# Patent

## Title
Layered heusler alloys and methods for the fabrication and use thereof

## Abstract

Disclosed herein are layered Heusler alloys. The layered Heusler alloys can comprise a first layer comprising a first Heusler alloy with a face-centered cubic (fcc) crystal structure and a second layer comprising a second Heusler alloy with a fcc crystal structure, the second Heusler alloy being different than the first Heusler alloy, wherein the first layer and the second layer are layered along a layering direction, the layering direction being the [110] or [111] direction of the fcc crystal structure, thereby forming the layered Heusler alloy.

## Background
STATEMENT OF GOVERNMENT SUPPORT
This invention was made with government support under Grant No. 1235396 awarded by the National Science Foundation and Agreement No. HR0011-13-3-0002 awarded by the Defense Advanced Research Projects Agency. The government has certain rights in this invention.


BACKGROUND
Memory and logic devices that utilize the electron's spin have elicited interest recently, in part because of scalability and power consumption issues associated with more conventional electronic devices. The performance of many of these “spintronic” devices can be enhanced by the availability of a material in the form of a thin film that combines highly spin-polarized electron currents with magnetic anisotropy perpendicular to the plane of the film.
SUMMARY
Disclosed herein are layered Heusler alloys. The layered Heusler alloys can comprise a first layer comprising a first Heusler alloy with a face-centered cubic (fcc) crystal structure and a second layer comprising a second Heusler alloy with a fcc crystal structure, the second Heusler alloy being different than the first Heusler alloy, wherein the first layer and the second layer are layered along a layering direction, the layering direction being the [110] or [111] direction of the fcc crystal structure, thereby forming the layered Heusler alloy. In some examples, the layered Heusler alloy can further comprise a third layer comprising a third Heusler alloy with a fcc crystal structure, and the first layer, the second layer, and the third layer are layered along the layering direction. The third Heusler alloy can be different than the first Heusler alloy and/or the second Heusler alloy.
In some examples, the first Heusler alloy can have a formula of ABC, wherein p is 1 or 2; A and B are each a transition metal, with the proviso that A and B are not the same transition metal; and C is an element from Group 13, 14, or 15. In some examples, A and B are selected from the group consisting of: scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, rhodium, and palladium. In some examples, A and B are selected from the group consisting of: titanium, vanadium, chromium, manganese, iron, cobalt, nickel, rhodium, and palladium. In some examples, C is selected from the group consisting of: boron, aluminum, gallium, indium, thallium, carbon, silicon, germanium, tin, lead, nitrogen, phosphorous, arsenic, antimony, and bismuth. In some examples, C is selected from the group consisting of: aluminum, gallium, silicon, germanium, tin, phosphorous, arsenic, and antimony.
In some examples, the second Heusler alloy can have formula of XqYZ, wherein q is 1 or 2; X and Y are each a transition metal, with the proviso that X and Y are not the same transition metal; and Z is an element from Group 13, 14, or 15. In some examples, X and Y are selected from the group consisting of: scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, rhodium, and palladium. In some examples, X and Y are selected from the group consisting of: titanium, vanadium, chromium, manganese, iron, cobalt, nickel, rhodium, and palladium. In some examples, Z is selected from the group consisting of: boron, aluminum, gallium, indium, thallium, carbon, silicon, germanium, tin, lead, nitrogen, phosphorous, arsenic, antimony, and bismuth. In some examples, Z is selected from the group consisting of: aluminum, gallium, silicon, germanium, tin, phosphorous, arsenic, and antimony.
In some examples, the first Heusler alloy and the second Heusler alloy can be selected from the group consisting of Co2CrSi, Co2CrSb, Co2FeAl, Co2FeGe, Co2FeSi, Co2MnAl, Co2MnGa, Co2MnGe, Co2MnSi, Co2MnSb, Co2TiGe, Co2VGa, Co2VSn, Cu2MnAl, Cu2MnIn, Cu2MnSn, Cu2MnBi, Fe2MnAl, Fe2MnGa, Fe2MnSi, Fe2TiGe, Fe2TiSi, Fe2VAl, Mn2VGa, Ni2MnAl, Ni2MnIn, Ni2MnGa, Pd2MnAl, Pd2MnIn, CoMnP, CoTiP, RhFeGe, RuMnAs, NiMnP, NiMnSi, and CoTiSi. In some examples, the first Heusler alloy and the second Heusler alloy can be selected from the group consisting of Co2CrSi, Co2CrSb, Co2FeSi, Co2MnAl, Co2MnSi, Co2MnSb, Co2TiGe, Co2VGa, Co2VSn, Fe2MnAl, Fe2MnGa, Fe2MnSi, Fe2TiGe, Fe2TiSi, CoMnP, CoTiP, RhFeGe, RuMnAs, NiMnP, NiMnSi, NiMnAs, NiMnSb, NiVSb, CoMnSb, and CoTiSi.
In some examples, the first Heusler alloy comprises a half metal or a near half metal. In some examples, the second Heusler alloy comprises a half metal or a near half metal. In some examples, the layered Heusler alloy comprises a half metal or a near half metal. In some examples, the layered Heusler alloy has a Fermi level and a gapped spin-channel with a gap, and wherein the Fermi level of the layered Heusler alloy falls within the gap of the gapped spin-channel of the layered Heusler alloy
In some examples, the layered Heusler alloy is layered along the [110] direction. In some examples, when the layered Heusler alloy is layered along the [110] direction, the first layer can a first number of sublayers; the second layer can comprise a second number of sublayers; and the first number of sublayers is the same as the second number of sublayers, such that the layered Heusler alloy has a unit cell comprising (ApBC)a(XqYZ)a, wherein a is the first number of sublayers and a is an integer from 1 to 1000. In other embodiments, more than 1000 layers can be present. The skilled artisan can use as many layers as desired.
In some examples, the layered Heusler alloy is layered along the [111] direction. In some examples, when the layered Heusler alloy is layered along the [111] direction, the first layer comprises a first number of sublayers, the first number of sublayers being 4, 6, or 8; the second layer comprises a second number of sublayers, the second number of sublayers being 4, 6, or 8; and the sum of the first number of sublayers and second number of sublayers is 12. In some examples, when the first number of sublayers is 4, the layered Heusler alloy has a unit cell comprising (ApBC)(XqYZ)2, wherein p and q are independently 1 or 2. In some examples, when the first number of sublayers is 8, the layered Heusler alloy has a unit cell comprising (ApBC)2(XqYZ), wherein p and q are independently 1 or 2. In some examples, when the first number of sublayers is 6, the layered Heusler alloy has a unit cell comprising: (ApBC)(Ap-1BZ)(XqYZ), wherein p and q are independently 1 or 2.
In some examples, the magnetocrystalline anisotropy of the layered Heusler alloy along a direction perpendicular to the layering direction can be from greater than 0 J/m3 to 106 J/m3.
In some examples, the layered Heusler alloy has a μ0Heff of from −10 to 1010N A−1 m−1. In some examples, the magnetocrystalline anisotropy of the layered Heusler alloy is large enough to overcome a demagnetization field of a thin film. In some examples, the layered Heusler alloy has a μ0Heff of greater than 0 N A−1 m−1.
In some examples, the layered Heusler alloys described herein can have high spin polarization at the Fermi energy, low damping, low resistivity, high spin-torque efficiency, high tunneling magnetoresistance, or a combination thereof. In some examples, the layered Heusler alloys described herein can be compatible with Heusler semiconductors.
Methods of making and uses of the layered Heusler alloys are also described herein.
Additional advantages will be set forth in part in the description that follows, and in part will be obvious from the description, or may be learned by practice of the aspects described below. The advantages described below will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive.



BRIEF DESCRIPTION OF THE FIGURES
FIG. 1A displays the schematic crystal structure for a L21 full Heusler A2BC. The crystalline structure is cubic in nature (fcc).
FIG. 1B displays the schematic crystal structure for a C1b half Heusler ABC. The crystalline structure is cubic in nature (fcc).
FIG. 2 displays a schematic representation of stacking in the [001] direction for full Heusler superlattice A2BC-X2YZ. The [100] and [010] directions indicated in the figure correspond to those in the fcc cell in FIG. 1A.
FIG. 3 displays a schematic representation of stacking in [110] direction for a full Heusler superlattice A2BC-X2YZ. The [001] and [110] directions indicated in the figure corresponds to those in the fcc cell in FIG. 1A.
FIG. 4 displays a schematic representation of stacking in [111] direction for full Heusler superlattice A2BC-X2YZ. The [112] and [110] directions indicated in the figure are relative to axes defined for the fcc cell in FIG. 1A.
FIG. 5A displays the density of states for Co2MnAl—Fe2MnAl stacked in [001] direction with n=0.5 layering. This superlattice is a near half-metal with gap width of 0.30 eV.
FIG. 5B displays the density of states for Co2TiGe—Fe2TiGe stacked in [001] direction with n=1.0 layering and gap width of 0.23 eV as a half-metal. The Fermi level is at 0 eV.
FIG. 6A displays the density of states for half-metallic Co2MnSi—CoTiSi superlattice stacked in [110] direction, n=1 with a band gap of 0.49 eV.
FIG. 6B displays the density of states for half-metallic CoMnP—CoTiP superlattice stacked in [111] direction with a big band gap of 1.35 eV. The Fermi level is at 0 eV.
FIG. 7A displays the density of states for a [001] stacked superlattice of Co2MnAl—Fe2MnAl is doped with Si atoms at the Al atoms site. In cases (i) and (ii), Al and Si atoms are not mixed in a (001) plane. In cases (iii) and (iv), both Al and Si atoms can be there in a plane. When 50% of the Al are replaced with Si, the Fermi level moves 0.05 eV into the band gap, relative to the valence band edge.
FIG. 7B displays the density of states for a Co2MnAl—Fe2MnAl superlattice doped with Fe and Cr atoms at the Mn atom site. Doping with Cr atoms move the Fermi level 0.05 eV into the band gap, but narrows the gap.



