Preferred number of flipped spins in Skyrmion excitation

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Abstract

We measured the activation energy of the Skyrmion excitations in the monolayer quantum Hall (QH) state at the Landau-level filling factor ν=1 and in the bilayer QH state at ν=2. The number of flipped spins Ns changes from 7 to 1 in the monolayer sample and in the bilayer sample with small tunneling energy gap, while Ns changes from 14 to 7 and finally to 1 in the bilayer sample with large tunneling energy gap. These experimental data suggest the existence of the preferred number of flipped spins Ns=7 for a Skyrmion-pair excitation.

Introduction

In the two-dimensional electron system, spin excitations of the Landau-level filling factor ν=1 quantum Hall (QH) state attracts much attention. Low-lying charged excitations are spin textures called Skyrmions [1], [2], [3], [4], [5], [6], [7], [8], [9]. They are characterized by the number of flipped spins Ns. While such excitations cost more Zeeman energy than a single spin flip, they save on Coulomb energy. Here, the excitation energy is written as [4]Δ=Δ0,Ns(B⊥)+Ns|g∗|μBBtot.The Zeeman energy depends on the total magnetic field Btot and contributes to the gap through the second term Ns|g∗|μBBtot; g∗ is the gyromagnetic ratio and μB is the Bohr magneton. The first term Δ0,Ns is the contribution to the gap from the non-Zeeman effect, which depends only on the perpendicular magnetic field B⊥. By changing Btot while keeping B⊥ fixed, the number of flipped spins Ns is determined from ∂Δ/∂(|g∗|μBBtot) by using Eq. (1).

Much more interesting are Skyrmion excitations in the bilayer system. In this system, various QH states are realized by adjusting the ratio of the tunneling and Zeeman effects. Particularly in the bilayer ν=2 QH state, a phase transition has been observed [10], [11], [12], [13], [14] between the spin polarized state and the spin unpolarized state. The ν=2 spin polarized bilayer QH state is realized when the electron density in each layer is equal and the total electron density nt is high enough [10], [15]. This state is identified as a compound state composed of two identical monolayer ν=1 states [10], where excitations are expected to be Skyrmions of the same type as in the monolayer ν=1 QH state.

In this work, we compare Skyrmions in the compound ν=2 state in the samples with different tunneling energy gap ΔSAS and in the induced monolayer ν=1 QH state. The induced monolayer system is realized by emptying the electrons in one of the layers. Such comparison will reveal the role of the interlayer Coulomb and tunneling interactions.

Section snippets

Experimental results

Three samples were grown by molecular beam epitaxy. They consist of two GaAs quantum wells of 200 Å width separated by a 31 Å thick barrier of AlxGa1−xAs (x=0.3, 0.33 and 1) [16]. We label them #10.9, #7.6 and #1 according to their ΔSAS; 10.9, 7.6 and 1 K, respectively. The electron densities of the front-layer nf and of the back-layer nb are controlled by adjusting the gate bias voltages. The low temperature mobility of samples #10.9 and #1 is 2×106 cm2/Vs with the electron density of 2×1011 cm−2,

Discussion

The energy ΔSky and the size κ of a Skyrmion are theoretically estimated for a large Skyrmion at ν=1 as [1], [2], [20]ΔSkye2/εℓ0≃π32+3β4κ,κ≃β1/32RZ/Cln2π32RZ/C+1−1/3,where β represents the strength of the Coulomb energy which depends on the sample parameter such as the layer thickness (β=3π2/64≃0.46 for a large Skyrmion in an ideal planer system). The creation energy of Skyrmion–anti-Skyrmion pair will be given by 2ΔSky. However, various factors affect the activation energy. In particular,

Acknowledgements

The research was supported in part by Grant-in-Aids for the Scientific Research from the Ministry of Education, Science, Sports and Culture (10203201, 10640244, 11125203, 11304019), the Asahi Glass Foundation, CREST-JST and NEDO “NT-D-P-98” projects.

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