First principles design of Ohmic spin diodes based on quaternary Heusler compounds
FFirst principles design of Ohmic spin diodes based on quaternary Heuslercompounds
T. Aull , a) E. Şaşıoğlu , and I. Mertig , Institute of Physics, Martin Luther University Halle-Wittenberg, D-06120 Halle (Saale),Germany Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle (Saale),Germany
The Ohmic spin diode (OSD) is a recent concept in spintronics, which is based on half-metallic magnets(HMMs) and spin-gapless semiconductors (SGSs). Quaternary Heusler compounds offer a unique platform torealize the OSD for room temperature applications as these materials possess very high Curie temperaturesas well as half-metallic and spin-gapless semiconducting behavior within the same family. Using state-of-the-art first-principles calculations combined with the non-equilibrium Green’s function method we design fourdifferent OSDs based on half-metallic and spin-gapless semiconducting quaternary Heusler compounds. Allfour OSDs exhibit linear current-voltage ( I − V ) characteristics with zero threshold voltage V T . We show thatthese OSDs possess a small leakage current, which stems from the overlap of the conduction and valence bandedges of opposite spin channels around the Fermi level in the SGS electrodes. The obtained on/off currentratios vary between and . Our results can pave the way for the experimental fabrication of the OSDswithin the family of ordered quaternary Heusler compounds.Spintronics is a rapidly emerging field in current nano-electronics. Due to their diverse and tunable electronicand magnetic properties, Heusler compounds receivedgreat interest for potential applications in spintronics.Especially, within the last two decades half metallicHeusler compounds with 100% spin polarization of theconduction electrons at the Fermi energy have been ex-tensively studied; both, theoretically and experimentally,for memory and sensor applications. Besides half metal-licity in ordinary X YZ-type Heusler compounds, severalquaternary Heuslers with chemical formula
XX’YZ , with X , X (cid:48) and Y are transition-metal atoms and Z is an sp el-ement, have been theoretically predicted to exhibit spin-gapless semiconducting behavior and some of them havebeen experimentally synthesized . Spin-gapless semi-conductors (SGSs) possess a unique electronic structure,in which conduction- and valence-band edges of oppositespins touch at the Fermi level and thus SGS behaviorleads to unique functionalities and device concepts.Half-metallic Heusler compounds have been consideredas ideal electrode materials in magnetic tunnel junctionsfor spin-transfer torque magnetic memory applicationsdue to their very high Curie temperatures. The use ofCo-based Heusler compounds in magnetic tunnel junc-tions made the experimental observation of high tunnelmagnetoresistance (TMR) effects possible. However,magnetic tunnel junctions constructed with half metalsdo not present any rectification (or diode effect) for logicoperations. Lately logic functionality in magnetic tunneljunctions is achieved by replacing one of the electrodes bya SGS material. In Ref. 13, based on HMMs and SGSs, areconfigurable magnetic tunnel diode and transistor hasbeen proposed. This concept combines logic and memoryon the diode and transistor level. Moreover, in a recent a) Electronic mail: [email protected] publication the present authors proposed another deviceconcept based on HMMs and SGSs, which is the so-calledOhmic spin diode (OSD) . It has been computationallydemonstrated that the OSD comprising two-dimensionalhalf-metallic Fe/MoS and spin-gapless semiconductingVS exhibits linear current-voltage ( I − V ) characteris-tics with zero threshold voltage V T . OSDs have a muchhigher current drive capability and low resistance, whichis advantageous compared to conventional semiconductor p − n junction diodes and metal-semiconductor Schottkydiodes.The aim of the present Letter is a computational de-sign of OSDs based on quaternary Heusler compoundsfor room temperature applications. Heusler compoundsoffer a unique platform to realize the OSD as these mate-rials possess very high Curie temperatures (much above FIG. 1. (Color online) (a) Upper part: Schematic represen-tation of the Ohmic spin diode and corresponding current-voltage ( I − V ) characteristics. Arrows show the magneti-zation direction of the HMM and SGS electrodes (ferromag-netic OSD). Lower part: Schematic representation of the den-sity of states for a HMM and SGS. (b) The same as (a) foranti-ferromagnetic coupling of the HMM and SGS electrodes(antiferromagnetic OSD). a r X i v : . [ c ond - m a t . m t r l - s c i ] F e b TABLE I. Material composition of the considered OSDs, coupling of