DETAILED DESCRIPTION
The compositions and methods described herein may be understood more readily by reference to the following detailed description of specific aspects of the disclosed subject matter and the Examples and Figures included therein.
Before the present compositions and methods are disclosed and described, it is to be understood that this disclosure is not limited to specific synthetic methods or to particular reagents, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting.
Also, throughout this specification, various publications are referenced. The disclosures of these publications in their entireties are hereby incorporated by reference into this application in order to more fully describe the state of the art to which the disclosed matter pertains. The references disclosed are also individually and specifically incorporated by reference herein for the material contained in them that is discussed in the sentence in which the reference is relied upon.
General Definitions
The term “comprising” and variations thereof as used herein is used synonymously with the term “including” and variations thereof and are open, non-limiting terms. Although the terms “comprising” and “including” have been used herein to describe various examples, the terms “consisting essentially of” and “consisting of” can be used in place of “comprising” and “including” to provide for more specific examples of the invention and are also disclosed. Other than in the examples, or where otherwise noted, all numbers expressing quantities of ingredients, reaction conditions, and so forth used in the specification and claims are to be understood at the very least, and not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, to be construed in light of the number of significant digits and ordinary rounding approaches.
As used in the description and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a composition” includes mixtures of two or more such compositions, reference to “an agent” includes mixtures of two or more such agents, reference to “the component” includes mixtures of two or more such components, and the like.
“Optional” or “optionally” means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where the event or circumstance occurs and instances where it does not.
It is understood that throughout this specification the identifiers “first”, “second” and “third” are used solely to aid in distinguishing the various components and steps of the disclosed subject matter. The identifiers “first”, “second” and “third” are not intended to imply any particular order, amount, preference, or importance to the components or steps modified by these terms.
Also, throughout this specification, various publications are referenced. The disclosures of these publications in their entireties are hereby incorporated by reference into this application in order to more fully describe the state of the art to which the disclosed matter pertains. The references disclosed are also individually and specifically incorporated by reference herein for the material contained in them that is discussed in the sentence in which the reference is relied upon.
Reference will now be made in detail to specific aspects of the disclosed materials, compounds, compositions, articles, and methods, examples of which are illustrated in the accompanying examples and figures.
Layered Heusler Alloys
Disclosed herein are layered Heusler alloys. The layered Heusler alloys can comprise a first layer comprising a first Heusler alloy with a face-centered cubic (fcc) crystal structure and a second layer comprising a second Heusler alloy with a fcc crystal structure, the second Heusler alloy being different than the first Heusler alloy, wherein the first layer and the second layer are layered along a layering direction, the layering direction being the [110] or [111] direction of the fcc crystal structure, thereby forming the layered Heusler alloy. As used herein, the layering direction being the [110] or [111] direction of the fcc crystal structure also includes those directions that are equivalent to the [110] or [111] direction of the fcc crystal due to symmetry of the fcc crystal. Directions equivalent to the [110] or [111] directions of the fcc crystal structure due to symmetry will be known to those of skill in the art. For example, in the fcc crystal structure, the [001], [010], [001], [010] and [100] directions are all equivalent by symmetry.
In some examples, the layered Heusler alloy can further comprise a third layer comprising a third Heusler alloy with a fcc crystal structure, and the first layer, the second layer, and the third layer are layered along the layering direction. The third Heusler alloy can be different than the first Heusler alloy and/or the second Heusler alloy.
The first Heusler alloy can comprise any full- or half-Heusler alloy. In some examples, the first Heusler alloy can have a formula of ABC, wherein p is 1 or 2; A and B are each a transition metal, with the proviso that A and B are not the same transition metal; and C is an element from Group 13, 14, or 15. When p is 2, the first Heusler alloy is a full-Heusler alloy with a L21 crystal structure and a unit cell formula of A2BC, as shown in FIG. 1A. The L21 structure is fcc with a 4 atom basis. When p is 1, the first Heusler alloy comprises a half-Heusler alloy with a C1b crystal structure and a unit cell formula of ABC, as shown in FIG. 1B. The C1b structure is fcc with a 3 atom basis. The description of the layered Heusler alloys herein will be based on the directions relative to the fcc cells, for example as shown in FIGS. 1A and 1B.
In some examples, A and B are selected from the group consisting of: scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, rhodium, and palladium. In some examples, A and B are selected from the group consisting of: titanium, vanadium, chromium, manganese, iron, cobalt, nickel, rhodium, and palladium.
In some examples, C is selected from the group consisting of: boron, aluminum, gallium, indium, thallium, carbon, silicon, germanium, tin, lead, nitrogen, phosphorous, arsenic, antimony, and bismuth. In some examples, C is selected from the group consisting of: aluminum, gallium, silicon, germanium, tin, phosphorous, arsenic, and antimony.
The second Heusler alloy can comprise any full- or half-Heusler alloy. In some examples, the second Heusler alloy can have formula of XqYZ, wherein q is 1 or 2; X and Y are each a transition metal, with the proviso that X and Y are not the same transition metal; and Z is an element from Group 13, 14, or 15. When q is 1, the second Heusler alloy is a half-Heusler alloy with a C1b crystal structure and a unit cell of XYZ. When q is 2, the second Heusler alloy is a full-Heusler alloy with a L21 crystal structure.
In some examples, X and Y are selected from the group consisting of: scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, rhodium, and palladium. In some examples, X and Y are selected from the group consisting of: titanium, vanadium, chromium, manganese, iron, cobalt, nickel, rhodium, and palladium.
In some examples, Z is selected from the group consisting of: boron, aluminum, gallium, indium, thallium, carbon, silicon, germanium, tin, lead, nitrogen, phosphorous, arsenic, antimony, and bismuth. In some examples, Z is selected from the group consisting of: aluminum, gallium, germanium, tin, phosphorous, arsenic, and antimony.
The first Heusler alloy and the second Heusler alloy are different. In some examples, when the first Heusler alloy is ABC and the second Heusler alloy is XqYZ, A and X are not the same transition metal. In some examples, when the first Heusler alloy is ABC and the second Heusler alloy is XqYZ, B and Y are not the same transition metal. In some examples, when the first Heusler alloy is ABC and the second Heusler alloy is XqYZ, C and Z are not the same element from Group 13, 14, or 15.
In some examples, the first Heusler alloy and the second Heusler alloy can be selected from the group consisting of Co2CrSi, Co2CrSb, Co2FeAl, Co2FeGe, Co2FeSi, Co2MnAl, Co2MnGa, Co2MnGe, Co2MnSi, Co2MnSb, Co2TiGe, Co2VGa, Co2VSn, Cu2MnAl, Cu2MnIn, Cu2MnSn, Cu2MnBi, Fe2MnAl, Fe2MnGa, Fe2MnSi, Fe2TiGe, Fe2TiSi, Fe2VAl, Mn2VGa, Ni2MnAl, Ni2MnIn, Ni2MnGa, Pd2MnAl, Pd2MnIn, CoMnP, CoTiP, RhFeGe, RuMnAs, NiMnP, NiMnSi, and CoTiSi. In some examples, the first Heusler alloy and the second Heusler alloy can be selected from the group consisting of Co2CrSi, Co2CrSb, Co2FeSi, Co2MnAl, Co2MnSi, Co2MnSb, Co2TiGe, Co2VGa, Co2VSn, Fe2MnAl, Fe2MnGa, Fe2MnSi, Fe2TiGe, Fe2TiSi, CoMnP, CoTiP, RhFeGe, RuMnAs, NiMnP, NiMnSi, NiMnAs, NiMnSb, NiVSb, CoMnSb, and CoTiSi.
In some examples, the first Heusler alloy comprises a half metal or a near half metal. As used herein, a Heusler alloy is a “half-metal” when the Fermi energy falls in a gap for one of the spin-channels, but not for the other. A “near half metal,” on the other hand, occurs when the Fermi energy falls slightly outside the gap for one of the spin channels (Munira K et al. J. Appl. Phys. 2014, 115, 17B731). In some examples, the second Heusler alloy comprises a half metal or a near half metal. In some examples, the layered Heusler alloy comprises a half metal or a near half metal. In some examples, the layered Heusler alloy has a Fermi level and a gapped spin-channel with a gap, and wherein the Fermi level of the layered Heusler alloy falls within the gap of the gapped spin-channel of the layered Heusler alloy
The highest Fermi-energy spin-polarization comes from ferromagnetic materials that exhibit half-metallic properties. In half-metals, the electronic structure of one of the spin channels is that of a metal while the other is that of an insulator or semiconductor (Munira K et al. J. Appl. Phys. 2014, 115, 17B731). In some examples, this can lead to 100% spin-polarization of the electron current, high magnetoresistance and high spin-torque efficiency. Half-metals can also have lower magnetic damping than typical ferromagnets (Liu C et al. J. Appl. Phys. 2009, 95, 2). Low damping can be beneficial for applications that utilize Spin-Torque transfer for switching of nanomagnets (Munira K et al. IEEE Transactions on Electron Devices. 2012, 59, 8).
In some examples, the layered Heusler alloy is layered along the [110] direction. In some examples, when the layered Heusler alloy is layered along the [110] direction, the first layer can a first number of sublayers; the second layer can comprise a second number of sublayers; and the first number of sublayers is the same as the second number of sublayers, such that the layered Heusler alloy has a unit cell comprising (ApBC)a(XqYZ)a, wherein a is the first number of sublayers and a is an integer from 1 to 1000. In some examples, there can be more than 1000 sublayers. In some examples, a is 1, 2, or 3.
When the layered Heusler alloy is formed by stacking layers along the [110] direction, each layer is stoichiometric. Referring now to FIG. 3, a schematic for a first Heusler alloy comprising A2BC and a second Heusler alloy comprising X2YZ being layered along the [110] direction, with the first layer and second layer each having one sublayer is shown. As shown in FIG. 3, atoms A, B and C are each present in the first (sub)layer and X, Y, and Z atoms are each present in the second (sub)layer. The unit cell in FIG. 3 corresponds to the first layer and second layer each having one sublayer, for which one layer of each constituent alternates one after another ( . . . -A2BC-X2YZ- . . . ). For two and three sublayers, the thickness of each layer of the layered Heusler alloy is increased by 2 ( . . . -A2BC-A2BC-X2YZ-X2YZ- . . . ) and 3 times ( . . . -A2BC-A2BC-A2BC-X2YZ-X2YZ-X2YZ- . . . ), respectively.
If the first Heusler alloy and the second Heusler alloy were each a half-Heusler, one of the A atoms in the A2BC layer and one of the X atoms in the X2YZ layer of FIG. 3 would be replaced by a vacancy. The layered Heusler alloy formed from two half-Heuslers (e.g., the first Heusler alloy being ABC and the second Heusler alloy being XYZ) with 1, 2 and 3 sublayers corresponds to ( . . . -ABC-XYZ- . . . ), ( . . . -ABC-ABC-XYZ-XYZ- . . . ) and ( . . . -ABC-ABC-ABC-XYZ-XYZ-XYZ- . . . ), respectively.
In some examples, when the layered Heusler alloy is layered along the [110] direction, the first Heusler alloy is ABC, and the second Heusler alloy is XqYZ, A and X are not the same transition metal. In some examples, when the layered Heusler alloy is layered along the [110] direction, the first Heusler alloy is ABC, and the second Heusler alloy is XqYZ, B and Y are not the same transition metal and C and Z are not the same element from Group 13, 14, or 15.
In some examples, the layered Heusler alloy is layered along the [111] direction. In some examples, when the layered Heusler alloy is layered along the [111] direction, the first layer comprises a first number of sublayers, the first number of sublayers being 4, 6, or 8; the second layer comprises a second number of sublayers, the second number of sublayers being 4, 6, or 8; and the sum of the first number of sublayers and second number of sublayers is 12. In some examples, when the first number of sublayers is 4, the layered Heusler alloy has a unit cell comprising (ApBC)(XqYZ)2, wherein p and q are independently 1 or 2. In some examples, when the first number of sublayers is 8, the layered Heusler alloy has a unit cell comprising (ApBC)2(XqYZ), wherein p and q are independently 1 or 2. In some examples, when the first number of sublayers is 6, the layered Heusler alloy has a unit cell comprising: (ApBC)(Ap-1XBZ)(XqYZ), when p and q are independently 1 or 2.
When the layered Heusler alloy is formed by stacking layers along the [111] direction, the layering can comprise the stacking of hexagonal nets, as can be seen from the depiction of layers perpendicular to the [111] direction shown in FIG. 4. The fcc cells shown in FIGS. 1A and 1B are also helpful in understanding [111] layering. The fcc lattice with a single atom basis can be viewed along the [111] direction as a succession of identical hexagonal layers with A-B-C stacking. The L21 structure is fcc but with a 4 atom basis. There is a single species on each layer. For full-Heuslers, for example with an X2YZ composition, the atomic layers perpendicular to the [111] direction follow the pattern of Y species on A, followed by X species on B, then Z species on C, X on A, Y on B, etc. In some examples, when the layered Heusler alloy is formed by stacking layers along the [111] direction, the correct stoichiometry for a full-Heusler (e.g., the first Heusler is A2BC and the second Heusler is X2YZ) requires a minimum of 4 sublayers for each of the first Heusler alloy and the second Heusler alloy (e.g., at least 4 sublayers in each of the first layer and the second layer), and the total number of repeating sublayers must be divisible by three to make the A-B-C sequence repeat. Thus for the case wherein the first Heusler alloy is A2BC and the second Heusler alloy is X2YZ, a minimum of 12 sublayers is required for the simulation of a Heusler superlattice stacked in this manner. As shown in FIG. 4, there may be six layers of A2BC and then six layers of X2YZ. One can also have 8 layers of A2BC followed by 4 layers of X2YZ or vice versa. Half-Heuslers do not contain any atoms in the second, sixth and tenth layers in the schematic structure of FIG. 4.
Due to the spin-orbit interaction and the symmetry of the crystal, the magnetic moments of a material will want to point in a particular direction in an infinite or spherical crystal. Meanwhile, layered systems can have a special direction perpendicular to the layers. The difference in the energy per unit volume of the layered material when the moments are pointed perpendicular to the layers compared to the minimum energy when they point in the plane of the layers is the magnetocrystalline anisotropy, K (sometimes with a subscript “u”, Ku). In other words, the magnetocrystalline anisotropy (K, sometimes with a subscript “u”, Ku) of a layered Heusler alloy can be calculated by using the energy differences, Ein-plane−Eperpendicular, where Eperpendicular represents the energy when magnetization orientation is perpendicular to the stacking planes and Ein-plane is the energy when magnetization orientation is along any direction in the stacking plane. For example, for layered Heusler alloys layered in the [110] direction, the energy calculated for the [110] magnetization can be compared to that calculated for the in-plane magnetization directions [001], [110], and [111]. For layered Heusler alloys layered in the [111] direction, for example, the energy calculated for the [111] magnetization can be compared to that calculated for the in-plane magnetization directions [112] and [110]. A positive value for the magnetocrystalline anisotropy (e.g., K>0) can indicate that the magnetization prefers to lie perpendicular to the Heusler planes, while a negative value indicates that the magnetization lies in-plane.
There is a different kind of anisotropy called shape anisotropy that can be important for a thin film. For a thin film, the moments want to lie head to tail (south adjacent to north), just like many small magnets, and they can best do this when they lie in-plane.
In some examples, the layered Heusler alloy can have a magnetocrystalline anisotropy of greater than 0 J/m3 along a direction perpendicular to the layering direction (e.g., 1 J/m3 or more, 2 J/m3 or more, 3 J/m3 or more, 4 J/m3 or more, 5 J/m3 or more, 6 J/m3 or more, 7 J/m3 or more, 8 J/m3 or more, 9 J/m3 or more, 10 J/m3 or more, 20 J/m3 or more, 30 J/m3 or more, 40 J/m3 or more, 50 J/m3 or more, 60 J/m3 or more, 70 J/m3 or more, 80 J/m3 or more, 90 J/m3 or more, 1×102 J/m3 or more, 2×102 J/m3 or more, 3×102 J/m3 or more, 4×102 J/m3 or more, 5×102 J/m3 or more, 6×102 J/m3 or more, 7×102 J/m3 or more, 8×102 J/m3 or more, 9×102 J/m3 or more, 1×103 J/m3 or more, 2×103 J/m3 or more, 3×103 J/m3 or more, 4×103 J/m3 or more, 5×103 J/m3 or more, 6×103 J/m3 or more, 7×103 J/m3 or more, 8×103 J/m3 or more, 9×103 J/m3 or more, 1×104 J/m3 or more, 2×104 J/m3 or more, 3×104 J/m3 or more, 4×104 J/m3 or more, 5×104 J/m3 or more, 6×104 J/m3 or more, 7×104 J/m3 or more, 8×104 J/m3 or more, 9×104 J/m3 or more, 1×105 J/m3 or more, 2×105 J/m3 or more, 3×105 J/m3 or more, 4×105 J/m3 or more, 5×105 J/m3 or more, 6×105 J/m3 or more, 7×105 J/m3 or more, 8×105 J/m3 or more, or 9×105 J/m3 or more).
In some examples, the magnetocrystalline anisotropy of the layered Heusler alloy along a direction perpendicular to the layering direction can be 106 J/m3 or less (e.g., 9×105 J/m3 or less, 8×105 J/m3 or less, 7×105 J/m3 or less, 6×105 J/m3 or less, 5×105 J/m3 or less, 4×105 J/m3 or less, 3×105 J/m3 or less, 2×105 J/m3 or less, 1×105 J/m3 or less, 9×104 J/m3 or less, 8×104 J/m3 or less, 7×104 J/m3 or less, 6×104 J/m3 or less, 5×104 J/m3 or less, 4×104 J/m3 or less, 3×104 J/m3 or less, 2×104 J/m3 or less, 1×104 J/m3 or less, 9×103 J/m3 or less, 8×103 J/m3 or less, 7×103 J/m3 or less, 6×103 J/m3 or less, 5×103 J/m3 or less, 4×103 J/m3 or less, 3×103 J/m3 or less, 2×103 J/m3 or less, 1×103 J/m3 or less, 9×102 J/m3 or less, 8×102 J/m3 or less, 7×102 J/m3 or less, 6×102 J/m3 or less, 5×102 J/m3 or less, 4×102 J/m3 or less, 3×102 J/m3 or less, 2×102 J/m3 or less, 1×102 J/m3 or less, 90 J/m3 or less, 80 J/m3 or less, 70 J/m3 or less, 60 J/m3 or less, 50 J/m3 or less, 40 J/m3 or less, 30 J/m3 or less, 20 J/m3 or less, 10 J/m3 or less, 9 J/m3 or less, 8 J/m3 or less, 7 J/m3 or less, 6 J/m3 or less, 5 J/m3 or less, 4 J/m3 or less, 3 J/m3 or less, 2 J/m3 or less, or 1 J/m3 or less).
The magnetocrystalline anisotropy of the layered Heusler alloy along a direction perpendicular to the layering direction can range from any of the minimum values described above to any of the maximum values described above. For example, the magnetocrystalline anisotropy of the layered Heusler alloy along a direction perpendicular to the layering direction can be from greater than 0 J/m3 to 106 J/m3 (e.g., from greater than 0 J/m3 to 1×103 J/m3, from 1×103 J/m3 to 106 J/m3, from 0 J/m3 to 1×102 J/m3, from 1×102 J/m3 to 1×104 J/m3, from 1×104 J/m3 to 106 J/m3, or from 10 J/m3 to 9×105 J/m3).
The effective anisotropy field of a thin magnetic film, Heff (or, μ0Heff where go is the magnetic permeability constant), can be described by:




