Magnetic Properties of Transition-Metal Adsorbed ot-Phosphorus Monolayer: A First-principles and Monte Carlo Study
MMagnetic Properties of Transition-Metal Adsorbed ot -PhosphorusMonolayer: A First-principles and Monte Carlo Study Zengyao Wang, Qingyun Wu, and Lei Shen ∗ Engineering Science Programme, Faculty of Engineering,National University of Singapore, Singapore 117575 Department of Materials Science Engineering,National University of Singapore, Singapore 117575 Department of Mechanical Engineering, Engineering Science Programme,National University of Singapore, Singapore 117575 (Dated: October 11, 2018)
Abstract
Using the first-principles and Monte Carlo methods, here we systematically study magneticproperties of monolayer octagonal-tetragonal phosphorus with 3 d transition-metal (TM) adatoms.Different from the puckered hexagonal black phosphorus monolayer (phosphorene or α -P), theoctagonal-tetragonal phase of 2D phosphorus (named as ot -P or ε -P in this article) is buckled withoctagon-tetragon structure. Our calculations show that all TMs, except the closed-shell Zn atom,are able to strongly bind onto monolayer ot -P with significant binding energies. Local magneticmoments (up to 6 µ B) on adatoms of Sc, Ti, V, Cr, Mn, Fe and Co originate from the exchange andcrystal-field splitting of TM 3 d orbitals. The magnetic coupling between localized magnetic statesof adatoms is dependent on adatomic distances and directions. Lastly, the uniformly magnetic orderis investigated to screening two-dimensional dilute ferromagnets with high Curie temperature forapplications of spintronics. It is found that ot -P with V atoms homogeneously adsorbed at thecentre of octagons with a concentration of 5% has the most stable ferromagnetic ground state. ItsCurie temperature is estimated to be 173 K using the Monte Carlo method. PACS numbers: 73.40.Ns, 73.20.At, 75.70.Rf, 52.65.Pp a r X i v : . [ c ond - m a t . m t r l - s c i ] A p r . INTRODUCTION The research scope of two-dimensional (2D) materials has developed from graphene inthe early stage into a vast range of layered materials including transition metal dichalcogenies(TMDs) and different 2D allotropes of silicon and phosphorus . In particular, monolayerblack phosphorus, known as phosphorene or α -P, has drawn great attentions since its firstsuccessful fabrication in 2014 . Comparing to carbon-based 2D materials, the extra pairof electrons in a P atom allows the phosphorene monolayer to have a band gap which canbe tuned by the strain, electric field or “cutting” into ribbons . Furthermore, phospho-rene shows good magnetic and/or magneto-optical properties . These properties makephosphorene a great potential in the applications of electronics, spintronics and photonics.The challenge of 2D black phosphorus for practical applications is its poor stability in theambient environment, and thus it needs to be capsuled by other inert 2D materials, such as h -BN . Recently, some other layered allotropes of phosphorus beyond black phos-phorus are proposed, such as blue phosphorus ( β -P) , γ -P and δ -P . Very recently,a new octagonal-tetragonal phosphorus is emerged, which is composed of alternate octagonand tetragon (coined as ot -P or ε -P) instead of puckered hexagons in mono-layered blackphosphorus as shown in Fig. 1 . The pristine monolayer ot -P is stable and exhibitssemiconducting properties [see APPENDIX ]. As an elemental semiconductor ot -P allowsits corresponding 2D type diluted magnetic semiconductors (DMSs) to have a more stableferromagnetic state than III-V and II-VI based DMSs by preventing the formation of anti-site defects . Furthermore, the anisotropic buckled structure of ot -P in principle allowsfor different coupling strength along different directions, which provides a way to tune themagnetic properties with doping. These properties suggest ot -P to be a promising materialfor 2D DMSs and spintronic applications.In this work, a systematic study of the magnetic properties of transition-metal (TM)atom (Sc-Zn) adsorbed ot -P monolayers ( ot -P+TM) is carried out by the first-principles andMonte-Carlo methods. It is found that except for closed-shell atom Zn all of TM atoms arefirmly binding onto the ot -P monolayer with significant binding energies. ot -P+TM systemsfor TM from Sc to Co exhibit local magnetic moments. The projected density of statesshows that the localized magnetism mainly originates from the crystal field and exchangesplitting of TM 3 d orbitals. The magnetic coupling and order acquired through the long-2ange interaction between diluted defects are investigated to screening possible ferromagnetsfor spintronic applications. Lastly, the Curie temperature of ferromagnets is estimated bythe Monte Carlo method. This article is organized as following: The computational detailsare given in Sec. II.
