United States

We study spin-dependent direct and Hall conductivities in the threshold region of Fermi energy, ε&lt;sub&gt;F&lt;/sub&gt; = 2J, where J is the exchange integral between the conduction electron spins and the skyrmion spin texture. For &lt;i&gt;ε&lt;sub&gt;F&lt;/sub&gt;&lt;/i&gt; at the threshold value and above the spin-down electrons are allowed to exist (sse Fig. 1). We find the two in the direct and four narrow peaks in the Hall conductivities for Fermi energies slightly below the threshold value. The found effects are dramatic because the electric current changes by approximately eight times in the narrow range of gate voltages (4 me). The values of the peaks strongly depend on skyrmion size. For small and very large skyrmion sizes the peak amplitudes are small compared to the conductivity absolute values. At the skyrmion radius &lt;i&gt;a=6 nm&lt;/i&gt; and very light conduction electrons, &lt;i&gt;m* = 10&lt;sup&gt;-2&lt;/sup&gt;m&lt;sub&gt;e&lt;/sub&gt;&lt;/i&gt;, the extrema are the most pronounced (see Fig. 2). The temperature evolution reveals the strong smearing effect where the peak-wise behavior completely disappears at room temperatures. Spin transistor could be considered for possible applications where in the narrow region of gate voltage the sharp conductivity change occurs.

![](https://assets.underline.io/uploads/markdown_image/1/image/343d329a55b5335e5f1e305059671557.jpg)

Fig. 1. Band structure for the spin-up (lower) and spin-down (upper) electrons. The splitting between the bands is equal to 2J. The positions of εF are shown by blue and red lines

![](https://assets.underline.io/uploads/markdown_image/1/image/8ec55eba5af5660c32367d098a503b93.jpg)

Fig. 2. Direct ((a) and (c)) and Hall ((b) and (d)) conductivities for spin-up ((a) and (b)) and spin-down ((c) and (d)) components for the various temperatures, kBT = 0 eV (the blue line), kBT = 0.002 eV (the red line), and kBT = 0.025 eV (the green line) with respect to εF for the skyrmion size a=6.0 nm.

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Threshold behaviors of direct and Hall currents in topological spin-Hall effect

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We study spin-dependent direct and Hall conductivities in the threshold region of Fermi energy, εF = 2J, where J is the exchange integral between the conduction electron spins and the skyrmion spin texture. For εF at the threshold value and above the spin-down electrons are allowed to exist (sse Fig. 1). We find the two in the direct and four narrow peaks in the Hall conductivities for Fermi energies slightly below the threshold value. The found effects are dramatic because the electric current changes by approximately eight times in the narrow range of gate voltages (4 me). The values of the peaks strongly depend on skyrmion size. For small and very large skyrmion sizes the peak amplitudes are small compared to the conductivity absolute values. At the skyrmion radius a=6 nm and very light conduction electrons, m* = 10-2me, the extrema are the most pronounced (see Fig. 2). The temperature evolution reveals the strong smearing effect where the peak-wise behavior completely disappears at room temperatures. Spin transistor could be considered for possible applications where in the narrow region of gate voltage the sharp conductivity change occurs.

![](https://assets.underline.io/uploads/markdown_image/1/image/343d329a55b5335e5f1e305059671557.jpg)

Fig. 1. Band structure for the spin-up (lower) and spin-down (upper) electrons. The splitting between the bands is equal to 2J. The positions of εF are shown by blue and red lines

![](https://assets.underline.io/uploads/markdown_image/1/image/8ec55eba5af5660c32367d098a503b93.jpg)

Fig. 2. Direct ((a) and (c)) and Hall ((b) and (d)) conductivities for spin-up ((a) and (b)) and spin-down ((c) and (d)) components for the various temperatures, kBT = 0 eV (the blue line), kBT = 0.002 eV (the red line), and kBT = 0.025 eV (the green line) with respect to εF for the skyrmion size a=6.0 nm.

