Main

Manipulation of magnetism by a gate electric field has been demonstrated in carrier-controlled ferromagnets by studies of the anomalous Hall effect10,11,12,13,14, resistance15,16 and splitting of a luminescence line17. Such studies provide information on spin polarization of itinerant carriers. To probe directly the effect of carrier localization on magnetism, we have developed superconducting quantum interference device (SQUID) magnetometry sensitive enough to quantitatively determine magnetization of (Ga, Mn)As constituting the channel of metal–insulator–semiconductor (MIS) structures. The (Ga, Mn)As film was grown on a GaAs (001) substrate and had a thickness t=3.5 nm and a nominal Mn cation concentration x=7±1%. For magnetic measurements, a series of (Ga, Mn)As-based parallel-plate capacitors with a gate area of about 10 mm2 and a HfO2 (dielectric constant ) gate insulator with a thickness d, ranging from 40 to 50 nm were prepared and found to sustain gate voltages VG up to ±(12–15) V, or electric fields EG=|VG|/d up to 3–4 MV cm−1 (see Fig. 1 and the Methods section for details as well as Supplementary Information, S1 for a transmission electron micrograph). Our as-grown material shows a Curie temperature TC<25 K, a typical value for very thin (Ga, Mn)As films18, and a reduced hole density, which brings the system near to the localization boundary, as illustrated for our channel in Supplementary Information, S2. The SQUID measurements are carried out along various crystallographic directions because of magnetic anisotropy. The results presented here correspond to the in-plane configuration, as we found that the magnetic moment remains in-plane even at low hole densities for which the easy axis assumes the perpendicular orientation in thick layers.

Figure 1: General layout and an example of an investigated MIS structure.
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a, The arrangement of the main components of devices fabricated for our studies. b, A view of one of the devices. The device is attached to the sample holder comprising a 2-mm-wide and 19-cm-long silicon strip using an equally long strip of a thin double-sided low-tack sticky tape. The connections to the voltage terminals at the far ends of the sample holder are made by a high-purity 50 μm copper wire.

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We obtain TC(VG) from the temperature dependence of the spontaneous magnetic moment mS(T) of the film during cooling the sample in zero magnetic field (<1 Oe) under constant VG applied at T>TC (see Fig. 2a) and from measurements of mS as a function of VG at various temperatures (see Fig. 2b). Absolute values of mS(T) are determined by a method outlined in the Supplementary Information, S3. From the results presented in Fig. 2a,b, we find that sample processing, presumably unintentional annealing, increases TC to 34 K at zero gate voltage. The magnitude of TC rises to 41 K under a negative bias of VG=−12 V, which increases the hole density, and can conversely be reduced to 24 K under a positive voltage VG=+12 V.

Figure 2: Magnetic studies of the (Ga, Mn)As channel under the influence of the electric fields.
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a, Experimental temperature dependence of the spontaneous moment mS for selected values of gate voltage VG. Temperatures at which mS disappears define the Curie temperature TC, as marked by arrows. b, Isothermal mS(VG). The arrows mark the Curie points for each T. c, Isothermal control of mS including complete switching ‘on’ and ‘off’ of the ferromagnetic state of the gated part of the sample at 1 K below TC=34 K. The temporal resolution of the experiment is limited mainly by the acquisition time of the SQUID, approximately 1.5 s per point. d, Experimental and calculated dependence of mSat on VG. e, Profile p(z) of the hole density in the channel for various VG computed assuming the interfacial donor concentration Ni=2.4×1013 cm−2 and the net acceptor concentration NA=2.0×1020 cm−3 in the 3.5-nm-thick channel. The dashed line exemplifies the method used to established Δz, defining the region populated by holes, required to calculate the saturation magnetic moment mSat. f, Experimental dependence of TC on VG: squares (from a) and circles (from b). The orange circles are calculated from equation (1) assuming the hole profiles of e.

