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Probing Spin Accumulation induced Magnetocapacitance in a Single Electron Transistor.

Lee TH, Chen CD - Sci Rep (2015)

Bottom Line: The latter is known as the magnetocapacitance effect.This dipole can effectively give rise to an additional serial capacitance, which represents an extra charging energy that the tunneling electrons would encounter.It is found that the extra threshold energy is experienced only by electrons entering the islands, bringing about asymmetry in the measured Coulomb diamond.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, National Taiwan University, Taipei 106, Taiwan.

ABSTRACT
The interplay between spin and charge in solids is currently among the most discussed topics in condensed matter physics. Such interplay gives rise to magneto-electric coupling, which in the case of solids was named magneto-electric effect, as predicted by Curie on the basis of symmetry considerations. This effect enables the manipulation of magnetization using electrical field or, conversely, the manipulation of electrical polarization by magnetic field. The latter is known as the magnetocapacitance effect. Here, we show that non-equilibrium spin accumulation can induce tunnel magnetocapacitance through the formation of a tiny charge dipole. This dipole can effectively give rise to an additional serial capacitance, which represents an extra charging energy that the tunneling electrons would encounter. In the sequential tunneling regime, this extra energy can be understood as the energy required for a single spin to flip. A ferromagnetic single-electron-transistor with tunable magnetic configuration is utilized to demonstrate the proposed mechanism. It is found that the extra threshold energy is experienced only by electrons entering the islands, bringing about asymmetry in the measured Coulomb diamond. This asymmetry is an unambiguous evidence of spin accumulation induced tunnel magnetocapacitance, and the measured magnetocapacitance value is as high as 40%.

No MeSH data available.


Related in: MedlinePlus

Illustration of charge and spin distributions in the AP-configuration.(a) Spin accumulation (and depletion). Blue and green arrows indicate magnetization direction of Co and Py, respectively. Current density J is composed of spin up (red) and spin down (blue) components, represented by corresponding colored arrows, whose width indicates the relative magnitude. Dotted black curve resembles the charge density decay in All-P configuration (Figure S1c, S1), and serves as a baseline. Smooth red and blue curves depict spin up depletion and spin down accumulation, respectively. Note that the areas enclosed between the red/blue curve and the equilibrium level n0 (gray dashed line) are the same. (b) A blow-up view of n(x) and V(x) around xc, at which n(x) crosses n0. Perturbation in n(x) (black curve) is composed of the spin up (red curve) and spin down (blue curve) contributions. The green curve shows charge potential V(x) with the block dotted line indicating the height of . (c) Deduction of inversed capacitance values from dV(x)/eΔn(x)Adx. All-P plateau (black dash line, left) is elevated to AP plateau (black dash line, right) for 1/CS after xc. The arrowed sphere (blue and red) represents a single electron spin right after experiencing sequential tunneling from tunnel barrier Al2O3, whereas the black dotted arrow indicates the flipping event at the cost of e2/2CS.
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f3: Illustration of charge and spin distributions in the AP-configuration.(a) Spin accumulation (and depletion). Blue and green arrows indicate magnetization direction of Co and Py, respectively. Current density J is composed of spin up (red) and spin down (blue) components, represented by corresponding colored arrows, whose width indicates the relative magnitude. Dotted black curve resembles the charge density decay in All-P configuration (Figure S1c, S1), and serves as a baseline. Smooth red and blue curves depict spin up depletion and spin down accumulation, respectively. Note that the areas enclosed between the red/blue curve and the equilibrium level n0 (gray dashed line) are the same. (b) A blow-up view of n(x) and V(x) around xc, at which n(x) crosses n0. Perturbation in n(x) (black curve) is composed of the spin up (red curve) and spin down (blue curve) contributions. The green curve shows charge potential V(x) with the block dotted line indicating the height of . (c) Deduction of inversed capacitance values from dV(x)/eΔn(x)Adx. All-P plateau (black dash line, left) is elevated to AP plateau (black dash line, right) for 1/CS after xc. The arrowed sphere (blue and red) represents a single electron spin right after experiencing sequential tunneling from tunnel barrier Al2O3, whereas the black dotted arrow indicates the flipping event at the cost of e2/2CS.

