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Coulomb blockade anisotropic magnetoresistance and voltage controlled magnetic switching in a ferromagnetic GaMnAs single electron transistor
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 310 (2007) 1883–1888 www.elsevier.com/locate/jmmm
Coulomb blockade anisotropic magnetoresistance and voltage controlled magnetic switching in a ferromagnetic GaMnAs single electron transistor J. Wunderlicha,, T. Jungwirthb,c, A.C. Irvined, B. Kaestnere, A.B. Shickf, R.P. Campionc, D.A. Williamsa, B.L. Gallagherc a
Hitachi Cambridge Laboratory, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK b Institute of Physics ASCR, Cukrovarnicka´ 10, 162 53, Praha 6, Czech Republic c School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK d Microelectronics Research Centre, University of Cambridge, Cambridge CB3 0HE, UK e National Physical Laboratory, Teddington T11 0LW, UK f Institute of Physics ASCR, Na Slovance 2, 182 21, Praha 8, Czech Republic Available online 14 November 2006
Abstract We observe low-field hysteretic magnetoresistance (MR) in a (Ga,Mn)As single electron transistor which can exceed three orders of magnitude. The sign and size of the MR signal is controlled by the gate voltage. Experimental data are interpreted in terms of electrochemical shifts associated with magnetization rotations. This Coulomb blockade anisotropic MR is distinct from previously observed anisotropic MR effects as it occurs when the anisotropy in a band structure derived parameter is comparable to an independent scale, the single electron charging energy. Effective kinetic-exchange model calculations in (Ga,Mn)As show chemical potential anisotropies consistent with experiment and ab initio calculations in transition-metal systems suggest that this generic effect persists to high temperatures in metal ferromagnets with strong spin–orbit coupling. In addition we observe a significant gate voltage dependence of the magnetic switching field which we attribute to carrier density variations in the electric field exposed GaMnAs regions causing a substantial change in the magneto-crystalline anisotropy profile. r 2006 Elsevier B.V. All rights reserved. Keywords: Magnetic semiconductors; Coulomb blockade; Single-electron tunneling; Magnetotransport phenomena; Materials for magnetotransport; Spin polarized resonant tunnel junctions
Single-electronics, which is based on the discrete charge of the electron [1], is the ultimate in miniaturization and electro-sensitivity. Spintronics, which is based on manipulating electron spins [2], delivers high magneto-sensitivity and nonvolatile memory effects. The potential of hybrid single-electronic/spintronic devices and the fundamental importance of spin phenomena at nanoscale have motivated number of studies of spin transport in the Coulomb blockade (CB) regime [3–7]. Experiments in single-electron transistors (SETs) in which the leads and island comprise different ferromagnetic materials [3] have shown both Corresponding author. Tel.: +44 1223 442901; fax: +44 1223 467942.
E-mail address: [email protected] (J. Wunderlich). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.676
electric and magnetic field dependent CB oscillations. These magneto-CB oscillations are due to the Zeeman energy changing the relative chemical potentials in the leads and in the island. They occur at high applied fields and are nonhysteretic. A small low-field hysteretic magnetoresistance (MR) effect has been demonstrated in SETs when the relative orientation of the magnetization of the leads is switched from parallel to antiparallel [3,7]. This gate-voltage dependent MR was attributed to resonant tunneling effects through quantized energy levels in the island. Here the magnetization reorientation induced by a weak magnetic field is attributed to subtle, spin-coherent resonant tunneling effects through quantized energy level in the island. It is much weaker than
ARTICLE IN PRESS 1884
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the response to the gate voltage, which is dominated by classical CB oscillations. We demonstrate that in ferromagnets with strong spin–orbit coupling, large chemical potential shifts can be induced by magnetization rotations leading to unprecedented characteristics of the ferromagnetic SET [4]. The signatures of this CB anisotropic magnetoresistance (CBAMR) effect are MR signals which can be hysteretic, which occur at magnetic fields corresponding to ferromagnetic anisotropy fields, which can have magnitudes approaching the resistance variations due to CB oscillations, and which show both positive and negative spin-valve-like characteristics controlled by the SET gate-voltage. Our SETs are fabricated from p-type (Ga,Mn)As, a ferromagnetic semiconductor for which parameters derived from the spin–orbit coupled band structure are known to be strongly anisotropic with respect to the magnetization orientation [8–14]. A schematic diagram of the device are shown in Fig. 1(a). The SET consists of a trench-isolated side-gated 40 nm wide channel aligned along the [1 1 0] direction. It was patterned by e-beam lithography and reactive ion etching in a 5 nm Ga0.98Mn0.02As epilayer, which was grown along the [0 0 1] crystal axis on an AlAs buffer layer by low-temperature molecular beam epitaxy [13]. The narrow channel technique is a simple approach to realize a SET and has been used previously to produce nonmagnetic thin film Si and GaAs-based SETs in which disorder potential fluctuations create small islands in the channel without the need for a lithographically defined island [15,16]. These SETs are well suited for exploring functionalities based on classical single-electron charging effects on which the CBAMR is based on. High precision electrical measurements were performed to exclude spurious effects associated with large changes in the resistance of the SETs. The DC currents were measured using sub-femtoampere source-measure units at a constant source–drain voltage. Simultaneously, voltage drops over constricted and unstructured parts of the bar were detected using a potentiometric method which achieves impedances
of the voltmeters larger than 1 GO. Fig. 1(b) shows clear CB oscillation diamonds [1] in the VGVSD plot, where VSD is the source–drain voltage and VG the gate voltage. Consistent with the CB phenomenology, the width of the low conductance parts of the oscillations gradually decreases with increasing VSD as the source–drain bias approaches the single-electron charging energy. We have investigated three different devices, all of which show the same qualitative behavior. Thermal cycling of the individual devices leads to only quantitative changes in the CB oscillation pattern as is typical of SETs realized in narrow channels [15,17]. All MR data were measured at 4.2 K. Magnetic fields were applied in the plane of the film at an angle y to the current I direction (By) or in the perpendicular-to-plane direction (Bptp). Examples of large, hysteretic, and gatevoltage dependent MRs of the SET are shown in Fig. 2 for magnetic field sweeps of B90 (a), (b) and Bptp (c), (d). At B9020 mT, the MR is 100% and negative for VG ¼ 0.94 V but is larger than 1000% and positive for VG ¼ 1.15 V. The shape of the hysteretic MR curves in Fig. 2(b) is reminiscent of spin-coherent resonant tunneling at different relative orientations of magnetizations in individual parts of a magnetic SET, reported, e.g., in Refs. [3,7]. It is, however, extremely improbable that these subtle quantum effects play an important role in our narrow channel (Ga,Mn)As SETs with islands created by disorder potential fluctuations, and we also emphasize that the magnitude of our hysteretic and gate-controlled MRs is incomparably larger. Figs. 2(c) and (d) show resistance
Fig. 1. (a) Schematics of our ferromagnetic SET. Trench isolated side-gate and channel aligned along the [1 1 0] direction were patterned by e-beamlithography and reactive ion etching in a 5 nm Ga0.98Mn0.02As epilayer. (b) CB conductance (I/VC) oscillations with gate voltage for different source–drain bias. The diamond patterns in this 2-D plot are clear fingerprints of single-electron transport.