the electrodes, lattice constants a , c/a ratio, sublatticeand total magnetic moments, work function ( Φ ), the magnetic anisotropy energy (MAE), Curie temperatures T C of the cubicphase and the electronic ground state. The T C values are taken from Ref. 7. a c/a m X m X (cid:48) m Y m total Φ MAE a T C GroundHMM-SGS junction Coupling Compound (Å) ( µ B ) ( µ B ) ( µ B ) ( µ B ) (eV) ( µ eV/at.) (K) stateMnVTiAl − FeVTaAl ↑↑ FeVTaAl 6.10 1.00 0.85 2.38 -0.19 3.00 3.75 0.63 681 SGSMnVTiAl 6.10 1.01 -2.42 2.61 0.86 1.00 3.59 11.94 963 HMMFeVHfAl − FeVTiSi ↑↑ FeVTiSi 5.91 1.00 0.57 2.33 0.10 3.00 3.52 -0.94 464 SGSFeVHfAl 5.91 1.12 -0.15 2.06 0.10 2.00 4.10 117.44 742 HMMFeVHfAl − FeVNbAl ↑↑ FeVNbAl 6.11 1.00 0.81 2.32 -0.11 3.00 3.72 0.25 693 SGSFeVHfAl 6.11 1.04 -0.68 2.41 0.29 2.00 3.45 62.44 742 HMMCo MnSi − FeVTaAl ↑↓ FeVTaAl 6.10 1.00 0.79 2.32 -0.11 3.00 3.75 0.63 681 SGSCoCoMnSi 6.10 0.86 1.01 1.01 3.18 5.00 3.83 57.50 920 HMM a Out-of-plane magnetisation is marked as negative MAE room temperature) as well as half-metallic and spin-gapless semiconducting behavior within the same family.To this end, the selection of the SGS and HMM elec-trode materials from the Heusler family for the designof OSDs is based on our recent study in Ref. 7, wherewe focus on Curie temperatures, spin-gaps, formationenergy, Hull distance for a large number of quaternaryHeusler compounds. Among the considered materialsthree SGSs (FeVNbAl, FeVTaAl, and FeVTiSi) turn outto be promising for device applications. As for the half-metallic Heusler compounds, we have a large variety ofchoice, but we stick to the quaternary ones (MnVTiAl,FeVHfAl) with similar lattice constants to the SGSs in or-der to ensure a coherent growth on top of each other. Ad-ditionally, we also consider the well-known half-metallicCo MnSi system among the ordinary full Heusler com-pounds as an electrode material.Our first-principles design of the OSDs is basedon the density functional theory (DFT) using the
QuantumATK package (version P-2019.12) . Asexchange-correlation functional we chose the Perdew-Burke-Ernzerhof (PBE) parametrization combinedwith norm-conserving PseudoDojo pseudopotentials and linear combinations of atomic orbitals (LCAO) asbasis-set. As k -point grid for the ground state prop-erties we use a × × Monkhorst-Pack grid anda density mesh cutoff of 120 Hartree. For the trans-port calculations we combined DFT with the nonequi-librium Green’s function method (NEGF). We use a × × k -point mesh in self-consistent DFT-NEGF calculations. The I − V characteristics were cal-culated within the Landauer approach , where I ( V ) = e/h (cid:80) σ (cid:82) T σ ( E, V ) [ f L ( E, V ) − f R ( E, V )] d E . V standsfor the bias voltage and the transmission coefficient T σ ( E, V ) depends additionally on spin σ of an electronand energy E . Furthermore, f L ( E, V ) and f R ( E, V ) de-note the Fermi-Dirac distribution of the left and rightelectrode, respectively. For the calculation of T σ ( E, V ) we chose a × k -point grid. In Fig. 1 we present schematically the structure of theOSD and the corresponding I − V characteristics. Theconcept of the OSD has been extensively discussed inRef. 14 and thus here we will only give a short overviewof the device. The OSD consists of HMM and SGS ma-terials and possesses linear I − V characteristics. Theschematic DOS of these materials are also shown inFig. 1. Depending on the choice of the junction materials,the HMM and SGS electrodes can couple ferromagneti-cally (ferromagnetic OSD) or antiferromagnetically (an-tiferromagnetic OSD) at the interface giving rise to cor-responding I − V curves shown in Fig. 1. The operationprinciple of the OSD relies on the unique spin-dependenttransport properties of HMMs and SGSs as discussed inRef. 14 in detail.In the proposal of the OSD , the proof of principlewas demonstrated by using two dimensional transition-metal dichalcogenides VS (SGS) and Fe/MoS (HMM)as electrode materials. Since VS possesses an estimatedCurie temperature of 138 K , it is not suitable for roomtemperature applications. For more realistic devices wenow consider six Heusler compounds as mentioned beforeand construct four different OSDs: i) FeVHfAl − FeVTiSi,ii) FeVHfAl − FeVNbAl, iii) MnVTiAl − FeVTaAl, and iv)Co MnSi − FeVTaAl. All six Heusler compounds possessextremely high Curie temperatures as presented in Ta-ble I. For the construction of the OSD we assume thesituation where one material needs to be grown on topof the other one. Thus, in our simulations we take oneelectrode (SGS) in the cubic structure and relax the sec-ond electrode material (HMM) with respect to the in-plane lattice parameter of the first one. Therefore, inTable I we include the c/a ratios for the half metallicelectrode materials which takes the tetragonal structure.In Table I we present also the obtained magnetic mo-ments, magnetic anisotropy energies (MAEs), and workfunctions. As expected, tetragonal distortion results in asignificant change in the magnetic anisotropy energy ofHMMs, which is at least two orders of magnitude larger
