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Title:
NANOWIRE AND MEMORY DEVICE USING IT AS A MEDIUM FOR CURRENT-INDUCED DOMAIN WALL DISPLACEMENT
Document Type and Number:
WIPO Patent Application WO/2009/072819
Kind Code:
A1
Abstract:
Disclosed herein are a nanowire and a current-induced domain wall displacement- type memory device using the same. The nanowire has perpendicular magnetic anisotropy and is configured in a manner that when a parameter Q, calculated by a saturation magnetization per unit area, a domain wall thickness and a spin polarizability of a ferromagnet that is a constituent material of the nanowire, has a value of (formula 1 should be inserted here) a domain wall thickness, a width ''*'" and a thickness -* of the nanowire satisfy the relationship of (formula 2 should be inserted here) The present invention can be designed such that a current density capable of driving a memory device utilizing the current-driven domain wall displacement has a value of less than (formula 3 should be inserted here), through the determination of the optimal nanowire width and thickness satisfying a value of a critical current density, Jc for the domain wall displacement below a certain value required for commercialization, for a given material in the nanowire with perpendicular anisotropy. According to such a configuration of the present invention, the current density required for the domain wall displacement can be at least 10 times or further lowered than the current density in currently available nano wires. Therefore, the present invention is capable of solving the problems associated with high power consumption and malfunction of the device due to generation of Joule heat and is also capable of achieving low-cost production of memory devices.

Inventors:
LEE, Kyung-Jin (# Samsung Raemian Apt, Jongam-dong Seongbuk-gu, Seoul 136-090, 104-1301, KR)
LEE, Hyun-Woo (# Gyosu Apt, Jigok-dong Nam-gu,Pohang-si, Gyeongsangbuk-do 790-834, 9-1902, KR)
JUNG, Soon-Wook (# Graduate School Apt, Pohang University of Science & TechnologyJigok-dong, Nam-g, Pohang-si Gyeongsangbuk-do 790-390, 1-1303, KR)
Application Number:
KR2008/007165
Publication Date:
June 11, 2009
Filing Date:
December 04, 2008
Export Citation:
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Assignee:
KOREA UNIVERSITY INDUSTRIAL & ACADEMIC COLLABORATION FOUNDATION (Anam-dong 5-ga 1, Seongbuk-gu, Seoul 136-701, KR)
POSTECH ACADEMY-INDUSTRY FOUNDATION (Pohang University of Science &, Technology San 31,Hyoja-dong, Nam-gu, Pohang-si, Gyeongsangbuk-do 790-784, KR)
LEE, Kyung-Jin (# Samsung Raemian Apt, Jongam-dong Seongbuk-gu, Seoul 136-090, 104-1301, KR)
LEE, Hyun-Woo (# Gyosu Apt, Jigok-dong Nam-gu,Pohang-si, Gyeongsangbuk-do 790-834, 9-1902, KR)
JUNG, Soon-Wook (# Graduate School Apt, Pohang University of Science & TechnologyJigok-dong, Nam-g, Pohang-si Gyeongsangbuk-do 790-390, 1-1303, KR)
International Classes:
G11B9/02; G11B5/00; G11B5/02
Attorney, Agent or Firm:
HYUN, Jong Cheol (Dooji Bldg. 4F, 353-18Sindang 2-dong,Jung-gu, Seoul 100-828, KR)
Download PDF:
Claims:

[CLAIMS] [Claim 1 ]

A nanowire with perpendicular magnetic anisotropy, wherein when a parameter calculated by a saturation magnetization per unit area, a domain wall thickness and a

spin polarizability of a ferromagnet that is a constituent material of the nanowire, has a value of a domain wall thickness a width and a thickness of the nanowire satisfy the relationship of Equation 10.

(Equation 10)

[Claim 2]

The nanowire according to claim 1 , wherein the nanowire is formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof.

[Claim 3]

The nanowire according to claim 1, wherein the nanowire is formed of a rare-earth metal.

[Claim 4] A nanowire with perpendicular magnetic anisotropy, wherein when a parameter calculated by a saturation magnetization per unit area, a domain wall thickness and a

spin polarizability of a ferromagnet that is a constituent material of the nanowire, has a

value of , a domain wall thickness * - , a

width and a thickness - of the nanowire satisfy the relationship of Equation 11.

[Claim 5]

The nanowire according to claim 4, wherein the nanowire is formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof.

[Claim 6]

The nanowire according to claim 4, wherein the nanowire is formed of a rare-earth metal.

[Claim 7] A nanowire with perpendicular magnetic anisotropy, wherein when a parameter , calculated by a saturation magnetization per unit area, a domain wall thickness and a

spin polarizability of a ferromagnet that is a constituent material of the nanowire, has a value of Z C( Z , a domain wall thickness a width and a thickness - of the nanowire satisfy the relationship of Equation 12.