  
    
      μ
      0
    
    ⁢
    
      H
      eff
    
  
  =
  
    
      
        2
        ⁢
        K
      
      -
      
        M
        s
        2
      
    
    
      M
      s
    
  




where μ0 is the magnetic permeability constant, K is the magnetocrystalline anisotropy, and Ms is the saturation magnetization of the magnetic film due to magnetic dipole interactions. Accordingly, a thin magnetic film with no magnetocrystalline anisotropy (K=0) will have an effective anisotropy field of μ0Heff=−Ms. A positive value of μ0Heff can indicate that the Heusler superlattice has enough perpendicular anisotropy to overcome the demagnetization field of a thin film.

In some examples, the layered Heusler alloy can have μ0Heff of −10 N A−1 m−1 or more (e.g., −5 N A−1 m−1 or more, 0 N A−1 m−1 or more, 5 N A−1 m−1 or more, 10 N A−1 m−1 or more, 20 N A−1 m−1 or more, 30 N A−1 m−1 or more, 40 N A−1 m−1 or more, 50 N A−1 m−1 or more, 60 N A−1 m−1 or more, 70 N A−1 m−1 or more, 80 N A−1 m−1 or more, 90 N A−1 m−1 or more, 1×102N A−1 m−1 or more, 2×102N A−1 m−1 or more, 3×102N A−1 m−1 or more, 4×102N A−1 m−1 or more, 5×102N A−1 m−1 or more, 6×102N A−1 m−1 or more, 7×102 N A−1 m−1 or more, 8×102N A−1 m−1 or more, 9×102 N A−1 m−1 or more, 1×103 N A−1 m−1 or more, 2.5×103 N A−1 m−1 or more, 5×103 N A−1 m−1 or more, 7.5×103 N A−1 m−1 or more, 1×104 N A−1 m−1 or more, 2.5×104N A−1 m−1 or more, 5×104N A−1 m−1 or more, 7.5×104N A−1 m−1 or more, 1×105 N A−1 m−1 or more, 2.5×105N A−1 m−1 or more, 5×105N A−1 m−1 or more, 7.5×105 N A−1 m−1 or more, 1×106N A−1 m−1 or more, 2.5×106N A−1 m−1 or more, 5×106N A−1 m−1 or more, 7.5×106N A−1 m−1 or more, 1×107 N A−1 m−1 or more, 2.5×107 N A−1 m−1 or more, 5×107 N A−1 m−1 or more, 7.5×107N A−1 m−1 or more, 1×108N A−1 m−1 or more, 2.5×108 N A−1 m−1 or more, 5×108N A−1 m−1 or more, 7.5×108N A−1 m−1 or more, 1×109N A−1 m−1 or more, 2.5×109 N A−1 m−1 or more, 5×109N A−1 m−1 or more, or 7.5×109 N A−1 m−1 or more).
In some examples, the layered Heusler alloy can have μ0Heff of 1010 N A−1 m−1 or less (e.g., 7.5×109N A−1 m−1 or less, 5×109N A−1 m−1 or less, 2.5×109 N A−1 m−1 or less, 1×109 N A−1 m−1 or less, 7.5×108N A−1 m−1 or less, 5×108N A−1 m−1 or less, 2.5×108 N A−1 m−1 or less, 1×108 N A−1 m−1 or less, 7.5×107N A−1 m−1 or less, 5×107N A−1 m−1 or less, 2.5×107 N A−1 m−1 or less, 1×107N A−1 m−1 or less, 7.5×106 N A−1 m−1 or less, 5×106 N A−1 m−1 or less, 2.5×106N A−1 m−1 or less, 1×106N A−1 m−1 or less, 7.5×105 N A−1 m−1 or less, 5×105N A−1 m−1 or less, 2.5×105N A−1 m−1 or less, 1×105N A−1 m−1 or less, 7.5×104 N A−1 m−1 or less, 5×104 N A−1 m−1 or less, 2.5×104N A−1 m−1 or less, 1×104N A−1 m−1 or less, 7.5×103 N A−1 m−1 or less, 5×103 N A−1 m−1 or less, 2.5×103 N A−1 m−1 or less, 1×103 N A−1 m−1 or less, 7.5×102 N A−1 m−1 or less, 5×102N A−1 m−1 or less, 2.5×102 N A−1 m−1 or less, 1×102 N A−1 m−1 or less, 90 N A−1 m−1 or less, 80 N A−1 m−1 or less, 70 N A−1 m−1 or less, 60 N A−1 m−1 or less, 50 N A−1 m−1 or less, 40 N A−1 m−1 or less, 30 N A−1 m−1 or less, 20 N A−1 m−1 or less, 10 N A−1 m−1 or less, 5 N A−1 m−1 or less, 0 N A−1 m−1 or less, or −5 N A−1 m−1 or less).
In some examples, the layered Heusler alloy has a μ0Heff of from −10 to 1010N A−1 m−1 (e.g., from −10 N A−1 m−1 to 1×105N A−1 m−1, from 1×105N A−1 m−1 to 1×10N A−1 m−1, from −10 N A−1 m−1 to 1×102N A−1 m−1, from 1×102 N A−1 m−1 to 1×104N A−1 m−1, from 1×104N A−1 m−1 to 1×106N A−1 m−1, from 1×106N A−1 m−1 to 1×108N A−1 m−1, from 1×108N A−1 m−1 to 1×1010 N A−1 m−1, or from 0 N A−1 m−1 to 1×1010 N A−1 m−1). In some examples, the magnetocrystalline anisotropy of the layered Heusler alloy is large enough to overcome a demagnetization field of a thin film. In some examples, the layered Heusler alloy has a μ0Heff of greater than 0 N A−1 m−1.
In some examples, the layered Heusler alloys described herein can have high spin polarization at the Fermi energy, low damping, low resistivity, high spin-torque efficiency, high tunneling magnetoresistance, or a combination thereof. In some examples, the layered Heusler alloys described herein can be compatible with Heusler semiconductors.
Methods of Making
The layered Heusler alloys described herein can be made, for example, by thin film processing techniques, such as sputtering, pulsed layer deposition, molecular beam epitaxy, evaporation, atomic layer deposition, or combinations thereof. In some examples, the layered Heusler alloys described herein can be made, for example, using equilibrium processing methods, such as arc melting, annealing, or combinations thereof.
Methods of Use
The layered Heusler alloys described herein can be used, for example, in spintronic devices, spin logic devices, spin valves, magnetic tunnel junctions, or a combination thereof.
In some examples, the layered Heusler alloys described herein can be used in Magnetoresistive random-access memory devices. Magnetoresistive random-access memory (MRAM) is a non-volatile random access-memory technology that uses magnetic storage elements to store data, unlike the electric charge or current flows used to store data in conventional RAM chip technologies.
In some examples, the layered Heusler alloys described herein can be used in spin-torque transfer devices, such as spin-transfer, torque-based logic devices that use spins and magnets for information processing. Spin-torque transfer is an effect in which the orientation of a magnetic layer can be modified using a spin-polarized current. Spin-torque transfer can be used to flip the active elements in magnetic random-access memory. Spin-torque transfer magnetic random-access memory (e.g., STT-RAM or STT-MRAM) has the advantages of lower power consumption and better scalability over conventional magnetoresistive random-access memory (MRAM) which uses magnetic fields to flip the active elements. Spin-torque transfer technology can combine lower current requirements and reduced cost in making MRAM devices. In some examples, the layered Heusler alloys described herein can form the free layer in a STT-RAM device. In some examples, the layered Heusler alloys described herein can form the reference (or pinned) layer in a STT-RAM device. In some examples, the layered Heusler alloys described herein can be used to form an all-Heusler magnetic tunnel junction, for example by layering a semiconducting Heusler alloy with a half-metallic Heusler alloy.
In some examples, the layered Heusler alloys can be used as the ferromagnetic free layer in spin memory devices.
EXAMPLES
The following examples are set forth below to illustrate the methods and results according to the disclosed subject matter. These examples are not intended to be inclusive of all aspects of the subject matter disclosed herein, but rather to illustrate representative methods and results. These examples are not intended to exclude equivalents and variations of the present invention which are apparent to one skilled in the art.
Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.) but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in ° C. or is at ambient temperature, and pressure is at or near atmospheric. There are numerous variations and combinations of reaction conditions, e.g., component concentrations, temperatures, pressures and other reaction ranges and conditions that can be used to optimize the product purity and yield obtained from the described process. Only reasonable and routine experimentation will be required to optimize such process conditions.
Example 1
Certain full-Heusler alloys (Skaftouros S et al. Phys. Rev. B. 2013, 87, 024420; Galanakis I et al. J. Phys. D: Appl. Phys. 2006, 39, 765) and half-Heusler alloys (Galanakis I et al. Phys. Rev. B. 2008, 77, 214417; Kandpal H C et al. J. Phys. D: Appl. Phys. 2006, 39, 5) have been shown (e.g., by calculation) to be half-metals or “near” half-metals. A half-metal occurs when the Fermi energy falls in a gap for one of the spin-channels, but not for the other. Thus electron transport at the Fermi energy (if spin-flip scattering and spin mixing effects are ignored) is metallic for the channel without a gap and activated for the gapped channel. The gap in the full- and half-Heusler alloys can occur such that the number of filled bands below the gap is three times the number of atoms per formula unit (i.e. for an average of three electrons per atom). Full and half-Heusler alloys can have a gap at three bands per atom. A “near half metal,” on the other hand, occurs when the Fermi energy falls slightly outside the gap for one of the spin channels (Munira K et al. J. Appl. Phys. 2014, 115, 17B731).
One drawback of Heusler alloys, for some applications, is that the symmetry of their L21 and C1b crystal structures can preclude uniaxial magnetocrystalline anisotropy. A uniaxial symmetry can be induced by a surface or an interface, for example when a thin layer of Heusler alloy has an interface with MgO (Munira K et al. J. Appl. Phys. 2014, 115, 17B731; Wen Z et al. Appl. Phys. Lett. 2011, 98, 242507) or GaAs (Wang W H et al. Phys. Rev. B. 2005, 71, 144416). However, such an induced magnetocrystalline anisotropy is proportional to the area of the interface rather than the volume of the alloy. If this interfacial anisotropy is perpendicular, it will eventually be counterbalanced by the demagnetization anisotropy as the thickness of the Heusler alloy is increased. One possible exception would be a ferrimagnetic Heusler alloy with zero net magnetic moment.
Herein, ab-initio simulations demonstrate that an intrinsic uniaxial anisotropy can be achieved by making layered superlattices of two Heusler alloys. Various full-full, full-half and half-half Heusler superlattices are studied and potential half-metallic superlattices with perpendicular magnetocrystalline anisotropy are identified. This uniaxial anisotropy in the superlattice can be caused by the different electronic configurations of the two Heusler alloys and/or by the distortion of the lattice, which can cause the local environment of each atom to be different in the direction perpendicular to the layers from that in the plane of the layers.
