Evidence for skyrmion crystallization from NMR relaxation experiments

Wigner solids of domain wall skyrmions

Detection and characterization of a different type of topological excitations, namely the domain wall (DW) skyrmion, has received increasing attention because the DW is ubiquitous from condensed matter to particle physics and cosmology. Here we present experimental evidence for the DW skyrmion as the ground state stabilized by long-range Coulomb interactions in a quantum Hall ferromagnet. We develop an alternative approach using nonlocal resistance measurements together with a local NMR probe to measure the effect of low current-induced dynamic nuclear polarization and thus to characterize the DW under equilibrium conditions. The dependence of nuclear spin relaxation in the DW on temperature, filling factor, quasiparticle localization, and effective magnetic fields allows us to interpret this ground state and its possible phase transitions in terms of Wigner solids of the DW skyrmion. These results demonstrate the importance of studying the intrinsic properties of quantum states that has been largely overlooked.

Skyrmions, a topological spin texture, have been found in a variety of magnetic systems, including quantum hall ferromagnets. Here, Yang et al demonstrate the existence of skyrmions in domain walls in a quantum Hall ferromagnet, and suggest that these skyrmions form a 1D Wigner crystal.

Enhanced stability of quantum Hall skyrmions under radio-frequency radiations

We present in this paper the results from a recent study on the stability of the quantum Hall skyrmions state at a Landau level filling factor (ν) close to ν = 1 in a narrow GaAs quantum well. Consistent with previous work, a resonant behavior is observed in the resistively detected NMR measurements. In the subsequent current-voltage (I-V) measurements to examine its breakdown behavior under radio frequency radiations, we observe that the critical current assumes the largest value right at the ⁷⁵As nuclear resonant frequency. We discuss possible origin for this unexpectedly enhanced stability.

Stable Skyrmions in SU(2) gauged Bose-Einstein condensates

We demonstrate that the three-dimensional Skyrmion, which has remained elusive so far, spontaneously appears as the ground state of SU(2) symmetric Bose-Einstein condensates coupled with a non-Abelian gauge field. The gauge field is a three-dimensional analogue of the Rashba spin-orbit coupling. Upon squashing the SO(3) symmetric gauge field to one- or two-dimensional shapes, we find that the ground state continuously undergoes a change from a three-dimensional to a one- or two-dimensional Skyrmion, which is identified by estimating winding numbers and helicity. All of the emerged Skyrmions are physically understandable with the concept of the helical modulation in a unified way. These topological objects might potentially be realizable in two-component Bose-Einstein condensates experimentally.

Low-frequency spin fluctuations in Skyrmions confined by wires: measurements of local nuclear spin relaxation

We investigate low-frequency electron spin dynamics in a quantum Hall system with wire confinement by nuclear spin relaxation measurements. We developed a technique to measure the local nuclear spin relaxation rate T(1)(-1). T(1)(-1) is enhanced on both sides of the local filling factor ν(wire)=1, reflecting low-frequency fluctuations of electron spins associated with Skyrmions inside the wire. As the wire width is decreased, the fast nuclear spin relaxation is suppressed in a certain range of Skyrmion density. This suggests that the multi-Skyrmion state is modified and the low-frequency spin fluctuations are suppressed by the wire confinement.

Fractional spin textures in the frustrated magnet SrCr(9p)Ga(12-9p)O₁₉

We consider the archetypal frustrated antiferromagnet SrCr(9p)Ga(12-9p)O₁₉ in its well-known spin-liquid state, and demonstrate that a Cr(3+) spin S=3/2 ion in direct proximity to a pair of vacancies (in disordered p<1 samples) is cloaked by a spatially extended spin texture that encodes the correlations of the parent spin liquid. In this spin-liquid regime, our analytic theory predicts that the combined object has a magnetic response identical to a classical spin of length S/2=3/4, which dominates over the small intrinsic susceptibility of the pure system. This fractional-spin texture leaves an unmistakable imprint on the measured ⁷¹Ga nuclear magnetic resonance line shapes, which we compute using Monte Carlo simulations and compare with experimental data.