FIG. 2. (Color online) (a) The atomic structure of the MnVTiAl − FeVTaAl Ohmic spin diode. The system is periodic in x - and y -direction in the plane orthogonal to the z -direction, which is the transport direction. The red arrows illustrate the directionas well as the magnitude of the magnetic moments within the scattering region. Small magnetic moments are overlayed bythe atomic radii. The black dashed box denotes the interface. (b) The calculated spin-resolved bulk electronic band structurealong the device stack direction, [001], for MnVTiAl (left panel) and FeVTaAl (right panel). For both compounds the Fermilevel is set to zero (dashed black line). than the SGSs, being in good agreement with the litera-ture .We now focus on the first OSD and discuss its struc-tural, electronic and magnetic properties. Fig. 2 (a) il-lustrates the atomic structure of the OSD based on half-metallic MnVTiAl (left electrode) and spin-gapless semi-conducting FeVTaAl (right electrode) quaternary Heuslercompounds. We use a minimal tetragonal unit cell alongthe [001] direction containing 8 atoms. For each electrodethis cells was repeated 5 times and defines the screeningregion. The length (screening region) of the device isaround 62 Å. In the other three OSDs, the consideredscreening region lies in between 61Å and 63Å, depend-ing on the materials. As the strength of the spin-orbitcoupling (SOC) is very weak in these materials we, ne-glect the SOC in transport calculations and thus we chosethe z -direction as the transport direction and also ad-justed the alignment of the magnetic moments to the z -axis. The red arrows and their size in Fig. 2 (a) representthe direction and magnitude of the atomic magnetic mo-ments in the junction materials. In this OSD, the HMMand SGS electrodes couple ferromagnetically at the in-terface, i.e., the energy difference between ferromagneticand antiferromagnetic coupling is about 400 meV.Looking at the magnetic moments at the interface re-gion in Fig. 2, we notice that the size of the arrows deviate from their bulk behavior, i.e, far from the interface. Espe-cially the magnetic moment of the Mn atom in MnVTiAlat the interface decreases from 2.42 µ B to 0.07 µ B . Thisis due to the fact, that at the interface region MnVTaAlis formed which also presents HMM behavior with bulkmagnetic moments of m Mn = 0 . µ B , m V = 1 . µ B , m T a = − . µ B and m Al = − . µ B . Therefore, thehalf metallic character of the MnVTiAl compound is re-tained at the interface. However, the FeVTaAl compoundloses its spin-gapless semiconducting nature near the in-terface region as it will be discussed later in detail.Next, we would like to discuss the electronic propertiesof the MnVTiAl − FeVTaAl junction at equilibrium, i.e.,at zero bias. The bulk band structure along the transportdirection of the junction materials is shown in Fig. 2 (b).MnVTiAl is a HMM with a band gap of around 650 meVin the minority-spin channel while FeVTaAl shows SGSproperties. Note that the spin-gapless semiconductingbehavior along the chosen directions is not well seen andfor a detailed discussion the reader is referred to Refs. 4and 7. Nikolaev et al. and Bai et al. provided a de-tailed discussion about the importance of band match-ing for the transport properties of giant magnetoresis-tance (GMR) spintronic devices. In our case, as seen inFig. 2 (b), there is a good band matching for the major-ity spin states near the Fermi level close to the Γ -point FIG. 3. (Color online) Projected device density of states (DDOS) at zero bias (equilibrium) for the majority (left panel) andminority spin channel (right panel) of the MnVTiAl − FeVTaAl OSD (the atomic structure is given in Fig. 2). The white dashedlines display the Fermi level while the vertical yellow dashed lines denote the interface. between the electrode materials, especially along the Γ -Rand Γ -A directions. Note that a good band matching sup-presses the electron back scattering at the interface andensures a smooth propagation of majority spin electronsfrom the FeVTaAl electrode to the MnVTiAl electrode.In Fig. 3 we present the device density of states (DDOS)of the MnVTiAl − FeVTaAl junction. As mentioned abovethe half metallicity of MnVTiAl is preserved at the inter-face which can be seen in the majority-spin and minority-spin channel DDOS presented in Fig. 3. However, theSGS character of FeVTaAl is lost near the