[Claim 8]

The nanowire according to claim 7, wherein the nanowire is formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof.

[Claim 9]

The nanowire according to claim 7, wherein the nanowire is formed of a rare-earth metal.

[Claim 10] A nanowire with perpendicular magnetic anisotropy, wherein when a parameter ss , calculated by a saturation magnetization per unit area, a domain wall thickness and a

spin polarizability of a ferromagnet that is a constituent material of the nanowire, has a value of Z Z , a domain wall thickness * , a

width and a thickness -* of the nanowire satisfy the relationship of Equation 13.

[Claim 11 ]

The nanowire according to claim 10, wherein the nanowire is formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof.

[Claim 12]

The nanowire according to claim 10, wherein the nanowire is formed of a rare-

earth metal.

[Claim 13]

A nanowire with perpendicular magnetic anisotropy, wherein when a parameter calculated by a saturation magnetization per unit area, a domain wall thickness and a

spin polarizability of a ferromagnet that is a constituent material of the nanowire, has a value of Z C( Z , a domain wall thickness ^ a width and a thickness of the nanowire satisfy the relationship of Equation 14.

(Equation 14)

[Claim 14]

The nanowire according to claim 13, wherein the nanowire is formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof.

[Claim 15]

The nanowire according to claim 13, wherein the nanowire is formed of a rare- earth metal.

[Claim 16]

A nanowire with perpendicular magnetic anisotropy, wherein when a parameter

3^, calculated by a saturation magnetization per unit area, a domain wall thickness and a

spin polarizability of a ferromagnet that is a constituent material of the nanowire, has a value of Z , a d omam wa u thickness , a width r and a

thickness ^* of the nanowire satisfy the relationship of Equation 15.

(Equation 15)

[Claim 17]

The nanowire according to claim 16, wherein the nanowire is formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof.

[Claim 18]

The nanowire according to claim 16, wherein the nanowire is formed of a rare- earth metal.

[Claim 19]

A memory device comprising the nanowire of any one of claims 1 to 18 and utilizing the current-induced domain wall displacement.

Description:

[DESCRIPTION] [Invention Title]

NANOWIRE AND MEMORY DEVICE USING IT AS A MEDIUM FOR CURRENT- INDUCED DOMA1N WALL DISPLACEMENT

[Technical Field]

The present invention relates to a nanowire. More specifically, the present invention relates to a nanowire which enables the construction of a memory device at a low current density by the application of an electric current to a ferromagnetic nanowire to induce the domain wall displacement and a current-induced domain wall displacement-type memory device using the same.

[Background Art] Ferromagnets refer to magnetic materials that become strongly magnetized in a magnetic field direction when exposed to an external strong magnetic field and retain their magnetism even when the external magnetic field is removed. In this case, individual atoms of the magnetic material behave like individual magnets.

That is, the ferromagnet is a material having magnet-like properties and typically includes iron, cobalt, nickel and their alloys. Individual atoms in the ferromagnetic material serve as individual magnets. The magnetic moments of these atoms are relatively less regularly aligned when they are not exposed to an external magnetic field, thus generally providing no magnet-like effects. However, when a magnet is brought close to the material, those atoms tend to align their magnetic moments with the external magnetic field and are therefore attracted to the magnet. Such regular alignment of atoms in a given direction under the influence of an external magnetic field is called "magnetization", and

the magnetized material per se can attract other ferromagnetic materials, as does a magnet. As is known in the related art, the spins of electrons in the ferromagnet are aligned parallel to one another in the same direction, so magnetic moments responsible for magnetization form and increase. Further, magnetic domains are considered as large groups of atoms whose spins are aligned parallel with one another. Within the magnetic field, the magnetic domains whose spins are aligned with a magnetic field direction are produced or enlarged. Even after the externally applied magnetic field is removed, the spins of atoms are still aligned in the same direction for a long period of time, consequently resulting in appearance of remanent magnetization. When a temperature is elevated, thermal motion of atoms takes place in the ferromagnet, which breaks up regular arrangement of atom spins, thus becoming paramagnetic with loss of ferromagnetism. This temperature is called the Curie temperature above which a ferromagnetic material loses its ferromagnetism and becomes paramagnetic. This phenomenon is exploited in a variety of applications such as permanent magnets, magnetic permeability materials, and magnetostrictive materials.

Recently, 1BM has proposed a new type of memory device, which consists of ferromagnetic nanowires and whose operation is based on the ferromagnetic domain wall displacement caused by the current injected into the magnetic nanowire.