We present details of the optimized geometric structures and originof local moments with an isolated adatom in Sec.
III and subsections. The long-rangemagnetic coupling, magnetic order, and the Curie temperature of ferromagnetic systems isstudied in Sec.
IV. and subsections. At the end, the conclusions and discussions of thisarticle are shown in Sec. V followed by the APPENDIX of the band structure and phonondispersion.
II. COMPUTATIONAL DETAILS
All the calculations are done via first-principles methods based on density functional the-ory (DFT) , as implemented in the
Vienna Ab Initio Simulation Package (VASP)46,47 . Theexchange correlation energy is simulated using generalized gradient approximation (GGA) inthe form of the Perdew-Burke-Ernzerhof approximation (PBE) functional, while the pro-jector augmented wave (PAW) approximation is used to describe the core electrons asexternal potentials to the orbitals of study. For structure relaxation and calculation of thebinding energies, a supercell of ot -P lattice with centered sampling point in the first Brillouinzone is used. In the perpendicular direction to the monolayer, a vacuum layer of 30 ˚A isused to eliminate interaction between adjacent slabs. The lattice constants for the primitiveunit cell of pristine ot -P monolayer used in this work are a = b =6.455 ˚A. the k-pointsmesh used for calculation carried out in a 2 × × ×
1. When studyingthe influence of adsorption concentration on Curie Temperature, systems with 5 differentadsorption concentrations, i.e. 3 . , , . , . , and 25% are studied, in whichthe adsorption concentration is defined to be the ratio of TM atoms vs P atoms in thesystem. Spin polarized calculations are performed throughout the work. The kinetic energycutoff for the plane wave basis set is chosen to be 255 eV, which yields well-converged totalenergies. All the structures are relaxed until the remaining force on each atom is reducedto less than 0.01 eV/˚A. 3 a)(b) (c)(d) (e) (f) (g) (h) (i) Charge density σσσ σ π ππ π FIG. 1.
Front view (a) and side view (b) of a 2D ot -P monolayer. The unit cell of ot -P consists of 8 atoms,which is denoted by a square in (a). The ot -P monolayer has a non-planar buckled structure, with half ofthe eight atoms at one side of a hypothetical middle plane and half at the other side. (c) Charge densitydistribution at the Γ point of the valence band of 2D ot -P. The atoms labeled with 1, 3, 5, and 7 are in frontof the hypothetic middle plane, while atoms labeled 2, 4, 6 and 8 are behind the middle plane. Each atomforms one π and one σ bonding with its two nearest-neighbor atoms through the occupied p orbital. Forclarity, in (a)(b) and all the following figures, we use orange color (dark grey) to represent atoms above themiddle plane and yellow color (light grey) to represent atoms below the middle plane. (d)-(i) ot -P monolayerwith adsorption of a TM atom at B , B , C C , T , and T sites respectively. Our calculation shows that C and T positions are two stable adsorption sites among the six configurations. III. ISOLATED ADATOM
First of all, we study geometric and electronic structures of a supercell of ot -P with anisolated TM adatom by placing a TM atom on a big supercell. The possible site of adsorptionand local structural deformation after adsorption is investigated for all 3 d transition metalson the ot -P supercell. The origin of the localized magnetic state induced by the adatom isdiscussed in detail. 4 .22.32.42.52.62.72.8 l l l l l l l Sc Ti V Cr Mn Fe Co Ni CuSc Ti V Cr Mn Fe Co Ni Cu B ond l eng t h ( A ) 。 B ond l eng t h ( A ) 。 (a) (b)(d) (c) l l l l l l l Local deformationLocal deformation (e) (f)
Sc Ti V Cr Mn Fe Co Ni Cu ZnSc Ti V Cr Mn Fe Co Ni Cu Zn B i nd i ng ene r g y ( e V ) B i nd i ng ene r g y ( e V ) c site t site @ c site PhysisorptionStrong chemisorption @ t site Chemisorption PhysisorptionStrong chemisorptionChemisorption
FIG. 2.
