Possibility of electrostatic control of magnetic moments in ferromagnetic semiconductors

Physica E 9 (2001) 295–299

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Possibility of electrostatic control of magnetic moments in ferromagnetic semiconductors T. Figielski ∗ , T. Wosinski Institute of Physics, Polish Academy of Sciences, Al. LotnikÃow 32=46, 02-668 Warszawa, Poland Received 23 March 2000; received in revised form 29 May 2000; accepted 23 June 2000

Abstract Semiconductor devices exploit electron charge to carry and process information, whereas magnetic materials make use of electron spin to store it. Hybridization of both the functions in one device is a goal that could be fully reached if we were able to manipulate magnetic moments by electric voltage. Having this in view we consider a rectangular island etched from a thin layer of a ferromagnetic semiconductor, which represents a single ferromagnetic domain. The island has suitably patterned Schottky gates deposited on the top of the layer. By applying a voltage to the gates, one could locally deplete carrier density beneath the gates and thus tailor ferromagnetic sub-domains of dierent shapes on the island. We show that it is possible in this manner to reverse the direction of magnetization of the island, which could constitute the principle of novel class of spintronic devices. ? 2001 Elsevier Science B.V. All rights reserved. PACS: 85.80.Jm; 85.90.+h; 75.50.Pp Keywords: Spintronic devices; Ferromagnetic semiconductors; Magnetic domains

Use of electron spin instead of (or in addition to) electron charge in electronics is nowadays an ambitious challenge for physicists and technologists of solid state. Various solid-state systems having potential applicability to this novel eld that is called sometimes spintronics or magnetoelectronics have been the subject of considerable recent study. Those systems may be classi ed as either vertical or planar devices, adopting the semiconductor terminology. To the rst class of devices belong magnetic multilayers and spin ∗

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tunnel junctions that exhibit giant magnetoresistance [1]. Such devices, in which current passes perpendicular to the layer plane, have already found practical application as read heads for magnetic hard disk drivers. In the context of the present letter it is noteworthy to add that current-induced realignment of magnetic domains in nanostructured Cu=Co multilayer pillar has been recently reported [2]. Very little has been done in the class of planar devices, despite that just such devices are more prospective for electronic applications as they could be easily incorporated into the planar semiconductor technology. An example of a new promising system in this class of devices, belonging to the mesoscopic

1386-9477/01/$ - see front matter ? 2001 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 0 ) 0 0 2 0 0 - 9

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structures, may be the quantum point contact [3]. As the recent experiments show, spin-polarized electrons probably dominate the single-channel conductance through such a contact even in nonmagnetic materials and in the absence of an applied magnetic eld [4]. A breakdown in the design of spintronic devices may be expected owing to the recent successful growth of ferromagnetic III–V semiconductors, like (Ga,Mn)As epitaxial layers [5,6]. Ferromagnetic semiconductor lms are expected to have, among others, this advantage over ferromagnetic metals that they could be tailored into regions of dierent carrier densities by applying electrostatic potential to suitably patterned metal electrodes (Schottky gates) deposited on the top of the layer [7]. Since just charge carriers assure ferromagnetic ordering in those materials, thus we could obtain a possibility of the voltage-controlled manipulation of magnetic moments in an electrostatically de ned ferromagnetic domain. We propose in this letter a class of submicron devices that make use of this principle, which could be used for both nonvolatile storage of information and simple logic operations. It should be noticed here that an alternative way of controlling spin by carrier density is to induce ferromagnetism by photogenerated carriers, which has been recently demonstrated in CdMnTe [7] and in (In,Mn)As [8]. We consider a thin monocrystalline layer of ferromagnetic semiconductor, say (Ga,Mn)As, below the Curie temperature. The layer is grown on a nonmagnetic, conducting substrate. We assume that the direction of easy magnetization lies in plane of the layer. We de ne a rectangular island in the layer (e.g. by mesa etching), separated from the rest of ferromagnetic semiconductor, whose size is small enough to contain a single ferromagnetic domain. The dominant forces inside the island, which are relevant to magnetic properties, are the exchange forces; they keep neighboring spins aligned parallel and thus produce a spontaneous magnetization, provided the temperature is not too high. It may be assumed that the exchange forces, which are short-range forces, do not depend on the specimen shape. Since in our case, these spins are localized at impurity Mn ions, which are randomly distributed in the matrix, the crystal is not expected to have distinguished crystallographic axes of easy magnetization. Instead, the magnetization directions are governed by long-range dipole interac-