FIG. 1 shows a conventional ferromagnetic nano wire-based memory device. As Fig. 1 illustrates, magnetization directions of magnetic domains 110,120 whose magnetization directions are different from each other and are parallel to the nanowire surface are recorded in a conventional ferromagnetic nanowire 100, and the magnetic domains 110,120 are then moved by means of a current-induced domain wall displacement phenomenon where positional displacement of domain walls takes place upon application of an electric current to the nanowire.

As can be seen from FIG. 1 , the conventional ferromagnetic nanowire 100 has a width ( ) of from several to several hundreds of nm and a thickness ( -^) of from

several to several hundreds of nm.

The information of the magnetic domains in the nanowire can be recorded and reproduced by recording and reproduction devices 130,140,150 positioned adjacent to the nanowire. Advantages of this technique are in that the positions of information recording and reproduction devices are fixed and the positions of information-containing magnetic domains can be electrically moved.

In spite of advantages such as a high recording density and non-volatility of information, conventional hard discs suffer from problems of impact susceptibility arising from a mechanically moving head of the device and also from high power consumption, which have been obstacles to the practical application of such hard discs to mobile storage devices.

On the other hand, flash memories, which are widely used as mobile storage devices, require very expensive production processes since one CMOS transistor should be inserted for each storage unit.

In contrast, the current-induced domain wall displacement-type memory device, to which the present invention pertains, is a storage device which is significantly advantageous as will be explained in the following. Specifically, the problems associated with high costs of flash memories can be solved because the memory device in accordance with the present invention requires only one CMOS transistor per nanowire where several tens to several hundreds of bits are stored. Further, as the mechanical rotational motion providing an important role in operation of the hard disc is replaced with the domain wall displacement which involves no mechanical motion, it is possible to achieve high impact

resistance and low power consumption while retaining advantages of conventional hard discs, i.e. high storage density and non-volatility of recorded information.

In other words, the device of the present invention is significantly attractive as a memory device that provides prominent strengths of the hard disc (including high storage density and non-volatility of recorded information) simultaneously with high impact resistance and low power consumption, through the replacement of a mechanical element with an electrical element.

The most important factor in this technique is a current-induced domain wall displacement phenomenon, which was first theoretically proposed in 1980's by L. Berger and was recently experimentally observed by Yamaguchi, Klaui, Parkin and many other research groups.

According to the experimental research results reported up to date, a critical current density for the domain wall displacement using an electric current alone without the application of a magnetic field is about 10 8 AZcm 2 , which is 10 to 100 times

greater than a value of required for commercial application.

Increases in the critical current density disadvantageously result in very high power consumption for application of an electric current, and incapability to control the domain wall displacement due to generation of Joule heat.

[Disclosure]

[Technical Problem]

Therefore, the present invention has been made in view of the above problems, and it is an object of the present invention to provide a nanowire which enables the construction of a low-current-density memory device, by establishing the conditions that

allow for the displacement of domain walls even when a low density current is applied to a nanowire formed of a ferromagnetic material.

It is another object of the present invention to provide a memory device including the same nanowire and utilizing the current-induced domain wall displacement.

[Technical Solution]

In accordance with an aspect of the present invention, the above and other objects can be accomplished by the provision of a nanowire with perpendicular magnetic anisotropy, wherein when a parameter Q reflecting properties of the nanowire (as defined in

Equation 3 below) has a value of 3X 10 8 AZcm 2 ≤ Q ≤ 10 10 9 AZcm , d omain wall

thickness , a width W and a thickness T of the nanowire satisfy the relationship of

In accordance with another aspect of the present invention, there is provided a nanowire with perpendicular magnetic anisotropy, wherein when a parameter ^

reflecting properties of the nanowire has a value of

10 AZcm ≤ C( < 3x10 AZcm , a domain wall thickness ^, a width ^ and

a thickness T of the nanowire satisfy the relationship of

In accordance with a further aspect of the present invention, there is provided a nanowire with perpendicular magnetic anisotropy, wherein when a parameter Q

reflecting properties of the nanowire has a value of

3χl0 7 AZcm 2 ≤ C( < 10 8 AZcm 2 , a domain wal i thickness λ a width W

and a thickness T of the nanowire satisfy the relationship of In accordance with a still further aspect of the present invention, there is provided a nanowire with perpendicular magnetic anisotropy, wherein when a parameter C(

reflecting properties of the nanowire has a value of

10 7 A/cm 2 ≤ C, < 3χ10 7 AZcm 2 , a domain wall thickness λ , a width W

and a thickness T of the nanowire satisfy the relationship of

In accordance with another aspect of the present invention, there is provided a nanowire with perpendicular magnetic anisotropy, wherein when a parameter Q

reflecting properties of the nanowire has a value of

7xlO 6 AZcm 2 < C( < 10 7 AZcm 2 ; a domain wall thickness λ , a

width W and a thickness T of the nanowire satisfy the relationship of

In accordance with yet another aspect of the present invention, there is provided a nanowire with perpendicular magnetic anisotropy, wherein when a parameter Q

reflecting properties of the nanowire has a value of Q ≤ 7x10 6 AZ cm 2 , a domain

wall thickness λ , a widt h W and a thickness T of the nanowire satisfy the

relationship of

A material for the nanowire may be any one selected from the group consisting of Fe, Co, Ni and any combination thereof. Alternatively, the nanowire may be formed of a rare-earth metal.