Fig. 2. Coulomb-blockade conductance oscillations measured at VSD ¼ 3 mV bias vs. gate voltage and in-plane, perpendicular to the channel direction (a), and perpendicular-to-plane magnetic field (c). (b) Spin-valve like MR signals of different magnitudes and opposite signs for gate voltages 1.15 and 0.94 V. (d) Huge MR signal for up and down sweeps of the perpendicular-to-plane magnetic field at VG ¼ 0.935 V.
ARTICLE IN PRESS J. Wunderlich et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 1883–1888
variations during magnetic field Bptp sweeps. A very large MR at VG ¼ 0.935 V due to the rotation of magnetization out of the plane of the (Ga; Mn)As epilayer. Resistance variations by more than 3 orders of magnitude are observed with the high resistance state realized at saturation. We explain below that these resistance changes are associated with (Ga, Mn)As magnetization rotations. The striking sensitivity to the orientation of the applied magnetic field hints to the anisotropic MR origin of the effect we observe. This is confirmed by the observation of comparably large and gate-controlled MR in our devices when saturation magnetization is rotated with respect to the crystallographic axes. These measurements, presented in the following paragraph, also help to elucidate the microscopic origin of the CBAMR. The anisotropic MR of our SET device is demonstrated in Figs. 3(c) and (d) and compared with normal anisotropic MR in the unstructured part of the (Ga,Mn)As bar, plotted in Figs. 3(a) and (b). Abrupt rotations via intermediate magnetization angles occur in the field sweep measurements (Figs. 3(a) and (c) as a result of the combined uniaxial and cubic in-plane anisotropies present in the (Ga,Mn)As epilayer [18,19]. As suggested above, we refrain from speculating on the details of magnetization reversals at low fields in the individual parts of our SET and focus on its behavior at saturation where magnetizations of all magnetic parts of the device are aligned with the external field [12,13,20]. This is explored systematically in Figs. 3(b) and (d) for a 5 T rotating magnetic field whose magnitude is well above any observed anisotropy field in our devices. (Note that
Fig. 3. (a) Resistance RS ¼ VS/I of the unstructured bar (see schematic diagram) vs. up and down sweeps of in-plane magnetic field parallel (blue/ green) and perpendicular (red /black) to the current direction. (b) RS vs. the angle between the current direction and an applied in-plane magnetic field of 5 T, at which MJB. (c) Channel resistance RC vs. gate voltage and down sweep of the magnetic field parallel to current. (d) RC vs. gate voltage and the angle between the current direction and an applied inplane magnetic field of 5 T.
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Lorentz force effects are negligible at these saturating fields, as the change in resistance with increasing magnetic field is independent of the field angle.) In the unstructured part of the bar, higher or lower resistance states correspond to magnetization along or perpendicular to the current direction, as seen from both Figs. 3(a) and (b). Similar behavior is seen in the SET part of the device at, e.g., VG ¼ 0.4 V [see Figs. 3(c) and (d)], but the anisotropic MR is now hugely increased and depends strongly on the gate voltage Fig. 4 demonstrates that the dramatic anisotropic MR effects in the SET are due to shifts in the CB oscillation pattern caused by the changes in magnetization orientation. The shifts are clearly seen in Fig. 4(a), which shows the CB oscillations for several magnetization angles. Blue curves indicate shifts in the oscillation pattern due to magnetization rotations. For example, at VG ¼ 0.4 V (highlighted in Fig. 4(a) by the red line) the oscillations have a peak for y ¼ 01 that moves to higher VG with increasing y until, for y ¼ 401, a minimum in the oscillatory resistance occurs. Figs. 4(a) and (b) show that the magnitude of the resistance variations with y at fixed VG and with VG at fixed y is comparable. As we point out below in the theory discussion, the key parameters for the CBAMR effect are the magnetization rotation induced electrochemical shifts relative to the CB charging energy. The charging energy obtained from experimental data in Fig. 4(c) is 4 meV. Note that the CB oscillation period inferred from data in Fig. 4(a) is 100 mV. As the CB charging energy and oscillation period for a single island are e2/2CS and e/ CG, respectively, this implies that CS, the total island capacitance, is much larger than CG, the gate–island capacitance. The experimental value of CS suggests that
Fig. 4. (a) Channel resistance vs. gate voltage and the angle between the current direction and applied in-plane saturation field of 5 T. (b) y sweep for fixed VG ¼ –0.4 V. (c) I–VC characteristic of the channel at 4.2 K (Coulomb blockade regime) and 50 K (Ohmic regime) used to determine the SET charging energy, as indicated by the red line. This inferred value remains constant with decreasing temperature below 4.2 K.
