Perpendicular magnetic anisotropy (PMA) in magnetic thin films has become a key driving force in the development of magnetic random-access memory (MRAM) devices and other information storage devices. Establishing of PMA in nanostructures and nanopatterned magnetic multilayers paves a new avenue of nano-magnetism, in which fascinating physics such as spin Hall switching and skyrmions are blooming.
Strong PMA enables a reduction in the size of magnetic logical domains, which facilitates increasingly high storage density in data storage devices. Logical bits in the atomic scale, considered as an ideal limit of the magnetic domain size, have also been raised as huge uniaxial magnetic anisotropy was found recently when single magnetic adatoms deposited on MgO (001). But magnetic anisotropy of about 100 meV, as is currently considered a maximum limit on a single atom, is still unable to approach the stability of written information against the thermal fluctuations which has the energy scale of 45KBT, about 1.2 eV when temperature T is chosen as 300 K for a 10-year retention.
The described embodiments of the invention are directed to the design and production of magnetic thin films with giant PMA, which is required for next generation data storage devices, for example spin transfer torque-MRAM. As used herein, the term “giant PMA” is used to describe a PMA that is more than one order of magnitude larger than the PMA associated with a Fe/MgO substrate.
As set forth in the described embodiments, such giant PMA may be achieved by growing Fe ultrathin films on top of nitrogen terminated (N-terminated) surface, i.e., a surface terminated by a thin layer of nitrogen. In the example embodiments described herein, the N-terminated surface may be grown upon a wurtzite GaN (000
In one aspect, the invention is a giant perpendicular magnetic anisotropy (PMA) material, comprising a III-V nitride substrate, and a layer of nitrogen disposed upon a surface of the III-V nitride substrate. The layer of nitrogen may form an N-terminated surface. The PMA material further comprises an iron film disposed upon the N-terminated surface.
The III-V nitride may be gallium nitride (GaN). The layer of nitrogen may be a monolayer of nitrogen atoms. The iron film may be less than or equal to three monolayers of iron atoms.
In another aspect, the invention is method of fabricating a giant PMA material, comprising exposing a surface of a III-V nitride substrate to one of (i) an atmosphere of nitrogen and (ii) an atmosphere of NH3, to form an N-terminated surface, and disposing an iron film upon the N-terminated surface.
In another aspect, the invention is a memory device comprising a memory element, an input/output interface, and a controller. The memory element may comprise a III-V nitride substrate, and a layer of nitrogen disposed upon a surface of the III-V nitride substrate. The layer of nitrogen may form an N-terminated surface. The memory element may further comprise an iron film disposed upon the N-terminated surface. The input/output interface may be configured to communicate an address signal, a read/write signal and a data signal. The controller may be configured to coordinate reading data from and writing data to the memory element.
In one aspect, the invention may be a giant perpendicular magnetic anisotropy (PMA) material, comprising a III-V nitride substrate, and a layer of nitrogen disposed upon a surface of the III-V nitride substrate. The layer of nitrogen forming a nitrogen terminated (N-terminated) surface. The PMA material may further comprise an iron film disposed upon the N-terminated surface. The III-V nitride may be gallium nitride (GaN). The layer of nitrogen may be a wurtzite GaN (000
In another aspect, the invention may be a method of fabricating a giant PMA material, comprising exposing a surface of a III-V nitride substrate to an atmosphere configured to provide a source of nitrogen, to dispose a layer of nitrogen on the surface of the III-V nitride substrate. The layer of nitrogen may form an N-terminated surface. The method may further comprise disposing an iron film upon the N-terminated surface. The atmosphere may be configured to provide a source of nitrogen comprises an atmosphere of nitrogen.
The atmosphere may be configured to provide a source of nitrogen comprises an atmosphere of excessive NH3. The method may further comprise sample annealing the III-V nitride substrate in the atmosphere of excessive NH3. The method may further comprise heating III-V nitride substrate to a temperature substantially equal to 1000° C., while exposing the III-V nitride substrate to a nitrogen plasma. The method may further comprise reducing the III-V nitride substrate to a temperature substantially equal to 685° C., thereby initiating growth of the N-terminated surface.
In another aspect, the invention may be a memory device, comprising a memory element. The memory element may comprise a III-V nitride substrate, a layer of nitrogen disposed upon a surface of the III-V nitride substrate. The layer of nitrogen may form an N-terminated surface. The memory element may further comprise an iron film disposed upon the N-terminated surface, an input/output interface configured to communicate an address signal, a read/write signal and a data signal. The memory element may further comprise a controller configured to coordinate reading data from and writing data to the memory element.
The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments.
A description of example embodiments follows.
