Soft Spin Wave nearν=1: Evidence for a Magnetic Instability in Skyrmion Systems

Abstract

The ground state of the two dimensional electron gas near ν=1 is investigated by inelastic light scattering measurements carried down to very low temperatures. Away from ν=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.In condensed matter physics, the competition between distinct correlated electron ground states follows from a delicate interplay between dimensionality, strength of Coulomb interactions, and disorder. Correlated states may possess long range spin and/or charge order that breaks a symmetry that, in turn, has profound consequences on the nature of the low-energy excitation spectrum [1,2]. One well-known example of the relationship between broken-symmetry and elementary excitations is the isotropic ferromagnet. The broken rotational spin symmetry leads to appearance of gapless spin wave excitations, Goldstone modes, that are fluctuations of the spin density around the magnetization direction.The ground state of the two-dimensional (2D) electron gas at Landau level filling factor ν=1 is a special kind of itinerant ferromagnet, the quantum Hall ferromagnet, where all electrons occupy the lowest orbital Landau level and their spins are aligned along the external magnetic field. The quantum Hall ferromagnet supports collective excitations similar to ferromagnetic spin-waves with a gap given by the bare Zeeman energy E z [3,4]. The quantum Hall ferromagnet also has spin texture excitations built from Skyrmions [5,6], a concept used to describe the emergence of nuclear particles in the context of field theories of nuclear matter [7]. Skyrmions are topological objects which smoothly distort the ferromagnetic order in a vortex-like configuration. Each individual Skyrmion involves several flipped spins and is therefore not favored by the Zeeman energy. On the other hand because the exchange energy is large in quantum Hall systems, and it prefers locally aligned spins, Skyrmions are cheaper than single spin-flips for sufficiently low E z . The relevance of Skyrmions has been demonstrated by a wide range of experiments probing the spin polarization of the 2DES [8,9,10,11].Near ν=1 the interaction between Skyrmions may lock orientations of spin in the XY plane to favor the formation of a Skyrme crystal of electron spin orientation that breaks spin rotational symmetry about the magnetic field axis [12]. As a consequence of the additional symmetry breaking, the 2D electron system supports spin waves which, contrary to the ferromagnetic spin wave, remain gapless in the presence of the magnetic field [13,14,15]. Both a jump in the specific heat and the very short T 1 observed away from ν=1 were inter...

Optical Emission Spectroscopy Study of Competing Phases of Electrons in the Second Landau Level

“…Softening of the spin wave from the Zeeman energy in this filling factor range is similar to the effect reported in the filling factor range 2/3 < ν < 1, which was interpreted as arising from the appearance of spin textures in the ground state [35]. Measurements of the spin wave by RILS thus allow to probe the spin rotational invariance of the competing phases observed through optical emission.…”

Goldstone mode stochastization in a quantum Hall ferromagnet

“…The QHF is in fact a high symmetry system for investigating the influence of many-particle Coulomb interactions on the spin excitation spectrum [3][4][5][6][7]. Research into the nonequilibrium spin system of the QHF is also a direct method of evaluating the influence of the many-particle Coulomb interactions on spin relaxation in 2D systems.…”

“…[15] regarding the influence of the spin rearrangement on nuclear spin relaxation. The reason is as follows: when the electron system undergoes the phase transition from the QHF to a less rigid spin state, several phase-destroying mechanisms for the coherent spin precession come into play due to low energy spin excitations [5,7,16]. Discussion.…”

Enhancement of theν=5/2Fractional Quantum Hall State in a Small In-Plane Magnetic Field

“…Recent numerical results indicate that the 5/2 state in a GaAs quantum well system is spin-polarized even in the limit of vanishing Zeeman energy [12]. Experimental investigations on spin polarization at 5/2 from electrical transport [13][14][15][16] and optical measurements [17][18][19] have been reported, but these results provide only indirect determination of the spin states. Recent resistively detected nuclear magnetic resonance measurements point to a fully spin-polarized ground state (GS) at 5/2 at a magnetic field around 5 T [20,21].…”