Further, the present invention provides a memory device including the aforesaid nanowire and utilizing the current-induced domain wall displacement.

[Advantageous Effects] The present invention can be designed such that a current density capable of driving a memory device utilizing the current-driven domain wall displacement has a value of less than , through the determination of the optimal nanowire width and

thickness satisfying a value of a critical current density, Jc for the domain wall displacement below a certain value required for commercialization, for a given material in the nanowire with perpendicular anisotropy. According to such a configuration of the present invention, the current density required for the domain wall displacement can be at least 10 times or further lowered than the current density in currently available nanowires. Therefore, the present invention is capable of solving the problems associated with high power consumption and malfunction of the device due to generation of Joule heat and is also capable of achieving low-cost production of memory devices.

[Description of Drawings]

FIG. 1 shows a conventional ferromagnetic nano wire-based memory device;

FIG. 2 shows a ferromagnetic nanowire-based memory device in accordance with the present invention;

FIG. 3a shows one embodiment of a domain wall being possible in a nanowire whose magnetization direction is perpendicular to the nanowire surface; FIG. 3b shows a conventional domain wall whose magnetization direction is parallel to the nanowire surface, which corresponds to a counterpart of FIG. 3a;

FIG. 3c shows another embodiment of a domain wall being possible in a nanowire whose magnetization direction is perpendicular to the nanowire surface;

FIG. 3d shows a conventional domain wall whose magnetization direction is parallel to the nanowire surface, which corresponds to a counterpart of FIG. 3c;

FIG. 4a shows changes of a domain wall thickness λ with respect to a

perpendicular magnetic anisotropy density

FIG. 4b shows changes of a domain wall anisotropic energy density K with

respect to a nanowire width

FIGS. 5 to 10 are graphs illustrating ranges of and satisfying the

condition of with respect to a range or , a parameter Q w hich is determined by the kinds of nano wire-forming materials;

FIGS. 11a to lie show contours for a thickness and a width of a

nanowire which is configured to have a parameter of less than

FIG. 12 is a graph illustrating a critical current density vs. nanowire width relationship for a memory device (1A) whose magnetization direction is parallel to the

nanowire surface and a memory device (PA) in accordance with the present invention; and FIGS. 13a and 13b are graphs illustrating a critical current density * c vs.

pinning potential relationship for a memory device (1A) whose magnetization

direction is parallel to the nanowire surface and a memory device (PA) in accordance with the present invention.

[Mode for Invention]

The present invention is aimed to lower a critical current density for induction of the domain wall displacement using an electric current alone without the application of a magnetic field to a level of less than . For this purpose, a manner whose

magnetization direction is perpendicular to the nanowire surface is employed instead of a conventional manner whose magnetization direction is parallel to the nanowire surface, and a structure of the nanowire is optimized.

As shown in FIG. 2, the present invention employs a scheme whose magnetization direction is perpendicular to the nanowire surface, not a conventional one whose magnetization direction is parallel to the nanowire surface.

FIG. 2 shows a ferromagnetic nanowire-based memory device in accordance with the present invention.

Referring to FIG. 2, magnetization directions of magnetic domains 210,220 whose magnetization directions are different from each other and are perpendicular to the nanowire surface are recorded in a conventional ferromagnetic nanowire 200, and the magnetic domains 210,220 are then motioned by means of a current-induced domain wall displacement phenomenon where positional displacement of domain walls takes place upon application of an electric current to the nanowire.

As can be seen from FIG. 1 , the conventional ferromagnetic nanowire 200 has a width ( ) of from several to several hundreds of nm and a thickness ( * ) of from

several to several hundreds of nm.

In this connection, the information of the magnetic domains is recorded and reproduced by recording and reproduction devices 230,240,250 positioned adjacent to the nanowire. Advantages of this technique are in that the positions of information recording and reproduction devices are fixed and the positions of information-containing magnetic domains can be electrically moved.

As to the nanowire formed of a ferromagnetic material, the current-induced magnetization behavior is depicted in terms of a motion equation according to Equation 1 below.

In Equation 1 , M represents a magnetization vector, Y represents a gyro magnetic coefficient, represents the total effective magnetic field vector, Ct represents a Gilbert attenuation coefficient, and * represents a saturation magnetization of a ferromagnet.

Meanwhile, a spin torque st caused by the applied current is calculated

according to Equation 2 below.