Mentions: In AP-configurations, the current flowing through Al for each spin is not steady (Fig. 3a), giving rise to spin accumulation. This accumulation, in turn, causes a difference between spin-up and spin-down diffusion lengths, λ±. This difference is taken into account in our finite element analysis described in S2, yielding a solution of different from that of All-P case. This is simply comprised of two spin-dependent components (Fig. 3b), i.e., , where is due to E-field penetration alone, which becomes negligible for x ≫ , while is due to spin-accumulation in AP-configuration. Note that each accumulated/depleted spin diffuses with different spin diffusion length, in contrary to spin-independent charge screening length ξ. This difference in λ is responsible for the location of xc, where and cancel each other out, forming a tiny charge dipole structure. In other words, xc is just the solution of , which serves as a critical point across where changes sign. In the limit of small current that occurs within Coulomb blockade regime, the difference between λ± is small such that the solution for xc fall within Al thickness, allowing the charge dipole to exist inside Al with at x = xc. Because of the finite value at x > xc, an extra serial capacitance CS in AP-configuration is generated, which can be calculated using , as shown in Fig. 3c. Note that the calculated 1/CS is only dependent on the magnetic configuration of our device since 1/CAl is used as a reference for calculation. The induced tiny charge dipole, having an equivalent capacitance CS, thus acts as a serial capacitance to CAl in the AP-configuration. The existence of this charge dipole requires that xc be greater than but close to the screening length ξ. While the lower limit of Al thickness is set by xc, the upper limit is set by the spin diffusion length λ and the effect of exchange proximity (see S1). Since it is a single electron sequential tunneling process, this implies an extra cost of “charging energy” for a single spin flip event, which takes place in AP-configuration. The positive side of the charge dipole is close to the Al2O3 interface, regardless of the current direction, as explained in S3. However, if the electrons flow in opposite direction to the one shown in Fig. 3a, i.e. from Py island towards Al2O3/Al interface, the charge accumulates from Al2O3/Al interface and compensates the positive side of the charge dipole. This would wash away the charge dipole, and the TMC diminishes, causing Coulomb diamond to display asymmetry with respect to the bias direction of Vb.


Probing Spin Accumulation induced Magnetocapacitance in a Single Electron Transistor.

Lee TH, Chen CD - Sci Rep (2015)

Illustration of charge and spin distributions in the AP-configuration.(a) Spin accumulation (and depletion). Blue and green arrows indicate magnetization direction of Co and Py, respectively. Current density J is composed of spin up (red) and spin down (blue) components, represented by corresponding colored arrows, whose width indicates the relative magnitude. Dotted black curve resembles the charge density decay in All-P configuration (Figure S1c, S1), and serves as a baseline. Smooth red and blue curves depict spin up depletion and spin down accumulation, respectively. Note that the areas enclosed between the red/blue curve and the equilibrium level n0 (gray dashed line) are the same. (b) A blow-up view of n(x) and V(x) around xc, at which n(x) crosses n0. Perturbation in n(x) (black curve) is composed of the spin up (red curve) and spin down (blue curve) contributions. The green curve shows charge potential V(x) with the block dotted line indicating the height of . (c) Deduction of inversed capacitance values from dV(x)/eΔn(x)Adx. All-P plateau (black dash line, left) is elevated to AP plateau (black dash line, right) for 1/CS after xc. The arrowed sphere (blue and red) represents a single electron spin right after experiencing sequential tunneling from tunnel barrier Al2O3, whereas the black dotted arrow indicates the flipping event at the cost of e2/2CS.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4562261&req=5

