Abstract:

The voltage-controlled magnetic anisotropy (VCMA) effect describes the fact that in a capacitor, in which one of electrodes is made of a thin ferromagnetic metal, the magnetic properties of the ferromagnetic metal changes, when a voltage is applied to the capacitor.

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Magnetic parameters, which depend on the gate voltage:

Coercive field H_c;Anisotropy field H_anis;Energy of perpendicular magnetic anisotropy (PMA) E_anis; Hall angle; Spin polarization; Logarithm of magnetization switching time Logarithm of Retention time Delta Δ

All these 8 parameters depend linearly on the gate voltage. They are linearly increases under a negative gate voltage and linearly decreases under a positive gate voltage.

High-precision measurements of gate voltage dependencies of these 8 magnetic parameters are described below.

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Content

click on the chapter for the shortcut

(1). Possible origins of VCMA in short

(2) Experimental measurements of VCMA

(measurement 1) Voltage-dependence of coercive field

(measurement 2) Voltage-dependence of anisotropy field

(measurement 3) Voltage-dependence of switching time, retention time, Δ and PMA energy

(measurement 4) Voltage-dependence of spin polarization

(measurement 5) Voltage-dependence of Hall angle

(3). Samples. Experimental setup

(4) Possible origins of VCMA effect:

group 1: due to modulation of Fermi level:

(origin 1) Change of magnetization due to to charge-accumulation/depletion under a gate voltage

(origin 2) Orbit reconstruction due to modulation of the Fermi level

group 2: without assumption of modulation of Fermi level:

(origin 3) Elastic strains

(origin 4) Orbit reconstruction

(origin 5) Rashba effect

(origin 6) Oxygen diffusion

(5). Enhancement Methods of VCMA effect

(5a) Work Function Engineering

(5b) (FeB/W) multilayers

(5c) optimization of gate oxide & gate metal

(6) Influence of the quality of the gate oxide on the VCMA effect

(7). Voltage-dependence of Left and Right edges of the coercive loop

(8) The dependence of the VCMA on an absolute value of H_anis and H_c

(7). The dependence of the VCMA on thickness of a ferromagnetic metal

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Questions & Answers

(q1) spin waves and VCMA

 

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working version of manuscript. Zayets July 14, 2018 & short version Nov. 2018

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Applications of the effect:

1) Voltage-switched magnetic random access memory (MRAM)

2) All-metal transistor

Under an applied voltage the magnetization direction of the ferromagnetic metal may be changed or even reversed. This magnetization-switching mechanism can be used as a data recording method. When an electrical pulse reverses magnetization direction, the data is memorized in the ferromagnetic metal by means of its two opposite magnetization directions. Such a recording mechanism is fast and energy-efficient. It may be used in magnetic the random access memory (MRAM) and the all-metal transistor.

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Possible origins of voltage-controlled PMA effect

 

detailed explanation is here

As Nov. 2018, the physical origin of the VCMA effect is still unclear. Many experimental and theoretical research are still going in order to clarify it.

Group 1:

Based on the Modulation of Fermi level

Problem: Estimated change of the Fermi level is small. It is only 4.5 eV per 1 V of gate voltage (see below)

Origin 1

- Modulation of magnetization

asymmetrical vs. voltage

Origin 2

- Modulation of orbit symmetry due to band intermixing

 

Group 2:

Not related to modulation of Fermi level

Origin 3

- magnetostriction effect

symmetrical vs. voltage

Origin 4

- Orbital reconstruction by electrical field

symmetrical+asymmetrical vs. voltage

Origin 5

- Rashba effect

magnitude of this contribution depends on the value of the bias current

 

Group 3:

Undesired effects

Origin 6

- Oxygen electro-diffusion

Response time ~ 30 sec. It makes a problem for usage of the VCMA for applications. This contribution is the feature of a gate oxide with defects.

 

 

 

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Experimental measurements

I use 5 independent measurements of the VCMA effect. All measurements have similar tendency of the linear dependence on gate voltage and the negative polarity of the dependence.

I have developed the following measurement methods in 2017-2018

Measurements 1

- gate voltage dependence of coercive field

slope: negative; gate-voltage polarity change: changes sign

For measurements, this method is used. It is very sensitive technique. It allows to detect a very tiny changes of the PMA under a gate voltage. The coercive field increases under a negative gate voltage and it decreases under a positive gate voltage. Most of samples show a perfect linear dependance.

 

 

 

 

 

 

 

Measurements 2

- gate voltage dependence of anisotropy field

slope: negative; gate-voltage polarity change: changes sign

The anisotropy field is the the field, at which initially-perpendicular magnetization turns completely to the in-plane direction. The anisotropy field increases under a negative gate voltage and it decreases under a positive gate voltage. The anisotropy field is proportional to the PMA energy (For details see here)

 

 

 

 

 

 

Measurements 3

slope: negative; gate-voltage polarity change: changes sign

- gate voltage dependence of switching time (retention time, Δ , PMA energy and magnetization)

For measurements, this method is used. It is very sensitive technique. It allows to detect a very small change of magnetic properties. This method allows to measure simultaneously the retention time and magnetization. Most of samples show substantial change of the retention time and Δ, In contrast, this method does not detect any modulation of the magnetization by the gate voltage.

Figure 11 (left) shows the dependence of the switching time on the magnitude of an external perpendicular magnetic field. On a logarithmic scale, the switching time is linearly proportional to the magnetic field. Therefore, the magnetization switching is well described by the Arrhenius law (Details see here) even in the case when magnetic properties are changed by a gate voltage. The switching time becomes longer at a negative gate voltage and shorter at a positive gate voltage. From this Eq, the slope of the lines is proportional to M_eff and the horizontal offset is proportional to retention time and consequently to E_PMA. Figure 11 (center) shows the measured dependence of the retention time on the gate voltage. On a logarithmic scale, the dependence is linear. The retention time increases at a negative gate voltage and decreases at a positive gate voltage. As can be seen from Fig. 11(left), the slope for each line is nearly the same. It means that the M_eff is not significantly affected by the gate voltage. The M_eff describes the average bulk magnetization during the magnetization reversal. It is not sensitive to a small change of magnetization in a thin region near the interface. Figure 11(right) shows the measured dependence of the Δ on the gate voltage. The dependence is linear. The Δ increases at a negative gate voltage and decreases at a positive gate voltage.