( q ,

In Equation 2, - represents wherein represents a spin

solarizability of a ferromagnet and has a value of 0 to 1 , represents a Bohr magneton, represents a current density, represents an electron charge quantity, and represents a saturation magnetization of a ferromagnet. In Equation 2, the first term is an adiabatic spin torque and the second term is a non-adiabatic spin torque, and a constant P is a relative magnitude of the non-adiabatic

spin torque vs. the adiabatic spin torque.

At present, an accurate value is not yet known for the magnitude of constant .

Meanwhile, a critical current density (Intrinsic for the domain wall

displacement is given according to Equation 3 below.

(Equation 3)

In Equation 3, represents a gyro-magnetic ratio,

and represents a value obtained when the distribution of magnetization components in

the nanowire thickness direction around the domain wall is approximated in terms of ✓ i ^ which corresponds to a domain wall thicknes and is determined by magnetic components of a ferromagnet.

In this connection, represents a position of the domain wall center, and

has a relationship defined by Equation 4 below.

In Equation 4 , represents an effective exchange constant of a ferromagnet, represents a perpendicular magnetic anisotropic energy density, represents a

demagnetization factor in the nanowire thickness direction, and represents a domain

wall demagnetizing factor corresponding to and is determined by the dipole-dipole

interaction of a magnetization vector constituting the domain wall.

Parameter & as previously defined in Equation 3, is a quantity determined by

components of the nanowire such as , etc., is a variable that is calculated by a saturation magnetization per unit area, a domain wall thickness and a spin polarizability of a ferromagnet, and has a value of

Equation 3 implies that the domain wall is displaced when the magnitude of current-induced spin torque overcomes the anisotropic domain wall energy.

From Equation 3, in order to satisfy the condition that a critical current density for the magnetic field-free current-induced domain wall displacement has a value of

less than usm g a scnerrie of the present invention whose magnetization

direction is perpendicular to the nanowire surface, it is required that meets the

requirements of Equation 5 below.

In Equation 5, is a domain wall demagnetizing factor and is therefore a

physical quantity that is determined upon the determination of a nanowire width , a

nanowire thickness and a domain wall thickness

That is, as depicted in Equations 6 and 7, is a function only of and

Then, when the parameter *■ " is determined with respect to the kinds of magnetic

materials, to satisfy the condition that has a value of less than due to Equation 5, that is, and correlated to a structure of

the nanowire are then determined. The present invention is directed to an optimum nanowire structure satisfying a va ilue o f f und A er „ Equation 5, that is optimum ranges of

and , for a given magnetic material.

As described above, when is made to have a value below the critical value

by controlling a nanowire width and a nanowire thickness in a given material,

the critical current density can be set to a value of w hich is the required

level for practical commercialization.

Meanwhile, can be calculated according to Equations 6 to 8.

In addition, disclosed in Equations 6 to 8 corresponds to disclosed

throughout the present invention, and corresponds to

As can be seen from Equation 6, N d i .s calculated from the difference between N dx and N dx, and values of N d and N dx, are also calculated according to

Equation 6.

Meanwhile, a value of N d is calculated using a value of F(x). Details for

calculation of ( ) are as defined in Equation 7. N d in Equation 7 is perfectly determined by T/ and W/λ, as the integration of x is carried out from - ∞ to

+ ∞

In addition, a value of is calculated using a value of ( ) . Details for

calculation of G are as defined in Equation 8. Similar to of Equation 7,

of Equation 8 is perfectly determined by T/λ and as the integration of

" is carried out from

FIGS. 3a and 3c show two types of domain walls being possible in a nanowire whose magnetization direction is perpendicular to the nanowire surface. In FIGS. 3a and 3c, -axis represents a length direction of the nanowire, -axis

represents a width direction of the nanowire, and -axis represents a thickness direction

of the nanowire. In FIGS. 3a and 3b, represents a thickness of the domain wall

magnetized in a given direction, and represents a nanowire width in a given material

and ^ represents a nanowire thickness in a given material.

On the basis of a magnetization direction, the magnetization configuration according to FIG. 3 a is referred to as a ^ domain wall which is a stable domain

wall when the condition of is satisfied. The corresponding conventional

counterpart nanowire whose magnetization direction is parallel to the nanowire surface is as shown in FIG. 3b.

On the basis of a magnetization direction, the magnetization configuration according to FIG. 3 c is referred to as a domain wall which is a stable domain wall with the condition of . The corresponding conventional counterpart : ! nanowire

whose magnetization direction is parallel to the nanowire surface is as shown in FIG. 3d. FIG. 4a shows changes of a domain wall thickness with respect to a

perpendicular magnetic anisotropy density , when the nanowire has a thickness

of 10 nm, a width of 77 nm, a saturation magnetization " of 400 emu/cm 3 , and

an effective exchange coefficient erg/cm.