Optimized geometry of (a)TM@ C and (c) TM@ T systems. The length of the TM-P bonds in (b)TM@ C systems and (d)TM@ T systems for TM from Sc to Cu. Notice that the Zn atom does not formbonds with nearby P atoms due to its closed-shell structure. Before adsorbing, l , l , l and l are equivalentin (a), and l / l (not l ) are equivalent in (c). After adsorbing, they may not be equivalent due to the localdeformation of the structure. The binding energies ( E b ) of the TM atoms on ot -P monolayers. Most of the3 d TM atoms, except for closed-shell Zn, have a chemisorption on the ot -P monolayer with a large bindingenergy ( > A. Stability of geometric structures
Before we study the magnetic property of ot -P monolayers with an isolated TM adatom,we first check their stability of the optimized geometric structure. Different from planarstructure of graphene or h -BN, the ot -P monolayer has a non-planar buckled structure. Aunit cell of ot -P consists of eight phosphorus atoms, denoted by a square in Fig. 1(a) . Ina unit cell, half of eight atoms are at one side of the hypothetical middle plane, while theother half are at the opposite side, as shown in
Figs. 1(b) and . Figure 1(c) showsthe charge density at the Γ point of the valence band. Atoms labeled with 1, 3, 5 and 7 arein front of the hypothetic middle plane, while atoms 2, 4, 6, and 8 are behind the middleplane. As can be seen, there is only occupied bonding orbital (no anti-bonding orbital) inbuckled ot -P. Each atom forms one π and one σ bonding with its two nearest-neighbor atomsthrough the occupied p orbital. Even in the graphene structure, there is no strong short-range π bonding between two adjacent carbon atoms, instead of a “big π ” bond floating5ver two sides of the graphene sheet. This all-bonding nature indicates an extremely stablestructure of buckled ot -P, which is further verified by the phonon dispersion [ APPENDIX ].For all ot -P+TM systems (TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn), six possibleadsorption sites are investigated, the bridge site over a P-P bond at the side of an octagonalring ( B ), the bridge site over a P-P bond at the side of a tetragonal ring ( B ), the center ofa tetragonal ring ( C ), the center of an octagonal ring ( C ), the top site of a P atom abovethe middle plain ( T ), and the top site of a P atom below the middle plain ( T ), as shownin Figs 1(d)-(i) . Through the optimization of the geometric structures of ot -P+TMs, wefind that the more preferred sites are C and T positions. Other four sites of adatoms arefound to be less energetically favourable. Regardless of their initial positions, the adatomswill spontaneously move to either C or T position after structural relaxation. Therefore,in the following studies only systems of ot -P+TM atoms adsorbed on C and T sites arediscussed.Except for closed shell atom Zn, other 3 d TM atoms at either C or T site is able tobond covalently with nearby P atoms. For adsorption at C positions, the four covalentbonds are formed between the adatoms and the four P atoms of an octagonal ring above themiddle plain. For T site, adatoms are covalently bond to the three nearest P atoms, whichtogether with the other P atom below form a valley at the joint corner of the octagonal andtetragonal rings. Graphical representation of the covalent bonds and their lengths are shownin Fig. 2 . Different values of the bond length indicate that the adsorption of TM atomsmay induce a local structural deformation. Mn and Fe can induce a large deformation atthe C site, while Cr makes a distinguished deformation at the T site. Different values ofbond length also mean different binding energies, E b , which is defined as E b = E T M + ot − P − E ot − P − E T M , (1)where E ot − P , E T M and E T M + ot − P are the total energies of the pristine ot -P