 

 

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Measurements 4

slope: negative; gate-voltage polarity change: changes sign

- gate voltage dependence of spin polarization

 

The spin polarization (sp) in a ferromagnetic metal linearly increases under a negative gate voltage and linearly decreases under a positive gate voltage.

 

The measurement method is described here. The facts about the spin polarization in a ferromagnetic metal are described here.

 

Measurements:

FeB (sp=81.7 %) : voltage-dependent change of sp=-0.245 %/V

FeCoB (sp=89.4 %) : voltage-dependent change of sp=-0.0068 %/V

Why voltage-dependent change of spin polarization is larger in FeB than in FeCoB?

A. The equilibrium spin polarization sp₀ is larger in FeCoB sample than in FeB sample. As a result, the same change of the sp-d spin pumping causes a smaller change of sp₀ in the FeCoB sample than in the FeB sample.

 

The spin polarization is different in a different ferromagnetic metal. The spin polarization is determined by a balance between the spin pumping and the spin damping. The spin pumping describes the conversion of spin-unpolarized electrons into the group of spin-polarized electrons. The spin damping describes the opposite conversion. (See details here). The origin of the spin pumping is the exchange interaction between conduction electrons and localized d-electrons (See here). The origin of the spin damping is scatterings on defects, the spin precession in an inhomogeneous magnetic field and so forth.

Since the gate voltage modulates the spin polarization, either the spin pumping or the damping or both are modulated by the gate voltage.

What does the gate voltage change? the spin pumping or the spin damping?

A. Probably the gate voltage changes the spin pumping. However, the change of the spin damping is also possible.

Possible mechanism of the gate-voltage modulation of the spin polarization:

It can be assumed that a negative gate voltage enlarges the metal magnetization in a very thin region close to the gate interface. Due to the larger magnetization, the sp-d spin pumping should be enhanced.  Such enhancement leads to a larger spin polarization.

 

 

 

 

 

Measurements 5

- gate voltage dependence of Hall angle

slope: negative; gate-voltage polarity change: changes sign

The Hall angle increases under a negative gate voltage and it decreases under a positive gate voltage.

Figure 9 shows the gate-voltage dependency of the Hall angle in the FeB film. (See here details about Hall angle) All measurement points fit well in a straight line with a negative slope.

The Hall angle is proportional to the magnetization of the ferromagnetic metal, the spin polarization of the conduction electrons and the strength of spin-orbit interaction (See here).

 

Note : The Hall angle is linearly proportional to the Hall resistance. In contrast to the Hall resistance, the Hall angle is only material dependent and does not depend on geometrical parameters like a film thickness.(Details see here)

 

 

 

 

 

 

 

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All measurements demonstrate the same tendency. The coercive field, anisotropy field, PMA energy, Hall rotation angle, and retention time decrease under a positive gate voltage and increase under a negative voltage.

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Samples

A thin nanowire of a ferromagnetic metal is used. A pair of Hall probe is used to extract magnetic properties of ferromagnetic nanowire. The source voltage is applied between two ends of the nanowire. The gate voltage was applied between one end of the nanowire and the gate electrode.

Which magnetic properties can be measured from the Hall measurements?

Coercive field; Retention time; effective magnetization; anisotropy field;delta;PMA energy Hall angle; spin polarization;

See here and here for details

Is there any tunneling current through 6-nm-thick MgO gate

Yes, there is, but it does not exceed 0.1 uA. It depends on the area of the gate. Typically it is 0.01-0.001 uA at the maximum- used gate voltage. Such small current does not influence the measurement. The measurements of the tunneling current is important. Measurements of the tunneling current is important to estimate the density of deep defects in the MgO gate oxide ( See below)

What is the main challenge in the fabrication of the VCMA samples?

It is the fabrication of the MgO gate oxide with the lowest density of the deep defects. I have developed an optimized growth method to reduce the density of the defect in the MgO gate oxide. However, some defect still remains and they influence the measured properties of the VCMA effect.

How to fabricate the gate oxide of a higher quality

In the case of MgO gate oxide, two growth methods can be used

1. Conventional growth method of MgO gate (a lower quality & larger amount of defects)

EB evaporation of MgO at room temperature. MgO thickness: 7-10 nm

2. Optimized growth method of MgO gate (a higher quality & lower amount of defects)

At first, a 1 nm MgO was deposited at room temperature, next the sample was annealed at 220⁰ C for 30' and the remaining of the MgO gate oxide was grown at 220⁰ C. Three 30-minute growth interruptions after each 1 nm of growth were used to improve the MgO crystal quality. Total MgO thickness is 7-10 nm

This fabrication method of MgO gate increases the break-down voltage and to suppress the oxygen diffusion in the gate.

Note: I have developed this method in 2005 for fabrication of the spin-photon memory.

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Possible origins of the VCMA effect

As on date (July 2018) the main origin of the VCMA is unclear for me.

The fact 1: The gate voltage modulates the perpendicular magnetic anisotropy (PMA)

Inside a metal the electrical field is screened by free electrons and cannot penetrate deep inside the metal. As a result, the voltage, which is applied to the capacitor dielectric (gate), may penetrate into and affect only the few uppermost atomic layers of the metal near the gate. However, the change of magnetic properties of the uppermost layer by the gate voltage affects the magnetic properties of the whole film. This can be only the case if the interfacial perpendicular magnetic anisotropy (PMA) is affected by the gate voltage.

  The interfacial PMA is the effect, which occurs due to a strong spin-orbit (SO) interaction in the upmost atomic layer of the metal[8]. As a result, the magnetic properties of only one upmost atomic layer strongly affect the magnetic properties of the whole film. Since the magnitude of the VCMA effect can be substantial, it is likely that the gate voltage affects the interfacial PMA. However, it is still unclear which particular properties of the upper layer or the whole film are changed by the gate voltage. The interfacial PMA depends on the magnetization of the film, atom arrangement and bonding at the interface. The gate-dependence of each of these properties may be the origin of the VCMA effect. The understanding of the details of the VCMA effect is important in order to optimize and possibly enhance the effect for a future practical application. In this paper we particularly emphasize our study on the symmetry and polarity the VCMA effect with respect to the reversal of the gate voltage. It might be a clue to clarify the origin of the VCMA effect.

How perpendicular magnetic anisotropy (PMA) may be changed?

PMA changes only in the case when

1. Magnetization is changed

2. Spatial symmetry of orbital is changed. (the orbital is deformed)

 

note: Only changes in uppermost layer affect the PMA.