As can be seen from FIG. 4a, it is possible to control a thickness of the domain

wall, by changing a value of at the thickness J and width y of a given nanowire. FIG. 4b shows changes of a domain wall anisotropic energy density of

Equation 3 with respect to a nanowire width , when the nanowire has a thickness

of 10 nm, a perpendicular magnetic anisotropy density of 1.5 χ 10 erg/cm , a

saturation magnetization of 400 emu/cm 3 , and an effective exchange coefficient As can be seen from FIG. 4b, it is possible to establish so that the domain wall

anisotropic energy density has a value of 0, by changing a nanowire width in

a nanowire having a given material and structure. In this connection, the point at which the

domain wall anisotropic energy density becomes zero is the point at which the Z domain wa n an( j the domain wall have the same energy level.

Therefore, through the adjustment of the nanowire thickness and nanowire

width of a given nanowire material according to Equations 6 to 8, it is possible to

design so that the domain wall demagnetizing factor * or the domain wall anisotropic

energy density approximates to 0. As a result, a critical current density for the

domain wall displacement can be lowered to a significantly small value according to Equation 3.

Then, for any magnetic material, a maximum value of the domain wall

. . , . . . , , J υ -2 demagnetizing factor satisfying a value of can be determined according to Equation 5.

When the domain wall demagnetizing factor ' d is determined, optimum ranges

of and satisfying the thus-determined value of can be determined,

and ranges of and can be determined according to Equation 9 below.

When the parameter is determined by a nanowire-forming material, ranges of

sa t ti-s f lyi ■ng a va ,lue o f l can , be d ,et.ermi .ned ,.

FIG. 5 shows ranges of and satisfying the condition of when a parameter determined by a constituent material of the

nanowire has a value of In this connection, the ferromagnetic nanowire with perpendicular magnetic anisotropy may be formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof. Alternatively, Examples of the material for the nanowire may include one or more rare-earth metals.

In FIG. 5, an area between the upper curve 410 and the lower curve 420

7 " Yi FP/J corresponds to ranges of and ' satisfying the condition of

, //" < X0 7 AZcm-

When values of in Equation 9 are calculated by matching of

Equation 9 with FIG. 5, they are as shown in Equation 10 below. In addition, ranges of and λ satisfying the conditions of

and * can be determined according to Equation 10.

Therefore, when the parameter S is determined and then and of

the nanowire are set to within the specified range according to Equation 10, it is possible to design so that a current density capable of driving a memory device taking advantage of

the current-driven domain wall displacement has a value of less than

FIG. 6 shows ranges of and " satisfying the condition of when a parameter d determined by a constituent material of the

nanowire has a value of In this connection, the ferromagnetic nanowire with perpendicular magnetic anisotropy may be formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof. Alternatively, examples of the material for the nanowire may include one or more rare-earth metals.

In FIG. 6, an area between the upper curve 510 and the lower curve 520 corresponds to ranges of and satisfying the condition of

When values of in Equation 9 are calculated by matching of

Equation 9 with FIG. 6, they are as shown in Equation 11 below. In addition, ranges of and λ satisfying the conditions of

and can be determined according to Equation 11.

Therefore, when the parameter Q is determined and then and of

the nanowire are set to within the specified range according to Equation 11, it is possible to design so that a current density capable of driving a memory device taking advantage of

the current-driven domain wall displacement has a value of less than

FIG 7 shows ranges of and satisfying the condition of when a parameter determined by a constituent materiall of the

nanowire has a value of In this connection, the ferromagnetic nanowire with perpendicular magnetic anisotropy may be formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof. Alternatively, examples of the material for the nanowire may include one or more rare-earth metals.

In FIG. 7, an area between the upper curve 610 and the lower curve 620 corresponds to ranges of λ and satisfying the condition of J J" < X Q 7 AfCm 2

When values of in Equation 9 are cakulated by matching of

Equation 9 with FIG. 7, they are as shown in Equation 12 below. In addition, ranges of ^ and satisfying the conditions of and j can be determined according to Equation 12.

0.91 W 2.18

+ 4.68 < -+ 4- I4 TM λ v λ / /\ (Equation 12)

Therefore, when the parameter 6? is determined and then and of

the nanowire are set to within the specified range according to Equation 12, it is possible to design so that a current density capable of driving a memory device taking advantage of

the current-driven domain wall displacement has a value of less than

FIG. 8 shows ranges of and satisfying the condition of when a parameter determined by a constituent material of the

nanowire has a value of In this connection, the ferromagnetic nanowire with perpendicular magnetic anisotropy may be formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof. Alternatively, the nanowire may also be formed of one or more rare-earth metals.

