Ising Quantum Hall Ferromagnet in Magnetically Doped Quantum Wells

We report on the observation of the Ising quantum Hall ferromagnet with Curie temperature $T_C$ as high as 2 K in a modulation-doped (Cd,Mn)Te heterostructure. In this system field-induced crossing of Landau levels occurs due to the giant spin-splitting effect. Magnetoresistance data, collected over a wide range of temperatures, magnetic fields, tilt angles, and electron densities, are discussed taking into account both Coulomb electron-electron interactions and $s\mathrm{\text{−}}d$ coupling to Mn spin fluctuations. The critical behavior of the resistance “spikes” at $T\to T_C$ corroborates theoretical suggestions that the ferromagnet is destroyed by domain excitations.

Figure 1

(a) Resistances ${\rho }_{xx}$ and ${\rho }_{xy}$ at $T=0.33\mathrm{K}$ for $n_s=2.97\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$ ($V_g=0$). Note the presence of a spike in ${\rho }_{xx}$ at $B_c\simeq 5.8\mathrm{T}$, shown at selected temperatures in (b). Inset: The nominal distribution of magnetic monolayers in the QW.

Figure 2

(a) Resistance ${\rho }_{xx}$ for $n_s=2.97\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$ for various tilt angles $\theta$ (a). Experimental and calculated [Eq. (1)] spike positions [(b),(c)] for two directions of the field sweep (c).

Figure 3

(a) Resistance ${\rho }_{xx}$ at 0.33 K for $n_s=2.31–3.44\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$. Traces are shifted vertically for clarity. Dashed lines mark resistance spikes at the crossing of LLs with the indices (2,5), (1,3), (0,2), and (0,1) as determined from LLs energies displayed in (b). The inset shows the height of the spike at $B_c\simeq 5.8\mathrm{T}$ as a function of the filling factor.

Figure 4

(a) The spike height as a function of $T$ for $n_s=2.97$ (squares) and $2.54\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$ (open circles). If the spike and the SdH peak overlap, the contribution of the latter is subtracted. Full circles show the width of hysteresis loops presented in (b), where ${\rho }_{xx}(B)$ is depicted in the region of the spike for two directions of the field sweep at various $T$. The sweep rate is $0.3\mathrm{T}/\min $. The resistance behavior, reminiscent of critical scattering, and the presence of magnetic hysteresis are taken as evidence for the phase transition to QHFM.