Fig. 1. Two dierent patterns of metallic gates deposited on a rectangular island made from ferromagnetic semiconductor layer.

tion that depends on the specimen shape. If to make lengths of perpendicular edges of the island considerably dierent, then internal magnetic forces will cause that the direction of magnetization along the longer edges will be the direction of stable equilibrium in zero magnetic eld. The mutual magnetic potential energy of a set of magnetic dipoles with moments i can be written as [9] P 0 P  · hji ; (1) Um = − 2 i i i6=j where 0 is the free-space magnetic permeability, and hji is the magnetic eld of dipole j at the position of dipole i, which expresses itself as " # 1 3rji (j rji ) j − 3 ; (2) hji = 4 rji5 rji where rji is the position vector of dipole i with respect to dipole j. Um should be minimum for the preferred directions of spontaneous magnetization of the domain. General tendency of the internal magnetic forces is to produce a magnetization distribution with no poles, i.e. a solenoidal distribution. For the ratio of the longer edge to the shorter edge of the island equal 4=3, as assumed in the included gures, and for the thickness of the layer much smaller than the island size, one gets by Eq. (1) the ratio of the corresponding magnetic energies equal approximately (−3)=(−2). On the other hand, magnetic energy of a square island that is uniformly magnetized in its plane is independent of the direction of magnetization. We assume now that metallic gates are deposited on the top of the island, where they pattern a cross that is composed of two perpendicular bars (Fig. 1a). Each bar acts as a single gate, called further gates X and Y , that can be biased independent of each other.

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Fig. 2. (a) Rectangular island representing single ferromagnetic domain. (b) Voltage applied to the gate Y , de ned in Fig. 1(a); the island becomes divided into two individual domains. (c) Voltage applied to the gates X and Y ; the island becomes divided into four domains. Arrows indicate the directions of magnetization. Force lines of magnetic eld emanating from the island are also sketched.

If we apply a suitable voltage between a gate and the substrate, the charge carriers will be repelled from the region of ferromagnetic layer beneath the gate. When this condition is met, we will speak shortly that the gate is biased. It should be noted that a small interruption in the gate Y has not to be accompanied by corresponding interruption in the carrier depletion region. When both gates are unbiased, the island behaves as a single ferromagnetic domain with spontaneous magnetization aligned with the y-axis (Fig. 2a). Magnetic ux closes outside the domain thus producing an external magnetic eld. After applying bias to the gate X or Y , the island splits up into two parts separated by a carrier depletion region (Fig. 2b). Energy of the system minimizes then by a turn of magnetization in one or two parts of the island to form two domains with antiparallel alignment. Although in this case magnetic ux closes also outside the island, magnetic energy of the system is roughly twice as small as that of a single domain. When the bias is switched o, two remnant domains transform into a single domain with magnetization vector aligned with the y-axis but whose sense is uncertain. When both gates are biased, the island becomes split up into four parts separated by carrier depletion regions (Fig. 2c). Each of these parts has also to carry a single domain. Now, the system lowers its energy by reorientation of the magnetization in each of the domains in such a way as to close magnetic ux inside the island (Fig. 2c). This case is sharply distinguished from that of a single domain, where the magnetic ux closes outside the island. So, in dependence on whether one, two or neither of the gates are

Fig. 3. Sequence of various voltage-induced con gurations of ferromagnetic domains, whose execution leads to reversal of magnetization direction in the island.

biased, this device is in one of three dierent states. We could in principle distinguish between these states either electrically, using magnetoresistive and Hall microsensors integrated with the device, or optically, exploiting the Faraday and Kerr magnetooptics rotation. The case just described illustrates well the principle of operation of the considered class of devices. The question arises if we could electrostatically reverse the direction of spontaneous magnetization of the island. The answer is yes and below we demonstrate how to achieve this goal. For this purpose we use the gate pattern forming a double cross. Each bar of this cross again acts as a single gate (gate X , Y1 and Y2 ) that could be biased independent each of the others (Fig. 1b). To de ne initial direction of the magnetization of the island, we rst apply for a while an external magnetic eld in the positive y-direction. The magnetization vector places itself parallel to the applied eld (Fig. 3, upper rectangle). Further, we manipulate this vector solely by applying external bias to dierent gates, keeping the following sequence. (i) Bias is applied to the gates X and Y1 , by which the island becomes divided into four unequal parts