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the characteristic size of the island is smaller than 20 nm. These rough estimates show that more than one island in the 40 nm channel SET may be contributing, consistent with the observed complex CB oscillations. We now analyze theoretically the microscopic origin of the CBAMR, which we attribute to the spin–orbit coupling induced anisotropy of the carrier chemical potential. As confirmed by detailed calculations below, we expect the nonuniform carrier concentration near the channel, implied by the existence of CB, to produce magnetization orientation dependent differences between chemical potentials of the lead and of the island in the constriction Dm(M). The schematic cartoons in Fig. 5 indicate the contributions to the Gibbs energy associated with the transfer of charge Q from the lead to the island. The energy can be written as a sum of the internal, electrostatic charging energy term and the term associated with, in general, different chemical potentials of the lead and of the island: Z
Q
dQ0 DV D ðQ0 Þ þ Q Dm=e;
U¼
(1)
0
Fig. 5. Schematics of the charging energy contribution (a) to the Gibbs energy and the contribution proportional to the difference Dm(M) in chemical potentials of the lead, DmL(M) and of the island, DmD(M) (b); (c) Calculated chemical potential anisotropy in (Ga, Mn)As as a function of carrier density for Mn local moment concentrations of 2% and 5%. The uniaxial anisotropy is modeled by introducing a weak shear strain exy ¼ 0.001. Insets: calculated chemical potential anisotropies in L10 FePtand CoPt-ordered alloys.
where DVD(Q) ¼ (Q+CGVG)/CS. The Gibbs energy U is minimized for Q0 ¼ CG(VG+VM), where the magnetization orientation dependent shift of the CB oscillations is given by VM ¼ CS/CG Dm(M)/e. Since |CGVM| has to be of order |e| to cause a marked shift in the oscillation pattern, the corresponding |Dm(M)| has to be similar to e2/CS, i.e., of the order of the island single-electron charging energy. The fact that CBAMR occurs when the anisotropy in a band structure derived parameter is comparable to an independent scale (single-electron charging energy) makes the effect distinct and potentially much larger in magnitude as compared to the previously observed anisotropic MR in the Ohmic regime (normal AMR) and in the tunneling regime (TAMR) [10,12,14,20,22]. We have performed microscopic calculations to estimate chemical potential anisotropies in (Ga, Mn)As epilayers. We use the effective kinetic-exchange model that has been frequently employed to study these dilute magnetic moment p-type semiconductors, particularly the properties related to the strong spin–orbit coupling in the valence band [8–13]. The zero-temperature calculations assume cubic magneto-crystalline anisotropy associated with the zinc-blende crystal structure plus an additional uniaxial field (as observed experimentally) modeled [19] by introducing a weak in-plane shear strain exy ¼ 0.001. Numerical results are presented in Fig. 5 for two Mn concentrations and over a range of carrier concentrations where the higher values are expected to correspond to the leads and the lower values to the constricted part of the bar. The data confirm that the chemical potential anisotropies in ferromagnetic (Ga,Mn)As are sensitive to the carrier and local moment density and may even change sign and that |Dm(M)| of a few meV that would explain the measured CB oscillation shifts are plausible. Note that CBAMR as analyzed above can occur for either a ferromagnetic or paramagnetic island. CBAMR should be generic to SETs fabricated in ferromagnetic systems with spin–orbit coupling. In ferromagnetic metals, highly accurate ab initio methods are available to study the spin–orbit coupled spectral properties. Recently, the technique has been successfully applied to describe magnetocrystalline anisotropies in L10 FePtand CoPt-ordered alloys and to predict the existence of the TAMR effect in transition metal tunnel junctions [23–26]. FePt and CoPt are useful model systems with both large exchange splitting resulting in the Curie temperatures well above room temperature and strong spin–orbit coupling. The calculated chemical potential anisotropies, shown in the inset in Fig. 5, are roughly an order of magnitude larger than in (Ga, Mn)As. This suggests that, building on the existing expertise in room-temperature nonmagnetic singleelectronic devices [27,28], metal based ferromagnetic SETs may offer a route to room-temperature CBAMR applications. In the following, we report from the observation of voltage controlled magnetic switching found in our (Ga, Mn)As SET devices. Voltage controlled magneto-crystalline anisotropy allows magnetization rotations to be triggered electrically
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[21]. In Fig. 6(a) the gate voltage dependence of a switching field (coercive field) is highlighted by the red dashed line. Electrical field assisted magnetization reorientation is illustrated in Fig. 6(b). (Ga, Mn)As epilayers show strong dependences of the uniaxial and cubic anisotropies on carrier
Fig. 6. (a) Channel conductance vs. gate voltage and in-plane, parallel to current magnetic field. The dashed red line highlights the critical reorientation field which is gate-bias dependent and decreases from about 40 mT at VG ¼ 1 V to less than 20 mT at VG ¼ 1 V. (b) CB oscillations at zero magnetic field where the system remains at magnetization M0 (gray) and at B0 ¼ 100 mT where the system remains at saturation magnetization M1 (black) over the gate voltage range between VG ¼ –1 and 1 V. Conductance measurements at intermediate field strengths of 35 mT (red circles) show a transition from M0 to M1 at critical gate voltages of about 0.5 V.