 

The interface PMA occurs due to the strong spin-orbit (SO) interaction in the uppermost atoms of a metal at the gate. The SO interaction is a relativistic effect, which states that an electron experiences an effective magnetic field when it moves in a static electrical field. The SO effective magnetic field is proportional to 1/c², therefore it is small.  Only in a strong static electrical field, an electron may experience a substantial SO effective magnetic field. In a solid the electrical field is only strong enough in the close proximity of the nucleus in order to induce a substantial SO magnetic field of 1 kGauss or greater. However, in a central-symmetric electrical field of a nucleus  the effective SO magnetic field is non-zero only when both the time-inverse symmetry and the spatial symmetry are broken. Otherwise, the effect cancels itself. The intrinsic magnetic field or the magnetization of a ferromagnetic metal breaks the time-inverse symmetry.  As a result, the strength of the SO effective magnetic field and the value of the PMA energy are proportional to the magnetization. (For more details see here)

The second condition for the existing of the SO magnetic field is the breaking of the spatial symmetry. For example, an electron of the symmetry, which has the spherical orbital, does not experience any SO interaction, because the spatial symmetry is not broken for such orbital. An external electrical field can break the spatial symmetry. There are several possible orbital deformations, which may lead to the breaking of the spatial symmetry. Firstly, the external electrical field may deform the orbital along its applied direction. Secondly, the electrical field may shift the center of the orbital from center of the nucleus.

The fact 2: There is only one major origin of the VCMA effect

All experimental measurements of the gate-voltage dependence of different magnetic parameters have the similar tendency and they related to each other. They linearly decrease when the gate voltage increases and they linearly increase when the gate voltage decreases. A sample, in which the voltage dependence is stronger for one magnetic parameter, has a stronger voltage dependence of other magnetic parameters.

 

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How deep does the gate voltage penetrate inside the ferromagnetic metal?

For all 5 possible origins, the magnitude of the VCMA effect strongly depends on the penetration depth of the gate voltage into the ferromagnetic metal.

 

The electrical field is screened in a metal. That means the following. The conduction electron move in the electrical field and they are accumulated at boundary of the gate oxide until their own electrical field fully compensates the applied electrical field and the total electrical field becomes zero.

In contrast to a semiconductor, which can be depleted, a metal can not be depleted and the conduction electrons are accumulated in a thin region at non-conductive gate oxide. This region is very thin, but not infinitely thin. Its thickness is about the size of electron or the electron mean-free path λ_mean (for details, see here and here). Along the thickness of this region, the electrical field decreases towards zero.

 

The smaller the thickness of electron accumulation region is, the larger the VCMA becomes. (independently from the VCMA origin!).

The smaller the thickness of electron accumulation region is:

the larger the density of electron accumulation becomes. As a result, the larger change of the Fermi level under a gate voltage becomes.

the larger the electrical field in this region becomes. As a result, the larger the orbital reconstruction becomes.

the larger the stress and magnetostriction effect. It is because of a larger electrical field in this region and the electrical field is compress force.

the stronger the oxygen electro diffusion becomes. It is because of a larger electrical field in this region, which induces the electro diffusion..

 

The larger metal resistivity is, the larger the VCMA effect is (independently on the VCMA origin)

Explanation: In a metal of a higher resistivity the mean free path of conduction electrons is shorter. As a result, the size of conduction electron is shorter, the penetration length of electrical field is shorter and therefore the VCMA is larger.

 

Note: AC electromagnetic field may also penetrates into a metal. This effect is called the skin effect. It has an electromagnetic origin, which is very different from the origin described above.

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Possible origin № 1 of VCMA effect: Change of magnetization due to to charge-accumulation/depletion under a gate voltage

Origin 1: Change of magnetization under a gate voltage

The gate voltage modulates the Fermi level at the Fe/MgO boundary. The gate voltage changes the Fermi level position . Because the density of states of the spin-up and spin-down localized d-electrons are different, the changes of number of spin-up and spin-down electrons are different. Therefore, the total magnetization changes under the gate voltage. A positive voltage is applied to gate (Ta). The conduction electrons are accumulated at MgO/Fe interface. As result, the Fermi level increases. More d-down electrons are filled up than the d-up electrons. Therefore, the magnetization decreases. A negative voltage is applied to gate (Ta). The conduction electrons are depleted at MgO/Fe interface. As result, the Fermi level decreases and the number of d-electrons decreases as well. The reduction of number of d-down is larger than the number of d-up electrons. Therefore, the total magnetization increases. click on image to enlarge it

Under the gate voltage, the electrons are accumulated or depleted in the metal in close proximity of gate. As a result, the Fermi level is changed. The cage of the Fermi level may be a cause of the VCMA effect. Note: the change of the Fermi level change is substantial in a semiconductor. For example, the MOSFET transistor utilizes this effect.

Supporting Facts: The predicted polarity of VCMA is exactly the same as observed experimentally. All experimental data point that the magnetization is change in a small region of metal close to the gate, which is predicted by this mechanism.This mechanism predicts the dependence of the VCMA effect on the position of the Fermi level in the ferromagnetic metal. There some experimental hints that it is the case (See FeB/W multilayer below). Still such dependence need be clarify carefully.

Problems: : Estimated change of the Fermi level is too small. It is only 4.5 eV per 1 V of gate voltage. In order to explain the experimental facts, it should be larger. This mechanism predicts the dependence of the VCMA effect depend on the material of the gate metal. Such dependence has not been observed experimentally yet. (I have checked W and Ta. I cannot find a substantial difference). A possible pinning of the Fermi level inside gate oxide make such experiment difficult.

Explanation of the mechanism:

Under a gate voltage the conduction electrons are accumulated or depleted in the vicinity the gate oxide. It changes the position of the Fermi level. When the Fermi level changes, the filling of the d-up and d-down electron bands changes as well. The density of states for the d-up and d-down bands are different. Therefore, the change of the numbers of d-up and d-down electrons are different. As result, the magnetization of the ferromagnetic metal, which is proportional to the difference between numbers of the d-up and d-down electrons, changes in the vicinity of the gate interface.

Why capacitor effect looks like the dominant effect of the controlled-magnetism in the FeB/MgO nanowire?

It is because:

1) All measurements show the asymmetrical dependence as a function of the gate voltage. It is the feature of the capacitor effect.