f3: Illustration of charge and spin distributions in the AP-configuration.(a) Spin accumulation (and depletion). Blue and green arrows indicate magnetization direction of Co and Py, respectively. Current density J is composed of spin up (red) and spin down (blue) components, represented by corresponding colored arrows, whose width indicates the relative magnitude. Dotted black curve resembles the charge density decay in All-P configuration (Figure S1c, S1), and serves as a baseline. Smooth red and blue curves depict spin up depletion and spin down accumulation, respectively. Note that the areas enclosed between the red/blue curve and the equilibrium level n0 (gray dashed line) are the same. (b) A blow-up view of n(x) and V(x) around xc, at which n(x) crosses n0. Perturbation in n(x) (black curve) is composed of the spin up (red curve) and spin down (blue curve) contributions. The green curve shows charge potential V(x) with the block dotted line indicating the height of . (c) Deduction of inversed capacitance values from dV(x)/eΔn(x)Adx. All-P plateau (black dash line, left) is elevated to AP plateau (black dash line, right) for 1/CS after xc. The arrowed sphere (blue and red) represents a single electron spin right after experiencing sequential tunneling from tunnel barrier Al2O3, whereas the black dotted arrow indicates the flipping event at the cost of e2/2CS.
Mentions: In AP-configurations, the current flowing through Al for each spin is not steady (Fig. 3a), giving rise to spin accumulation. This accumulation, in turn, causes a difference between spin-up and spin-down diffusion lengths, λ±. This difference is taken into account in our finite element analysis described in S2, yielding a solution of different from that of All-P case. This is simply comprised of two spin-dependent components (Fig. 3b), i.e., , where is due to E-field penetration alone, which becomes negligible for x ≫ , while is due to spin-accumulation in AP-configuration. Note that each accumulated/depleted spin diffuses with different spin diffusion length, in contrary to spin-independent charge screening length ξ. This difference in λ is responsible for the location of xc, where and cancel each other out, forming a tiny charge dipole structure. In other words, xc is just the solution of , which serves as a critical point across where changes sign. In the limit of small current that occurs within Coulomb blockade regime, the difference between λ± is small such that the solution for xc fall within Al thickness, allowing the charge dipole to exist inside Al with at x = xc. Because of the finite value at x > xc, an extra serial capacitance CS in AP-configuration is generated, which can be calculated using , as shown in Fig. 3c. Note that the calculated 1/CS is only dependent on the magnetic configuration of our device since 1/CAl is used as a reference for calculation. The induced tiny charge dipole, having an equivalent capacitance CS, thus acts as a serial capacitance to CAl in the AP-configuration. The existence of this charge dipole requires that xc be greater than but close to the screening length ξ. While the lower limit of Al thickness is set by xc, the upper limit is set by the spin diffusion length λ and the effect of exchange proximity (see S1). Since it is a single electron sequential tunneling process, this implies an extra cost of “charging energy” for a single spin flip event, which takes place in AP-configuration. The positive side of the charge dipole is close to the Al2O3 interface, regardless of the current direction, as explained in S3. However, if the electrons flow in opposite direction to the one shown in Fig. 3a, i.e. from Py island towards Al2O3/Al interface, the charge accumulates from Al2O3/Al interface and compensates the positive side of the charge dipole. This would wash away the charge dipole, and the TMC diminishes, causing Coulomb diamond to display asymmetry with respect to the bias direction of Vb.

Bottom Line: The latter is known as the magnetocapacitance effect.This dipole can effectively give rise to an additional serial capacitance, which represents an extra charging energy that the tunneling electrons would encounter.It is found that the extra threshold energy is experienced only by electrons entering the islands, bringing about asymmetry in the measured Coulomb diamond.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, National Taiwan University, Taipei 106, Taiwan.

ABSTRACT
The interplay between spin and charge in solids is currently among the most discussed topics in condensed matter physics. Such interplay gives rise to magneto-electric coupling, which in the case of solids was named magneto-electric effect, as predicted by Curie on the basis of symmetry considerations. This effect enables the manipulation of magnetization using electrical field or, conversely, the manipulation of electrical polarization by magnetic field. The latter is known as the magnetocapacitance effect. Here, we show that non-equilibrium spin accumulation can induce tunnel magnetocapacitance through the formation of a tiny charge dipole. This dipole can effectively give rise to an additional serial capacitance, which represents an extra charging energy that the tunneling electrons would encounter. In the sequential tunneling regime, this extra energy can be understood as the energy required for a single spin to flip. A ferromagnetic single-electron-transistor with tunable magnetic configuration is utilized to demonstrate the proposed mechanism. It is found that the extra threshold energy is experienced only by electrons entering the islands, bringing about asymmetry in the measured Coulomb diamond. This asymmetry is an unambiguous evidence of spin accumulation induced tunnel magnetocapacitance, and the measured magnetocapacitance value is as high as 40%.

No MeSH data available.


Related in: MedlinePlus