pubs.acs.org/NanoLett
Electrically Defined Ferromagnetic Nanodots Daichi Chiba,†,‡ Fumihiro Matsukura,†,§ and Hideo Ohno*,†,§ †
Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan, ‡ Institute for Chemical Research, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan, and § Center for Spintronics Integrated Systems, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan ABSTRACT While ferromagnetic nanodots are being widely studied from fundamental as well as application points of views, so far all the dots have been physically defined; once made, one cannot change their dimension or size. We show that ferromagnetic nanodots can be electrically defined. To realize this, we utilize an electric field to modulate the in-plane distribution of carriers in a ferromagnetic semiconductor (Ga,Mn)As film with a meshed gate structure having a large number of nanoscaled windows. KEYWORDS Spintronics, ferromagnetic dots, electric-field controlled ferromagnetism, ferromagnetic semiconductor, (Ga,Mn)As
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tudies of ferromagnetic nanoparticles/dots have established fundamental understanding of many important phenomena in magnetism such as thermal fluctuation aftereffects and superparamagnetism and at the same time have laid the foundation of modern magnetic recording technology.1-8 In addition, advancement of nanotechnology for patterning and/or formation of nanoparticles/ dots, ranging from top-down electron-beam lithography to bottom-up self-assembly, has made it possible to fabricate ferromagnetic nanodots for magnetoresistive random access memories9 and patterned media.10 Nonmagnetic semiconductor nanodevices (nanowires and dots),11-14 on the other hand, are being used to investigate quantum phenomena for semiconductor physics and applications, where an electric field E plays a significant role in realizing low dimensional structures by modulating carrier density. In this study, we show the formation of ferromagnetic nanodots defined by the application of E in a ferromagnetic semiconductor (Ga,Mn)As thin film,15 which exhibits carrier (hole)-induced ferromagnetism.16 Its Curie temperature TC, coercivity Hc, and magnetocrystalline anisotropy are tunable by electrical gating through the modulation of hole concentration p.17-22 Figure 1a shows a meshed gate with nanoscaled windows formed on the gate insulator deposited onto (Ga,Mn)As channel. The high p regions remain only under the windows by the application of positive gate voltage VG, i.e., ferromagnetic dots can be defined by electrical gating. The anomalous Hall effect is employed to investigate the magnetization behavior15,17-20 of the electrically defined ferromagnetic dots. The magnetization process of the ferromagnetic dot ensemble showing superparamagnetic behavior including blocking is compared with a simulation based on single domain magnets which reproduces its
behavior well, showing the formation of electrically defined nanodots. A photomicrograph of the fabricated device with measurement configuration is shown in Figure 1b. A 3.6 nm thick Ga0.93Mn0.07As channel is grown at 220 °C by molecular beam epitaxy. The underneath buffer layer grown on a semi-insulating GaAs(001) substrate consists of 4.0 nm GaAs/30 nm Al0.75Ga0.25As/420 nm In0.15Ga0.85As/ 30 nm GaAs. The (In,Ga)As layer introduces tensile strain in the (Ga,Mn)As layer, which makes its magnetic axis along the growth direction.23 The sample is processed into a Hall bar geometry with a 30 µm wide and 200 µm long channel. Metal electrode pads (40 nm Au/5 nm Cr) are evaporated and lifted-off to form voltage probes as well as source and drain contacts. Then, a 40 nm thick HfO2 gate insulator (dielectric constant κ ) 21) is formed by atomic layer deposition. Finally, two regions of the electrically connected Au/Cr gate electrodes (G), meshed gate for dot formation and unpatterned gate for reference, are formed by electron-beam lithography and lift-off process. The meshed gate, the right-half of G in Figure 1b, forms an array of windows defining the dots. Scanning electron microscope images of the meshed gate region are shown in Figure 1c. The ∼400 × 400 nm2 windows are arranged in a square lattice with a 500 nm pitch in horizontal and vertical directions. The left-half of G is unpatterned and is fully covered by Au/Cr. The maximum applied VG is 16 V, which corresponds to an electric field E of 4 MV/cm. Four-terminal measurements are performed to probe the Hall resistance under the unpatterned and the meshed gate regions (RHallu and RHallm) and the sheet resistance under the unpatterned gate as functions of E, temperature T, and external out-of-plane magnetic field H. We first describe the magnetic properties of the region under the unpatterned gate. Figure 2a shows the RHallu versus H at 60 K under seven different E. The curve at -4 MV/cm shows a square hysteresis, reflecting a ferromagnetic order.