interface re-gion due to the charge transfer from the half-metallicelectrode to the SGS (see the left panel of Fig. 3). Thischarge transfer stems from the work function differenceof 160 meV between the two electrode materials. As Mn-VTiAl has the lower work function, electrons flow fromthe majority-spin channel of MnVTiAl to the majorityspin-channel of FeVTaAl. Once the charge redistributionreaches equilibrium, MnVTiAl will be positively chargednear the interface region, whereas FeVTaAl will be neg-atively charged and hence an electric dipole will be in-duced. This dipole influences the electronic and mag-netic properties of both materials. Since the magneticmoment of the Mn atom in the MnVTiAl electrode hasalready been discussed above, we will briefly commenton the magnetic moment of the V atoms near the in-terface region.The magnetic moment of the V atoms inMnVTiAl is reduced to 2.25 µ B close to the interface andrecovers to the bulk value within two unit cells. On theother hand, the variation of magnetic moments in theFeVTaAl electrode near the interface region is around0.1 µ B . Thus, the affected region by the charge transferis restricted to five atomic layers for the majority-spinchannel. The minority-spin channel is not substantiallyaffected for both junction materials.Up to now, we discussed the properties of the OSD forzero bias and will now focus on the current-voltage ( I − V ) characteristics when a bias voltage is applied. Therefore,Fig. 4 (a) and 4 (b) illustrate the DDOS for both spinchannels for the MnVTiAl − FeVTaAl junction under abias voltage of +0.3 V and -0.3 V, respectively. Also thecorresponding transmission spectra are presented there.For both, forward and reverse bias, the electronic andmagnetic properties of both materials are not influencedby the bias voltage. The I − V characteristics of theMnVTiAl − FeVHfAl junction presented in Fig. 5 (a) canbe explained on the basis of the DDOS. Under a for-ward bias voltage majority spin electrons from the oc-cupied states below the Fermi level in FeVTaAl can betransmitted to unoccupied states above the Fermi levelin MnVTiAl. Thus, the transmission coefficient has afinite value in this case. However, for the minority spinelectrons the transmission coefficient is zero because bothmaterials have no states that could contribute to trans-port in the given voltage window. Thus, the forward cur-rent (on-current) is 100% spin polarized. Also under anapplied reverse bias voltage the transmission coefficientfor minority-spin electrons is zero due to the energy gapin both materials. On the other hand, the overlap ofconduction and valence bands of opposite spin channelsaround the Fermi energy in FeVTaAl gives rise to a non-zero transmission coefficient for majority-spin electrons,which leads to a leakage current that will be discussed indetail in the following paragraph.Before we discuss the origin of the leakage current, wewill briefly comment on the I − V characteristics of theother three OSDs, which are also presented in Fig. 5.As seen there, for all OSDs we obtain a linear behav-ior starting from around +0.15 V for the ferromagneticOSDs (MnVTiAl − FeVTaAl, FeVHfAl − FeVTiSi andFeVHfAl − FeVNbAl junctions) and around -0.15 V in thecase of the antiferromagnetic OSD Co MnSi − FeVTaAl.For the three ferromagnetic OSDs, the I − V curvesare more or less similar to each other, while the FIG. 4. (Color online) (a) Projected local device density of states (DDOS) for the majority (left panel) and minority (rightpanel) spin channel in MnVTiAl − FeVTaAl OSD (the atomic structure of an OSD is provided in Fig. 2) for a bias voltage of V = 0 . V. In the middle panel we present the calculated transmission spectrum for both spin channels. The dashed linesindicate the Fermi energy of the left and right electrode. (b) displays the same as (a) for a bias voltage V = − . V. Co MnSi − FeVTaAl junction is in the off state for a for-ward bias and in the on state for a reverse bias, whichis somewhat similar to the backward diode . An in-teresting feature of this latter OSD would be its dynam-ical configuration since the magnetic coupling strengthof the electrodes at the interface is rather weak ( ∼ I − V curves of the diode can be reversed similar tothe case of reconfigurable magnetic tunnel diode con-cept in Ref. 13. Returning back to the discussion of the I − V characteristics, all four OSDs exhibit exactly zerothreshold voltage V T under forward bias. It is worth tonote that all semiconductor diodes have sizeable thresh-old voltages V T (V T ∼ p − n diodes),which gives rise to the power dissipation ( P = V T · I ) inform of heat and thus this is an undesirable effect. Thelarger the value of the threshold voltage V T , the higheris the