In FIG. 8, an area between the upper curve 710 and the lower curve 720 corresponds to ranges of and satisfying the condition of

When values of in Equation 9 are calculated by matching of

Equation 9 with FIG. 8, they are as shown in Equation 13 below. In addition, ranges of a nd satisfying the conditions of

and can be determined according to Equation 13.

Therefore, when the parameter Q is determined and then and of

the nanowire are set to within the specified range according to Equation 13, it is possible to design so that a current density capable of driving a memory device taking advantage of

the current-driven domain wall displacement has a value of less than

FIG. 9 shows ranges of and satisfying the condition of when a parameter ^A determined by a constituent material of the

nanowire has a value of /

In this connection, the ferromagnetic nanowire with perpendicular magnetic anisotropy may be formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof. Alternatively, the nanowire may also be formed of one or more rare-earth metals.

In FIG. 9, an area between the upper curve 810 and the lower curve 820 corresponds to ranges of and satisfying the condition of

When values of in Equation 9 are calculated by matching of

Equation 9 with FIG. 9, they are as shown in Equation 14 below. In addition, ranges of and W satisfying the conditions of and can be determined according to Equation 14.

(Equation 14)

Therefore, when the parameter is determined and then and of

the nanowire are set to within the specified range according to Equation 14, it is possible to design so that a current density capable of driving a memory device taking advantage of

the current-driven domain wall displacement has a value of less than

FIG 10 shows ranges of and satisfying the condition of when a parameter determined by a constituent material of the

nano wire has a value of C( Z

In this connection, the ferromagnetic nanowire with perpendicular magnetic anisotropy may be formed of any one selected from the group consisting of Fe, Co, Ni and any combination thereof. Alternatively, the nanowire may also be formed of one or more rare-earth metals.

In FIG. 10, an area under the curve 910 corresponds to ranges of and sa + ti-s f fyi ■ng λ the cond jivtion or .

When values of α in Equation 9 are cakulated by matching of

Equation 9 with FIG. 10, they are as shown in Equation 15 below. In addition, ranges of T and satisfying the conditions of Z and can be determined according to Equation 15.

Therefore, when the parameter Q is determined and then and of

the nanowire are set to within the specified range according to Equation 15, it is possible to design so that a current density capable of driving a memory device taking advantage of the current-driven domain wall displacement has a value of less than

The aforesaid method of lowering a domain wall anisotropic energy density

through the control of a nanowire thickness and a nanowire width in the

nanowire made of a ferromagnet is also applicable to a nanowire whose magnetization direction is perpendicular to the nanowire surface. This is because the domain wall anisotropic energy density becomes zero at

the point where the domain wall and the domain wall have the same

energy level, as shown in FIGS. 4a and 4b. Therefore, the same basic principle applies to both of the nanowire whose magnetization direction is perpendicular to the nanowire surface and the nanowire whose magnetization direction is parallel to the nanowire surface. However, upon practical fabrication of the nanowire, it will have the distribution of a critical current density with respect to overall nanowire thickness and

nanowire width , due to various reasons accompanied by a manufacturing process.

FIGS. 11a to lie show contours for a thickness and a width of a

nanowire configured to design so that a current density capable of driving a memory device utilizing the current-driven domain wall displacement has a value of less than with respect to each perpendicular magnetic anisotropy density

Referring to FIGS. 1 In to 1 Ic, it can be confirmed that a thickness and a

width of the nanowire configured to have a memory device-driving current density

of less than h ave different values depending on each perpendicular

magnetic anisotropy density ". When a nanowire is configured with the thickness

and width *-' of the nanowire conforming to the aforementioned contour, it is possible to

design so that a memory device-driving current density has a value of less than

FIG. 12 is a graph illustrating a critical current density vs. nanowire width

* ' " relationship for a memory device (1A) 1110 whose magnetization direction is parallel

to the nanowire surface and a memory device (PA) 1120 in accordance with the present invention.

Referring to FIG. 12, the conventional memory device (1A) with a magnetization direction parallel to the nanowire surface should be fabricated with the precision of less than 0.1 nm in terms of nanowire width or thickness in order to obtain a value of However, it is impossible to fabricate such a high-precision device

due to the occurrence of many errors accompanied during practical processes.

On the other hand, the memory device (PA) in accordance with the present invention can achieve the condition of > / , ^ ^ j s fabricated with the

precision of less than 3 nm.

Further, the conventional memory device (1A) with a magnetization direction parallel to the nanowire surface should be fabricated with the precision of less than 1 nm in terms of nanowire width or thickness in order to satisfy the condition of Similarly, it is impossible to fabricate such a high-precision device

due to the occurrence of many errors accompanied during practical processes.

On the other hand, the memory device (PA) in accordance with the present invention can satisfy the condition of , if it is fabricated with the

precision of less than 27 nm.