a
doping [19] and the electric field control achieved here is most probably due to gate control of the local carrier density. Finally, we discuss a new functionality concept offered by the CBAMR effect. The huge and hysteretic MR signals show that CBAMR-SETs can act as nonvolatile memories. In nonmagnetic SETs, the CB ‘‘on’’ (low-resistance) and ‘‘off’’ (high-resistance) states are used to represent logical ‘‘1’’ and ‘‘0’’ and the switching between the two states can be realized by applying a gate voltage, in analogy with a standard field-effect transistor. Our ferromagnetic SET can be addressed also magnetically with comparable ‘‘on’’ to ‘‘off’’ resistance ratios in the electric and magnetic modes. The functionality is illustrated in Fig. 7. The inset of panel (a) shows two CB oscillation curves corresponding to magnetization states M0 and M1. As evident from panel (b), M0 can be achieved by performing a small loop in the magnetic field, B-B0-0 where B0 is larger than the first switching field Bc1 and smaller than the second switching field Bc2, and M1 is achieved by performing the large fieldloop, B-B1-0 where B1oBc2. The main plot of Fig. 7(a) shows that the high resistance ‘‘0’’ state can be set by either the combinations (M1, VG0) or (M0, VG1) and the low resistance ‘‘1’’ state by (M1, VG1) or (M0, VG0). We can therefore switch between states ‘‘0’’ and ‘‘1’’ either by changing VG in a given magnetic state (the electric mode) or by changing the magnetic state at fixed VG (the magnetic
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Fig. 7. (a) Two opposite transistor characteristics (blue and green) in a gate-voltage range 1 V (VG0) to 1.04 V (VG1) for two different magnetization orientations M0 and M1; corresponding Coulomb blockade oscillations in a larger range of VG ¼ 0.6–1.15 V are shown in the inset. Switching between low-resistance (‘‘1’’) and high-resistance (‘‘0’’) states can be performed electrically or magnetically. (b) Hysteretic magnetoresistance at constant gate voltage VG1 illustrating the nonvolatile memory effect in the magnetic mode. (c) Illustration of integrated transistor (electric mode) and permanent storage (magnetic mode) functions in a single nanoscale element. (d) The transistor characteristic for M ¼ M1 is reminiscent of an n-type field effect transistor and is inverted (reminiscent of a p-type field effect transistor) for M ¼ M0; the inversion can also be realized in the nonvolatile magnetic mode.
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mode). Due to the hysteresis, the magnetic mode represents a nonvolatile memory effect. The diagram in Fig. 7(c) illustrates one of the new functionality concepts our device suggests in which lowpower electrical manipulation and permanent storage of information are realized in one physical nanoscale element. Panel (d) then highlights the possibility to invert the transistor characteristic; for example, the system is in the low-resistance ‘‘1’’ state at VG1 and in the high-resistance ‘‘0’’ state at VG0 (reminiscent of an n-type field effect transistor) for the magnetization M1 while the characteristic is inverted (reminiscent of a p-type field effect transistor) by changing magnetization to M0. In the ferromagnetic semiconductor epilayer used in our study the gate voltage alters significantly the magnetocrystalline anisotropy and can, therefore, be used to trigger magnetization rotations solely electrically. To conclude, we have observed a new type of MR effect, CBAMR, in a ferromagnetic semiconductor SET and explained its origin in terms of electrochemical shifts that are anisotropic with respect to the magnetization orientation. The effect should be generic and offers new functionality concepts combining electrical transistorlike action with permanent information storage or utilizing magnetization controlled transistor characteristics in a single nanoscale element. In parallel, we observed a significant effect of the electric field on the critical magnetic reorientation field which we attribute to the carrier dependent magnetic anisotropy in our GaMnAs-SET. The coercive field changes by more than 50% during gate-voltage variation of only 2 V. Acknowledgments The authors acknowledge discussions with Allan MacDonald and Jairo Sinova and support from the EPSRC through Grant no. GR/S81407/01, from the Grant Agency
and Academy of Sciences of the Czech Republic through Grant nos. 202/05/0575 and AV0Z10100521, from the Ministry of Education of the Czech Republic Grant no. LC510, from the EU Project NANOSPIN (FP6-2002-IST015728), and from the EU EUROCORES Project SPICO (FON/06/E002). References [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] [26] [27] [28]
K.K. Likharev, Proc. IEEE 87 (1999) 606. S.A. Wolf, et al., Science 294 (2001) 1488. K. Ono, et al., J. Phys. Soc. Japan 66 (1997) 1261. J. Wunderlich, et al., Phys. Pev. Lett. 97 (2006) 077201. M.M. Deshmukh, et al., Phys. Rev. Lett. 89 (2002) 266803. A.N. Pasupathy, et al., Science 306 (2004) 86. S. Sahoo, et al., Nat. Phys. 1 (2005) 99. T. Dietl, et al., Science 287 (2000) 1019. M. Abolfath, et al., Phys. Rev. B 63 (2001) 054418. T. Jungwirth, et al., Appl. Phys. Lett. 83 (2003) 320. L. Brey, et al., Appl. Phys. Lett. 85 (2004) 1996. C. Gould, et al., Phys. Rev. Lett. 93 (2004) 117203. A.D. Giddings, et al., Phys. Rev. Lett. 94 (2005) 127202. H. Saito, et al., Phys. Rev. Lett. 95 (2005) 086604. M.A. Kastner, Rev. Mod. Phys. 64 (1992) 849. K. Tsukagoshi, et al., Appl. Phys. Lett. 73 (1998) 2515. As expected, Coulomb staircase effects, i.e., quasiperiodic fluctuations, in dI/dVSD vs. VSD related to the multiple electron tunneling through the dot are not well pronounced in our data. These oscillations can be strong in lithographically defined SETs with large differences between resistances of tunnel barriers separating the island and the two leads [1]. K.Y. Wang, et al., Phys. Rev. B 72 (2005) 085201. M. Sawicki, et al., Phys. Rev. B 71 (2005) 121302(R). C. Ruester, et al., Phys. Rev. Lett. 94 (2005) 027203. D. Chiba, et al., Science 301 (2003) 943. F. Matsukura, et al., Physica (Amsterdam) 21E (2004) 1032. A.B. Shick, et al., Phys. Rev. B 67 (2003) 172407. A.B. Shick, et al., Phys. Rev. B 73 (2006) 024418. K.I. Bolotin, et al., Cond-mat/0602251. M. Viret, et al., Cond-mat/0602298. Matsumoto, et al., Appl. Phys. Lett. 68 (1996) 34. Saitoh, et al., Appl. Phys. Lett. 85 (2004) 6233.