Previous theoretical calculations have shown that it is possible for half-metallic Heusler superlattices comprising multiple Heusler alloys layered perpendicular to the [001] direction to retain their half-metallicity (Culbert C A et al. J. Appl. Phys. 2008, 103, 07D707; Tirpanci S et al. J. Appl. Phys. 2013, 113, 043912; Liu C et al. arXiv:1103.3855, 2011). Herein, the possibility of Heusler alloys layered perpendicular to the [110] and [111] directions retaining half-metallicity is investigated. In addition, the effects of symmetry reduction due to said layering is investigated, particularly with respect to magnetocrystalline anisotropy. The identification of Heusler superlattices that are half-metallic and also have sufficient perpendicular magnetic anisotropy to off-set the demagnetization field of a thin ferromagnetic layer that might occur, for example, in the ferromagnetic layers of an Spin-Torque Transfer Random Access Memory (STT-RAM) device (Apalkov D et al. J. Emerg. Technol. Comput. Syst. 2013, 9, 2), is discussed herein.
Layering in the [001] Direction
In bulk full-Heusler alloys, A2 and BC planes are stacked alternately along the [001] direction. For half-Heuslers, A and BC planes alternate. For both alloy types, four of these atomic layers stacked along the [001] direction are needed to complete a supercell with the correct symmetry for all atoms. FIG. 2 illustrates the unit cell of a superlattice with layers stacked along the [001] direction and composed of two full-Heusler alloys, A2BC and X2YZ. This unit cell corresponds to n=0.5 layering (in the terminology of Tirpanci S et al. J. Appl. Phys. 2013, 113, 043912), for which layers of each Heusler alloy alternate one after another, with each Heusler alloy having two layers. In other words, the unit cell for the Heusler superlattice comprising two full-Heusler alloys, namely A2BC and X2YZ, would comprise a first layer populated by A atoms, followed by a second layer populated by B and C atoms, a third layer populated by X atoms, and a fourth layer populated by Y and Z atoms. Thus, an n=0.5 superlattice comprising two full-Heusler alloys can be described by . . . -A2-BC-X2-ZY- . . . where “ZY” (rather than “YZ”) indicates that the positions of the transition and non-transition metal have been interchanged between the second and fourth layers. As used herein, this stacking is also referred to as “two layer stacking,” indicating there are two atomic layers per Heusler alloy in the super lattice. For half-Heusler superlattices, the second and fourth layers are the same, but one of the two atomic sites in layers 1 and 3 that would have been occupied by an A or X atom in the full-Heusler is vacant, with the positions of the atom and vacancy alternating between layers 1 and 3.
Two layer stacking is called n=0.5 because the representation of a pure full-Heusler with cubic symmetry requires a supercell with 4 atomic [001] layers. When the number of layers for each constituent alloy is doubled (e.g., four layer stacking), the resulting superlattice will be said have n=1.0 layers (e.g., . . . -A2-BC-A2-CB-X2-YZ-X2-ZY- . . . ). Similarly, n=1.5 corresponds to 6 layers each of A2BC and X2YZ ( . . . -A2-BC-A2-CB-A2-BC-X2-ZY-X2-YZ-X2-ZY- . . . ).
Layering in the [110] Direction
When the superlattice is formed by stacking layers along the [110] direction, each layer is stoichiometric. As shown in FIG. 3, A, B and C atoms are present in each layer. The unit cell in FIG. 3 corresponds to n=0.5 layering of a full-Heusler alloy, for which one layer of each constituent alternates one after another ( . . . -A2BC-X2YZ- . . . ). For n=1 and n=1.5, the thickness of each constituent of the superlattice is increased by 2 ( . . . -A2BC-A2BC-X2YZ-X2YZ- . . . ) and 3 times ( . . . -A2BC-A2BC-A2BC-X2YZ-X2YZ-X2YZ- . . . ), respectively.
For a half-Heusler, one of the A atoms in the A2BC layer and one of the X atoms in the X2YZ layer would be replaced by a vacancy. For the half-Heusler superlattice, n=0.5, 1.0 and 1.5 layering corresponds to ( . . . -ABC-XYZ- . . . ), ( . . . -ABC-ABC-XYZ-XYZ- . . . ) and ( . . . -ABC-ABC-ABC-XYZ-XYZ-XYZ- . . . ), respectively. Symmetry does not allow perpendicular magnetic anisotropy for Heusler superlattices stacked in the [110] direction for n=0.5 if A=X or if B=Y and C=Z, because, in such cases, the superlattice is geometrically equivalent in the [110] and [110] directions. Systems with this degeneracy are omitted from Table 3.
As described in more detail below, the results of the investigations discussed herein indicate that (110) textured Heuslers and half-Heuslers can retain their half-metallicity. In this context “textured” means that the film is growing in such a manner that the atomic planes parallel to the plane of the film are perpendicular to the [110] direction. This may be useful in growing textured Heusler films. A full-Heusler alloy with random site occupation would be bcc. Alloys with bcc structure often prefer [110] growth because the atomic planes tend to be most dense for this growth direction. Denser planes that are further apart can lead to a lower surface energy. Herein, values of the formation energy per atom for the different layering directions and layer thicknesses were calculated in lieu of calculating surface energies.
Layering in the [111] Direction
Layering in the [111] direction comprises the stacking of hexagonal nets, as can be seen from the depiction of layers perpendicular to the [111] direction shown in FIG. 4. The fcc cells shown in FIGS. 1A and 1B are also helpful in understanding [111] layering. The fcc lattice with a single atom basis can be viewed along the [111] direction as a succession of identical hexagonal layers with the familiar A-B-C stacking. The L21 structure is fcc but with a 4 atom basis. There is a single species on each layer. For full-Heuslers with an X2YZ composition, the atomic layers perpendicular to the [111] direction follow the pattern of Y species on A, followed by X species on B, then Z species on C, X on A, Y on B, etc. The correct stoichiometry for a full-Heusler requires a minimum of 4 layers for each type of Heusler and the total number of repeating layers must be divisible by three to make the A-B-C sequence repeat. Thus for the case A2BC-X2YZ, a minimum of 12 layers is required for the simulation of a Heusler superlattice stacked in this manner. As shown in FIG. 4, there may be six layers of A2BC and then six layers of X2YZ. One can also have 8 layers of A2BC followed by 4 layers of X2YZ or vice versa. Half-Heuslers do not contain any atoms in the second, sixth and tenth layers in the schematic structure of FIG. 4.
Computational Approach
Calculations were performed using the Vienna Ab-Initio Simulation Package (VASP) (Kresse G and Hafner J. Phys. Rev. B. 1993, 47, 558; Kresse G and Furthmüller J. Phys. Rev. B. 1996, 54, 11169) with the Perdew-Burke-Ernzerhof formulation of the generalized gradient approximation (GGA) (Wang Y and Perdew J P. Phys. Rev. B. 1991, 44, 13298) for the exchange-correlation potential. The superlattices were relaxed without any constraint on shape or volume, using the conjugate-gradient algorithm. A high kinetic energy cutoff of 520 electron volts (eV) was used during unit cell relaxation in order to guarantee accuracy and ensure that the calculated atomic forces are consistent with the energy (i.e., to ensure that the forces vanish at the energy minimum). The Brillouin zone sampling was performed according to the Monkhorst-Pack scheme. The Kohn-Sham equations were solved to find the charge distribution of the ground state system without taking spin-orbit interactions into account. Finally, the total energy of the system was calculated for a given orientation of magnetic moments in the presence of spin-orbit coupling.
Due to the spin-orbit interaction and the symmetry of the crystal, the magnetic moments of a material will want to point in a particular direction in an infinite or spherical crystal. Meanwhile, layered systems can have a special direction perpendicular to the layers. The difference in the energy per unit volume of the layered material when the moments are pointed perpendicular to the layers compared to the minimum energy when they point in the plane of the layers is the magnetocrystalline anisotropy, K (sometimes with a subscript “u”, Ku). In other words, the magnetic anisotropy of a superlattice (K, sometimes with a subscript “u”, Ku) is calculated by using the energy differences, Ein-plane−Eperpendicular. Eperpendicular represents the energy when magnetization orientation is perpendicular to the stacking planes. Ein-plane is the energy when magnetization orientation is along any direction in the stacking plane.
For [001]-stacked superlattices, the energy calculated for the [001] magnetization direction was compared to that calculated for the [110] and [100] directions. For superlattices stacked in the [110] direction, the energy calculated for the [110] magnetization was compared to that calculated for the in-plane magnetization directions [001], [110], and [111]. For superlattices stacked in the [111] direction, the energy calculated for the [111] magnetization was compared to that calculated for the in-plane magnetization directions [112] and [110]. A positive value for K indicates that the magnetization prefers to lie perpendicular to the Heusler planes, while a negative value indicates that the magnetization lies in-plane.
The formation energy per atom for the layered superlattice was calculated by subtracting the energies of the individual elements in pure form from the superlattice's total energy. For a layered n=0.5 A2BC-X2YZ superlattice, the formation energy per atom (Eform) is:




  
    E
    form
  
  =
  
    
      (
      
        
          E
          
            
              