power dissipation in a diode. Furthermore, for allOSDs the leakage currents are small compared to the on-currents. The leakage current can be traced back to thesmall overlap of conduction and valence band edges of op-posite spin channels around the Fermi level in the SGSelectrode as schematically shown in Figs. 5 (e) and 5 (f)(see Refs. 4 and 7 for the band structure and DOS of theSGS materials). Band overlaps allow in the ferromag-netic (antiferromagnetic) OSD the flow of majority spinelectrons from the occupied states of the HMM (SGS)material into the unoccupied states of the SGS (HMM)electrode. Thus, this process gives rise to a small leak-age current. However, the leakage current is absent in the minority-spin channel in both cases due to the en-ergy gaps in the electrode materials. Therefore, leakagecurrents can be prevented by using ideal SGS materi-als, i.e., without an overlap in conduction and valenceband edges of opposite spin channels around the Fermienergy. Since FeVTiSi exhibits an overlap of 150 meVwhile FeVNbAl and FeVTaAl possess overlaps of 45 meVand 60 meV, respectively, the FeVHfAl − FeVTiSi junctionshows the largest leakage current.Finally, we would like to comment on the on/off ratiosand current densities of the OSDs. The I ON /I OFF ra-tios at ± . V vary between (FeVHfAl − FeVTiSi) and (MnVTiAl − FeVTaAl) at zero temperature. SinceFeVTiSi possesses the largest overlap between the con-duction and valence band edges of opposite spin chan-nels around E F , the FeVHfAl − FeVTiSi junction showsthe largest leakage current as discussed above and thusthe lowest on/off ratio. From that point of view, also theon/off current ratios can be increased by using materialswith ideal spin-gapless semiconducting behavior. Here,the MnVTiAl − FeVTaAl junction seems to be the bestcandidate for realizing the OSD. Another aspect that in-fluences the on/off ratios is temperature, which is ne-glected in our transport calculations due to the technicallimitation of the
QuantumATK package for spintronicmaterials as discussed in Ref. 14. Temperature effectsas well as the spin-flip excitations can further reduce theon/off current ratio in OSDs (see Ref. 14 for a detaileddiscussion). As for the current densities, the calculatedvalues are comparable to the elementary metals and much
FIG. 5. (Color online) Calculated current-voltage ( I − V ) characteristics for all HMM-SGS junctions (a-d). The red linesdisplay a linear fit. The coupling of the electrodes is displayed by a small image in the lower right corner. (e) and (f) show theorigin of the leakage current under reverse and forward bias for ferromagnetically and antiferromagnetically coupled HMM andSGS electrodes, respectively. higher than conventional p − n or p − i − n diodes .It is worth to note that in transport calculations withinthe QuantumATK package all inelastic scattering pro-cesses stemming from phonons as well as electrons andmagnons are neglected. All these neglected processes cansubstantially reduce the current density of the OSDs.In conclusion, the OSD is a recently proposed con-cept in spintronics and requires materials with uniqueelectronic properties, in particular half-metallic and spin-gapless semiconducting behavior. Since both propertieshave already been identified in the family of orderedquaternary Heusler compounds, this family is a prefer-able choice for the realization of such devices. Moreover,most of the compounds within this family possess veryhigh Curie temperatures making them potential candi-dates for spintronic applications at room temperature.By using first principles DFT calculations combined withthe NEGF method, we proposed four different HMM-SGS junctions (or OSDs) within the family of quaternaryHeusler compounds. All four OSDs show linear I − V characteristics with zero threshold voltage V T in the onstate and small leakage currents in the off state whichcan be attributed to the small overlap of conduction andvalence band edges of opposite spin channels around theFermi level in the SGS electrode. In three of the designedOSDs, the HMM and SGS electrodes couple ferromag-netically, while in the Co MnSi − FeVTaAl junction thiscoupling is antiferromagnetic and thus this diode can beconfigured dynamically via an external magnetic field.Furthermore, the zero threshold voltage V T is importantfor reducing the power consumption in a diode as it scales linearly with V T . We hope that our results pave the wayfor the experimental fabrication of OSDs based on qua-ternary Heusler compounds. ACKNOWLEDGMENTS
This work was supported by the European Union(EFRE), Grant No: ZS/2016/06/79307 and by DeutscheForschungsgemeinschaft (DFG) SFB CRC/TRR 227.
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