2) The polarity of effect is the same as the polarity of the capacitor effect. The coercive field, the Hall angle, the anisotropy field, all increase under a negative gate voltage and decrease under a positive gate voltage.

Unclear point: How such a small gate voltage and corresponded small charge accumulation can change substantially the position of the Fermi level in a metal.

The number of conduction electrons in a metal is large. At gate voltage of 1 or 2 V the charge accumulation on sides of the capacitor is not very large. In order to change magnetization of the ferromagnetic metal, the change of the Fermi level should be at least of a ten millivolts or more. However, the density of states of the conduction electrons large and it can be suggested that much larger charge accumulation is required to required change the Fermi level.

Possible answer 1:

The electron accumulation occurs within a very small region in the vicinity of the gate. Even though the amount of the accumulated electrons might be not very large, the density of the accumulated electrons can be very large, because of very small region of the accumulation. In the contrast to a semiconductor, a metal can not be depleted. Therefore, in a metal the charge is accumulated in the region, which size is about the size of an electron. Therefore, the accumulation region should be at least smaller than the electron mean free path and larger than lattice parameter.

Note: the length of a conduction electron equals to the mean free path (see here)

Possible answer 2:

At the interface between the ferromagnetic electrode and the gate oxide, the conduction electrons are different than in the bulk of the metal. They bound to oxide, they have a different wave function and they are often called the surface states. The density of the surface states is much smaller than the number of stated of the conduction electrons in the bulk of a metal. Therefore, even a small change of the electrons of the surface states causes a substantial change of the Fermi level.

 

 

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Possible origin № 2 of VCMA effect: Orbit reconstruction due to modulation of the Fermi level

C.G. Duan et al., Phys. Rev. Lett. 101 (2008) 1–4

Explanation of the mechanism:

The second possible mechanism of the VCMA effect is the modulation of the spatial symmetry of localized d-electrons by the modulation of the Fermi level.  This mechanism is similar to the mechanism of the modulation of the SO interaction of the conduction electrons in a semiconductor [J.M. Luttinger, W. Kohn, Phys. Rev. 97 (1955) ], which occurs due to the mixing between bands of p- and s- symmetry. A conduction electron, whose energy is at the bottom of the conduction band, has symmetry and does not experience any SO interaction. A conduction electron of a higher energy has a component of the p-symmetry and does experiences the SO interaction. By a modulation of the Fermi level, the strength of the SO interaction can be modulated. A similar mechanism was suggested [] for the localized electrons in a ferromagnetic metal. As a result of a shift of the Fermi level, the spatial symmetry of the localized electrons changes. This leads to the modulation of the strength of the SO interaction and the PMA. The contribution of this mechanism to the VCMA may be substantial only in the case when there are at least two types of states for localized electrons of substantially-different spatial symmetry. However, it is accepted that in bcc Fe only d-electrons of the e.g. symmetry are localized [] and there are no localized states of a substantially different symmetry. As a result, a substantial contribution of this mechanism to the VCMA is not expected. It should be noted that the hybridization of the localized d-electrons with p-electrons at the gate interface []may increase the diversity of the spatial symmetry of the localized electrons and therefore increase the contribution of this mechanism.

Supporting Facts: ???

Problems: It requires unrealistically large change of the Fermi energy; There is no evidence that localized d- electron in Fe or Co has two bands or states of substantially different symmetries and close energies as required by this mechanism.

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Possible origin № 3 of VCMA effect: Elastic strains

Supporting Facts: The magnitude of the magnetostriction effect in substantial in the Fe and Co; The ferromagnetic metal is stressed under a gate voltage in a small region near the gate

Problems: The symmetry of the contribution should be symmetrical with respect to the polarity of the gate voltage. However, measured voltage-dependence of different magnetic parameters are asymmetric and linear.

Explanation of the mechanism:

This mechanism does not require the modulation of the Fermi level.

The third possible mechanism of the VCMA effect is the modulation of the PMA by the strains. Under a gate voltage, the gate is compressed. Since the electrical field slightly penetrates into a metal, a few uppermost layers of the metal may be compressed as well.  Due to the compressive strains the electron orbital is deformed, which may modulate the SO and the PMA. The gate voltage of both polarities equally compresses the gate. As a result, the VCMA induced by the strains should not depend on the polarity of the gate voltage. In the case of a large VCMA effect (see above) the measured polarity of the VCMA is opposite for the opposite gate voltages. It can be concluded that the strain-induced mechanism is a minor contributor to the VCMA effect in the studied samples. 

Why the gate are stressed under a gate voltage?

The positive and negative charges at opposite electrodes attract each other. Under this force the gate is compressed.

Why the stressed induced VCMA is independent on the polarity of the gate voltage?

The positive charge attracts the negative charge the same force as the negative charge attracts the positive charge. Therefore, the attractive force between two charged electrodes does depend on relative polarity, but it is only depend the difference of charges.

The gate oxide is stressed under the gate voltage. It is OK. But why the ferromagnetic metal is stressed?

The electromagnetic field penetrates into the ferromagnetic over size of a conduction electron (See here). This region is stressed for the same reason why the gate is the stressed: the attraction between the positive and negative charges.

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Possible origin № 4 of VCMA effect: Orbit reconstruction

Supporting Facts: The predicted polarity of VCMA is exactly the same as observed experimentally. This mechanism does not contradict with any experimental fact.

Problems: ???

Explanation of the mechanism:

This mechanism does not require the modulation of the Fermi level.

