Antiferromagnetic material with large anomalous hall effect

Abstract

This antiferromagnetic material has a hexagonal crystal structure (space group P63 / mmc) and has a composition of (Mn1-xAx)3Sn (0<x<0.15, A=Ti, V, Cr, Zr, Nb, Mo, Tc, Hf, Ta, W, Re) or Mn3Sn1-yBy (0<y<0.35, B=Sc, Ti, V, Ga, Y, Zr, Nb, In, Hf, Tl). A is preferably at least one of V and Cr. Also, B is preferably at least one of Ga, In, and Tl.

Description

Antiferromagnetic Material with Large Anomalous Hall Effect

[0001] This disclosure relates to antiferromagnetic materials with giant anomalous Hall conductivity. This application claims priority based on U.S. Provisional Patent Application 63 / 609,965 filed in the United States on December 14, 2023, the content of which is incorporated herein by reference.

[0002] Antiferromagnets are known to have advantages in magnetic device applications such as magnetic memories and HDDs, such as having a fast response to external magnetic fields and spin currents compared to ferromagnets, and being easy to highly integrate because there is no magnetization and no leakage magnetic field. Applications to devices have been studied (see, for example, H. Tsai, et al., “Electrical manipulation of a topological antiferromagnetic state,” Nature, 580, 608 (2020)). In hexagonal Mn3X (X = Sn, Ge, Ga), it has a non-collinear antiferromagnetic state and almost no magnetization, while the spins are polarized in cluster magnetic octupoles. Therefore, by applying a magnetic field or flowing a spin current, it is possible to rapidly rotate and control the net spin polarization defined by the magnetic octupoles, and it is also possible to indirectly observe the direction of the spin polarization through the anomalous Hall conductivity.

[0003] According to one aspect of this disclosure, the antiferromagnetic material consists of (Mn 1-x A x )3Sn (0 < x < 0.15, A = Ti, V, Cr, Zr, Nb, Mo, Tc, Hf, Ta, W, Re), or Mn3Sn 1-y B y (0 < y < 0.35, B = Sc, Ti, V, Ga, Y, Zr, Nb, In, Hf, Tl) and has a hexagonal crystal structure (space group P63 / mmc).

[0004] A more complete understanding of the present disclosure and many of the attendant advantages thereof will be readily obtained by reference to the following detailed description when considered in conjunction with the accompanying drawings, in which: Figure 1 is a conceptual diagram illustrating the atomic and magnetization arrangements of a Mn3Sn-type magnetic material; Fig. 2(a) shows the energy dependence of AHC at the Fermi surface when the magnetization configuration in Fig. 1 is partially substituted with Cr at T = 50 K. Fig. 2(b) shows the substitution dependence of AHC at the Fermi surface when the magnetization configuration in Fig. 1 is partially substituted with Cr at T = 50 K. Fig. 2(c) shows the energy dependence of AHC at the Fermi surface when the magnetization configuration in Fig. 1 is partially substituted with In at T = 50 K. Fig. 2(d) shows the substitution dependence of AHC at the Fermi surface when the magnetization configuration in Fig. 1 is partially substituted with In at T = 50 K.

[0005] As used herein, terms such as "a" and "an" mean "one or more." When an amount, concentration, or other value or parameter is expressed as a range, and / or the description includes a list of upper and lower limits, this is understood to specifically disclose all integers and fractions within the stated range, as well as all ranges formed from any pair of any upper and lower limits, whether or not subranges are individually disclosed. When a range of numerical values ​​is recited herein, unless otherwise specified, the range is intended to include all integers and fractions within the range, as well as its endpoints. As an example, the range of 1 to 10 fully describes and includes the independent subranges 3.4 to 7.2, as well as the listing of the values ​​1, 4, 6, and 10.

[0006] In the embodiment of the present disclosure, the antiferromagnetic material Mn3Sn having a hexagonal crystal structure (space group P63 / mmc) does not undergo element substitution (Mn 1-x A x)3Sn (0 < x < 0.15, A = Ti, V, Cr, Zr, Nb, Mo, Tc, Hf, Ta, W, Re), or Mn3Sn 1-y B y (0 < y < 0.35, B = Sc, Ti, V, Ga, Y, Zr, Nb, In, Hf, Tl), by doing so, it exhibits a larger anomalous Hall conductivity compared to Mn3Sn. The anomalous Hall conductivity of the above antiferromagnetic material is caused by the spin clustering magnetic octupole polarization, and an anomalous Hall voltage occurs in the direction perpendicular to the spin polarization and the external voltage. Therefore, by using the above antiferromagnetic material, more accurate observation regarding its magnetic state becomes possible using the anomalous Hall conductivity. Hereinafter, embodiments will be described.