Journal of Magnetism and Magnetic Materials 310 (2007) 1883–1888 www.elsevier.com/locate/jmmm
Coulomb blockade anisotropic magnetoresistance and voltage controlled magnetic switching in a ferromagnetic GaMnAs single electron transistor J. Wunderlicha,, T. Jungwirthb,c, A.C. Irvined, B. Kaestnere, A.B. Shickf, R.P. Campionc, D.A. Williamsa, B.L. Gallagherc a
Hitachi Cambridge Laboratory, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK b Institute of Physics ASCR, Cukrovarnicka´ 10, 162 53, Praha 6, Czech Republic c School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK d Microelectronics Research Centre, University of Cambridge, Cambridge CB3 0HE, UK e National Physical Laboratory, Teddington T11 0LW, UK f Institute of Physics ASCR, Na Slovance 2, 182 21, Praha 8, Czech Republic Available online 14 November 2006
Abstract We observe low-field hysteretic magnetoresistance (MR) in a (Ga,Mn)As single electron transistor which can exceed three orders of magnitude. The sign and size of the MR signal is controlled by the gate voltage. Experimental data are interpreted in terms of electrochemical shifts associated with magnetization rotations. This Coulomb blockade anisotropic MR is distinct from previously observed anisotropic MR effects as it occurs when the anisotropy in a band structure derived parameter is comparable to an independent scale, the single electron charging energy. Effective kinetic-exchange model calculations in (Ga,Mn)As show chemical potential anisotropies consistent with experiment and ab initio calculations in transition-metal systems suggest that this generic effect persists to high temperatures in metal ferromagnets with strong spin–orbit coupling. In addition we observe a significant gate voltage dependence of the magnetic switching field which we attribute to carrier density variations in the electric field exposed GaMnAs regions causing a substantial change in the magneto-crystalline anisotropy profile. r 2006 Elsevier B.V. All rights reserved. Keywords: Magnetic semiconductors; Coulomb blockade; Single-electron tunneling; Magnetotransport phenomena; Materials for magnetotransport; Spin polarized resonant tunnel junctions
Single-electronics, which is based on the discrete charge of the electron [1], is the ultimate in miniaturization and electro-sensitivity. Spintronics, which is based on manipulating electron spins [2], delivers high magneto-sensitivity and nonvolatile memory effects. The potential of hybrid single-electronic/spintronic devices and the fundamental importance of spin phenomena at nanoscale have motivated number of studies of spin transport in the Coulomb blockade (CB) regime [3–7]. Experiments in single-electron transistors (SETs) in which the leads and island comprise different ferromagnetic materials [3] have shown both Corresponding author. Tel.: +44 1223 442901; fax: +44 1223 467942.