The fourth possible mechanism of the VCMA effect is the modulation of the PMA due to an orbital deformation in an electric field . The deformation of the orbital induces an electrical dipole moment. Due to this induced dipole moment, the permittivity of a metal becomes different from the vacuum permittivity. The deformation of the orbital enhances the SO interaction See here and here). The larger the orbital deformation is and the larger the SO enhancement becomes. The polarity of this contribution can be both symmetrical and asymmetrical with respect to the polarity of the gate voltage. The schematic diagrams in Fig.5 illustrate both the symmetrical ((a)-(c)) and the asymmetrical ((d)-(e)) contributions. In the case of a centrosymmetric orbital in the absence of an external electrical field, there are neither a net electrical dipole moment P nor an effective SO magnetic field H_SO(Fig.5a). In an electrical field, the electron orbital and the nucleus are slightly shifted relatively to each other and the electrical dipole moment P is induced. The breaking of the spatial symmetry along the M direction induces H_SO(Fig.5(b,c)).  The polarity of H_SO does not depend on the polarity of the electrical field. It is always directed along M. As a result, the change of H_SO and correspondingly the PMA energy do not depend on the polarity of the gate voltage. The case of an elliptical orbital is different. For example, the electron orbital may be elongated toward the gate due to an attraction of an oxygen atom. In this case, the P and H_SO are non-zero even in the absence of an external electrical field (Fig.5d). An electrical field either reduces or enhances P and H_SO(Figs. 5(e,f) depending on its polarity. Even though the H_SO does not reverse its own direction, the changes of H_SO are opposite for the opposite polarities of the gate voltage. As shown in Figs. 5(e,f), the H_SO and correspondingly the PMA energy are larger under a positive gate voltage and smaller under a negative gate voltage. This predicted polarity of VCME is opposite to the polarity of our measurements (Figs. 2-4). In the case when the orbital deformation could be opposite to that shown in Fig.5d, the VCME polarity would be the same as in our experiment.
As was mentioned above, only the regions with the highest electrical field contribute substantially to the SO effective magnetic field. As a result, the region of close proximity to the nucleus (Fig.5) is mostly important to determine the strength of the SO interaction. This is the reason why the simplified description of Fig.5 is valid for the electrons of p- and d-symmetries as well.

Nakamura et. al PRB 2009;Ibrahim et.al. PRB 2016;

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Possible origin № 5 of VCMA effect: Rashba effect

Supporting Facts: ????

Problems: Since only relatively-small gate electrical field can be applied and the drift movement of electron is slow, Rashba-effect contribution should be very smallThis contribution should depend on the polarity of bias current, which has not been observed experimentally

 

In this case the strength of the VCMA effect should depend on current density in the nanowire. Such dependence has not been yet experimentally detected.

Major difference between Rashba-effect contribution and all other discussed contributions is :

all other discussed contributions: the spin-orbit (SO) interaction is induced by electrical field of a atomic nucleus and orbital movement of an electron

Rashba-effect contribution: the SO interaction is induced by the gate electrical field and the drift movent of electrons along the bias voltage.

 

Note: Since only relatively-small gate electrical field can be applied and the drift movement of electron is slow, Rashba-effect contribution should be very small

L.Xu et.al. JAP (2012); S.E.Barnes et.al.Sci.Rep. (2014)

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Possible origin № 6 of VCMA effect:Oxygen diffusion

Supporting Facts: The oxygen diffusion through the gate oxide is the major mechanism of the VCMA in the case of a gate with a substantial number of defects and a slow-response of the VCMA. It is well experimentally verified fact.

Problems: The diffusion of the oxygen is relatively slow process (it takes minutes and hours). However, the VCMA effect has been measured at a high frequency of FMR (~ 10 GHz). In this case, the time response of the VCMA effect is too fast for any sizable oxygen diffusion to occur in the gate oxide.

Explanation of the mechanism:

This mechanism does not require the modulation of the Fermi level.

This mechanism is a feature of samples, in which the gate oxide has many defects.

The covalent bonding between oxygen and iron deforms substantially the d-orbit of Fe. As a result, the spin-orbit interaction the d-electrons is enhanced and consequently the PMA is enhanced as well. Up to some limit, a larger amount of oxygen ions at interface causes a larger PMA.

In case when the crystal quality of the gate oxide is not perfect, the oxygen ion may diffuse through it. Under a negative gate voltage, the oxygen ions diffuse toward gate/ferromagnetic-metal interface, it makes the PMA larger. Under a positive gate voltage, the oxygen ions diffuse out from interface, it makes the PMA smaller. It is the same polarity of the VCMA as was observed in experiment.

GdOx gate: C. Bi et al, PRL (2014); U. Bauer et al, Nat.Mat (2015); AlOx gate S. Baek et al, Nat. Elect (2018)

The oxygen diffusion is a very clear feature of samples with a low-quality of the gate oxide. In this case, the oxygen diffusion contributes greatly to the VCMA. Сan the oxygen diffusion be the origin of the VCMA effect even in the case of a sample with a high quality of gate oxide?

A. Yes. A shift of oxygen position under a gate voltage may be the origin of the VCMA in the case of a high-quality of the gate oxide.

Samples with a large number of defect in gate oxide show a large VCMA effect. However, the features of the VCMA is very peculiar. For example, the response time of the VCMA effect is very slow and there is a hysteresis loop vs gate voltage (See below). Such properties are not acceptable for any practical application. Therefore, the fabrication technology of the gate oxide is optimized to reduce the number of defects. As a result, the VCMA effect becomes weaker (but still substantial), the response time of VCMA effect becomes very fast (at least 1 ns) and there is no hysteresis loop in a sample of a high-quality of the gate oxide.

 

The number of defects in the gate oxide can be measured using the capacitance-voltage measurements, DLTS (deep level transition spectroscopy) and DLCS (deep level conduction spectroscopy). When there are enough defects and vacancies, under a negative-gate voltage the negatively-charged oxygen ion jumps from a site to site in gate oxide towards the ferromagnetic metal. When there are more oxygen at interface, the stronger the perpendicular magnetic anisotropy (PMA) becomes. Under a negative-gate voltage the oxygen ions moves out of the interface and the PMA becomes smaller. The same polarity of VCMA is observed in samples with quality of the gate oxide.

There is no oxygen diffusion in a sample of a high quality of gate oxide. However, even a slight shift of the oxygen ion towards or backwards to a Fe atom is sufficient to enhance substantially the PMA. As explained here, the strength of the PMA is related to the deformation of the Fe orbital. Such deformation depends substantially on mutual positions of iron and oxygen at the interface.

For example, in phase-change memory (PRAM) the properties of GeTe–Sb2Te3 superlattice is utilized. Under an electrical or optical pulse the position of Ge atom is slightly shifted. Even a slight shift of Ge atom causes a substantial change of the electrical and optical properties of the superlattice. Even though the effect is related to the shift of atom, the effect is fast (response time ~ 100 ps). Similarly, the VCMA effect originated from the slight shift of oxygen atoms may have a very fast response.