technical paper

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An experimental realization of the Haldane conjecture of a gapped spin liquid is of great interested among condensed matter scientists. The conjecture is implemented in the chains of Heisenberg integer spins bounded by identical intrachain exchange interactions J and could be realized in uniform quasi-one-dimensional integer spin compounds [1]. The Haldane phase has to compete with magnetic anisotropy and long-range ordered phases, depending on the ratio of interchain J' and intrachain J exchange interactions and uniaxial D and rhombic E single-ion anisotropy. The critical ratios J'/J and D/J for Haldane phase, easy axis long ordered AFM and easy plane long ordered XY-AFM were first discovered by Sakai and Takahashi [2]. Many compounds, both organic and inorganic, have been studied to verify this idea, some of them have been identified as belonging to the Haldane sector of the Sakai-Takahashi phase diagram. In this work, the position on Sakai-Takahashi phase diagram was determined for the novel integer spin S = 1 chain compound, strontium nickel selenite chloride Sr2Ni(SeO3)2Cl2. XRD measurements showed that the crystal structure of the compound contains the NiO4Cl2-octahedra bridged by the SeO3-pyramids into uniform spin chains. These chains are well separated by strontium cations and cavities of selenium’s lone pair of electrons that could lead to 1D-dimensionality of magnetic subsystem. In magnetic measurements it was determined that strontium nickel selenite chloride, Sr2Ni(SeO3)2Cl2, is a spin S = 1 chain system which passes through a correlations regime at Tmax ~ 12 K to long-range order at TN = 6 K. The values of J'/J = 0.083 and D/J = 0.357 place this compound into a hitherto unoccupied XY-AFM sector of the Sakai-Takahashi phase diagram. The results was recently published in Scientific reports journal [3]. Support by the P220 program of Government of Russia through the project 075-15-2021-604 is acknowledged. We also acknowledge the support of the HLD-HZDR, member of the European Magnetic Field Laboratory (EMFL).

![](https://assets.underline.io/uploads/markdown_image/1/image/ac2674811e3113c6c930d976a3efd7a0.jpg)

Sakai-Takahashi phase diagram for uniform spin-1 chain compounds, novel compound Sr2Ni(SeO3)2Cl2 is also marked.

Magnetic properties of S = 1 spin chain in Sr2Ni(SeO3)2Cl2: XY-antiferromagnet at Sakai-Takahashi phase diagram

Spin-crossover (SCO) complexes form an interesting class of switchable materials that can exist in two different spin states, known as the low-spin (LS) and high-spin (HS) states. These complexes may be switched between the two spin states under various stimuli including temperature, pressure, light, magnetic and electrical fields [1]. Among these stimuli, pressure is one of the most appealing thermodynamic parameters used to probe the spin transition properties of spin-crossover materials since it allows for tuning both the crystal field as well as the interactions between SCO centers. Since the pioneering works of Drickamer [2], Konig [3] and Gutlich[4], the pressure effect has continuously attracted the interest of the scientific community, being intensively studied until nowadays. In general, the application of an external pressure induces a transformation of the SCO complex to the low-spin state, i.e. to the state of lower molecular volume, and has the effect of shifting the switching temperatures towards higher values. However, the interpretation of the pressure effect on molecular SCO phenomena has been, in some cases, compromised by the relatively poor or incomplete information resulted from experimental difficulties related to the need for hydrostatic conditions at low temperatures. In this work I will talk on both hydrostatic [5, 6] and non-hydrostatic [7] pressure effects on the spin transition properties of molecular spin crossover complexes in terms of major thermal hysteresis loop and FORC diagram methods. We have shown that for high pressure gradients, the thermal hysteresis loop becomes asymmetric. Remarkably, the FORC diagram method has been proved to be much more sensitive to local changes than the “bulk” parameters, which characterize the major hysteresis loop. This makes the FORC diagram method a suitable technique to characterize the hydrostaticity degree of a pressure cell. Acknowledgements. This work was partially funded by UEFISCDI, project number PN-III-P1-1.1-TE-2019-2194 (Contract No: TE 123/2020)