monolayer, theisolated TM atom, and the system of ot -P monolayer with TM atoms adsorbed respectively.The calculated binding energies are shown in Figs. 2(c) and . It shows that exceptfor the closed shell transition metal atom Zn that is physisorbed to ot -P monolayer witha binding energy as low as 0.17 ∼ ype IType II Type II (a)(b) (e) (f) M agne t i c m o m en t ( B ) μ Sc Ti V Cr Mn Fe Co Ni Cu Zn @ c site @ t site Type IIIType I Type III Δ cf Δ exType IHigh spin V @ c site Δ cf Δ exType IILow spin Fe @ c site E F -1.0 -0.5 0 0.5 1.0 P D O S ( a . u ) V @ c site Fe @ c site (c) (d) Energy (eV) Energy (eV) -3.0 -2.0 -1.0 0 1.0
Type I Type IIType II spinspin spinspin Δ cf Δ ex Δ cf Δ ex FIG. 3.
Magnetic moments of (a) ot -P+TM@ C and (b) ot -P+TM@ T systems. Each kind of systems isfurther divided into three types, Type I (high spin state), Type II (low spin state), and Type III (non-spinstate). Partial density of states of (c) ot -P+V@ C and (d) ot -P+Fe@ C systems. Schematics of 3 d energylevels of (e) V (type I) and (f) Fe (type II) atom after adsorption on the C sites of ot -P monolayer. In ot -P+V@ C , the type I system, the crystal field splitting ∆ cf is smaller than the exchange splitting ∆ ex ,leading a high spin state and high total magnetic moment. On the other hand, in ot -P+Fe@ C , the type IIsystem, ∆ ex is comparable to ∆ cf , resulting a low spin state and low total magnetic moment of 2 µB due tothe spin-moment compensation. B. Origin and classification of localized magnetic states
The magnetic moments of different ot -P+TM systems are shown in Figs. 3(a) and .The ot -P+TM systems are magnetic for TM atoms from Sc to Co for adsorption at both C and T sites. For transition metal atoms of Ni, Cu and Zn, the ot -P+TM systems arenonmagnetic regardless of their adsorption sites.It can be seen in Fig. 3(a) that the highest magnetic moment for ot -P+TM systems canreach 6 µB per adatom due to the extra contribution from 4 s electrons. In an isolated TMatom, the 4 s orbitals are of lower energies than the 3 d orbitals. However, after adsorptionon pristine ot -P monolayer, the large coulomb repulsion between the monolayer and the 4 s s orbitals. Electrons, originally in 4 s orbitals,would instead occupy lower 3 d orbitals. These electrons would therefore also contribute tomagnetism of the systems. ot -P+TM systems can be further classified into three types foreach adsorption sites, the high spin state (type I), the low spin state (type II), and non-spinstate (type III). The classification is made basing on the degree of crystal field splitting ∆ cf and exchange splitting ∆ ex of 3 d orbitals in different ot -P+TM systems.The effect of crystal field splitting ∆ cf originates from symmetry breaking when intro-ducing the TM atoms to the ot -P monolayer system. ot -P+TM systems with adsorption on C sites are of D symmetry, i.e. there is a four-fold axis perpendicular to the hypotheti-cal middle plane of ot -P and four two-fold axis normal to the four-fold axis. On the otherhand, ot -P+TM systems with adsorption on T sites are of C s symmetry, which is lowerthan the D symmetry. The crystal field splitting effect in such systems is therefore morepronounced, resulting in a lower degeneracy of 3 d orbital energy levels. Comparing to thePDOS of V@ C , there are more well-spaced discrete peaks in the PDOS of V@ T (not shownhere), suggesting a lower degeneracy of energy levels in the V@ T system. In the meantime,different TM atoms would also induce different extend of lattice distortion at the adsorptionsites, which further breakdown the symmetry of the system. For this reason, different TMatoms adsorbed at the same site also have different degrees of crystal field splitting of their3d orbital energy levels. The relative values of the crystal field splitting of the system totheir exchange