Pinning-mode resonance of a Skyrme crystal near Landau-level filling factor ν=1

Microwave pinning-mode resonances found around integer quantum Hall effects, are a signature of crystallized quasiparticles or holes. Application of in-plane magnetic field to these crystals, increasing the Zeeman energy, has negligible effect on the resonances just below Landau-level filling ν=2, but increases the pinning frequencies near ν=1, particularly for smaller quasiparticle or hole densities. The charge dynamics near ν=1, characteristic of a crystal order, are affected by spin, in a manner consistent with a Skyrme crystal.

Hamiltonian theory of disorder at nu = 1/3

The Hamiltonian theory of the fractional quantum Hall regime provides a simple and tractable approach to calculating gaps, polarizations, and many other physical quantities. In this Letter we include disorder in our treatment and show that a simple model with minimal assumptions produces results consistent with a range of experiments. In particular, the interplay between disorder and interactions can result in experimental signatures which mimic those of spin textures.

Topological Hall effect in the A phase of MnSi

Recent small angle neutron scattering suggests that the spin structure in the A phase of MnSi is a so-called triple-Q state, i.e., a superposition of three helices under 120 degrees. Model calculations indicate that this structure in fact is a lattice of so-called Skyrmions, i.e., a lattice of topologically stable knots in the spin structure. We report a distinct additional contribution to the Hall effect in the temperature and magnetic field range of the proposed Skyrmion lattice, where such a contribution is neither seen nor expected for a normal helical state. Our Hall effect measurements constitute a direct observation of a topologically quantized Berry phase that identifies the spin structure seen in neutron scattering as the proposed Skyrmion lattice.

Soft spin wave near nu=1: evidence for a magnetic instability in Skyrmion systems

The ground state of the two-dimensional electron gas near nu=1 is investigated by inelastic light scattering measurements carried down to very low temperatures. Away from nu=1, the ferromagnetic spin wave collapses and a new low-energy spin wave emerges below the Zeeman gap. The emergent spin wave shows soft behavior as its energy increases with temperature and reaches the Zeeman energy for temperatures above 2 K. The observed softening indicates an instability of the two-dimensional electron gas towards a magnetic order that breaks spin rotational symmetry. We discuss our findings in light of the possible existence of a Skyrme crystal.

NMR probing of spin excitations in the ring structure of a two-subband system

Resistively detected nuclear magnetic resonance (NMR) is observed inside the ringlike structure, with a quantized Hall conductance of 6e(2)/h, in the phase diagram of a two-subband electron system. The NMR signal persists up to 470 mK and is absent in other states with the same quantized Hall conductance. The nuclear spin-lattice relaxation time T1, is found to decrease rapidly towards the ring center. A strong dynamic nuclear polarization by the biasing current has also been observed only inside the ring. These observations are consistent with the assertion of the ringlike region being a ferromagnetic state that is accompanied by collective spin excitations.

Low-Frequency Spin Dynamics in a Canted Antiferromagnet

Resistively detected nuclear spin relaxation measurements in closely separated two-dimensional electron systems reveal strong low-frequency electron-spin fluctuations in the quantum Hall regime. As the temperature is decreased, the spin fluctuations, manifested by a sharp enhancement of the nuclear spin-lattice relaxation rate 1/T1, continue to grow down to the lowest temperature of 66 millikelvin. The observed divergent behavior of 1/T1 signals a gapless spin excitation mode and is a hallmark of canted antiferromagnetic order. Our data demonstrate the realization of a two-dimensional system with planar broken symmetry, in which fluctuations do not freeze out when approaching the zero temperature limit.

Dynamic nuclear polarization and nuclear magnetic resonance in the vicinity of edge states of a 2DES in GaAs quantum wells

Nuclear magnetic resonance is detected via the in-plane conductivity of a two-dimensional electron system at unity Landau level filling factor in the regime of the quantum Hall effect in narrow and wide quantum wells. The NMR is spatially selective to nuclei with a coupling to electrons in the current carrying edge states at the perimeter of the 2DES. Interpretation of the electron-nuclear double resonance signals is facilitated by numerical simulations. A new RF swept method for conductivity-detected NMR is introduced which offers more efficient signal averaging. The method is applied to the study of electric quadrupole interactions, weakly allowed overtone transitions, and evaluation of the extent of electron wave function delocalization in the wide quantum well.