Pressure effect on spin-crossover materials: Experiment vs theory

Recently, 5d and 4d oxides and halides with honeycomb lattice structures are of great interest [1-2] for exhibiting an interplay between an isotropic Heisenberg-type exchange interaction (J) and an anisotropic Kitaev-type exchange interaction (K), see Fig. 1a. We predict that such an interplay can lead to topological edge states with chiral conduction when the anisotropic interaction is at least twice the strength of the isotropic interaction (i.e. K ≥ 2J), see Figs. 1b-c. We show that these interactions give rise to new types of antiferromagnetic orders, which determine the chirality of the edge atomic chain. We show calculations for sodium iridate and alpha-ruthenium chloride, both known to exhibit a zigzag antiferromagnetic order at low temperatures, and discuss the chiral edge conduction in the context of the relative strength between J and K. The edge conduction in the presence of a zigzag antiferromagnetic order will be manifested as a quantized Hall conductance when the number of zigzag atomic chains is odd (see Fig. 1b) since both edges will have the same magnetic orders. On the other hand, the Hall conductance will be zero when the number of zigzag atomic chains is even (see Fig. 1c) since the edges will have opposite magnetic orders. These signatures of the exchange interaction induced chiral edge conductions in odd and even numbers of two-dimensional atomic chains are similar to the well-known signatures of a quantum anomalous Hall insulator and an axion insulator states typically observed in a three-dimensional magnetic topological insulator [3-4], respectively. We further use a widely used model for two-dimensional topological materials to analyze the underlying mechanisms of the predicted phenomena.

![](https://assets.underline.io/uploads/markdown_image/1/image/b67aecaae65e534de04962906894efe1.jpg)

(a) Honeycomb lattice with isotropic (J) and anisotropic (K) exchange interactions. Hall conductance Gxy = Vx / Iy is calculated when the number of zigzag atomic chains is (b) odd and (c) even, as a function of K / J.

Chiral edge conduction induced by large anisotropic exchange interactions.

Materials exhibiting high degree of spin polarization such as half-metals or spin-gapless semiconductors are in demand for spin-transport-based devices. Especially, half metallic Heusler compounds have attracted much attention because they have tunable magnetic properties and exhibit high Curie temperature much above room temperature. We have synthesized one such predicted half metal, FeCrVAl, using arc melting and annealing. The vacuum annealing was done at 600oC for 48 hours. In addition, we also studied the effect of Mn substitution on the structural, magnetic, and electronic band properties of FeCrVAl synthesizing samples with compositions FeCr0.5Mn0.5VAl and FeCrV0.5Mn0.5Al. The room temperature, x-ray diffraction patterns indicate that FeCrVAl and FeCrV0.5Mn0.5Al are cubic in structure with A2 type disorder, whereas FeCr0.5Mn0.5Val is more ordered as evidenced by the presence of superlattice peaks. All samples show small saturation magnetizations at room temperature and the thermomagnetic curves M(T) are similar to that of a paramagnetic material. However, as shown in Fig.1 below, the M(T) of FeCr0.5Mn0.5VAl is different and shows a slow magnetic transitionat 800 K similar to that of a ferrimagnetic material. In this presentation, we will discuss the structural, magnetic and electron band properties of the synthesized materials and the effect of disorder on the properties of FeCrVAl. This research is supported by the National Science Foundation (NSF) under Grant Numbers 2003828 and 2003856 via DMR and EPSCoR.

![](https://assets.underline.io/uploads/markdown_image/1/image/671008ce0e34982996f2b9cfad55899c.jpg)

Figure 1: Thermomagnetic curve M(T) of FeCr0.5Mn0.5VAl alloy. The inset shows the M (H) curve recorded at 300 K.