E-mail address: [email protected] (J. Wunderlich). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.676
electric and magnetic field dependent CB oscillations. These magneto-CB oscillations are due to the Zeeman energy changing the relative chemical potentials in the leads and in the island. They occur at high applied fields and are nonhysteretic. A small low-field hysteretic magnetoresistance (MR) effect has been demonstrated in SETs when the relative orientation of the magnetization of the leads is switched from parallel to antiparallel [3,7]. This gate-voltage dependent MR was attributed to resonant tunneling effects through quantized energy levels in the island. Here the magnetization reorientation induced by a weak magnetic field is attributed to subtle, spin-coherent resonant tunneling effects through quantized energy level in the island. It is much weaker than
ARTICLE IN PRESS 1884
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the response to the gate voltage, which is dominated by classical CB oscillations. We demonstrate that in ferromagnets with strong spin–orbit coupling, large chemical potential shifts can be induced by magnetization rotations leading to unprecedented characteristics of the ferromagnetic SET [4]. The signatures of this CB anisotropic magnetoresistance (CBAMR) effect are MR signals which can be hysteretic, which occur at magnetic fields corresponding to ferromagnetic anisotropy fields, which can have magnitudes approaching the resistance variations due to CB oscillations, and which show both positive and negative spin-valve-like characteristics controlled by the SET gate-voltage. Our SETs are fabricated from p-type (Ga,Mn)As, a ferromagnetic semiconductor for which parameters derived from the spin–orbit coupled band structure are known to be strongly anisotropic with respect to the magnetization orientation [8–14]. A schematic diagram of the device are shown in Fig. 1(a). The SET consists of a trench-isolated side-gated 40 nm wide channel aligned along the [1 1 0] direction. It was patterned by e-beam lithography and reactive ion etching in a 5 nm Ga0.98Mn0.02As epilayer, which was grown along the [0 0 1] crystal axis on an AlAs buffer layer by low-temperature molecular beam epitaxy [13]. The narrow channel technique is a simple approach to realize a SET and has been used previously to produce nonmagnetic thin film Si and GaAs-based SETs in which disorder potential fluctuations create small islands in the channel without the need for a lithographically defined island [15,16]. These SETs are well suited for exploring functionalities based on classical single-electron charging effects on which the CBAMR is based on. High precision electrical measurements were performed to exclude spurious effects associated with large changes in the resistance of the SETs. The DC currents were measured using sub-femtoampere source-measure units at a constant source–drain voltage. Simultaneously, voltage drops over constricted and unstructured parts of the bar were detected using a potentiometric method which achieves impedances
of the voltmeters larger than 1 GO. Fig. 1(b) shows clear CB oscillation diamonds [1] in the VGVSD plot, where VSD is the source–drain voltage and VG the gate voltage. Consistent with the CB phenomenology, the width of the low conductance parts of the oscillations gradually decreases with increasing VSD as the source–drain bias approaches the single-electron charging energy. We have investigated three different devices, all of which show the same qualitative behavior. Thermal cycling of the individual devices leads to only quantitative changes in the CB oscillation pattern as is typical of SETs realized in narrow channels [15,17]. All MR data were measured at 4.2 K. Magnetic fields were applied in the plane of the film at an angle y to the current I direction (By) or in the perpendicular-to-plane direction (Bptp). Examples of large, hysteretic, and gatevoltage dependent MRs of the SET are shown in Fig. 2 for magnetic field sweeps of B90 (a), (b) and Bptp (c), (d). At B9020 mT, the MR is 100% and negative for VG ¼ 0.94 V but is larger than 1000% and positive for VG ¼ 1.15 V. The shape of the hysteretic MR curves in Fig. 2(b) is reminiscent of spin-coherent resonant tunneling at different relative orientations of magnetizations in individual parts of a magnetic SET, reported, e.g., in Refs. [3,7]. It is, however, extremely improbable that these subtle quantum effects play an important role in our narrow channel (Ga,Mn)As SETs with islands created by disorder potential fluctuations, and we also emphasize that the magnitude of our hysteretic and gate-controlled MRs is incomparably larger. Figs. 2(c) and (d) show resistance
Fig. 1. (a) Schematics of our ferromagnetic SET. Trench isolated side-gate and channel aligned along the [1 1 0] direction were patterned by e-beamlithography and reactive ion etching in a 5 nm Ga0.98Mn0.02As epilayer. (b) CB conductance (I/VC) oscillations with gate voltage for different source–drain bias. The diamond patterns in this 2-D plot are clear fingerprints of single-electron transport.
Fig. 2. Coulomb-blockade conductance oscillations measured at VSD ¼ 3 mV bias vs. gate voltage and in-plane, perpendicular to the channel direction (a), and perpendicular-to-plane magnetic field (c). (b) Spin-valve like MR signals of different magnitudes and opposite signs for gate voltages 1.15 and 0.94 V. (d) Huge MR signal for up and down sweeps of the perpendicular-to-plane magnetic field at VG ¼ 0.935 V.
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variations during magnetic field Bptp sweeps. A very large MR at VG ¼ 0.935 V due to the rotation of magnetization out of the plane of the (Ga; Mn)As epilayer. Resistance variations by more than 3 orders of magnitude are observed with the high resistance state realized at saturation. We explain below that these resistance changes are associated with (Ga, Mn)As magnetization rotations. The striking sensitivity to the orientation of the applied magnetic field hints to the anisotropic MR origin of the effect we observe. This is confirmed by the observation of comparably large and gate-controlled MR in our devices when saturation magnetization is rotated with respect to the crystallographic axes. These measurements, presented in the following paragraph, also help to elucidate the microscopic origin of the CBAMR. The anisotropic MR of our SET device is demonstrated in Figs. 3(c) and (d) and compared with normal anisotropic MR in the unstructured part of the (Ga,Mn)As bar, plotted in Figs. 3(a) and (b). Abrupt rotations via intermediate magnetization angles occur in the field sweep measurements (Figs. 3(a) and (c) as a result of the combined uniaxial and cubic in-plane anisotropies present in the (Ga,Mn)As epilayer [18,19]. As suggested above, we refrain from speculating on the details of magnetization reversals at low fields in the individual parts of our SET and focus on its behavior at saturation where magnetizations of all magnetic parts of the device are aligned with the external field [12,13,20]. This is explored systematically in Figs. 3(b) and (d) for a 5 T rotating magnetic field whose magnitude is well above any observed anisotropy field in our devices. (Note that
Fig. 3. (a) Resistance RS ¼ VS/I of the unstructured bar (see schematic diagram) vs. up and down sweeps of in-plane magnetic field parallel (blue/ green) and perpendicular (red /black) to the current direction. (b) RS vs. the angle between the current direction and an applied in-plane magnetic field of 5 T, at which MJB. (c) Channel resistance RC vs. gate voltage and down sweep of the magnetic field parallel to current. (d) RC vs. gate voltage and the angle between the current direction and an applied inplane magnetic field of 5 T.