* Author to whom correspondence should be addressed: phone, +81-22-2175553; fax, +81-22-217-5553; e-mail,
[email protected]. Received for review: 07/8/2010 Published on Web: 10/05/2010 © 2010 American Chemical Society
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DOI: 10.1021/nl102379h | Nano Lett. 2010, 10, 4505–4508
FIGURE 1. Schematics of electrically defined ferromagnetic nanodots and the device structure. (a) The device is made of ferromagnetic semiconductor (Ga,Mn)As, a HfO2 gate insulator, and a meshed Au/Cr gate electrode. The gate voltage VG depletes the holes underneath the meshed gate, making the region paramagnetic and creating an array of ferromagnetic nanodots under the nanoscaled windows. (b) Hall bar shaped device structure and measurement configuration. The device has two gate (G) regions (equipotential unpatterned and meshed gates). 400 × 400 nm2 windows are formed by the meshed gate having a 500 nm pitch. The area of unpatterned gate is covered by Au/Cr. dc source (S)-drain (D) current IDS of 4 µA is applied during the Hall measurement. VG is applied between G and S. (c) Scanning electron microscope images of the meshed gate. The black regions indicate windows.
FIGURE 2. Magnetic properties of the channel under the unpatterned and meshed gates. (a) Magnetic hysteresis curves probed by Hall resistance of unpatterned gate (RHallu) part and (b) the meshed gate (RHallm) part at 60 K. The sweep rate of the applied magnetic field µ0H (µ0: permeability in free space) is 1.9 mT/min. (c) Temperature T dependence of remanent RHallu (unpatterned gate part, RHall,ru) and (d) RHallm (meshed gate part, RHall,rm) as a function of applied electric field E. The Curie temperature TC of the channel under the unpatterned gate is modulated from ∼58 to ∼74 K by changing E from +4 to -4 MV/cm.
The remanent Hall resistance RHall,ru (|RHallu| at H ) 0) and Hc are reduced as E increases toward positive and becomes zero at +3 MV/cm. T dependence of RHall,ru under each E is presented in Figure 2c: From the figure, TC of the channel defined as temperature at which RHall,ru becomes zero is determined to be 58, 67, and 74 K at E ) +4, 0, and -4 MV/cm, respectively. © 2010 American Chemical Society
We now turn to the region of the meshed gate. The RHallm versus H at 60 K under E and T dependence of RHall,rm are shown in panels b and d of Figure 2, respectively. While the suppression of the ferromagnetic order at 60 K under E ) +3 MV/cm or above can be seen in Figure 2a for the region under the unpatterned gate, we see a clear hysteresis under 4506
DOI: 10.1021/nl102379h | Nano Lett. 2010, 10, 4505-–4508
FIGURE 3. Measured and simulated magnetic hysteresis curves. (a) Hysteresis curves of the Hall resistance under the unpatterned gate (RHallu) and (b) the meshed gate (RHallm) at a gate electric field of E ) +4 MV/cm and T ) 50-66 K. (c) Simulated hysteresis curves of the normalized average magnetization Mave/Ms(0 K) of the ensemble of ferromagnetic nanodots. The relaxation time is assumed to have a distribution due to the variation of the out-of-plane uniaxial anisotropy constant K and the volume V of dots. Here, Ms(0 K) ) 0.07 T, Kmax(0 K) ) 400 J/m3, Kmin/Kmax ) 0.5, Vmax ) 0.95Vnom, and Vmin ) 0.8Vnom are used for simulation, where Vnom is nominal volume of a dot. Experimental and simulated results show good agreement, particularly when T is higher than TC of the region underneath the unpatterned gate (T > ∼58 K).
FIGURE 4. Electric-field dependence of the coercivity: (a) coercivity of the unpatterned gate region (Hcu) and (b) the meshed gate region (Hcm) as a function T.