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Within the impurity-band models of electronic states in ferromagnetic (Ga, Mn)As (refs 3, 5, 8, 9), the magnitude of TC is expected to reach a maximum, when the Fermi level is shifted across the peak in the density of the impurity states. So far, however (Fig. 2 and refs 12, 13), a monotonic decrease of TC is observed when the channel is depleted by the gate voltage.

Figure 2c shows the isothermal switching among different magnetic states in the time domain, which provides the absolute scale of the magnetic moment changes reported previously for (In, Mn)As (refs 10, 12) and (Ga, Mn)As (refs 13, 14). In Fig. 2a, mSat=mS(T→0) changes monotonically in the whole range of VG (see also Fig. 2d), indicating that the channel is partially depleted at VG=0 as no increase of magnetic response is expected once all of the moments are involved in the ferromagnetic phase.

To find out to what extent one can describe the data without considering effects of localization, we calculate the hole density p along the growth direction z by using a Poisson solver under the Thomas–Fermi approximation (ref. 19; we have also developed a Poisson solver with Fermi–Dirac integration for highly degenerated semiconductors at low temperatures). As in (Ga, Mn)As, the mean free path is shorter than the channel width and so the dimensional quantization is smeared out, which makes this semi-classical approach valid. We calculate p(z) and then mSat(VG) and TC(VG) in a self-consistent way adopting the hole density-of-states effective mass from the 6×6 kp model2. Furthermore, as the density of the surface states and the degree of compensation are unknown, we treat the concentration of positive interface states Ni and the net concentration NA of Mn acceptors in the (Ga, Mn)As channel as two adjustable parameters to obtain a p(z) that describes the experimental values of mSat(VG)/mSat(0).

As shown in Fig. 2d, the calculated dependence of the relative magnetic moment mSat(VG)/mSat(0)=Δz(VG)/Δz(0), where Δz(VG) is the thickness of the layer populated by the holes (see Fig. 2e), reproduces well the experimental values. This points to a strongly non-uniform hole distribution across the width of the channel for all gate voltages examined here. Furthermore, the presence of a surface depletion layer shows that an efficient steering of the hole density towards enhanced TC or anisotropy switching at the high-p end20 requires the reduction of interface states.

To calculate TC(VG), we noted that the phase coherence length of holes, as extrapolated from the low-temperature data21, is expected to exceed the width of (Ga, Mn)As channel, which implies a collective two-dimensional behaviour of the Mn spins across the channel. In this case, in terms of the sheet hole density and the corresponding thermodynamic density of states at the Fermi level ρs(EF)=∂ ps/∂ EF, TC according to the p–d Zener model2,22 can be written in the form,

where TC[p, xeff] is the Curie temperature computed earlier2 for (Ga, Mn)As as a function of the hole concentration and the effective concentration of Mn participating in the ferromagnetic ordering xeffN0, where N0 is the cation concentration. As shown in Fig. 2f, on the basis of profiles from Fig. 2e, equation (1) can explain the dependence of TC(VG)/TC(0) reasonably well. We note also that, although with the fixed values of Ni and NA we can describe both mSat(VG)/mSat(0) and TC(VG)/TC(0), the fitting could be improved by taking the thickness of (Ga, Mn)As, owing to the possible existence of a native oxide layer16, and/or the concentration of As-antisite donors in the GaAs buffer layer as extra adjustable parameters.

In (Ga, Mn)As, the self-compensation proceeds through the creation of Mn interstitial double donors of concentration23 xI N0=(x N0−NA)/3. According to both theoretical24,25 and experimental26 findings, they do not couple to the hole spins, so that xeff=x−xI. Indeed, by fitting the absolute values of TC(VG) and mSat(VG), we obtain reduced values of x, xeff (fromTC)=0.028 and xeff (from mSat)=0.017, as shown in Fig. 2f and d, respectively. According to the determined values of NA=2.0×1020 cm−3, xI is 0.020, which gives xeff=0.05. We see that xeff determined from experiments is smaller than this value, particularly in the case of mSat(VG). In the search for the missing magnetic moments, we have undertaken an elaborated method of magnetization determination for this sample.