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Lorentz force effects are negligible at these saturating fields, as the change in resistance with increasing magnetic field is independent of the field angle.) In the unstructured part of the bar, higher or lower resistance states correspond to magnetization along or perpendicular to the current direction, as seen from both Figs. 3(a) and (b). Similar behavior is seen in the SET part of the device at, e.g., VG ¼ 0.4 V [see Figs. 3(c) and (d)], but the anisotropic MR is now hugely increased and depends strongly on the gate voltage Fig. 4 demonstrates that the dramatic anisotropic MR effects in the SET are due to shifts in the CB oscillation pattern caused by the changes in magnetization orientation. The shifts are clearly seen in Fig. 4(a), which shows the CB oscillations for several magnetization angles. Blue curves indicate shifts in the oscillation pattern due to magnetization rotations. For example, at VG ¼ 0.4 V (highlighted in Fig. 4(a) by the red line) the oscillations have a peak for y ¼ 01 that moves to higher VG with increasing y until, for y ¼ 401, a minimum in the oscillatory resistance occurs. Figs. 4(a) and (b) show that the magnitude of the resistance variations with y at fixed VG and with VG at fixed y is comparable. As we point out below in the theory discussion, the key parameters for the CBAMR effect are the magnetization rotation induced electrochemical shifts relative to the CB charging energy. The charging energy obtained from experimental data in Fig. 4(c) is 4 meV. Note that the CB oscillation period inferred from data in Fig. 4(a) is 100 mV. As the CB charging energy and oscillation period for a single island are e2/2CS and e/ CG, respectively, this implies that CS, the total island capacitance, is much larger than CG, the gate–island capacitance. The experimental value of CS suggests that
Fig. 4. (a) Channel resistance vs. gate voltage and the angle between the current direction and applied in-plane saturation field of 5 T. (b) y sweep for fixed VG ¼ –0.4 V. (c) I–VC characteristic of the channel at 4.2 K (Coulomb blockade regime) and 50 K (Ohmic regime) used to determine the SET charging energy, as indicated by the red line. This inferred value remains constant with decreasing temperature below 4.2 K.
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the characteristic size of the island is smaller than 20 nm. These rough estimates show that more than one island in the 40 nm channel SET may be contributing, consistent with the observed complex CB oscillations. We now analyze theoretically the microscopic origin of the CBAMR, which we attribute to the spin–orbit coupling induced anisotropy of the carrier chemical potential. As confirmed by detailed calculations below, we expect the nonuniform carrier concentration near the channel, implied by the existence of CB, to produce magnetization orientation dependent differences between chemical potentials of the lead and of the island in the constriction Dm(M). The schematic cartoons in Fig. 5 indicate the contributions to the Gibbs energy associated with the transfer of charge Q from the lead to the island. The energy can be written as a sum of the internal, electrostatic charging energy term and the term associated with, in general, different chemical potentials of the lead and of the island: Z
Q
dQ0 DV D ðQ0 Þ þ Q Dm=e;
U¼
(1)
0
Fig. 5. Schematics of the charging energy contribution (a) to the Gibbs energy and the contribution proportional to the difference Dm(M) in chemical potentials of the lead, DmL(M) and of the island, DmD(M) (b); (c) Calculated chemical potential anisotropy in (Ga, Mn)As as a function of carrier density for Mn local moment concentrations of 2% and 5%. The uniaxial anisotropy is modeled by introducing a weak shear strain exy ¼ 0.001. Insets: calculated chemical potential anisotropies in L10 FePtand CoPt-ordered alloys.
where DVD(Q) ¼ (Q+CGVG)/CS. The Gibbs energy U is minimized for Q0 ¼ CG(VG+VM), where the magnetization orientation dependent shift of the CB oscillations is given by VM ¼ CS/CG Dm(M)/e. Since |CGVM| has to be of order |e| to cause a marked shift in the oscillation pattern, the corresponding |Dm(M)| has to be similar to e2/CS, i.e., of the order of the island single-electron charging energy. The fact that CBAMR occurs when the anisotropy in a band structure derived parameter is comparable to an independent scale (single-electron charging energy) makes the effect distinct and potentially much larger in magnitude as compared to the previously observed anisotropic MR in the Ohmic regime (normal AMR) and in the tunneling regime (TAMR) [10,12,14,20,22]. We have performed microscopic calculations to estimate chemical potential anisotropies in (Ga, Mn)As epilayers. We use the effective kinetic-exchange model that has been frequently employed to study these dilute magnetic moment p-type semiconductors, particularly the properties related to the strong spin–orbit coupling in the valence band [8–13]. The zero-temperature calculations assume cubic magneto-crystalline anisotropy associated with the zinc-blende crystal structure plus an additional uniaxial field (as observed experimentally) modeled [19] by introducing a weak in-plane shear strain exy ¼ 0.001. Numerical results are presented in Fig. 5 for two Mn concentrations and over a range of carrier concentrations where the higher values are expected to correspond to the leads and the lower values to the constricted part of the bar. The data confirm that the chemical potential anisotropies in ferromagnetic (Ga,Mn)As are sensitive to the carrier and local moment density and may even change sign and that |Dm(M)| of a few meV that would explain the measured CB oscillation shifts are plausible. Note that CBAMR as analyzed above can occur for either a ferromagnetic or paramagnetic island. CBAMR should be generic to SETs fabricated in ferromagnetic systems with spin–orbit coupling. In ferromagnetic metals, highly accurate ab initio methods are available to study the spin–orbit coupled spectral properties. Recently, the technique has been successfully applied to describe magnetocrystalline anisotropies in L10 FePtand CoPt-ordered alloys and to predict the existence of the TAMR effect in transition metal tunnel junctions [23–26]. FePt and CoPt are useful model systems with both large exchange splitting resulting in the Curie temperatures well above room temperature and strong spin–orbit coupling. The calculated chemical potential anisotropies, shown in the inset in Fig. 5, are roughly an order of magnitude larger than in (Ga, Mn)As. This suggests that, building on the existing expertise in room-temperature nonmagnetic singleelectronic devices [27,28], metal based ferromagnetic SETs may offer a route to room-temperature CBAMR applications. In the following, we report from the observation of voltage controlled magnetic switching found in our (Ga, Mn)As SET devices. Voltage controlled magneto-crystalline anisotropy allows magnetization rotations to be triggered electrically
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[21]. In Fig. 6(a) the gate voltage dependence of a switching field (coercive field) is highlighted by the red dashed line. Electrical field assisted magnetization reorientation is illustrated in Fig. 6(b). (Ga, Mn)As epilayers show strong dependences of the uniaxial and cubic anisotropies on carrier
Fig. 6. (a) Channel conductance vs. gate voltage and in-plane, parallel to current magnetic field. The dashed red line highlights the critical reorientation field which is gate-bias dependent and decreases from about 40 mT at VG ¼ 1 V to less than 20 mT at VG ¼ 1 V. (b) CB oscillations at zero magnetic field where the system remains at magnetization M0 (gray) and at B0 ¼ 100 mT where the system remains at saturation magnetization M1 (black) over the gate voltage range between VG ¼ –1 and 1 V. Conductance measurements at intermediate field strengths of 35 mT (red circles) show a transition from M0 to M1 at critical gate voltages of about 0.5 V.