                A
                2
              
              ⁢
              BC
            
            -
            
              
                X
                2
              
              ⁢
              YZ
            
          
        
        -
        
          2
          ⁢
          
            E
            A
          
        
        -
        
          E
          B
        
        -
        
          E
          C
        
        -
        
          2
          ⁢
          
            E
            X
          
        
        -
        
          E
          Y
        
        -
        
          E
          Z
        
      
      )
    
    8
  




where EA2BC-X2YZ is the total energy of the superlattice unit cell containing 8 atoms (two A, one B, one C, two X, one Y and one Z), and EA, EB, EC, EX, EY, and EZ stand for the energies when each of the A, B, C, X, Y and Z elements crystallize in pure metals, respectively. If the formation energy per atom is positive, the superlattice is unstable and cannot be formed in equilibrium conditions. A negative formation energy per atom suggests that such a superlattice film can be grown. However, a negative formation energy does not, for example, guarantee against formation of binary or ternary phases comprising any two or three of the available six elements.
Results and Discussion
For this study, sixteen Heusler superlattices were simulated for layering perpendicular to the [001] and [110] directions and eight were simulated for layering perpendicular to the [111] direction. The 16 superlattices for the layered Heuslers are composed of 14 distinct full Heuslers and 7 distinct half-Heusler alloys. The bulk properties of these Heusler alloys are listed in Table 1. Individual Heusler alloys which are already experimentally realized are noted with a t sign. The alloys that have citations but no t signs are those for which theoretical predictions are available in the art, but not experimental confirmation. Compounds without citations are alloys that were found to have a negative formation energy herein, but for which no other experimental or theoretical reports were available.
The 21 Heusler alloys listed in Table 1 have gaps in the minority spin channel density of electronic states at 3 electrons per atom. This gap is referred to herein as the Slater-Pauling gap because Slater and Pauling noted in the 1930s that certain bcc-based alloys tend to maintain approximately three electrons per atom in the minority spin-channel. Table 1 also gives the calculated width of this gap. For some of the alloys, the Fermi energy is in (or is calculated to be in) this gap, generating a half-metal (e.g., Co2MnSi, NiMnP) which are denoted by (HM) in the column of Table 1 that lists the width of the gap.
For three of the alloys listed in Table 1, namely Fe2TiSi, Fe2TiGe, and CoTiP, there is an average of 6 valence electrons per atom, such that it is possible to have a Slater-Pauling gap in both spin channels. The results of the calculations discussed herein indicated that these Heusler alloys have identical gaps in both channels. These alloys are denoted by (SC) adjacent to the gap width values in Table 1.
For CoTiSi, the Fermi energy is not in the gap, but is within 0.03 eV of falling in the gap. Herein, alloys whose Fermi energy falls outside the gap but within an energy distance from the gap of 0.05 eV are referred to as “near half-metals” and denoted by (NHM) in the column with the gap width values in Table 1. For five of the alloys in Table I, the Fermi energy falls outside of the gap and is further than 0.05 eV from the gap. Even though these alloys are not predicted to be half-metals or near half-metals as bulk alloys, they can be used in certain layered systems to make near half-metal or half-metal superlattices.
The column in Table 1 labeled “Distance from EF to gap” gives the distance (in eV) from the Fermi energy to the gap edge. Thus, for the half-metals, it gives the distance to the nearest band edge and the notation in parentheses indicates whether the nearest band edge is the conduction band (CB) or the valence band (VB). For some applications of half-metals, it can be desirable to have the Fermi energy as far from a band edge as possible. For the alloys that are not predicted to be half-metals, the number in the “Distance from EF to gap” column gives the energy difference between the Fermi energy and the closest band edge, and the notation in parentheses tells whether the Fermi energy falls below (VB) or above (CB) the gap. For some applications it might be desirable for this energy distance to be small, e.g. to make it easier to use alloying or electrochemical potentials to move the Fermi energy into the gap.







TABLE 1







Lattice constants, magnetic moments, formation energies, and calculated energy gaps of


14 full-Heusler and 7 half-Heusler alloys.
















Formation







Magnetic
energy

Distance




Lattice
moment
per
Gap
from EF




constant
per unit
atom
Width*
to gap



Heusler
a (A)
cell (μB)
(eV)
(eV)
(eV)
Curie temperature (K)
















Co2MnAl†
5.71
4.009
−0.349
0.477
0.149
950


(Sakuraba Y et al. Appl. Phys. Lett.




(VB)
(Kim K et al. Physica


2006, 88, 022503)





Status Solidi B. 2004, 241, 7)


Fe2MnAl†
5.67
2.002
−0.183
0.376
0.0886
400


(Ando Y et al Spintronics. ed Felser C and Fecher 




(VB)
(Vinesh A et al. J. Appl. Phys.


G H. Springer Netherlands, 2013, p. 355-366)





2009, 105, 07A309)


Fe2MnGa†
5.69
2.0145
−0.067
0.083
0.2374
750


(Kudryavtsev Y V et al. Acta Materialia 2012, 60, 




(VB)
(Gasi T et al. J. Appl. Phys.


12; Gasi T et al. J. Appl. Phys. 2013, 113, 17E301)





2013, 113, 17E301)


CO2MnSi†
5.63
5
−0.433
0.669
0.310
985


(Picozzi S et al. Phys. Rev. B. 2004, 69, 094423; 



(HM)
(VB)
(Sakuraba Y et al. Appl.


Kämmerer S et al. Appl. Phys. Lett. 2004, 85, 79)





Phys. Lett. 2006, 88, 192508)


Fe2MnSi
5.56
3
−0.332
0.405
0.067
215


(Mori H et al. Thin Solid Films. 2012, 520, 15; 




(VB)
(Brown P J et al. J. Magnetism


Hamad B and Hu Q. Physica Status Solidi (b).





and Magnetic Mater. 1985, 50, 2)


2011, 248, 12)








Co2FeSi†
5.66
5.4642
−0.349
0.040
0.628
1100 


(Kandpal H C et al. Phys. Rev. B. 2006, 73, 094422; 




(CB)
(Wurmehl S et al. Phys.


Inomata K et al. J. Phys. D: Appl. Phys. 2006, 39, 816)





Rev. B. 2005, 72, 184434)


Fe2TiSi†
5.69
0
−0.666
0.32
—
—


(Meinert M et al. Phys. Rev. B. 2014, 90, 085127)



(SC)




Co2VGa†
5.76
2
−0.277
0.14
0.025
369


(Han H et al. J. Phys. D: Appl. Phys. 2012, 111, 9; 



(HM)
(CB)
(Kübler J et al. Phys. Rev. B.


Kanomata T et al. Phys. Rev. B. 2010, 82, 144415)





2007, 76, 024414)


CO2VSn
6.07
3
−0.041
0.376
0.093
103


(Mahmoud N T et al. Intermetallics. 2013, 33, 0)



(HM)
(CB)
(Kübler J et al. Phys. Rev. B.








2007, 76, 024414)


Co2TiGe†
5.84
2
−0.470
0.425
0.0813
380


(Prathiba G et al. J. Magnetism and Magnetic



(HM)
(CB)
(Barth J et al. Phil. Trans. R.


Mater. 2011, 323, 1)





Soc. A. 2011, 369, 3588)


Fe2TiGe
5.78
0
−0.452
0.1
—
—


(Luo H et al. J. Magnetism and Magnetic Mater.



(SC)




2012, 324, 20)








Co2MnSb
6.02
6
−0.069
0.486
0.063
600


(Huang H M et al. Physica B: Condensed Matter.



(HM)
(CB)
(Manea A S et al. J. Crystal


2011, 406, 8)





Growth. 2005, 205, 1)


Co2CrSb
6.01
5
0.066
0.385
0.088
—


(Kanbur U and Gokoglu G. J. Magnetism and



(HM)
(CB)



Magnetic Mater. 2011, 323, 9)








CO2CrSi
5.66
4
−0.305
0.682
0.3336
747


(Rai D P et al. Bull. Mater. Sci. 2011, 34, 6)



(HM)
(VB)
(Chen X W et al. J. Appl.








Phys. 2006, 100, 113901)


CoMnP
5.34
3
−0.325
1.1
0.493
583


(Fujii S et al. J. Phys. F: Metal Phys. 1988, 18, 5)



(HM)
(CB)
(Fruchart R et al. J. Appl.








Phys. 1969, 40, 1250)


CoTiP
5.43
0
−0.988
1.37
—
—






(SC)




RhFeGe
5.77
3
-0.128
0.46
0.077
—






(HM)
(CB)



RuMnAs
5.76
2
−0.032
0.78
0.012
—


(Antonov V N et al. Phys. Rev. B. 1997, 56, 20)



(HM)
(VB)



NiMnSi
5.43
3
−0.139
0.87
0.325
715


(Galanakis I et al. J. Appl. Phys. 2008, 104, 083916)



(HM)
(VB)
(Dinh V A et al. J. Phys. Soc.








Jpn. 2008, 77, 014705)


NiMnP
5.46
4
−0.193
0.89
0.302
1050 


(Singh M et al. AIP Conf. Proceed.. 2011, 1393, 1)



(HM)
(CB)
(Dinh V A et al. J. Phys. Soc.








Jpn. 2008, 77, 014705)


CoTiSi
5.58
0.998
−0.561
1.16
0.0291
—


(Kawaharada Y et al. J. Alloys and Compounds.



(NHM)
(VB)



2004, 384, 1)





*In column “Gap Width”: NHM indicates a nearly half-metallic alloy with Fermi level within 0.05 eV of the bandgap. HM indicates a half-metallic superlattice with the Fermi level inside the band gap. SC indicates that the material is predicted to be a semiconductor with a Slater-Pauling gap in both spin-channels.






The results of calculations of the properties of certain layered Heusler alloys for layering in the [001], [110], and [111] directions are listed in Tables 2, 3, and 4, respectively. Generally, the Slater-Pauling gaps were found to be robust. The size of the gap in the multi-layer and its position relative to the Fermi energy varies with the direction of layering and with the thickness of the layers. In general, the results indicated the gap width for the layered Heusler will be between those of the individual Heuslers that comprise the layered Heusler system. Similarly, the results indicated that layering half-metals generally yields half-metallic multilayers.
One exception to these general trends is the layered system Co2TiGe—Fe2TiGe [001] n=0.5. The parent alloys are a Slater-Pauling half-metal (CO2TiGe) and a Slater-Pauling semiconductor (Fe2TiGe), respectively. The results of the calculations indicated the layered structure was a half-metal for [001] n=1.0 and n=1.5 layering, but not for n=0.5. This can be due to the nature of the semiconductor Fe2TiGe, which is predicted to be a non-magnetic semiconductor despite being 50% Fe. The energy reduction achieved by making a Slater-Pauling semiconductor can be sufficient to “kill” the magnetic moment of Fe. Other Heuslers which show this effect are Fe2VAl and Fe2TiSi. The results discussed herein suggest that it is more difficult, however, to kill the Fe moment when the Fe atoms have second neighbors that are Co, for example as occurs in Co2TiGe—Fe2TiGe [001] n=0.5, when the layers are extremely thin.
The results discussed herein indicate that layering of gapped Heuslers that are not half-metals or near-half-metals can, in some examples, move the Fermi energy closer to the gap or even into the gap. One example is a layered Heusler structure comprising Co2MnAl and Fe2MnAl. Both of the parent alloys have Slater-Pauling gaps, but the Fermi energy falls at least 0.88 eV below the gap edge for both parent alloys. However, all of the layered Co2MnAl—Fe2MnAl systems investigated herein had a Fermi energy closer to the gap edge than either of the parent alloys.
One strategy for moving the Fermi energy into the gap can be layering a Heusler that has its Fermi energy in the valence band with another Heusler that has its Fermi energy in the conduction band. An example of this is layering Co2MnAl with Co2FeSi. The latter has a tiny gap that is far from the Fermi energy in DFT calculations, although it can be made into a half-metal by application of a sufficiently large U in a LDA+U calculation (Balke B et al. Phys. Rev. B. 2006, 74, 104405). However, Co2MnAl—Co2FeSi can yield half-metals when layered in the [001], [110], or [111] directions.
Table 2 lists the geometric and magnetic properties of superlattice systems layered along the [001] direction for three different values of the constituent thicknesses as labeled by n. Since the x- and y-directions perpendicular to the layering direction, (z), are equivalent, these superlattices will have tetragonal symmetry after relaxation. For these systems, both the in-plane lattice constant, “a”, and a ratio labeled “c/a” that indicates the degree of tetragonal distortion of the lattice, are reported. The c/a number is actually C/(2na), where C is the length of the supercell in the [001] direction. A value of c/a of 1.0000 indicates no tetragonal distortion. For most of the systems herein, this distortion was small.
The magnetocrystalline anisotropy (K) is calculated by taking the difference between the energy when magnetization is aligned in the [001] direction and the lowest energy in-plane. The direction of the magnetization when the energy is the lowest in-plane is indicated in the magnetocrystalline anisotropy column (K) in Table 2.
The effective anisotropy field of a thin magnetic film, Heff (or, μ0Heff where go is the magnetic permeability constant), can be described by:




  
    
      μ
      0
    
    ⁢
    
      H
      eff
    
  
  =
  
    
      
        2
        ⁢
        K
      
      -
      
        M
        s
        2
      
    
    
      M
      s
    
  




where μ0 is the magnetic permeability constant, K is the magnetocrystalline anisotropy, and Ms is the saturation magnetization of the magnetic film due to magnetic dipole interactions. Accordingly, a thin magnetic film with no magnetocrystalline anisotropy (K=0) will have an effective anisotropy field of μ0Heff=−Ms. Even if K is greater than 0, μ0Heff can be negative. A negative value of μ0Heff indicates that the magnetic dipole interactions of the thin film are strong enough to pull the magnetic moment directions into the plane of the film. Conversely, a positive value of μ0Heff, for example as shown in Table 2, can indicate that the Heusler superlattice has enough perpendicular anisotropy to overcome the demagnetization field of a thin film.