As shown in Fig. 3a, by cooling in the magnetic field we reveal the presence of an increased (with respect to mS) low-temperature magnetic remanent signal. This extra contribution becomes visible only below a certain characteristic temperature Tσ<TC. Whereas the already discussed spontaneous magnetic moment mS shows properties expected for standard ferromagnets, the properties of this extra magnetic moment mσ are similar to those shown by a collection of magnetic nanoparticles. We hereafter call it a superparamagnetic-like moment and identify Tσ as a relevant blocking temperature. Interestingly, as shown in Fig. 3b, the moments mσ (circles) and mS (triangles) are oriented in the mutually perpendicular directions, along [110] and [−110], respectively. This behaviour is typical for (Ga, Mn)As, according to results of SQUID measurements for other samples collected in the Supplementary Information, S4. At the same time, a Brillouin-like character of the critical decay of magnetization at T→TC−, shown in Figs 2 and 3, and Supplementary Information, S4a,b, demonstrates the collective behaviour of the Mn spins across the channel, which confirms that the phase coherence length of holes is longer than the channel width in these samples.

Figure 3: Experimental evidence for the coexistence of ferromagnetic and superparamagnetic-like regions specified by differing magnetic anisotropy.
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a, After field cooling in H=1 kOe, a standard measurement of thermoremanent magnetization [t r m(T), red points] along the [100] direction starts at the initial temperature T0=6 K (point A) after the field quenching. Then, instead of warming the system directly to above TC=34 K (T5, point B), the temperature sweep is interrupted at some intermediate temperatures (T1 to T4) and redirected back to T0—where the warming is restarted to the next Ti. After exceeding a characteristic temperature Tσ≈19 K (point D), all of the experimental points fall onto the same temperature-reversible line (C–D–B, dashed yellow). The procedure allows us then to identify in general: (1) the temperature-reversible component mS (the grey area under the C–D–B line) and (2) the history-dependent part mσ (cross hatched triangle A–D–C ‘above’ the C–D–B line); or in particular their projections. b, Temperature dependence of [−110] (filled points) and [110] (open points) components of mS (triangles) and mσ (circles), showing that the easy axis for most of mσ is [110], that is perpendicular to the easy axis of mS. c, Demonstration that Tσ (black arrows) and uniaxial magnetic anisotropy of mσ (difference between open and filled points) decreases with the channel depletion, the anisotropy vanishing entirely for VG=+12 V.

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To interpret these observations, we note that according to some of the present authors8,27, properties of carrier-mediated ferromagnets are strongly influenced by the vicinity of the metal-to-insulator transition (MIT), particularly by the corresponding quantum critical fluctuations in the local density of states. These fluctuations break the spatial continuity of the ferromagnetic order, leading to a nanoscale phase separation, a scenario suggested also by Monte Carlo simulations7 and X-ray magnetic dichroism28 as well as providing an explanation for unexpected Coulomb blockade features29,30 in macroscopically uniform constrictions of (Ga, Mn)As. This process is seen by inspecting the data in Figs 2e and 3c for VG≤0, where the relative contribution mσ(T→0) to mSat increases on going towards more positive VG. On further depletion of the channel (VG>0), a reduction in the volume of superparamagnetic regions is expected owing to a shortening of the localization length. The presence of this effect is corroborated by the low-field studies pointing to a rapid fall of Tσ and progressive randomization of the easy-axis orientations, as seen in Fig. 3c.