Experimental and theoretical investigation of FeCrVAl and related compounds

Heusler alloys have been investigated intensively as a potential spin source with 100% spin polarisation at room temperature [1,2]. Theey can be used in magnetoresistive junctions for a next generation read head and a magnetic memory cell [3]. We have recently reduced their crystallisation temperature by growing on the (110) plane [4]. This can be achieved by growing on a body-centred cubic seed layer [5],[6]. In this study, we systematically investigate the effect of seed and capping layers on Co2FeAl0.5Si0.5 (CFAS) Heusler-alloy films. Heusler alloy films were grown on a thermally oxidised Si substrate in the form of Cr (0 and 3)/W (10)/CF(A)S (10)/X (5)/Ru (3) (thickness in nm, X: W, Ta, V, Ag and Pt) using a high target utilisation sputtering system at room temperature. These films were annealed at 300~350°C for 1~3 hours. The structural and magnetic properties were characterised by X-ray diffraction (XRD) and vibrating sample magnetometry. The magnetisation reversal process was also imaged using magnetic force microscope. Figure 1(a) confirms all films show W crystallisation along the (110) surface orientation, promoting the CFAS crystallisation as confirmed by the CFAS(220) peak. As shown in Fig. 1(b), all CFAS films exhibit perpendicular magnetic anisotropy but with clear deviations under the influence of top-interfaces. The magnetisation curve of the W cap exhibits the highest squareness. In-plane magnetisation measurements also confirm the CFAS/W top interface shows single-step reversal. This means that the sample consisting of a W/CFAS/W trilayer shows the ideal magnetic properties for junction applications. As listed in Fig. 1(d), all films show MS within the range of 650~850 emu/cm3, which is almost 30% smaller than the bulk value. This work was partially supported by EPSRC (EP/M02458X/1 and EP/V007211/1) and JST CREST (No. JPMJCR17J5).

![](https://assets.underline.io/uploads/markdown_image/1/image/71da82cf3408d23ffc6e5565bf99a0d6.jpg)

(a) XRD θ-2θ scans and (b) out-of-plane and (c) in-plane magnetisation curves of Si/SiO2//W (10)/CFAS (10)/Y (5)/Ru (3) (thickness in nm, Y: W, Ta, V, Ag and Pt). (d) Saturation magnetisation of these films calculated from (c).

Perpendicular Anisotropy Controlled by Seed and Capping Layers of Heusler Alloy Films

Co-based Heusler alloys are currently exploited in several interesting spintronics applications, such as magnetic electrodes in spin-valve and magnetic tunnel junction devices, due to their half-metallic ferromagnetic properties [1]. Their magnetic and electronic transport behavior at room temperature are intensely studied and tuned to meet several applications demands. In particular, the electronic transport properties display an unusual trend of Seebeck coefficient and electrical conductivity proving the half-metallic ferromagnetic behavior of these compounds [2]. In this work, Co2HfSn and Co2ZrSn bulk alloys are synthetized by arc-furnace in which the melt contains pure elements in the appropriate stoichiometric quantities; subsequent, annealing at 800 °C for 6 days is performed to release stress and reach the equilibrium phase. Magnetic properties were investigated in the wide temperature range from 2 to 500 K by SQUID and VSM magnetometers; isothermal hysteresis loops M(H) and magnetization as a function of temperature curves M(T) have been measured. Magnetic results are in excellent agreement with the mean-field model of itinerant ferromagnetism (Stoner model) in the limit of very weak ferromagnetism. The linear relationship between M2 and H/M (i.e. Arrott plot) is maintained at all studied temperatures, both well below and above the Curie temperature (see Fig. 1a). The weak itinerant ferromagnetism model, by means of its temperature-dependent coefficients, is successfully used to determine the Curie temperature resulting at 432 K and 458 K for the Co2HfSn and Co2ZrSn alloy, respectively. In addition, the extrapolation of the experimental M(T) curve at T = 0 K reveals a magnetic moment of 2.0 μB/f.u. 1.81 μB/f.u. for the Co2HfSn and Co2ZrSn samples, respectively. Electric and magnetic experimental results are compared with the ab-initio calculation, which provides the spin-polarized density of states (DOS) confirming that Co2HfSn and Co2ZrSn alloys are half-metallic compounds with a majority-spin channel across the Fermi surface, whereas the minority-spin channel shows a small band gap (see Fig. 1b).