a
doping [19] and the electric field control achieved here is most probably due to gate control of the local carrier density. Finally, we discuss a new functionality concept offered by the CBAMR effect. The huge and hysteretic MR signals show that CBAMR-SETs can act as nonvolatile memories. In nonmagnetic SETs, the CB ‘‘on’’ (low-resistance) and ‘‘off’’ (high-resistance) states are used to represent logical ‘‘1’’ and ‘‘0’’ and the switching between the two states can be realized by applying a gate voltage, in analogy with a standard field-effect transistor. Our ferromagnetic SET can be addressed also magnetically with comparable ‘‘on’’ to ‘‘off’’ resistance ratios in the electric and magnetic modes. The functionality is illustrated in Fig. 7. The inset of panel (a) shows two CB oscillation curves corresponding to magnetization states M0 and M1. As evident from panel (b), M0 can be achieved by performing a small loop in the magnetic field, B-B0-0 where B0 is larger than the first switching field Bc1 and smaller than the second switching field Bc2, and M1 is achieved by performing the large fieldloop, B-B1-0 where B1oBc2. The main plot of Fig. 7(a) shows that the high resistance ‘‘0’’ state can be set by either the combinations (M1, VG0) or (M0, VG1) and the low resistance ‘‘1’’ state by (M1, VG1) or (M0, VG0). We can therefore switch between states ‘‘0’’ and ‘‘1’’ either by changing VG in a given magnetic state (the electric mode) or by changing the magnetic state at fixed VG (the magnetic
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Fig. 7. (a) Two opposite transistor characteristics (blue and green) in a gate-voltage range 1 V (VG0) to 1.04 V (VG1) for two different magnetization orientations M0 and M1; corresponding Coulomb blockade oscillations in a larger range of VG ¼ 0.6–1.15 V are shown in the inset. Switching between low-resistance (‘‘1’’) and high-resistance (‘‘0’’) states can be performed electrically or magnetically. (b) Hysteretic magnetoresistance at constant gate voltage VG1 illustrating the nonvolatile memory effect in the magnetic mode. (c) Illustration of integrated transistor (electric mode) and permanent storage (magnetic mode) functions in a single nanoscale element. (d) The transistor characteristic for M ¼ M1 is reminiscent of an n-type field effect transistor and is inverted (reminiscent of a p-type field effect transistor) for M ¼ M0; the inversion can also be realized in the nonvolatile magnetic mode.
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mode). Due to the hysteresis, the magnetic mode represents a nonvolatile memory effect. The diagram in Fig. 7(c) illustrates one of the new functionality concepts our device suggests in which lowpower electrical manipulation and permanent storage of information are realized in one physical nanoscale element. Panel (d) then highlights the possibility to invert the transistor characteristic; for example, the system is in the low-resistance ‘‘1’’ state at VG1 and in the high-resistance ‘‘0’’ state at VG0 (reminiscent of an n-type field effect transistor) for the magnetization M1 while the characteristic is inverted (reminiscent of a p-type field effect transistor) by changing magnetization to M0. In the ferromagnetic semiconductor epilayer used in our study the gate voltage alters significantly the magnetocrystalline anisotropy and can, therefore, be used to trigger magnetization rotations solely electrically. To conclude, we have observed a new type of MR effect, CBAMR, in a ferromagnetic semiconductor SET and explained its origin in terms of electrochemical shifts that are anisotropic with respect to the magnetization orientation. The effect should be generic and offers new functionality concepts combining electrical transistorlike action with permanent information storage or utilizing magnetization controlled transistor characteristics in a single nanoscale element. In parallel, we observed a significant effect of the electric field on the critical magnetic reorientation field which we attribute to the carrier dependent magnetic anisotropy in our GaMnAs-SET. The coercive field changes by more than 50% during gate-voltage variation of only 2 V. Acknowledgments The authors acknowledge discussions with Allan MacDonald and Jairo Sinova and support from the EPSRC through Grant no. GR/S81407/01, from the Grant Agency
and Academy of Sciences of the Czech Republic through Grant nos. 202/05/0575 and AV0Z10100521, from the Ministry of Education of the Czech Republic Grant no. LC510, from the EU Project NANOSPIN (FP6-2002-IST015728), and from the EU EUROCORES Project SPICO (FON/06/E002). References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
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