PMA is originated from the spin-orbit coupling (SOC), where the orbital angular momentum L is coupled with the spin momentum S according to the spin-orbit Hamiltonian HSO=λL·S. The strength of the PMA is exactly the energy correction from the SOC perturbation. As all five d-orbitals, xy, yz, xz, x2-y2, and 3z2-r2, in the ligand field theory have zero Lz due to the time reversal symmetry, the first order perturbation of SOC vanishes if these orbitals are nondegenerate. The dominant contribution thus comes from the second order perturbation, which is the scenario in most thin film systems. The energy scale of PMA is thus λ2/Δ with Δ designating the band width of states crossing the Fermi level. For a typical 3d magnetic element, λ˜0.03 eV and Δ˜1 eV, PMA is only on the scale of 1 meV, which is consistent with numerous experimental and theoretical studies on well-known PMA systems such as a Fe(Co)/MgO-based system and a CoFeB/MgO-based system.
A regime where the first order perturbation of SOC is dominant would escalate the PMA, such that the PMA will be proportional to λ instead. Such a regime may occur for partially filled degenerate orbitals around the Fermi surface. This scenario is known to take place when single adatoms or dimers are deposited on particular substrates. However, once a thin film is formed, PMA in these systems are greatly reduced.
As set forth in the example embodiments herein, giant PMA approaching the atomic limit may occur in Fe ultrathin films grown on top of wurtzite GaN (000
The above-described calculations were carried out in the framework of the non-collinear spin-polarized first-principles calculations with the projector augmented wave (PAW) pseudopotential implemented in the Vienna ab initio simulation package (VASP). Employed were the generalized gradient approximation (GGA) of Perdew, Burke-Ernzerhof (PBE) formation plus Hubbard U (GGA+U) with U=4.0 eV for Fe(3d) orbitals.
To build the slab supercell, four Ga—N principal layers are used as the substrate, and one to three Fe monolayers (MLs) are deposited on the N-terminated (000
Charge density of the SOC-free ground state was used as the initial state. Self-consistent total energy calculations were employed to derive the non-collinear calculation with SOC included. Γ-centered 25×25×1 K-point meshes in the two-dimensional Brillouin zone were used with an energy cutoff of 600 eV for the plane-wave expansion. The accuracy of the total energy is thus guaranteed to be better than 0.1 meV per unit cell (u.c.).
As a central result of this work, energies of different magnetization orientations of 1 ML Fe on GaN were obtained. Spin moment, mainly attributed to the Fe(3d) electrons, is 3.84 μB from self-consistent calculations. The relative total energy as a function of sin2 θ is shown in
TABLE I shows Bader charges on Fe and the top N atom. ‘Bulk’ refers to the bulk Fe and GaN, respectively. ‘Surface’ refers to the clean GaN (000
The giant PMA in Fe/GaN of the described embodiments cannot be explained by the second order perturbation of SOC. To explain the origin of this giant PMA, an analysis of the electronic structures of Fe(3d) orbitals are presented below.
The ionic behaviors of Fe are double confirmed by the Bader charge results (see TABLE I), of which the difference corresponds to the charge increasing/decreasing on one atom. About 0.4 e− electrons per Fe atom are transferred to N atoms on the interface. TABLE I shows Bader charges on Fe and the top N atom. ‘Bulk’ refers to the bulk Fe and GaN, respectively. ‘Surface’ refers to the clean GaN (000
To explain the charge transfer from xz/yz to x2-y2/xy orbitals and thereby identify valence states of Fe cations, results of an investigation into the crystal field and orbital-resolved projected density-of-state (PDOS) of Fe(3d) without SOC first is presented. As shown in
Once SOC is included, one can expect the lift of degeneracy between x2-y2 and xy. It is confirmed by the PDOS shown in
√{square root over (α)}(i|xy+|x2−y2)+√{square root over (β)}(i|xz−|yz)
or, equivalently,
√{square root over (2α)}|Y22+√{square root over (2β)}|Y21
where α=0.458 and β=0.042. This nearly fully filled state is one branch of the original degenerate e states without SOC and predominated by Y22. The other e state predominated by Y2−2 is hybrid with e′ states and the occupation numbers for those three states are 0.042, 0.033 and 0.032 respectively, that is, almost empty. The 3z2-r2 or Y20-dominated state, which is insensitive to SOC, has the occupation number of 0.293. Therefore, the net orbital magnetic moment on Fe(3d) along z direction is 1.54 μB, consistent with Lz=2 due to the splitting into Y22 and Y2−2 in e states near the Fermi level. This result is demonstrated by
Large band splitting and the partial occupation in consequence are the precursor of large PMA according to the discussions above. However, one should note that the SOC of Fe(3d) is no larger than 20 meV, two orders of magnitudes smaller than the band width (˜2.0 eV) of x2-y2/xy orbitals [see trace 210 of