 

 

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How to enhance the VCMA effect

A possible method to enhance the VCMA effect may depend on the origin of the VCMA effect, which is still unknown (Feb. 2019).

method 1: Work-Function Engineering of magnetic properties

This method may be only effective if the origin of the VCMA is related to the change of the Fermi level in ferromagnetic metal by the gate voltage. The Work-Function Engineering may optimize the Fermi energy in the metal at energy, where a smallest modulation of the position of the Fermi energy causes the largest modulation of the density of states of d-electrons (See below for details)

method 2: Optimization of the metal-oxide interface

The strength of the PMA depends on the orbital deformation of iron and oxygen atoms at the metal-gate interface (See details here). Due to the orbital deformation these atoms experiences a large spin-orbit (SO) interaction (See details here and here). The gate voltage modifies such deformation and therefore it modifies the PMA. This fact is independent on the origin of the VCMA. The chemistry of the interface should be optimized such that the deformation of orbitals by the electrical field of the gate voltage should cause the largest change of the strength of the spin-orbit interaction and consequently the largest change of the PMA.

method 3: The reduction of the penetration depth of the electrical field of the gate voltage into the metal.

This method is independent on the origin of the VCMA. In the case of the shorter penetration depth, the electrical field of the gate voltage at the interface is large and its influence on the PMA is larger.

method 4: The use of a ferromagnetic metal with more localized d- electrons (or f-electrons).

The more localized the d-electrons ( or f-electrons) are, the sharper their corresponding peak in DOS is. The VCMA is enlarged in the case when the Fermi level is at a slope of this peak. The VCMA is is larger, when the DOS of the localized electrons has a greater slope near the Fermi level. See Work-Function Engineering below for more details.

 

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Work-Function Engineering of magnetic properties

In the case if the origin of VCMA effect is related to the gate-voltage modulation of the Fermi energy at the interface of a metal, the strength of the VCMA should depend on the metal material of the buffer layer. As Feb. 2019, I have measured several near-identical samples, where either Ta or W is used as the buffer. It is hard to make a clear conclusion, because other magnetic properties of a nanomagnet substantially depends on the material of the buffer.

In the case if the origin of VCMA effect is related to the gate-voltage modulation of the Fermi energy at the interface of a metal, in ferromagnetic-metal/non-magnetic-metal super lattice the strength of the VCMA should depend on the metal material of the non-magnetic metal. A FeB/W multi layer is a good candidate to test such dependence. The VCMA strength is substantially depends on the W thickness in this multi layer. The VCMA may be either substantially enhanced or substantially suppressed depending on the W thickness. However, since other magnetic parameters also depend substantially on the W thickness, it is hard to make a clear conclusion.

Note: A thick bcc W/FeB multilayer has substantial PMA. Their properties are similar to a fcc Co/Pt multilayer. Note: A W/FeB multilayer with a thick W layer (1-2 nm) has a greater VCMA effect than that in a FeB film. A W/FeB multilayer with a thin W layer (0.1-0.5 nm) has a small VCMA effect. Note: Both crystal and magnetic properties of FeB/W multi layers are influenced substantially by the thickness of the W layer.

 

 

 

 

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FeB/W multi layers

FeB/W multi layer might be a good candidate for the Work-Function Engineering in order to enhance the VCMA effect

 

Note: A thick bcc W/FeB multilayer has substantial PMA. Their properties are similar to a fcc Co/Pt multilayer.

 

Note: A W/FeB multilayer with a thick W layer (1-2 nm) has a greater VCMA effect than that in a FeB film. A W/FeB multilayer with a thin W layer (0.1-0.5 nm) has a small VCMA effect.

 

Note: Both crystal and magnetic properties of FeB/W multi layers are influenced substantially by the thickness of the W layer.

 

Influence on the crystal quality: At a thinner W layer, the multi layer becomes rougher. As the result, the VCMA strength decreases. At the W thickness of 0.2 nm and thinner, the multi layer surface becomes too rough so that the FeB becomes not-continuous and consequently it changed to be paramagnetic.

 

Influence on the magnetic properties: The strength and the polarity of the exchange coupling between FeB layers depend substantially on the thickness of the W layer. I have not checked the full dependence of the exchange coupling on the W thickness. However, the measured magnetization of FeB/W multilayer is smaller that that of FeB It implies the exchange coupling might be anti ferromagnetic.

 

 

 

The Work-Function Engineering may enhance the VCMA effect only if the modulation of the Fermi energy at metal/oxide interface is the main origin of the VCMA effect.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Dependence of VCMA on a material of the gate metal

In the case if the origin of VCMA effect is related to the gate-voltage modulation of the Fermi energy at the interface of a metal, the strength of the VCMA should depend on material of the gate metal. As Feb. 2019, I have measured several samples with Ta and W gates. However, I have not found any clear dependence of VCMA on the material of the gate metal.

Challenges of this experiment:

It is only possible to detect the dependence of the VCMA on the material of the gate metal if the Fermi level is not pinned or partially pinned inside the gate oxide. It still a challenging task to fabricate the gate oxide of the required quality.

 

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Opposite polarity of VCMA for nearly-identical samples

 

Case 1: different buffer layer

:Y. Shiota et al, APL (2013)

It was experimentally demonstrated that the insertion of a Ru layer between CoFeB and Ta changes the polarity of the VCMA effect

explanation of polarity change:

possible explanation 1: The insertion of the Ru changes the position of the Fermi level at the CoFeB/MgO interface.

possible explanation 2: The crystal quality of the CoFeB/MgO interface degrades due to insertion of the Ru layer. As a result, the type of oxygen-iron bonding is slightly changed, which leads to the change of the PMA and the VCMA

 

Case 2 Excess of oxygen at gate/metal interface

:S. Baek et al, Nat. Elect (2018)

It was experimentally demonstrated that a longer exposure of AlO in oxygen plasma changes the polarity of the VCMA effect.

explanation of polarity change:

In the case of a longer plasma exposure, the amount of oxygen at the CoFeB/MgO interface. It is known that the PMA at the CoFeB/MgO interface substantially depends on the amount of oxygen at it (). In the case of the gate oxide of Fig.24(b), the VCMA mechanism is oxide diffusion in the gate, which is influence by initial amount of oxygen at the interface.

 

 

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Influence of the quality of the gate oxide on the VCMA effect

In the case of sample with gate oxide of a higher quality, there is not any hysteresis loop. There is a hysteresis loop in the case of a sample with gate of lower quality. The hysteresis loop is originated due to a capture of electrons into deep defect states in the gate oxide. It also may cause the pinning of the Fermi level at the defect energy level. In this case, the gate voltage, which is applied to the metal/gate interface, is reduced. Consequently, the VCMA effect is reduced as well.