The model presented here reaches beyond the case of very thin films. For any thickness, the depletion of the near-surface region or interface will introduce this superparamagnetic-like response in a proportion depending on the thickness of the film. Analogously, if a film of any thickness is brought to the MIT, for example, by decreasing xeff and, thus, p and ρ(EF), its magnetic properties will also be affected by the carrier localization. However, similarly to other thermodynamic properties, ferromagnetic characteristics do not show any critical behaviour at the MIT. Instead, within the present scenario, washing out of ferromagnetism by carrier localization proceeds by means of nanoscale phase separation, resulting in the gradual appearance of superparamagnetic-like properties. This means that in the insulating phase, ferromagnetic ordering is maintained only locally but, nevertheless, the apparent TC is still satisfactorily described by the p–d Zener model8. A further shortening of the correlation length (which corresponds to a mean localization length in this case) brings relevant blocking temperatures towards zero, so that no magnetic moments are observed without an external magnetic field at non-zero temperatures. Experimentally, a jump of the apparent TC to zero occurs rather abruptly15. In the case of (Ga, Mn)As, where the MIT appears at relatively high values of xeff, and ρ(EF), the reported Curie temperatures at the ferromagnetism boundary group around a common value of , before jumping to zero. In agreement with this conjecture, lower than ∼15 K values of TC* have been reported for, for example, (Zn, Mn)Te (ref. 8) and (In, Mn)Sb (ref. 31), in which the MIT occurs at smaller values of xeff and ρ(EF), respectively. We note that this reasoning does not rule out a continuous decay of TC* with p, it rather calls for more elaborate magnetic studies in this region of the magnetic phase diagram.

We have developed a method to monitor experimentally and to describe theoretically changes in the magnetic moment and ordering temperature induced by an electric field in MIS structures of ferromagnets in which the spin–spin coupling is mediated by carriers. We have found that further progress in magnetization manipulations by an electric field requires a better control over interface states. Furthermore, our data demonstrate the coexistence of ferromagnetic-like, superparamagnetic-like and paramagnetic regions. We assign this phase separation to quantum critical fluctuations in the local density of hole states, specific to doped semiconductors in the vicinity of the Anderson–Mott MIT. Within this model, the portion of the spins that contribute to the long-range ferromagnetic order diminishes when electronic disorder increases, which eventually results in the loss of spontaneous magnetization. This occurs at higher values of disorder than that corresponding to the MIT (ref. 32). According to our results, magnetic anisotropy undergoes significant changes in this region. Although the distribution of magnetic ions has been assumed to be uniform, in many systems magnetic ions tend to aggregate. In such a case, the magnitude of the apparent Curie temperature is determined rather by a non-random distribution of magnetic ions27 than by the fluctuations in the local carrier density.

Methods

Sample growth and device fabrication for magnetic measurements.

A 3.5-nm-thick film of Ga0.93Mn0.07As and 4 nm GaAs are grown at 195 ∘C following 30 nm of Al0.8Ga0.2As and 30 nm of GaAs buffers grown at 220 ∘C and 560 ∘C, respectively, on a semi-insulating GaAs(001) substrate by molecular beam epitaxy (see Supplementary Information, S1 for other details and cross-sectional TEM of the structure). After placing the In contact on top of the (Ga, Mn)As channel, the as-grown material is introduced to an atomic layer deposition chamber for a high-κ dielectric-oxide gate insulator at a substrate temperature of 130 ∘C. Despite a relatively low deposition temperature, a 30–100% increase of TC is always recorded after processing, indicating an increase of hole density and/or effective Mn concentration. MIS structures of the required dimension are defined by ∼0.5-mm-wide stripes of photoresist put down on the surface before deposition of a 3 nm Cr/50 nm Au gate electrode. After the lift-off, the final electrical connections to the (Ga, Mn)As channel and the gold metal electrode are attached by a silver-based conductive epoxy. We regard a device as a prospective one if during room-temperature current–voltage (I–V) characteristics tests within ±4 V (±∼1 MV cm−1), the capacitor shows no indication of leaking (flat I–V ‘curve’ on the 100 pA range indicating a leakage current below 10−10 A cm−2). Finally, typically one third of the devices survive multiple mounting on a magnetometer sample holder and low-temperature energizing up to the gate voltage of 12–15 V (3–4 MV cm−1). The use of indium for contacting the (Ga, Mn)As channel and some technical details of the experimental set-up limit reliable magnetometry of these devices to temperatures above 6 K and magnetic fields below a few kilo-oersted, respectively.