![](https://assets.underline.io/uploads/markdown_image/1/image/df3139ef06e4c7e8a2379ed3a8f014a3.jpg)

a) Arrott plot for the Co2HfSn sample; b) DOS by ab-initio calculation for the Co2ZrSn sample

Weak ferromagnetism and electronic properties of half-metallic Co2HfSn and Co2ZrSn Heusler alloys

Exceptional tunability in the electronic and magnetic properties makes Heusler compounds very promising from both the fundamental and applied perspectives. Half-metallic ferromagnetism, half-metallic fully-compensated ferrimagnetism, spin-gapless semiconducting behavior, and fully-compensated ferrimagnetic spin-gapless semiconducting behavior have been predicted or demonstrated experimentally in Heusler compounds which makes them suitable for applications in a number of novel spintronic devices1,2,3,4,5. Half-metallic Co-based Heusler alloys are among the most attractive systems due to their high Curie temperatures, high spin polarization and the structural similarity to binary semiconductors6,7,8. Spin-gapless semiconductors can be regarded as a combination of gapless semiconductors and half-metallic ferromagnets where the conducting electrons or holes are not only 100% spin polarized but also easily excited. The realization of spin-gapless semiconducting behavior in Heusler alloys is expected to fulfill the needs for semiconductor spintronics. In this work, we have introduced the substitution of low valence transition metal atoms Y = Ti, V, Cr, Mn, and Fe to Co atoms in the parent Co2FeGa system, and examined the properties of quaternary Heusler compounds Co2-xYxFeGa (x = 0.50), both experimentally and theoretically to get a global overview of the electronic, magnetic, electron transport and mechanical properties. All single-phase alloys exhibit Heusler like L21 ordering, as corroborated by X-ray diffraction. The low-temperature saturation magnetic moments agree fairly well with the values expected from a Slater-Pauling rule for half metals (Fig.1). Electrical transport measurements are performed to explain the electronic structure of the alloys. The temperature dependence of electrical resistivity for Mn substituted alloy shows semiconducting nature in the complete temperature regime (5-400)K (Fig.2). Ab initio calculations are also performed to understand the experimental findings.

![](https://assets.underline.io/uploads/markdown_image/1/image/14f7b59db99b038cf74a4718f8f85273.jpg)

The variation of saturation magnetic moment with valence electron counts per formula units with element Y.

![](https://assets.underline.io/uploads/markdown_image/1/image/4d76d8c1a433798c5183033756315811.jpg)

Temperature dependence of electrical resistivity in Co1.50Mn0.50FeGa at zero magnetic field showing semiconducting behavior.

Possible half-metallic and spin-gapless semiconducting behavior in quaternary Heusler compounds Co2-xYxFeGa (Y = Ti, V, Cr, Mn, Fe, and Co, x = 0.50)

Quantized electronic transport in magnetic topological insulators is intertwined with spontaneous magnetic ordering, as magnetization controls band topology through the exchange interaction. We show that considering the exchange gaps at the mean-field level is inadequate to predict phase transitions between electronic states of distinct topology. Thermal spin fluctuations that disturb the magnetization can act as frozen disorders, which strongly scatter electrons and thus reduce the onset temperature of quantized transport appreciably even in the absence of structural impurities. This effect, which has hitherto been overlooked, provides an alternative explanation of recent experiments on magnetic topological insulators.