TABLE 2







Lattice constants, c/a, magnetic moments and formation energies of various Heusler


superlattices layered in [001] direction for three different thicknesses, n.




















Magnetic









Lattice

moment

Formation


Distance




constant

per unit
K × 105
energy per
μ0Heff
Gap Width
from Ef to


Superlattice
n
a (Å)
c/a
cell (μB)
(J/m3)
atom (eV)
(N A−1m−1)
(eV)
gap (eV)





















Co2MnAl—Fe2MnAl
0.5
5.70
0.9993
6.000
 6.807 [110]
−0.263
1.50
0.30
(NHM)
0.015
(VB)


















1.0
5.68
1.0024
12.015
−0.687 [110]
−0.264
−0.99
0.37
0.072
(VB)



1.5
5.70
0.9973
18.039
 1.253 [110]
−0.266
−0.35
0.31
0.087
(VB)


















Co2MnAl—Co2FeSi
0.5
5.70
0.9921
10.000
−1.646 [100]
−0.405
−1.60
0.19
(HM)
0.019
(CB)



1.0
5.69
0.9935
20.000
 0.105 [110]
−0.392
−1.26
0.23
(HM)
0.067
(CB)


















1.5
5.73
0.9849
29.772
−2.765 [110]
−0.366
−1.82
0.01
0.165
(CB)


Co2MnAl—Fe2MnGa
0.5
5.72
0.9964
6.013
 7.175 [110]
−0.205
1.64
0.11
0.124
(VB)



0.5
5.72
1.0000
6.014
 7.365 [110]
−0.203
1.72
0.08
0.120
(VB)



1.0
5.70
1.0020
12.086
 1.275 [110]
−0.208
−0.34
0.10
0.169
(VB)



1.5
5.71
0.9966
18.164
 1.099 [110]
−0.210
−0.39
0.06
0.181
(VB)


Co2MnSi—Fe2MnSi
0.5
5.57
1.0056
8.013
−2.940 [110]
−0.379
−1.76
0.33
0.065
(VB)



















1.0
5.57
1.0053
16.001
−2.631 [100]
−0.379
−1.46
0.51
(HM)
0.095
(VB)



1.5
5.57
1.0077
24.000
−0.324 [110]
−0.380
−1.15
0.47
(HM)
0.108
(VB)

















Co2MnSi—Co2FeSi
0.5
5.60
1.0072
10.979
−2.134 [110]
−0.397
−1.82
0.14
0.388
(CB)



1.0
5.60
1.0033
21.598
−1.027 [110]
−0.394
−1.61
0.28
0.244
(CB)



1.5
5.61
1.0054
31.994
−1.009 [110]
−0.390
−1.59
0.08
0.429
(CB)


















Co2MnSi—Fe2TiSi
0.5
5.78
0.9688
5.000
−0.280 [100]
−0.543
−0.75
0.36
(HM)
0.152
(VB)



1.0
5.69
0.9915
10.000
 0.118 [110]
−0.550
−0.60
0.42
(HM)
0.172
(CB)



1.5
5.67
0.9968
15.000
−0.989 [100]
−0.557
−1.03
0.41
(HM)
0.194
(CB)


Co2VGa—Co2VSn
0.5
5.94
0.9875
5.000
 0.520 [110]
−0.211
−0.34
0.26
(HM)
0.028
(CB)



1.0
5.90
0.9963
9.999
 1.164 [100]
−0.180
−0.06
0.31
(HM)
0.072
(CB)



1.5
6.00
0.9688
15.000
 4.668 [100]
−0.157
1.47
0.23
(HM)
0.012
(CB)
















Co2TiGe—Fe2TiGe
0.5
5.72
1.0216
0.620
 0.643 [110]
−0.446
2.11
No gap
—



















1.0
5.86
0.9868
4.000
 3.421 [100]
−0.460
3.39
0.23
(HM)
0.057
(CB)



1.5
5.81
0.9725
5.996
 2.246 [100]
−0.430
1.99
0.14
(HM)
0.020
(CB)


Co2MnSb—Co2CrSb
0.5
6.04
0.9938
11.000
 0.721 [110]
−0.019
−1.02
0.43
(HM)
0.116
(CB)



1.0
6.02
0.9981
22.000
−0.109 [110]
−0.017
−1.20
0.43
(HM)
0.083
(CB)



1.5
6.02
0.9987
33.000
−0.032 [110]
−0.016
−1.18
0.43
(HM)
0.084
(CB)


Co2CrSi—Fe2MnAl
0.5
5.79
0.9637
6.000
−0.641 [110]
−0.298
−0.98
0.42
(HM)
0.112
(VB)



1.0
5.68
0.9912
12.000
−1.864 [110]
−0.268
−1.38
0.38
(HM)
0.076
(VB)



1.5
5.67
0.9956
18.000
−1.647 [100]
−0.261
−1.31
0.37
(HM)
0.063
(VB)


Co2CrSi—Fe2MnGa
0.5
5.82
0.9581
6.000
−2.199 [110]
−0.237
−1.49
0.33
(NHM)
0.018
(VB)



1.0
5.71
0.9879
12.000
−3.157 [110]
−0.210
−1.80
0.27
(NHM)
0.037
(VB)


















1.5
5.68
0.9937
18.012
−2.833 [100]
−0.203
−1.69
0.23
0.062
(VB)


















Co2CrSi—Fe2MnSi
0.5
5.69
0.9781
7.000
 0.074 [100]
−0.333
−0.90
0.48
(HM)
0.136
(VB)



1.0
5.69
0.9772
14.000
−0.427 [110]
−0.329
−1.04
0.48
(HM)
0.111
(VB)



1.5
5.67
0.9823
21.000
−0.097 [100]
−0.327
−0.95
0.45
(HM)
0.094
(VB)


CoMnP—CoTiP
0.5
5.39
1.0049
3.000
 3.106 [110]
−0.740
1.33
1.32
(HM)
0.594
(CB)



1.0
5.40
1.0012
6.000
−1.326 [110]
−0.754
−1.19
1.32
(HM)
0.595
(CB)



1.5
5.40
1.0025
9.000
−1.333 [110]
−0.761
−1.20
1.33
(HM)
0.604
(CB)

















RhFeGe—RuMnAs
0.5
5.79
1.0002
5.136
−2.281 [110]
−0.088
−1.55
0.18
0.173
(VB)



















1.0
5.78
1.0025
10.000
−2.537 [100]
−0.095
−1.66
0.48
(NHM)
0.016
(VB)



1.5
5.77
1.0041
14.998
−0.280 [100]
−0.096
−0.72
0.41
(HM)
0.023
(VB)


NiMnSi—NiMnP
0.5
5.47
0.9959
7.000
 0.303 [100]
−0.345
−0.93
0.84
(HM)
0.409
(VB)



1.0
5.47
0.9981
14.000
−0.369 [100]
−0.343
−1.09
0.82
(HM)
0.404
(CB)



1.5
5.46
1.0005
21.000
 0.496 [110]
−0.340
−0.88
0.77
(HM)
0.369
(CB)

















Co2MnSi—CoTiSi
0.5
5.63
0.9867
4.015
−7.817 [110]
−0.509
−4.19
0.04
0.136
(VB)

















0.5
5.63
1.0000
4.081
−1.692 [100]
−0.468
−1.33
No gap
—


















1.0
5.62
0.9897
8.067
−3.945 [110]
−0.537
−2.37
0.26
0.082
(VB)



1.5
5.61
0.9935
12.267
−1.366 [110]
−0.528
−1.17
0.17
0.135
(VB)









In Table 3, the analogous properties for layering along the [110] direction are presented. A [110] layered Heusler alloy can be represented by a supercell with 2 atomic layers. Thus for layering, n=0.5 would represent alternating layers A2BC-X2YZ.
For a [110]-layered superlattice with n=0.5, the [110] (in-plane) direction can be geometrically equivalent to the [110] (perpendicular) direction in certain cases, i.e. for A=X, or for B═Y and C═Z. Thus, for these cases, perpendicular magnetocrystalline anisotropy can only be obtained for layer thicknesses of n=1 or greater. As such, n=0.5 layering for [110] was not calculated herein for these cases.
For [110] layering, both c/a and c/b are reported. Both of these columns have been adjusted so that layering of two Heusler alloys with identical lattice constants and no distortions would yield c/a=c/b=1.0000. Thus, the reported c/a is actually c√{square root over (2)}/(na) and c/b is actually 2C/(nb), where C is the dimension of the superlattice in the direction of layering.
The results discussed herein indicate that the gaps are generally slightly larger for [110] layering than for [001] layering. Furthermore, when the Fermi energy falls outside the gap, the [110] layered systems tend to have the Fermi energy closer to the gap than the corresponding [001] layered systems.
Layering in the [110] direction offers the opportunity for magnetic anisotropy in the plane of the layers as well as for a difference between the energy between the in-plane and perpendicular directions. The direction for which the lowest energy was found is indicated in Table 3.







TABLE 3







Summary of the geometric and magnetic properties of various Heusler superlattices for


three different thicknesses n, layering in [110] direction.






















Magnetic

Formation







Lattice


moment

energy per


Distance




constant


per unit
K × 105
atom
μ0Heff
Gap Width
From Ef to


Superlattice
n
a (Å)
c/a
c/b
cell (μB)
(J/m3)
(eV)
(N A−1m−1)
(eV)
gap (eV)






















Co2MnAl—Fe2MnAl
1.0
5.71
0.9955
1.0012
12.001
 1.654 [001]
−0.262
−0.21
0.40
(NHM)
0.046
(VB)



1.5
5.71
0.9941
1.0013
18.000
 1.350 [001]
−0.258
−0.31
0.37
(NHM)
0.011
(VB)


Co2MnAl—Co2FeSi
1.0
5.66
1.0007
0.9989
20.000
−2.201 [110]
−0.398
−1.71
0.33
(HM)
0.153
(CB)



1.5
5.66
1.0007
0.9989
29.999
−3.029 [110]
−0.389
−1.87
0.22
(HM)
0.013
(CB)


















Co2MnAl—Fe2MnGa
0.5
5.73
0.9921
0.9916
6.004
−0.199 [110]
−0.191
−0.82
0.16
0.074
(VB)



1.0
5.73
0.9948
1.0013
12.057
 1.540 [001]
−0.204
−0.25
0.22
0.164
(VB)



1.5
5.73
0.9947
1.0013
18.045
 1.159 [001]
−0.201
−0.37
0.21
0.116
(VB)



















Co2MnSi—Fe2MnSi
1.0
5.57
1.0079
0.9990
16.000
−7.431 [110]
−0.385
−2.82
0.58
(HM)
0.066
(VB)



1.5
5.56
1.0117
0.9994
24.000
−4.901 [110]
−0.387
−2.22
0.59
(HM)
0.108
(VB)


















Co2MnSi—Co2FeSi
1.0
5.63
1.0009
1.0001
21.778
−0.497 [110]
−0.405
−1.50
0.34
0.204
(CB)