[0007] [Antiferromagnetic Material with Giant Anomalous Hall Conductivity] The antiferromagnetic material with giant anomalous Hall conductivity of the present disclosure has a hexagonal crystal structure (space group P63 / mmc), and (Mn 1-x A x )3Sn (0 < x < 0.15, A = Ti, V, Cr, Zr, Nb, Mo, Tc, Hf, Ta, W, Re), or Mn3Sn 1-y B y (0 < y < 0.35 B = Sc, Ti, V, Ga, Y, Zr, Nb, In, Hf, Tl) composition. The substitution amount of each element of A is more preferably in the range of the values shown in Table 1, and as the substitution element, V and Cr are more preferable. The substitution amount of each element of B is more preferably in the range of the values shown in Table 2, and as the substitution element, Ga, In, and Tl are more preferable.

[0008] The inventor of the present disclosure found that by performing a simulation as described below, by partially substituting the constituent elements of the antiferromagnetic material Mn3Sn with specific elements, the anomalous Hall conductivity is improved.

[0009] (Simulation method) To search for antiferromagnetic materials with improved anomalous Hall conductivity, we performed simulations in the following three steps: (1) Using the antiferromagnetic material Mn3Sn with a hexagonal crystal structure as the reference material, we searched for two types of materials: [1] materials in which Mn is partially substituted with another element, and [2] materials in which Sn is partially substituted with another element, and searched for materials with improved anomalous Hall conductivity compared to the reference material; (2) among these, we searched for materials whose magnetism disappearance temperature (Néel temperature) does not drop dramatically compared to the reference material; and (3) among these, we searched for materials whose structure can exist stably or metastable. Each of these steps is explained in order below.

[0010] (1) Using the antiferromagnetic material Mn3Sn with a hexagonal crystal structure as the base material, we search for two types of materials: [1] materials in which Mn is partially randomly substituted with other elements, and [2] materials in which Sn is partially randomly substituted with other elements, to find materials whose anomalous Hall conductivity is improved compared to the base material.

[0011] The elements to be substituted are 54 elements from the periodic table with atomic numbers 11 (Na) to 83 (Bi), excluding rare gas elements, lanthanides, and the same elements as the original substitution. The maximum substitution amount is 15% for Mn and 35% for Sn. Furthermore, the crystal structure (lattice constant and internal coordinates) uses the values ​​of Mn3Sn, and changes in lattice constant due to element substitution are not taken into account. For the crystal structure determined above, material systems whose anomalous Hall conductivity, calculated based on first-principles electronic structure calculations, is higher than the standard Mn3Sn value are selected as search candidates. The specific calculation method is as follows:

[0012] First-principles calculations of random substitution systems were performed using the virtual crystal approximation (VCA) implemented in the Quantum ESPRESSO (QE) code (see P. Giannozzi, et al., J. Phys: Condens. Matter 21, 395502 (2009)).

[0013] Figure 1 is a conceptual diagram showing the atomic and magnetization configurations of an Mn3Sn-type magnetic material. The arrows indicate the direction of the magnetic moment. In Figure 1, the coordinate positions of the Sn and Mn atoms are shown along with the reference plane. The white circles are Sn atoms, and the gray circles are Mn atoms. The z-coordinate position of the circle surrounded by a solid line is 0.25 relative to the reference plane, and the z-coordinate position of the circle surrounded by a dotted line is 0.75 relative to the reference plane.

[0014] Mn3Sn-type magnetic materials exhibit the magnetization configuration shown in Figure 1 at room temperature, and when an electric field is applied in the z direction, a Hall voltage is generated in the y direction (Nat. Phys.13, 1085 (2017)). This anomalous Hall conductivity (AHC, σ zy ) is calculated by Kubo's formula in the clean limit as follows: where f n is the Fermi-Dirac distribution function of the nth band at k, Equation (2) is the Berry curvature of the nth band at k. |nk> (|mk>) is the Bloch state with band index n(m) and wave vector k, is an eigenvalue. is the velocity operator in the α direction. For the AHC calculations, we used norm-conserving fully relativistic pseudopotentials generated by the Optimized Norm-Conserving Vanderbilt Pseudopotential (ONCVP) code (see DR Hamann, Phys. Rev. B88, 085117 (2013)) obtained from PseudoDojo (see MJ van Setten, et al., Comput. Phys. Commun. 226, 39 (2018)). Spin-orbit coupling was self-consistently included to handle relativistic effects. After the self-consistent calculations by QE were completed, the Bloch functions were Fourier transformed into maximally localized Wannier functions (MLWFs) using the Wannier90 package (see N. Marzari, et al., Rev. Mod. Phys. 84, 1419 (2012)). The energy cutoff of the wave functions was 100 Ry, N k is set to a value of 7 × 7 × 8, and the band structure obtained by MLWFs is F -15 eV to E F +1.5 eV (E FThe DFT band structure was perfectly reproduced in the range of k = 1 / k (where k is the Fermi energy). MLWFs were used to calculate the Berry curvature of equation (2) on a dense k-lattice of 63 × 63 × 66 in the BZ using the WANNIER-BERRI package (S.S. Tsirkin, npj Comput. Mater. 7, 33 (2021)). As an example, the following results (Fig. 2 (a)-(d)) are obtained. Figure 2(a) shows the energy dependence of AHC when a portion of Mn is substituted with Cr at T = 50 K in the magnetization configuration shown in Figure 1 (Fig. 1), (b) shows the Fermi surface dependence of AHC on the amount of element substitution when a portion of Mn is substituted with Cr at T = 50 K in the magnetization configuration shown in Figure 1 (Fig. 1), (c) shows the energy dependence of AHC when a portion of Sn is substituted with In at T = 50 K in the magnetization configuration shown in Figure 1 (Fig. 1), and (d) shows the Fermi surface dependence of AHC on the amount of element substitution when a portion of Sn is substituted with In at T = 50 K in the magnetization configuration shown in Figure 1 (Fig. 1). Here, σ x = σ yz is.