![](https://assets.underline.io/uploads/markdown_image/1/image/7c46726549c088ed001f510b9339cdce.jpg)

Spin Fluctuations in Quantized Transport of Magnetic Topological Insulators

Inorganic chiral crystals have attracted much recent interest for their potential topological quantum properties1. In particular, β-Ag2Te was shown to be a bulk insulator hosting a topological surface state (TSS) of highly anisotropic Dirac dispersion2. On the other hand, in chiral materials, an electric current along the helical axis produces a collinear spin polarization; this is known as chirality-induced spin selectivity (CISS)3. This raises the intriguing possibility that Ag2Te may be a material that simultaneously exhibits TSS and CISS. Here we report on electrical transport measurements on oriented films of nonmagnetic Ag2+δTe. The films were grown by electron-beam evaporation on quartz, which were shown to be highly textured by XRD. With decreasing temperature, the film resistivity shows semiconducting behavior at high temperatures, and plateaus below ~50 K, consistent with the predominance of a TSS (Fig. 1). The in-plane field magnetoresistance (MR) of the samples exhibits qualitatively different behavior for the longitudinal and transverse configurations. The transverse MR is positive and of a similar magnitude to polycrystalline Ag2Te samples4. In contrast, the longitudinal MR is negative in the semiconducting temperature range, and remains substantial at 300 K. At lower temperatures, the longitudinal MR shows a non-monotonic behavior, with sign reversals for the slope and even magnitude with increasing field (Fig. 2). The unusual MR in the oriented films of Ag2+δTe implies two competing mechanisms behind the magnetotransport properties of Ag2+δTe, possibly reflecting the coexistence of a TSS on the surface and CISS in the bulk. *Work supported by NSF grant DMR-1905843

![](https://assets.underline.io/uploads/markdown_image/1/image/3dbdf24c4831393f5bc0415e2f16b80a.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/b148479fb729dd5560b9b113714769b9.jpg)

Sign Reversal and Large Anisotropy in the Magnetoresistance of Oriented Thin Films of Ag2+δTe

Sign Reversal and Large Anisotropy in the Magnetoresistance of Oriented Thin Films of Ag2+δTe

The search for magnetic topological semimetals has been one of the most intriguing issues in the field of spintronics because they exhibit anomalous transport properties that can be utilized for novel spintronic devices. Quite recently, it was theoretically predicted that an inverse spinel compound VMg2O4 is a good magnetic Weyl semimetal [1,2]. The Weyl points are found just above the Fermi energy in the eg-band formed by the 3d-orbitals of the tetravalent V on the diamond lattice. Stimulated by these previous works, here we study the electronic states and transport properties of another spinel compound MnMg2O4, in which V is totally substituted for Mn with a smaller ionic radius. The significant difference between V and Mn is that, if they maintain the nominal tetravalent configuration, V has one electron in the eg-orbital while Mn also has one hole in the eg-orbital in the low-spin state or one electron in the t2g orbital in the high-spin state. Here we focus on how the topological properties found in VMg2O4 can be affected by the orbital symmetry by first-principles calculations using WIEN2k code. The band structure and the density of states of MnMg2O4 are shown in Figure 1 (a) and (b), respectively. We find that the Fermi energy lies at the t2g band and high-spin state is realized in the 3d electrons of Mn. The resulting band structure is half-metallic with the minority band gap is found to be 3eV. We note that, unlike the eg-band lies around 1eV below the Fermi level, there is no obvious linear crossing in the t2g band. We also compute the intrinsic anomalous Hall conductivity (AHC) within the linear-response theory in the clean limit, and the energy dependence of the AHC is shown in Fig. 2. As expected from the band structure in Fig. 1(a), the AHC is very small at the Fermi energy, shown with black line. We also examine the effects of the compressive strain on the electronic structures and AHC of the systems. Lifting the degeneracy of the t2g band, the Weyl points appears slightly above the Fermi energy, resulting in a large AHC ( -144 S/cm ).

![](https://assets.underline.io/uploads/markdown_image/1/image/b9452ae2fe6ff8055dc1e70c5a891907.jpg)

Fig.1
(a) The band structure and (b) the density of states of MnMg2O4.

![](https://assets.underline.io/uploads/markdown_image/1/image/d084731d45c35b3bbf4ae0675c47bd19.jpg)

Fig.2
The energy dependences of the anomalous Hall conductivity with several compressive strains.

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