In the graph of FIG. 12, the spin polarizability is 0.7, the saturation magnetization per unit area s is ^ me p er p enc ii cu i ar magnetic

anisotropy density is the effective exchange coefficient A

i s , and the nan owire thickness is 10 nm.

In this connection, a thickness of the thus-formed domain wall is 13 nm, and

then the parameter t^, which is calculated by a saturation magnetization per unit area, a

domain wall thickness and a spin polarizability of a ferromagnet, has a value of about In this case, the ferromagnet falls within the specified range of FIG. 7 which was previously defined by Equation 12. When this value is assigned to Equation 12, the critical

< ■ r- „ J , . . . , , , current density satisfies a range or which is sought by the present invention, for all the values of the nanowire width within the range of

Referring to FIG. 12, a range of the nanowire width satisfying the condition

of is This range encompasses a range

of the nanowire width calculated by the parameter of p rom

these results, it is validated for a range of the nanowire width depicted by Equation

12 of the present invention. The reason why the memory device (PA) in accordance with the present invention

has a low critical current density at a much broader nanowire width or thickness is because the domain wall anisotropic energy density is relatively significantly less sensitive to a width or thickness of the nanowire in the memory device (PA) of the present invention, as compared to the conventional memory device (1A) which was fabricated with a magnetization direction parallel to the nanowire surface.

Due to process and material heterogeneities upon practical fabrication of the nanowire, there may be a variety of pinning potentials for the domain wall displacement.

Further, as described above, the present invention is required to satisfy the characteristics that the critical current density is not sensitive to a value of P of

Equations 1 and 2 and a Gilbert damping constant determining energy loss of domain

walls upon the displacement of domain walls.

FIGS. 13a and 13b are graphs illustrating a critical current density * vs.

pinning potential ° relationship for a memory device (1A) whose magnetization

direction is parallel to the nanowire surface and a memory device (PA) in accordance with the present invention.

Referring to FIGS. 13a and 13b, a critical current density vs. pinning

potential relationship is shown with respect to and P values.

Regarding FIG. 13 a, in the conventional memory device 1210 with a magnetization direction parallel to the nanowire surface, the critical current density is

highly sensitive to the pinning potential, and , when a value of * is 0.1. As the

critical current density exhibits a critical current density value of more than

at pratical pinning potential value , practical

application thereof is not feasible.

On the other hand, when a thickness of the nanowire is 10 nm and a width

of the nanowire is 81 nm, the memory device 1220 in accordance with the present

invention exhibits a critical current density of Z at a practical pinning potential value of , thus representing superior critical current density

properties, i.e. a 10 to 100 times lower critical current density value than the conventional memory device.

Regarding FIG. 13b, in the conventional memory device 1210 with a magnetization direction parallel to the nanowire surface, the critical current density *

exhibits a critical current density value of at a practical pinning potential

value of g/ i when a value of is 0.01. Therefore, the conventional

memory device 1210 lacks commercial viability.

On the other hand, when a thickness of the nanowire is 10 nm and a width

of the nanowire is 81 nm, the memory device 1220 in accordance with the present

invention exhibits a critical current density of at a practical pinning potential value of , thus representing superior critical current density

properties, i.e. a 100 to 1000 times lower critical current density value than the conventional memory device. Referring to FIGS. 13a and 13b, it can be seen that the critical current density

is more susceptible to the pinning potential, ^ and , in conjunction with a higher

critical current density value of more than at a practical pinning potential

value of in the conventional memory device 1210 with the surface-

parallel magnetization direction than in the memory device 1220 of the present invention with the perpendicular magnetization direction, thus confirming that the memory device in accordance with the present invention exhibits superior properties in terms of critical current density value.

[Industrial Applicability] As apparent from the above description, the present invention can be designed such that a current density capable of driving a memory device utilizing the current-driven domain wall displacement has a value of less than ^ through the

determination of the optimal nanowire width and thickness satisfying a value of a critical current density (Jc) for the domain wall displacement below a certain value required for commercialization, for a given material in the nanowire with perpendicular anisotropy. According to such a configuration of the present invention, an at least 10 times lower or still smaller value is obtained than a current density required for the domain wall displacement in currently commercially available nano wires. Therefore, the present invention is capable of solving the problems associated with high power consumption and malfunction of the device due to generation of Joule heat and is also capable of achieving low-cost production of memory devices.

Although the present invention has been described herein with reference to the foregoing embodiments and the accompanying drawings, those embodiments are provided

for illustrative purposes only. Accordingly, those skilled in the art will appreciate that various substitutions, modifications and changes are possible, without departing from the technical spirit of the present invention as disclosed in the accompanying claims. It is to be understood that such substitutions, modifications and changes are within the scope of the present invention. Therefore, the scope of the present invention should be defined by attached claims only.