1.5
5.63
1.0005
1.0001
32.357
−0.092 [111]
−0.403
−1.42
0.24
0.299
(CB)



















Co2MnSi—Fe2TiSi
0.5
5.66
1.0056
0.9958
5.000
−1.193 [001]
−0.530
−1.11
0.36
(HM)
0.135
(VB)



1.0
5.64
1.0059
1.0026
10.000
−0.096 [110]
−0.543
−0.68
0.50
(HM)
0.194
(VB)



1.5
5.65
1.0038
1.0022
15.000
−0.289 [110]
−0.552
−0.76
0.47
(HM)
0.193
(VB)


Co2VGa—Co2VSn
1.0
5.89
0.9983
1.0020
10.000
 0.001 [001]
−0.210
−0.57
0.30
(HM)
0.041
(CB)



1.5
5.91
0.9963
1.0010
15.000
−0.285 [001]
−0.209
−0.63
0.28
(HM)
0.045
(CB)


Co2TiGe—Fe2TiGe
1.0
5.77
1.0107
0.9976
4.000
−0.909 [110]
−0.459
−1.20
0.26
(HM)
0.064
(VB)



1.5
5.79
1.0046
0.9974
6.000
 0.455 [110]
−0.460
0.24
0.24
(HM)
0.095
(CB)


Co2MnSb—Co2CrSb
1.0
6.02
0.9981
0.9997
21.998
 1.149 [001]
−0.019
−0.93
0.43
(HM)
0.092
(CB)



1.5
6.01
0.9998
0.9996
33.000
−0.308 [001]
−0.017
−1.24
0.43
(HM)
0.079
(CB)


Co2CrSi—Fe2MnAl
0.5
5.62
0.9979
1.0131
6.000
−0.857 [001]
−0.282
−1.05
0.48
(HM)
0.083
(VB)



1.0
5.68
0.9939
0.9884
11.999
−3.021 [001]
−0.275
−1.75
0.45
(HM)
0.054
(VB)



1.5
5.63
1.0048
0.9988
18.000
−1.254 [001]
−0.269
−1.18
0.41
(HM)
0.097
(VB)


Co2CrSi—Fe2MnGa
0.5
5.65
0.9930
1.0071
6.000
−1.852 [001]
−0.216
−0.77
0.31
(NHM)
0.048
(VB)



1.0
5.68
0.9892
0.9883
12.000
−3.615 [001]
−0.214
−1.95
0.32
(NHM)
0.035
(VB)



1.5
5.64
1.0036
0.9985
18.000
−1.800 [001]
−0.208
−1.36
0.26
(NHM)
0.015
(VB)


Co2CrSi—Fe2MnSi
0.5
5.55
1.0087
1.0209
7.000
−0.840 [001]
−0.330
−1.15
0.51
(HM)
0.134
(VB)



1.0
5.58
1.0059
0.9971
14.000
−1.653 [001]
−0.325
−1.37
0.56
(HM)
0.140
(VB)



1.5
5.54
1.0191
1.0016
21.000
−2.409 [001]
−0.326
−1.58
0.59
(HM)
0.140
(VB)


CoMnP—CoTiP
1.0
5.41
0.9997
0.9980
6.000
−0.188 [001]
−0.747
−0.55
1.35
(HM)
0.561
(CB)



1.5
5.41
0.9976
0.9985
9.000
 0.360 [001]
−0.720
−0.24
1.32
(HM)
0.624
(CB)


















RhFeGe—RuMnAs
0.5
5.76
1.0085
1.0054
5.069
−5.910 [110]
−0.093
−3.05
0.17
0.265
(VB)




















1.0
5.77
0.9999
0.9949
10.000
 3.820 [111]
−0.100
0.99
0.47
(NHM)
0.012
(VB)



1.5
5.78
1.0016
1.0011
15.001
−2.234 [110]
−0.099
−1.53
0.43
(NHM)
0.037
(VB)


NiMnSi—NiMnP
1.0
5.45
1.0024
0.9983
14.000
 0.409 [111]
−0.348
−0.90
0.83
(HM)
0.407
(CB)



1.5
5.45
1.0010
0.9980
21.000
 0.026 [001]
−0.232
−0.99
0.81
(HM)
0.380
(VB)


















Co2MnSi—CoTiSi
0.5
5.64
0.9846
0.9867
4.015
 7.817 [001]
−0.509
3.11
0.04
0.136
(VB)




















1.0
5.59
0.9921
0.9965
8.000
 2.699 [001]
−0.553
0.72
0.49
(HM)
0.125
(VB)



1.5
5.59
0.9968
0.9981
12.000
 2.418 [001]
−0.552
0.59
0.47
(HM)
0.083
(VB)









Table 4 presents results for layering along the [111] direction for eight Heusler pairs for the minimal 12 layer geometry required to represent the full-Heusler alloy geometry. For [111] layering, each atomic layer is a relatively sparsely populated hexagonal net containing only a single species. The column labeled “Lattice constant” gives the in-plane nearest neighbor distance a multiplied by √{square root over (2)}, which would correspond to the Heusler lattice constant for the pure Heusler system. The column labeled c/a lists the c-axis of the supercell divided by √{square root over (6)}a, where a is the in-plane nearest neighbor distance. This ratio would be 1.000 for the cubic Heusler lattice. A value in this column greater than unity indicates that the lattice is stretched in [111] direction relative to the in-plane direction.
Three types of stacking within this twelve layer supercell were investigated: 8-4, meaning 8 layers of Heusler 1 followed by 4 layers of Heusler 2; 4-8, meaning 4 layers of Heusler 1 followed by 8 layers of Heusler 2; and 6-6, meaning 6 layers of Heusler 1 followed by 6 layers of Heusler 2.







TABLE 4







Summary of the geometric and magnetic properties of various Heusler superlattice,


stacked in [111] direction. Heusler A2BC is followed by layers of Heusler X2YZ. For half-


Heuslers, O represents a vacant layer.




















Magnetic









Lattice

moment

Formation


Distance




constant

per unit
K × 105
Energy per
μ0Heff
Gap Width
from Ef to


Superlattice
Stacking order
a (Å)
c/a
cell (μB)
(J/m3)
atom (eV)
(N A−1m−1)
(eV)
gap (eV)





















Co2MnSi—Fe2MnSi
BACABACAYXZX
5.61
1.0035
13.000
−3.924 [112]
−0.404
−2.01
0.62
(HM)
0.084
(VB)



BACABAZXYXZX
5.61
1.0022
12.000
−5.770 [110]
−0.385
−2.43
0.62
(HM)
0.123
(VB)



YXZXYXZXBACA
5.60
1.0012
11.000
−5.091 [112]
−0.370
−2.29
0.60
(HM)
0.080
(VB)

















Co2MnAl—Fe2MnAl
BACABACAYXZX
5.69
1.0201
10.022
 1.602 [112]
−0.292
−0.36
0.45
0.085
(CB)



















BACABAZXYXZX
5.69
1.0183
9.000
 1.230 [110]
−0.262
−0.35
0.39
(NHM)
0.017
(CB) 


















YXZXYXZXBACA
5.68
1.0180
8.005
 1.011 [110]
−0.234
−0.30
0.42
0.055
(CB) 


















Co2MnAl—Co2FeSi
BACABACAYXZX
5.68
1.0155
14.000
−0.221 [110]
−0.390
−1.24
0.43
(HM)
0.068
(VB)



BACABAZXYXZX
5.66
1.0116
15.000
−1.011 [112]
−0.407
−1.48
0.42
(HM)
0.187
(CB)


















YXZXYXZXBACA
5.66
1.0123
15.880
−1.160 [110]
−0.390
−1.57
0.25
0.161
(VB) 



















YXZXYXCABACA
5.68
1.0165
15.000
−2.206 [110]
−0.382
−1.71
0.24
(HM)
0.086
(CB)

















Co2MnAl—Fe2MnGa
BACABACAYXZX
5.70
1.0218
10.060
 3.060 [110]
−0.255
0.07
0.35
0.148
(CB)



BACABAZXYXZX
5.71
1.0212
9.015
 1.800 [112]
−0.186
−0.15
0.20
0.145
(CB)



YXZXYXZXBACA
5.70
1.0213
8.076
 2.303 [112]
−0.160
0.18
0.21
0.188
(CB)



YXZXYXCABACA
5.70
1.0197
9.002
 1.244 [110]
−0.225
−0.34
0.31
0.075
(CB)


















Co2MnSi—Fe2TiSi
BACABACAYXZX
5.65
1.0002
10.000
−0.529 [110]
−0.504
−1.02
0.59
(HM)
0.244
(VB)



BACABAZXYXZX
5.64
0.9998
9.000
−1.361 [112]
−0.497
−1.22
0.59
(HM)
0.161
(VB)



YXZXYXZXBACA
5.67
1.0037
5.000
−2.456 [110]
−0.585
−1.87
0.48
(HM)
0.169
(VB)



YXZXYXCABACA
5.68
1.0057
6.000
−2.487 [112]
−0.594
−1.74
0.52
(HM)
0.124
(VB)


Co2MnSi—Co2FeSi
BACABACAYXZX
5.63
0.9994
15.998
−0.301 [112]
−0.418
−1.44
0.46
(NHM)
0.013
(VB)


















YXZXYXZX-BACA
5.63
0.9987
16.401
−0.206 [112]
−0.388
−1.46
0.24
0.357
(VB)


















CoMnP—CoTiP
BOCABOCAYOZX
5.39
0.9522
6.000
 3.784 [112]
−0.452
1.00
1.39
(HM)
0.693
(CB)



YOZXYOCABOCA
5.42
0.9578
3.000
 5.019 [110]
−0.624
4.01
1.39
(HM)
0.576
(CB)


Co2MnSi—CoTiSi
BACABACAYOZX
5.60
0.9999
9.000
 5.108 [112]
−0.506
0.81
0.73
(HM)
0.361
(CB)



YOZXYOZXBACA
5.57
0.9905
3.000
 5.457 [112]
−0.607
4.78
0.56
(HM)
0.023
(VB)