activation energy Eact.1,5,6,8 The magnitudes of Eact needed to overcome to reach the +(-) state from -(+) state is expressed as Eact+(-) ) KV(1 - H/Hsw)R, where K is the perpendicular uniaxial anisotropy constant, V is the volume of a dot, and Hsw ()2K/Ms, where Ms is the T dependent spontaneous magnetization) is the switching magnetic field. We adopt R ) 2 because H is applied along the uniaxial easy axis. The thermally activated magnetization switching of a dot is characterized by the time constant τ+(-) following the Ne´el-Arrhenius law, τ+(-) ) τ0 exp(-Eact+(-)/kBT), where the inverse of the attempt frequency τ0 is assumed to be 10-9 s and kB is the Boltzmann constant.2 The probability that the magnetization of a dot resides in the + direction is given by solving the probability equation of motion. We consider a distribution of τ+(-) because of the variation of K and V of each dot in our system. The maximum and the minimum of τ+(-) depend on those of K and V (Kmax, Kmin, Vmax, and Vmin). The Brillouin function with spin S ) 5/2 is used for the T dependent Ms, and Kmax is assumed to be proportional to Ms.2,24 The averaged magnetization Mave of the dot ensemble in Figure 3c is then calculated (the parameters used for the calculation are presented in the caption). The calculated curves capture the salient features in Figure 3b very well, particularly above 58 K, e.g., the constriction near H ) 0 in the experimental curves is well-reproduced, suggesting that the each isolated dot is in a single domain state. The same set of parameters also explains well the behavior of the magnetization relaxation (see Supporting Information). These good agreements show that the ferromagnetic nanodots are electrically created by the application of E. Finally, we focus on the coercivity Hc. Parts a and b of Figure 4 show E dependence of Hc under the unpatterned (Hcu) and meshed gate (Hcm) regions, respectively. For the
the same E in Figure 2b, indicating that the ferromagnetic order remains below the windows. The hysteresis curves at E ) +3 and +4 MV/cm show a pronounced constriction near H ) 0. We also note that the shape of the hysteresis is skewed extending to H higher than Hc at E ) 0. These two features can readily be explained by the presence of ferromagnetic dots having a distribution of Hc as we discuss in the next section. The influence of the presence of the windows is also seen in positive E side in Figure 2d, as compared to Figure 2c. Parts a and b of Figure 3 show RHallu and RHallm versus H observed at T ) 50-66 K under E ) +4 MV/cm. The magnitudes of Hc and the shape of the two sets of curves are dramatically different at all temperatures. While RHall curves are moderately square at T < 58 K, above which it becomes paramagnetic (Figure 3a), the shape of RHallm curves changes from a moderate rounded one at low temperatures to the one with a clear constriction at T > 58 K (58 K corresponds to TC under the gate at E ) +4 MV/cm (see Figure 2c)) and finally to a superparamagnetic one without hysteresis above 63 K (Figure 3b). Figure 3c shows the result of simulation. The magnetization curves are calculated by using the Ne´el-Brown model (see Supporting Information) for single-domain dots with two stable states (+ and - states with the magnetization directions parallel and antiparallel to H, respectively) separated by an H and T dependent © 2010 American Chemical Society
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case of the unpatterned gate, Hcu decreases with increasing E at all temperatures, in accordance with our previous studies; this was attributed to the p dependence of the domain-nucleation magnetic field.19 Comparison of Figure 4b with Figure 4a reveals two features of Hcm. While the negative E produces qualitatively the same dependence, under E > 0, Hcm is found to be always larger than Hcu at all temperatures. In addition, one notices that there are ranges of T and E under which Hcm increases with increasing E toward positive direction. In these ranges, both the regions of (Ga,Mn)As layer underneath the windows and under the meshed gate are ferromagnetically ordered. In view of our earlier work,25 we believe the observed increase of Hcm is due to the suppression of domain wall propagation from one window region to another across the meshed gated region. Consequently, the magnetization reversal in each region under a window takes place independently. In summary, we have shown an electrical formation of ferromagnetic nanodots. The temperature dependence of magnetization curves, coercivity, and magnetization relaxation all show clear signatures of the nanodot formation. This approach will enable us to electrically tune the size of the ferromagnetic dot as well as the interaction among them. In view of the recent studies on the electrical control of ferromagnetism in thin metallic films26-28 and multiferroics29-31 and on electric-field induced superconductivity,32 electrical definition of nanostructures is believed to become a powerful tool for controlling and studying collective phenomena at nanoscale.
of this paper published ASAP October 5, 2010. The correct version published October 11, 2010. Supporting Information Available. Information on the Monte Carlo simulation of hysteresis curves of ferromagnetic dot ensemble and magnetization relaxation of the ferromagnetic dot ensemble. This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES AND NOTES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25)
Acknowledgment. We thank R. Sasaki and T. Meguro for their technical support as well as T. Ono for discussion. The work was supported in part by ERATO from JST, Grant-inAids from MEXT/JSPS, the “High-Performance Low-Power Consumption Spin Devices and Storage Systems” program under R & D for Next-Generation IT of MEXT, the Funding Program for World-Leading Innovative R & D on Science and Technology (FIRST) Program from JSPS, and the GCOE program at Tohoku University.
(26) (27) (28) (29) (30)
Note Added after ASAP Publication. Due to a production error, Figures 1, 2, 3, and 4 were reprocessed in the version
© 2010 American Chemical Society
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DOI: 10.1021/nl102379h | Nano Lett. 2010, 10, 4505-–4508
