling. Overall, the behavior of GaV4Se8 in many respects is similar to that of the skyrmion host GaV4S8, exhibiting a complex interplay of orbital, spin, lattice, and polar degrees of freedom. However, its dielectric behavior at the polar transition markedly differs from that of the Jahn-Teller driven ferroelectric GeV4S8, which can be ascribed to the dissimilar electronic structure of the Ge compound.Comment: 7 pages, 6 figures. Revised version according to suggestions of referee