The fabrication of a high-quality oxide is critically important in order to obtain a strong VCMA effect.

I have developed a growth method of MgO to fabricate a high-quality gate with a high break-down voltage (0.8-1 V/nm) and a low-density of defects.

The defects in the MgO gate were characterized and measured using the capacitance-voltage measurements, DLTS (deep level transition spectroscopy) and DLCS (deep level conduction spectroscopy).

How does the defect density in the gate oxide influence the VCMA effect

1. The Fermi level can be pinned inside the gate oxide. In this case, the applied voltage at the gate/metal interface is substantially reduces. That causes the reduction of VCMA.

2. Oxygen ions diffuses in a gate oxide with defects under a gate voltage. The PMA at an Fe/oxide or Co/oxide interface increases when there are more oxygen ions at interface. That causes a substantial modulation of the PMA. It is undesirable effect, because its very slow response.

3. The electrons can be capture into deep defect levels in the gate oxide. These electrons are slowly released under an opposite gate voltage. The captured electrons modify the distribution of the electrical field in the gate oxide and correspondingly the voltage applied to the oxide/ferromagnetic-metal interface.

 

Is it possible to measure the VCMA using a sample with low quality of the gate oxide?

A. It is very difficult and often impossible. For example, the measurement becomes dependent on the time constant of measurement. Such measurements are very confusing. Additionally, the hysteresis loop of Fig.22 (b), which is also may be observed for different voltage-dependent parameters, can completely overlap the intrinsic properties of the VCMA effect.

The fabrication technology of a high-quality of the gate oxide is well-established for a MOSFET transistor. What is the problem?

A. For the fabrication of the gate oxide the thermo-oxidation of Si or the atomic layer epitaxy (ALE) is often used. These technologies yields a very high quality of the gate oxide. It is still challenging to apply the similar technologies for the studied VCMA devices. Mainly, the sputtering of the oxide is used. In this case, the quality of the gate oxide is moderate. I have tried the sputtering of different oxides: MgO, Al2O3, MgO+SiO2. In each case, it is possible to obtain acceptable quality and to measure the VCMA. However, the quality is still very far from the best. The fabrication of the high-quality of the gate oxide is still a challenging task in the field.

How to grow a high-quality gate oxide?

Several condition should be satisfied:

The ferromagnetic metal should not be oxidized or the oxidation should be controllable. It can be achieved at a low growth temperature. the surface of gate oxide should smooth. It can be achieved at a high growth temperature, when the mobility of atoms on the surface is high. The growth initialization should be 2d-type (not 3D-type). It can be achieved by suppressing atom mobility at a low temperature. The number of defects in gate oxide should be low. It can be achieved at a higher growth temperature. Also, the metal - oxygen ratio should be optimized.

My method to optimize the crystal quality of the sputtered MgO:

At first, a 1 nm MgO was deposited at room temperature, next the sample was annealed at 220 deg C for 30 minutes and the remaining of the MgO gate oxide was grown at 220 deg C. Three 30-minute growth interruptions after each 1 nm of growth were used to improve the MgO crystal quality.  

 

 

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Voltage-dependence of left and right edges of the coercive loop

A coercive loop has two switching points: (1) from magnetization-up to magnetization-down; (2) from magnetization-down to magnetization-up. In the case of the SOT effect these two magnetization switchings are affected differently by the SOT effect.

Is the voltage-dependence of the coercive fields for the switchings from spin-down to up and from spin-up to down different?

A. No. Both switchings are absolutely identical and their voltage-dependence is the same

 

Why there is a slight offset between spin down-to-up and up-to-down switchings in Fig.11(a)?

It is because the size of nucleation domain for magnetization switching depends slightly on the magnetization switching direction (See here for more details)

 

 

 

 

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The dependence of the VCMA on an absolute value of H_anis and H_c

 

As Feb.2019, I have not found a substantial dependence of the VCMA strength on an absolute value of H_anis and H_c

The coercive and anisotropy fields may be substantially different for devices fabricated on different sides of the same wafer due a slight variation of the thickness of the ferromagnetic metal. However, in case if the quality of the gate oxide remains the same, the measured VCMA is identical for such sample despite of a substantial difference of their H_anis and H_c.

 

It implies that the strength of the VCMA might not depended on absolute values H_anis and H_c. Note :

I have studied the FeCoB samples having H_c from 0 Oe to ~800 Oe and corresponding H_anis from 1.6 kG to ~25 kG. Perhaps, for the samples of a larger variation of H_anis and H_c, the dependence of VCMA strength on H_anis and H_c might exist.

 

Thicker FeB: H_c-> larger; H_anis-> larger; retention time ->larger; nucleation domain size->the same

Thinner FeB: H_c-> smaller; H_anis->smaller; retention time ->smaller; nucleation domain size->the same

 

How large is the possible variation of the FeB thickness?

From ~0.8 nm to ~1.2 nm. The magnetization of a thicker film becomes in-plane. A thinner film becomes a paramagnetic.

Can the thickness of a ferromagnetic FeB film be thinner than 0.8 nm? Is it possible to grow such a thin ferromagnetic FeB film?

Using a direct growth it is impossible. At the beginning of the FeB growth, the clusters of FeB is formed, they are not connected, the FeB is not continuous film and it is paramagnetic. When the growth proceeds, the clusters collapse and form a continuous smooth film, which becomes ferromagnetic.

The growth type depends on the material of the buffer layer. Above description is for the case of the FeB growth on the W or Ta buffer.

In order to fabricate a smooth continuous ferromagnetic film the following advanced growth procedure should be used:

step 1: growth of a thicker FeB film (~1.5-2.5 nm)

step 2: Ar milling of FeB film down to the designed thickness

step 3: proceeding of the growth of the remaining of the film

I have designed and used this growth procedure for a while now. It is working very well. This growth procedure takes a longer time and the growth facilities should have an Ar milling equipment. Its main benefit is a smoother film.

The ferromagnetic FeB film of thickness ~0.1-0.2 nm can be fabricated by this method. The magnetization of such film is perpendicular-to-plane. The thickness of the FeB can be evaluated by this method.

Note: there is no problem to grow directly a smooth continuous Co film with thickness of 0.1-0.2 nm on Pt and on some other buffer metals.

 

Does the film roughness influence the VCMA?