The energy contribution from Hubbard U can be given by the single-particle expression under the Dudarev formation of L(S)DA+U; Vmσ=(U−J)(1/2−nmσ), where U−J=4.0 eV is the U value chosen for our first-principles calculations and nmσ denotes the occupation number of orbital m in spin channel σ. The result is 1.62 eV for the Y22-dominated state with occupation number 0.904, and 1.98 eV for three empty states, leading to a total splitting is 3.6 eV, consistent with the splitting in PDOS [see
To further confirm this conclusion, we performed the SOC-included self-consistent calculations with multiple values of Hubbard U. As shown in the top portion 302 of
Finally, we further investigated the thickness dependence of PMA in this system. Slab supercells with 2 ML and 3 ML Fe cations on top of GaN were built following the hexagonal closed packing along wurtzite GaN (000
As a sided discovery, we found that in Fe(1 ML)/GaN thin film, the nearest neighbor Heisenberg exchange between Fe is in the plane and antiferromagnetic with a weak exchange coupling of J=0.8 meV. It might lead to spin frustration in this 2D hexagonal lattice. For Fe(2 ML)/GaN or Fe(3 ML)/GaN, however, the nearest neighbors of Fe are the interlayer instead, since the Fe—Fe distances between first-second, second-third and first-third layers are 2.444 Å, 2.385 Å, and 3.130 Å, respectively. All of them are smaller than intra-layer Fe—Fe distance of 3.183 Å. In the Fe(3 ML)/GaN thin film, the exchange couplings are −75 meV, −11 meV and −32 meV for first-second, second-third and first-third interlayer couplings, respectively, all ferromagnetic. The corresponding intra-layer exchanges are 14 meV, 13 meV and 2 meV for the first, second and top layers, respectively. Therefore, since the ferromagnetic coupling is much stronger than antiferromagnetic coupling, ferromagnetic films with giant PMA are identified.
In summary, based on non-collinear spin-polarized first-principles calculations, we discovered giant PMA in Fe/GaN thin films. For Fe(1 ML)/GaN film, we obtained a PMA of 32 meV/u.c. (50.5 erg/cm2), which approaches the limit of the energy of SOC for an isolated Fe. Electronic structure calculations and ligand field analysis show that each Fe cation has a net orbital angular momentum Lz=2. It is originated from the SOC driven splitting of the degeneracy between x2-y2 and /xy orbitals. The on-site correlation interaction amplifies the splitting so that PMA is linearly proportional to the SOC. Thickness dependence shows that PMA is still large for multiple Fe layers deposited on GaN. Experimental results suggest that a Fe(1 ML)/GaN tiny square unit with only 2.0 nm in length has a total uniaxial magnetic anisotropy energy about 1.2 eV, reaching the criteria for 10-year data retention at room temperature. Therefore, giant PMA in this thin film can ultimately lead to nanomagnetism and promote revolutionary ultra-high storage density in the future.
Although the example embodiments described herein are directed to forming an N-terminated surface on a GaN substrate, it should be understood that other III-V nitride substrates may also be used. For example, Fe/InN has been shown to exhibit a PMA of 30.8 meV, and Fe/AlN has shown to exhibit a PMA of 60.1 meV.
The N-terminated surfaces associated with giant PMA materials of the described embodiments may be fabricated by growing, or otherwise procuring, a GaN substrate (or other III-V nitride), and exposing the GaN substrate under a nitrogen atmosphere. In one example embodiment, the substrate may be heated to about 1000° C. while exposed to a nitrogen plasma. After about 30 minutes under the nitrogen plasma, the temperature of the substrate may be reduced to about 685° C., initiating growth of the N-terminated surface. It should be understood that this example embodiment is not intended to be limiting, that other specific techniques known in the art may be employed for growth of the N-terminated surface described herein, and that the underlying requirement is the exposure of the substrate to a nitrogen atmosphere. In other embodiments, the N-terminated surface may be fabricated by exposing the nitride substrate to a NH3 atmosphere, for example by sample annealing the substrate in a NH3 atmosphere.
The exposure of the substrate to the nitrogen atmosphere may cause a monolayer of nitrogen atoms to form as the top surface of the GaN substrate. The monolayer of nitrogen atoms constitutes the N-terminated surface.
The giant PMA materials according to the described embodiments may be used the underlying storage mechanism for data storage devices such as MRAM and hard disk memory devices. For examples of such storage devices, see “The emergence of spin electronics in data storage,” C. Chappert, A. Fert, and F. N. Van Dau, Nat. Mater. 6, 813 (2007); “Current-induced torques in magnetic materials,” A. Brataas, A. D. Kent, and H. Ohno, Nat. Mater. 11, 372 (2012); and “Perpendicular magnetic anisotropy at transition metal/oxide interfaces and applications,” B. Dieny and M. Chshiev, Rev. Mod. Phys. 89, 025008, (2017).
While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims.
This application claims the benefit of U.S. Provisional Application No. 62/589,399, filed on Nov. 21, 2017. The entire teachings of the above application are incorporated herein by reference.
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