[0015] (2) Search for materials whose magnetism disappearance temperature (Neel temperature) is not significantly lower than that of the reference material. From the material system obtained in (1) above, select those whose Neel temperature maintains 90% or more of that of the original Mn3Sn.

[0016] (3) Search for materials that can exist stably or metastably in terms of structure For the material system obtained in (2) above, while fixing the elemental composition ratio, calculate the energies in crystal structures of Tetragonal (collinear ferrimagnetism) and Cubic (collinear ferrimagnetism) in addition to the original Hexagonal crystal structure, and calculate the energy differences between Hexagonal and these crystal structures. The lattice constants in each crystal structure are optimized by first-principles calculations, and the relative positions of the internal coordinates are fixed. At this time, regarding the calculation codes and pseudopotentials used, as well as the calculation conditions and the introduction methods of element substitution systems, they shall conform to the descriptions in (1). Perform a relative comparison of the energies in the three crystal structures obtained thereby. Select as materials that can be considered to have a Hexagonal structure existing stably or metastably in a material system where “Energy in Tetragonal structure” − “Energy in Hexagonal structure” > −0.05 eV / atom and “Energy in Cubic structure” − “Energy in Hexagonal structure” > 0.05 eV / atom.

[0017] Through the above simulations, in an antiferromagnetic material having a hexagonal crystal structure (space group P63 / mmc), (Mn 1-x A x )3Sn (0 < x < 0.15, A = Ti, V, Cr, Zr, Nb, Mo, Tc, Hf, Ta, W, Re), or Mn3Sn 1-y B y (0 < y < 0.35, B = Sc, Ti, V, Ga, Y, Zr, Nb, In, Hf, Tl), it has been found that the thermal stability of magnetism (Neel temperature) does not decrease significantly and can exist stably in terms of energy.

[0018] In one embodiment of the present disclosure, the Neel temperature (calculated value) of the antiferromagnetic layer has a Neel temperature that is 90% or more of the Neel temperature of Mn3Sn.

[0019] In one embodiment of the present disclosure, the energy difference between the Tetragonal structure and the Hexagonal structure with the same composition in the antiferromagnetic layer has a value equal to or less than that of Mn3Sn.

[0020] [Method for Manufacturing Antiferromagnetic Materials with Giant Anomalous Hall Conductivity] The materials used in this disclosure can be manufactured using known film-forming techniques, such as sputtering and epitaxial growth (MBE, MOCVD, etc.). Alternatively, bulk crystal growth techniques (Czochralski method, vertical Bridgman method, etc.) can also be used. For example, when using sputtering, targets of Mn, Sn, and elements A and B listed in Tables 1 and 2 can be attached to a DC magnetron gun in a multi-target magnetron sputtering system, and the materials can be co-sputtered. The atomic ratio of each element can be easily controlled by the amount of power applied. The manufactured film may be heat-treated for crystallization. Heat treatment conditions are preferably a temperature of 300°C to 600°C and a heating time of 10 minutes to 50 hours.

[0021] Obviously, numerous modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that, within the scope of the appended claims, the invention may be practiced otherwise than as specifically described herein.

Claims

1. The antiferromagnet with giant anomalous Hall conductivity of the present disclosure has a hexagonal crystal structure (space group P63 / mmc) and has the composition of (Mn 1-x A x )3Sn (0 < x < 0.15, A = Ti, V, Cr, Zr, Nb, Mo, Tc, Hf, Ta, W, Re), or Mn3Sn 1-y B y (0 < y < 0.35, B = Sc, Ti, V, Ga, Y, Zr, Nb, In, Hf, Tl).

2. The antiferromagnetic material of claim 1 having substitution amounts corresponding to the following table:

3. The antiferromagnetic material of claim 1 having substitution amounts corresponding to the following table:

4. The antiferromagnetic material of claim 1, wherein A is at least one of V and Cr.

5. The antiferromagnetic material of claim 1, wherein B is at least one of Ga, In, and Tl.