A. Both the PMA and VCMA are influenced by the film roughness very much. It is hard to show it in numbers. However, this fact is very obvious. The VCMA of a rougher film is smaller. See for example Fig.31 here.

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The dependence of the VCMA on thickness of a ferromagnetic metal

As Feb. 2019, I have not found any dependence on the VCMA strength on the thickness of the ferromagnetic metal.

The dependence of VCMA on the film thickness was reported in this reference.

 

Is the VCMA effect is stronger in a thinner sample?

A. No.

When the film thickness may influence the VCMA?

A. The film thickness may influence the VCMA only when the penetration depth of the gate electrical field into the ferromagnetic field becomes comparable to the film thickness. Also, such influence strongly depends on the main origin of the VCMA. It is clear that the VCMA is an effect of an interface, but not of bulk of material. Only some influence of film thickness on the interface properties may change the VCMA.

How deep the electrical field of the gate voltage can penetrate into the ferromagnetic metal?

A. It is very hard to estimate. It may varies from a material to a material. Also, it should depend substantially on the type and density of the surface states at the metal oxide-interface. Maybe it could be estimated from the capacitance-voltage measurements or DLTS (deep level transition spectroscopy) or DLCS (deep level conduction spectroscopy) measurements. As Feb. 2019 I do not know any report on a successful measurement of the penetration depth. My suggestion is that the penetration depth is about 0.01-01 nm.

 

 

The gate voltage affects the ferromagnetic metal only in a very thin region of the gate oxide, which is very close to the gate oxide.

 

 

 

 

 

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History

1. 1st demonstration

A gate voltage is applied to magnetic wire through electrolyte. The change of coercive field under the gate voltage was detected

M. Weisheit et al, Science (2007)

2. 1st solid-state device (practical device)

 

T. Maruyama et al, Nature Nanotech. (2009)

3. 1st high-speed voltage-induced magnetization reversal

It is a breakthrough result in the field, because it opened a possibility of the fabrication of a new type of high-speed low- power- consumption magnetic random access memory (MRAM)

Y. Shiota et al, APL(2012)

 

 

 

 

 

Members of our Spintronics center Prof. Suzuki, Dr. Shiota and Dr. Nozaki did pioneering research in this field

 

 

 

 

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VCMA and TMR effects. It would be interesting to correlate this gate tuning of spin polarization with the bias-dependent TMR experiments which have been traditionally explained with barrier height modulation.

A. I guess there are several contributions to the bias-dependence of TMR. The voltage dependence may have some contribution. However, it should be a contribution, which is polarity dependent. The voltage-control change of the spin polarization always changes its sign, when the voltage polarity is reversed. I have checked many samples already. The spin polarization always linearly increases under a negative gate voltage and it always linearly decrease under a positive gate voltage.

 

 

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Publications

Intermag (Singapore) March 2018 presentation

SSDM (Tokyo) Sep. 2018 presentation and abstract

long version of manuscript. July 14, 2018 &

short version Nov. 2018

Arxiv Dec.2018

 

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Video. Youtube

 

 

Intermag 2023. Sendai, Japan		The 67th Annual Conference on Magnetism and Magnetic Materials (MMM 2022)
click on image to see Youtube Video		click on image to see Youtube Video
(title): Systematic study of the strength of VCMA effect in nanomagnets of small and large strength of spin-orbit interaction.		(title:) Modulation of spin-orbit interaction by a gate voltage. VCMA effect

 

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Questions & Answers

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(spin waves and VCMA)

Recently, I read a research article (See link here) and I felt a huge confusion. In the article, the authors said that, 'the SO interaction depends on an orthogonality between the applied electric field, the equilibrium magnetization, and the wave vector of the spin waves'. Their main observation is that, when the External Electric field and Equilibrium magnetic field are orthogonal, then they observed spin orbit coupling (they applied out of plane E field). But when they changed E field direction in plane, they didn't observe the spin orbit coupling. Actually, this makes me confused. It makes some queries in my mind: 1. Is it mandatory of being orthogonal of both E field and magnetization for observing E field driven spin orbit interaction? 2. If needed, what is the reason or facts?

To grasp the concept of how a gate voltage affects the spin waves, it's crucial to have a clear understanding of spin-orbit interaction.

The spin- orbit interaction describes a magnetic field of relativistic origin and nothing else. This magnetic field Hso of spin- orbit interaction possesses unique properties and characteristics.Once you comprehend these features, it will be easier for you to understand any effect related to spin- orbit interaction.

(feature 1 of SO) The direction of the magnetic field Hso of spin- orbit interaction consistently aligns with the direction of the total magnetic field Htotal applied to the electron orbital. Hso is linearly proportional to Htotal. The proportionality coefficient is called the coefficient kso of spin- orbit interaction. The method for measuring kso is relatively straightforward. I have been doing measurements of kso for many years now.

Inside a ferromagnetic film, Htotal is referred to as the internal magnetic field, comprising the sum of the magnetic field along the magnetization M and the demagnetization field Hdemag. Hso approximately tracks M with some deviation attributable to Hdemag.

(feature 2 of SO): The strength of the spin-orbit interaction (SO) is proportional to the orbital deformation. kso is substantially larger when Htotal is directed along the deformation compared to when it is perpendicular to the deformation.

When an electric field is applied, the orbital is deformed along the electrical field, leading to an increase in kso. This effect is referred to as the Voltage-Controlled Magnetic Anisotropy (VCMA) effect.

In the case of a metal, the voltage is applied only to the interface, deforming the orbital there and modulating Hso only for interface orbitals. In the case of a dielectric material (like a garnet), the voltage is applied through the bulk of the film, modulating Hso for orbitals in the bulk.

(spin waves): In the dynamic LL equation for spin waves, it is necessary to include Hso and its modulation by the gate voltage. I believe that considering this modulation of spin-orbit interaction by the gate voltage will provide a comprehensive explanation of the properties of spin waves.

Is it mandatory of being orthogonal of both E field and magnetization for observing E field driven spin orbit interaction?

Absolutely not. To measure the gate-voltage modulation of kso and for magnetization reversal induced by a gate voltage, an in-plane bias magnetic field is necessary. The VCMA effect exhibits similar strength in this scenario. This fact is undeniable.

(about paper) I am confident that the correct description of the spin-orbit interaction (SO), as explained above, accounts for all the observed experimental features of the spin waves.