The magnetic anisotropy of a layered Heusler system (e.g., a Heusler superlattice) can stem from two factors: (1) the difference in the electronic system between the two Heuslers in the superlattice and (2) lattice distortion. Most of the Heusler superlattices discussed herein have a relatively small stretching or contraction in the stacking direction compared to the in-plane direction. Moreover, no strong or obvious correlation between the anisotropy and the lattice distortion was observed. These observations suggest that the induced magnetic anisotropy can be due to the difference in the electronic structure of the two Heusler constituents.
In order to test the hypothesis that the contrast in electronic structure can be more important for anisotropy than the changes in atomic positions, the electronic structure of two systems was recalculated for the ideal layered structure and compared the to the result for the relaxed layered structure. For Co2MnAl—Fe2MnGa, the effect of the distortion was small. The undistorted calculation is listed in Table 2 as the row with c/a=1.0000. On the other hand, for Co2MnSi—CoTiSi, the relaxation seemed to be important both for the anisotropy and for the existence of the gap.
As discussed above, for some superlattices, even though the system has perpendicular anisotropy, the perpendicular anisotropy field is not strong enough to overcome the demagnetization field of a thin film (e.g., Co2MnAl—Fe2MnAl with n=1.5 layering and [001] stacking, Co2MnAl—Fe2MnGa with n=1.0 or 1.5 layering and [110] stacking).
The calculated magnetic anisotropy for the sixteen [001]-layered Heusler alloys is shown in Table 2. For each system, the anisotropy was calculated for n=0.5, 1.0 and 1.5. Sixteen of these 48 systems were found to have perpendicular anisotropy. Of these 16 with perpendicular anisotropy, 7 were found to have sufficient perpendicular anisotropy to exceed the thin film demagnetization field.
Co2MnAl—Fe2MnAl with n=0.5 is predicted to be a near half-metal with perpendicular magnetic anisotropy; the density of states for this layered system is shown in FIG. 5A. Co2TiGe—Fe2TiGe with n=1.0 is predicted to be a half-metal with perpendicular magnetic anisotropy; the density of states for this layered system is shown in FIG. 5B. CoMnP—CoTiP with n=0.5 is a layered combination of half-Heuslers that combines a relatively strong perpendicular anisotropy with wide band-gap half-metallicity. Interestingly, both Fe2TiGe and CoTiP are Slater-Pauling semiconductors.
For [110] layering, the same 16 Heusler combinations as for [001] layering were investigated. For some of the n=0.5 thickness systems with [110] layering, the [110] direction is equivalent to the [110] direction. These systems cannot have perpendicular anisotropy in the [110] direction. This consideration reduces the number of systems to 39 compared to 48 for the [001] direction. Thirteen of the 39 [110] systems were found to have perpendicular magnetocrystalline anisotropy. Of the 13 with perpendicular magnetocrystalline anisotropy, 5 had sufficient perpendicular magnetic anisotropy to be perpendicular as a thin film. Of these 5 predicted to be perpendicular as a thin film, 3 were also half metals. The full-Heusler-half-Heusler combination, Co2MnSi—CoTiSi with n=1 is predicted to have perpendicular magnetic anisotropy and to be a half-metal with a relatively large band gap. The density of states for this superlattice is shown in FIG. 6A.
For [111] layering we investigated 8 pairs of Heuslers. Even for a minimal 12 atomic layer supercell (9 atomic layers if both are half-Heuslers) there are several ways the layers can be arranged while still maintaining the local Heusler environment. In all we investigated 24 [111] layered systems. Of these 24, 11 were calculated to have perpendicular magnetic anisotropy and of the 11 with perpendicular magnetic anisotropy we calculated that 6 would be perpendicular as thin films. The sign of the magnetocrystalline anisotropy was consistent for all of the [111] layer schemes that we tried for a given pair of Heuslers. The [111] layered half-Heusler system CoMnP—CoTiP is predicted to be half metallic as well as perpendicular with a large band gap. The density of states for this superlattice is shown in FIG. 6B.
For some applications of half-metals, it can be desirable to have the Fermi energy fall near the center of the gap of the gapped spin-channel. Many of the half-metallic Heusler superlattices with perpendicular anisotropy investigated herein have a Fermi level close to the valence band edge (e.g., [001] direction stacked, n=0.5 superlattice of Co2MnAl—Fe2MnAl). The position of the Fermi level and the gap width can be engineered by doping the superlattice with atoms with a higher or lower count of valence electrons (Balke B et al. Phys. Rev. B. 2006, 74, 104405; Miura Y et al. Phys. Rev. B. 2004, 69, 144413; Antonov V N et al. Phys. Rev. B. 2005, 72, 054441).
In order to move the Fermi level away from the valence band edge toward the band gap in the [001] direction stacked n=0.5 superlattice of Co2MnAl—Fe2MnAl, the alloy was doped with Si atoms at the Al atom sites or with Cr atoms at the Mn sites to add electrons and thereby move the Fermi energy up relative to the gap. FIG. 7A shows the density of states of the [001] direction stacked superlattice of Co2MnAl—Fe2MnAl with Si doping. For cases (i) and (ii), the Al and Si atoms were not mixed in a (001) plane. For case (i) one in every four Mn—Al atomic planes were replaced with Mn—Si planes ( . . . —Co2—MnAl—Fe2—MnAl—Co2—MnAl—Fe2—MnSi— . . . ). In case (ii), two of the Mn—Al planes were replaced with Mn—Si ( . . . —Co2—MnAl—Fe2—MnAl—Co2—MnAl—Fe2—MnSi— . . . ). For cases (iii) and (iv), both Al and Si atoms can be in a (001) plane.
For Co2MnAl—Fe2MnAl, the Fermi Level is 0.015 eV inside the valence band. In all cases of doping, addition of Si atoms shifted the Fermi level into the band gap. When 50% of the Al atoms were replaced with Si atoms (cases (ii) and (iv)), the Fermi level moved 0.05 eV into the band gap relative to the valence band edge. For 25% doping, the Fermi level moved 0.03 eV into the band gap. The improvement in half-metallicity came at the cost of the perpendicular anisotropy. For 25% Si doping at the Al sites, the anisotropy dropped from 6.08×105 J/m3 to 5.02×105 J/m3 and 4.8×105 J/m3 for cases (i) and (iii), respectively. For 40% Si doping, the anisotropy dropped to 2.16×105 J/m3 and 1.08×105 J/m3 for cases (ii) and (iv), respectively.
FIG. 7B shows the effect of Fe or Cr doping at the Mn atom sites. Addition of Fe atoms moved the Fermi level 0.043 eV into the valence band. Addition of Cr atoms placed the Fermi level in the middle of the band gap. However, the bandgap was reduced to 0.1 eV and the anisotropy dropped to 1.47×105 J/m3.
One drawback of half-metallic Heusler alloys for application as ferromagnetic layers in certain spintronic devices is that they do not have uniaxial magnetocrystalline anisotropy. To address these and other issues, layered Heusler alloys were investigated by studying superlattices stacked in the [001], [110], or [111] directions for different thickness. The results indicate that two Heusler alloys stacked in the [001], [110], or [111] directions for various thicknesses to form a superlattice, can still satisfy the Slater-Pauling rule and the resulting superlattice can be half-metallic with gaps comparable to or larger than those of its constituents. The Slater-Pauling gaps characteristics of many L21 (full) and C1b (half) Heusler alloys were found to be robust in the presence of layering in the [001], [110], or [111] directions. This was found for L21-L21, L21-C1b, and C1b-C1b combinations. The results discussed herein also predicted that it is possible to achieve uniaxial anisotropy by layering two Heusler alloys and that said uniaxial magnetocrystalline anisotropy can be due to the differences in the electronic structure of the two Heuslers in the superlattice.
Other advantages which are obvious and which are inherent to the invention will be evident to one skilled in the art. It will be understood that certain features and sub-combinations are of utility and may be employed without reference to other features and sub-combinations. This is contemplated by and is within the scope of the claims. Since many possible examples may be made of the invention without departing from the scope thereof, it is to be understood that all matter herein set forth or shown in the accompanying drawings is to be interpreted as illustrative and not in a limiting sense.

## Claims

1. A layered Heusler alloy, comprising:
a first layer comprising a first Heusler alloy with a face-centered cubic (fcc) crystal structure;
a second layer comprising a second Heusler alloy with a fcc crystal structure, the second Heusler alloy being different than the first Heusler alloy;
wherein the first layer and the second layer are layered along a layering direction, the layering direction being the [110] or [111] direction of the fcc crystal structure, thereby forming the layered Heusler alloy;
wherein the layered Heusler alloy has a magnetocrystalline anisotropy of greater than 0 J/m3 along a direction perpendicular to the layering direction, and
wherein the layered Heusler alloy has a Fermi level and a gapped spin-channel with a gap, and wherein the Fermi level of the layered Heusler alloy falls within the gap of the gapped spin-channel of the layered Heusler alloy.

2. The layered Heusler alloy of claim 1, wherein:
the layered Heusler alloy is layered along the [110] direction;
the first Heusler alloy has a formula ABC, wherein:
p is 1 or 2;
A and B are each a transition metal, with the proviso that A and B are not the same transition metal; and
C is an element from Group 13, 14, or 15;

the first layer comprises a first number of sublayers;
the second Heusler alloy has a formula XqYZ, wherein:
q is 1 or 2;
X and Y are each a transition metal, with the proviso that X and Y are not the same transition metal; and
Z is an element from Group 13, 14, or 15;

the second layer comprises a second number of sublayers; and
the first number of sublayers is the same as the second number of sublayers, such that the layered Heusler alloy has a unit cell comprising (ApBC)a(XqYZ)a, wherein a is the first number of sublayers and a is an integer from 1 to 1000.

3. The layered Heusler alloy of claim 2, wherein:
A and B are selected from the group consisting of: scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, rhodium, and palladium; and
X and Y are selected from the group consisting of: scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, rhodium, and palladium.

4. The layered Heusler alloy of claim 2, wherein:
A and B are selected from the group consisting of: titanium, vanadium, chromium, manganese, iron, cobalt, nickel, rhodium, and palladium; and
X and Y are selected from the group consisting of: titanium, vanadium, chromium, manganese, iron, cobalt, nickel, rhodium, and palladium.

5. The layered Heusler alloy of claim 2, wherein C and Z are independently selected from the group consisting of: boron, aluminum, gallium, indium, thallium, carbon, silicon, germanium, tin, lead, nitrogen, phosphorous, arsenic, antimony, and bismuth.

6. The layered Heusler alloy of claim 2, wherein C and Z are independently selected from the group consisting of: aluminum, gallium, silicon, germanium, tin, phosphorous, arsenic, and antimony.

7. The layered Heusler alloy of claim 1, wherein
the layered Heusler alloy is layered along the [111] direction;
the first Heusler alloy has a formula ApBC, wherein:
p is 1 or 2;
A and B are each a transition metal, with the proviso that A and B are not the same transition metal; and
C is an element from Group 13, 14, or 15;

the first layer comprises a first number of sublayers, the first number of sublayers being 4, 6, or 8;
the second Heusler alloy has a formula XqYZ, wherein:
q is 1 or 2;
X and Y are each a transition metal, with the proviso that X and Y are not the same transition metal; and
Z is an element from Group 13, 14, or 15;

the second layer comprises a second number of sublayers, the second number of sublayers being 4, 6, or 8; and
the sum of the first number of sublayers and second number of sublayers is 12, such that:
when the first number of sublayers is 4, the layered Heusler alloy has a unit cell comprising (ApBC)(XqYZ)2, wherein p and q are independently 1 or 2;

when the first number of sublayers is 8, the layered Heusler alloy has a unit cell comprising (ApBC)2(XqYZ), wherein p and q are independently 1 or 2; and
when the first number of sublayers is 6, the layered Heusler alloy has a unit cell comprising (ApBC)(Ap-1XBZ)(XqYZ), wherein p and q are independently 1 or 2.

8. The layered Heusler alloy of claim 7, wherein:
A and B are selected from the group consisting of: scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, rhodium, and palladium; and
X and Y are selected from the group consisting of: scandium, titanium, vanadium, chromium, manganese, iron, cobalt, nickel, yttrium, zirconium, niobium, molybdenum, technetium, ruthenium, rhodium, and palladium.

9. The layered Heusler alloy of claim 7, wherein:
A and B are selected from the group consisting of: titanium, vanadium, chromium, manganese, iron, cobalt, nickel, rhodium, and palladium; and
X and Y are selected from the group consisting of: titanium, vanadium, chromium, manganese, iron, cobalt, nickel, rhodium, and palladium.

10. The layered Heusler alloy of claim 7, wherein C and Z are independently selected from the group consisting of: boron, aluminum, gallium, indium, thallium, carbon, silicon, germanium, tin, lead, nitrogen, phosphorous, arsenic, antimony, and bismuth.

11. The layered Heusler alloy of claim 7, wherein C and Z are independently selected from the group consisting of: aluminum, gallium, silicon, germanium, tin, phosphorous, arsenic, and antimony.

12. The layered Heusler alloy of claim 1, wherein the first Heusler alloy and the second Heusler alloy are selected from the group consisting of Co2CrSi, Co2CrSb, Co2FeSi, Co2MnAl, Co2MnSi, Co2MnSb, CO2TiGe, Co2VGa, Co2VSn, Fe2MnAl, Fe2MnGa, Fe2MnSi, Fe2TiGe, Fe2TiSi, CoMnP, CoTiP, RhFeGe, RuMnAs, NiMnP, NiMnSi, NiMnAs, NiMnSb, NiVSb, CoMnSb, and CoTiSi.

13. The layered Heusler alloy of claim 1, wherein the first Heusler alloy comprises a half metal or a near half metal.

14. The layered Heusler alloy of claim 1, wherein the second Heusler alloy comprises a half metal or a near half metal.

15. The layered Heusler alloy of claim 1, wherein the layered Heusler alloy comprises a half metal or a near half metal.

16. The layered Heusler alloy of claim 1, wherein the magnetocrystalline anisotropy of the layered Heusler alloy along a direction perpendicular to the layering direction is from greater than 0 J/m3 to 106 J/m3.

17. The layered Heusler alloy of claim 1, wherein the μ0Heff of the layered Heusler alloy is from −10 to 1010 N A−1 m−1.

18. The layered Heusler alloy of claim 1, wherein the layered Heusler alloy has a μ0Heff of greater than 0 N A−1 m−1.

19. The layered Heusler alloy of claim 1, wherein the layered Heusler alloy further comprises:
a third layer comprising a third Heusler alloy with a fcc crystal structure, the third Heusler alloy being different than the first Heusler alloy, the second Heusler alloy, or combinations thereof; and
the first layer, the second layer, and the third layer are layered along the layering direction.