Hysteretic Resistance Spikes in Quantum Hall Ferromagnets without Domains

We use spin-density-functional theory to study recently reported hysteretic magnetoresistance ${\rho }_{xx}$ spikes in Mn-based 2D electron gases [Phys. Rev. Lett. 89, 266802 (2002)]. We find hysteresis loops in our calculated Landau fan diagrams and total energies signaling quantum Hall ferromagnet phase transitions. Spin-dependent exchange-correlation effects are crucial to stabilize the relevant magnetic phases arising from distinct symmetry-broken excited- and ground-state solutions of the Kohn-Sham equations. Besides hysteretic spikes in ${\rho }_{xx}$, we predict hysteretic dips in the Hall resistance ${\rho }_{xy}$. Our theory, without domain walls, satisfactorily explains the recent data.

Figure 1

Hysteretic magnetoresistance ${\rho }_{xx}$, Hall resistance ${\rho }_{xy}$, and total energy $E$, as a function of $B$ for a quantum well [inset in (a)]. For the $\mathrm{\text{up}}\rightleftharpoons \mathrm{\text{down}}$ $B$ sweeps, hysteretic spikes and dips appear in ${\rho }_{xx}$ and ${\rho }_{xy}$, respectively, at $B\sim 5.8\mathrm{T}$ (a). For increasing temperatures, the hysteretic loops become less pronounced (${\rho }_{xy}$ not shown) and disappear above a critical temperature $T_c\sim 2.1\mathrm{K}$ (b). The total energy $E$ (c) shows hysteretic loops [see blowup of the loops in (d)] because the KS equations have two distinct solutions (ground and excited states), e.g., for $B_c^d<B<B_c^u$. These are quantum Hall ferromagnet phases with distinct spin polarizations (Fig. 2). The curves in (b) are displaced vertically for clarity.

Figure 2

(a) Landau-level fan diagram [Eq. (4)], (b) spin-dependent electron densities $n_{2\mathrm{D}}^{\uparrow ,\downarrow }$, and (c) spin polarization $\zeta$ of our 2DEG [Fig. 1a]. In (a), we plot the center of each LL with a phenomenological Gaussian broadening $\Gamma =0.36\sqrt{B}\mathrm{meV}{\mathrm{T}}^{-1/2}$ [11]. The $s\mathrm{\text{−}}d$-induced nonlinear behavior of the energy spectrum ($B<2\mathrm{T}$) allows for nontrivial LL crossings near the chemical potential $\mu$ (curve at $\sim 74\mathrm{meV}$). Inset (a): Blowup of the hysteretic crossings between the states with $n=1$ and spin down (${\epsilon }_{1,1}^{\downarrow }$) and that with $n=0$ and spin up (${\epsilon }_{1,0}^{\uparrow }$) at $B\sim 5.8\mathrm{T}$ for the $\mathrm{\text{up}}\rightleftharpoons \mathrm{\text{down}}$ $B$ sweeps. The discontinuous change in the spin polarization $\zeta$ signals a transition between distinct quantum Hall ferromagnet phases. We have adjusted $x_p$ and $\Gamma$ so the levels would cross at $\sim 5.8\mathrm{T}$ as in the experimental data [7].

Figure 3

Magnetoresistance ${\rho }_{xx}$ vs $B\cos (\theta )$ for several tilt angles $\theta$ between the $B$ field and the growth direction. Similarly to the data in Ref. 7, the spike shifts to lower fields as $\theta$ increases, while the ordinary Shubnikov–de Haas peaks do not.

Figure 4

Temperature dependence of the ${\rho }_{xx}$ spike positions $B_c$ (a) and amplitudes (b) for $\mathrm{\text{up}}\rightleftharpoons \mathrm{\text{down}}$ $B$ sweeps. Inset in (a): $\Delta B_c=B_c^d-B_c^u$ versus $T$, from which we extract a critical temperature $T_c$; for $T>T_c$, the hysteresis disappears. The asymmetric shape of our hysteretic loops [Figs. 1b, 1c, 1d] is clearly manifest in (b).