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(square and rectangular ones). Energy of the system minimizes by reorientation of the magnetization in each part in such a way as to maximize magnetic ux enclosed inside the island. This is likely realized by a large turn of magnetization in the square parts of the island and a small turn in the rectangular parts (Fig. 3). (ii) Bias is switched o from the gate Y1 and applied to the gate Y2 . Magnetization of the domains adjusts itself to the new con guration that represents a mirror re ection of the former con guration with respect to the y-axis. Energy of the new con guration is evidently the same as that of the former one. (iii) Bias is switched o from the gates X and Y2 . Single domain is restored on the island but now the magnetization direction is opposite to the initial one (Fig. 3, lower rectangle). So, in this manner we have achieved a reversal of the magnetization of the ferromagnetic island. We can come back to the initial direction of magnetization by executing either the same or reverse bias sequence. These both ways are illustrated in Fig. 3 where subsequent bias con gurations are arranged around a circle. We can pass from a given direction of magnetization to the opposite one going either clockwise or counterclockwise in this diagram. It re ects an important property of the device that its operation is completely reversible. This device has two dierent nonvolatile states, corresponding to uniform magnetization of the island in opposite directions along its longer edges, which could represent two binary digits. The scheme just described is certainly not the only one but one of the simplest by which the reversal of magnetization could be achieved without applying magnetic eld. Consider now, whether the just described idea can nowadays be realized in practice. We focus our attention on (Ga,Mn)As, which can be grown by the low-temperature molecular-beam-epitaxy [5,6]. Ferromagnetic (Ga,Mn)As so obtained is of p-type with hole concentration 1018 –1020 cm−3 in undoped crystals. The Curie temperature, Tc , is approximately proportional to Mn atomic fraction, x, up to x = 0:053, above which it starts to decrease. The highest Tc so far obtained is 110 K. The origin of ferromagnetism is likely the Ruderman–Kittel–Kasuya–Yoshida

(RKKY) interaction between Mn spins (SMn = 5=2 for Mn2+ charge state), mediated by holes. The easy axis of magnetization is in plane of the layer due to compressive strain in the layer [6]. We can calculate the bias voltage, V , necessary to deplete carrier density in the layer using simple capacitor formula V = Q=C, where Q is the charge accumulated in the capacitance C (in our case it is a capacitance between the substrate and a gate). To obtain a small value of V , crystals with the lowest hole density, p, are preferred. If to assume p = 1018 cm−3 , and the thickness of the layer equal to 50 nm, then the bias voltage required to deplete the layer is ∼ 2 V. That voltage could be safely applied to a Schottky metal gate deposited on p-type GaAs previously covered by a thin (5 –10 nm) cap layer of undoped GaAs. To supply the layer with the assumed hole concentration, x should be close to 0.01, which gives rise to ferromagnetic transition at Tc ≈ 10 K [6]. Let us assume the island size to be 0:75 × 1 m2 , which is easily attainable by the present time nanotechnology. That size likely assures formation of a single domain on the island [10]. Then, widths of the gate stripes might amount to about 100 nm. The question arises whether the direction of spontaneous magnetization of that island will be stable against thermal uctuations. For the assumed parameters of the ferromagnetic island we have estimated by Eq. (1) a dierence in the magnetic energies,
Um , for two perpendicular orientations of the magnetization vector. The obtained value is ∼ 1:5 meV in favor of the orientation parallel to the longer edge of the island. This value corresponds to a thermal energy kT at a temperature of 17 K, which exceeds expected Tc for the assumed Mn content. So, the conditions required for the operation of the proposed device can likely be ful lled in case of (Ga,Mn)As at low temperatures. In conclusion, we have proposed to use ferromagnetic III–V semiconductors, like (Ga,Mn)As, for design of novel class of devices that could serve for both nonvolatile storage of information and simple logic operations. The idea is to reverse the direction of spontaneous-magnetization of a single-domain island by manipulating voltages applied to suitably patterned Schottky gates deposited on the top of

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ferromagnetic island, which allows tailoring dierent sub-domains. Such a tailoring resembles the split gate technique used for de ning quantum wires and dots in semiconductor heterostructures, cf. [11]. References [1] J.S. Moodera, J. Nassar, G. Mathon, Ann. Rev. Mater. Sci. 29 (1999) 381. [2] J.A. Katiro, F.J. Albert, R.A. Bukman, Appl. Phys. Lett. 76 (2000) 354. [3] H. Imamura, N. Kobayashi, S. Takahashi, S. Maekawa, Phys. Rev. Lett. 84 (2000) 1003. [4] C.T. Liang, M.Y. Simmons, C.G. Smith, G.H. Kim, D.A. Ritchie, M. Pepper, Phys. Rev. B 60 (1999) 10 687.

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