Magnetic anisotropy control by applying an electric field to the side surface of ferromagnetic films

Reducing the power consumption necessary for magnetization reversal is one of the most crucial issues facing spintronics devices. Electric field control of the magnetic anisotropy of ferromagnetic thin films is a promising method to solve this problem. However, the electric field is believed to be effective only within several nanometres of the surface in ferromagnetic metals because of its short Thomas-Fermi screening length, which prevents its practical application to devices. Herein, we successfully modulate the magnetic anisotropy of the entire region of the ferromagnetic layers in the elongated mesas of vertical spin field-effect transistors with widths as large as ~500 nm by applying an electric field to the side surface of the metallic GaMnAs-based mesas through an electric double layer. Our results will open up a new pathway for spintronics devices with ultra-low power consumption.

In order to verify that the MR characteristics obtained in the main manuscript originates from TMR rather than TAMR, we measured TAMR in a GaMnAs-based heterostructure that has a single ferromagnetic layer. We have grown Ga 0.94 Mn 0.06 As (20 nm)/ AlAs (6 nm)/ GaAs: Be (100 nm) on a p + GaAs (001) substrate, and have prepared a cylindrical mesa diode with 200 μm in diameter as shown in Supplementary Fig. S1(a). We measured the MR varying the in-plane magnetic-field direction φ at V = -80 mV at 3.8 K. The φ dependence of the MR is measured in the same procedure as we performed in the main manuscript. Supplementary Fig. S1(c) shows the MR characteristics measured at φ = 35°, and 75°. When φ = 75°, the MR characteristics showed positive hysteresis signals; however, when φ = 35°, the MR showed negative hysteresis signals, which are not observed in the usual TMR characteristics regardless of φ. These are TAMR characteristics and are summarized in Supplementary Fig. S1(e). The obtained TAMR (0.2%) is negligibly small in comparison with the value of the TMR ratio (~5%) shown in the main manuscript. In order to understand these MR characteristics, we calculated the TAMR characteristics of a tunnel junction with a ferromagnetic GaMnAs electrode whose easy axis is in the [1 � 10] direction. In the calculation, we used the Stoner-Wohlfarth model in the same way as we did in the main manuscript. Here, we assumed H B = 0.1 (kOe), H U[010] = 0 (kOe), U[1 � 10] = 0.5 (kOe), and U[1 � 10] , ε, and M are the biaxial anisotropy field along <100>, the uniaxial anisotropy field along [010], the uniaxial anisotropy field along [1 � 10], the domain nucleation/propagation energy, and the magnetization, respectively.
In this case, using the concept of TAMR, the tunnel resistance R can be expressed by where, R 0 and ΔR are fitting parameters. θ is the in-plane magnetization direction with respect to the [100] direction in GaMnAs. Then, the TAMR ratio is expressed by The peak positions of calculated result shown by red curves reproduce that of experimentally obtained results. Although, when we fit the MR characteristics at fixed φ, we can find some sets of parameters, when we fit the MR characteristics at all φ simultaneously, the parameters are determined almost uniquely.
We can determine the fitting parameters for top and bottom GaMnAs layers rather independently. Generally, the top GaMnAs layer has a smaller coercive field than the bottom layer. This is because the Mn interstitial defects can be more easily diffused out from the top  Supplementary Fig. S2).

Supplementary Note 3. Influence of the parasitic resistance in the device performance
The resistance of our device is dominated by the tunnel resistance at the GaAs barrier and the influence of the parasitic resistance is negligibly small as shown below.
Supplementary Fig. S3 shows the resistance area product (RA) of the device prepared in the main manuscript (GaMnAs (9.2 nm)/ GaAs (11 nm)/ GaMnAs (3 nm)/ GaAs: Be (100 nm) on a p + GaAs (001) substrate) and that of the diode without the GaAs barrier layer which is composed of GaMnAs (10 nm)/ GaAs: Be (100 nm) on a p + GaAs (001) substrate. The RA of the diode without a GaAs barrier layer is ~10 -3 -10 -4 times smaller than the device which has a GaAs barrier layer. Thus, the resistance originating from the GaAs: Be layer and the substrate is estimated to be only ~10 -1 -10 -2 % of that of the whole MTJ. Because the Be concentration of the GaAs: Be layer is high (1×10 18 cm -3 ) and it is metallic, the influence of the gate electric field modulation of GaAs: Be is smaller than ~10 -1 -10 -2 % of the total resistance of the MTJ. It is negligibly small in comparison with the change of the resistance obtained in our main manuscript (~20%).

Supplementary Figure S3 | Influence of the parasitic resistance in the device performance.
Bias voltage dependence of the RA of the diode composed of GaMnAs/GaAs/GaMnAs/GaAs:Be on a p+ GaAs (001) substrate, and GaMnAs/GaAs:Be on a p + GaAs (001) substrate at ~4 K.

Supplementary Note 4. Temperature dependence of magnetic anisotropy
We show that the Joule heating, which may be induced by the change in the current due to the electric field, is not the origin of the change in the anisotropy fields of the GaMnAs layers. We measured tunnel magnetoresistance (TMR) for a reference sample of a GaMnAs-based magnetic tunnel junction varying the (source-drain) bias voltage V and thus the tunneling current I. The reference sample is composed of Ga 0.94 Mn 0.06 As (10 nm)/ GaAs (9 nm)/ Ga 0.94 Mn 0.06 As (3 nm)/ GaAs: Be (100 nm) grown on a p + GaAs (001) substrate by low temperature molecular beam epitaxy. We fabricated a simple cylindrical mesa diode with 100 μm in diameter. This device does not have a gate electrode. Here, we note that this reference sample is more sensitive to the influence of Joule heating than the sample used in the main manuscript. Because this reference sample has a thinner tunnel barrier than the sample prepared in the main manuscript, the generated heat per unit area becomes larger when the applied voltages are fixed. In addition, because the total surface area per unit volume of the reference sample is smaller than the sample prepared in the main manuscript which has an elongated shape, heat exchange from the surface is less efficient in this reference sample. The TMR measurements were performed in the same way as described in the main manuscript. Supplementary Fig. S4a-c shows the magnetic-field direction φ dependence of the MR ratio at V = 5 mV, 10 mV and 15 mV, respectively. The corresponding I which flows in the diode are 105 nA, 341 nA and 787 nA at V = 5 mV, 10 mV, and 15 mV when the magnetic field H is 0 kOe, respectively. Despite this large change in I (105 nA→787nA), the symmetry of the MR patterns looks very similar in Supplementary Fig.   S4a-c. This means that the magnetic anisotropy is not changed by changing I or the Joule heating in this experiment. In our study shown in the main manuscript, the modulation ratio of the drain current by the gate electric field is only 20% at most (Fig. 2b in the main manuscript), which is much smaller than the change in I in this experiment (105 nA→787nA, 650%). Thus, we can conclude that the effect of the Joule heating is negligibly small for the change in the anisotropy fields.