field splitting of 3 d orbitals under external magnetic field is the essentialcriterion for determination of the high spin and low spin type of the system.The exchange splitting ∆ ex is the energy difference of two electronic states due to exchangeinteractions, i.e., direct overlap of electronic wavefunctions. When the crystal field splitting∆ cf is less pronounced than the exchange splitting ∆ ex , the energy levels are of higherdegeneracy, as shown in Figs. 3(c) and . the schematic representation of energy levelsof V@ C . It is easier for the system to occupy all the spin-up states first before starting tooccupy the spin-down states. Thus, such systems are expected to be able to reach highertotal magnetic moment. This type of systems is of high spin case and is classified as type Iin this work. On the contrary, when the crystal field splitting ∆ cf is more pronounced thanthe exchange field splitting ∆ ex , such system has a small amount of magnetic moments, asshown in Figs. 3(d) and . It is because of the occupation of the spin-down states ofthe lower energy levels, thus cancels the total spin of electrons and results in a lower total8agnetic moment. For this reason, this type of systems is classified as type II – the lowspin type. When the the exchange field splitting ∆ ex is zero, for example the absorptionsof Ni, Cu and Zn atoms on ot -P monolayers at both C and T sites, these systems arenonmagnetic, defined as type III.Using the above definition for type I (high spin), type II (low spin), and type III (non-spin), we can classify all cases of ot -P+TM at both C and T sites. For systems withadsorption at C sites, systems with TM = Sc, Ti, V and Cr are of Type I, and systemswith TM = Mn, Fe and Co are of type II [ Fig. 3(a) ]. For systems with adsorption at T sites, systems with TM = Sc, Ti, Cr, Mn, Fe and Co are of type II and the system with TM= V is of type I [ Fig. 3(b) ]. The all rest are of type III [
Fig. 3(a) and
Fig. 3(b) ]. Inparticular, the highest magnetic moment in TM@ C systems is 6 µB per adatom, whereasthe highest magnetic moment in TM@ T systems is 5 µB per adatom. This is becausefor adsorption at C sites there is higher symmetry and less splitting of 3 d orbital energylevels than that at T sites. Meanwhile, the exchange field splitting effect is large enough tocompletely separate the spin-up and spin-down states of in total six 3 d +4 s orbitals, resultingin a high total magnetic moment. Our PDOS results show that for Ni+ ot -P systems theten outmost electrons exactly fill up the 3d orbitals, thus having a spin configuration ofno total magnetic moment. For ot -P+Cu systems, the left one electron after filling up thespin-up and spin-down states of 3d orbitals has a delocalized nature and does not contributeto the local magnetic moment. As for Zn, the close-shell atom is physisorbed onto the ot -Pmonolayer, thus is able to maintain its atomic state without magnetism. IV. MAGNETIC COUPLING, ORDER AND CURIE TEMPERATURE
After studying the localized magnetic state of ot -P with a single adatom, we next in-vestigate the long-range magnetic coupling and order under different concentrations anddirections of adatoms. After getting configurations with ferromagnetic order, the Curietemperature of ferromagnets is estimated and discussed for the application of spintronics.In this section, V and Cr are chosen as examples to study the effect of adsorption distance,direction, and concentration on magnetic properties of ot -P+TM systems. They are cho-sen over other TM atoms because these two elements exhibit a high magnetic moment andstrong binding energy at both C and T adsorption sites as what has been shown in the9 rigin a ba a a b b b (a) (b)(c) Origin a ba a a a b b b b E - E ( m e V )
14 16 18
V@C2 siteAFMFM b b b a a a Distance (A) 。 (d) E - E ( m e V ) Cr@T2 siteAFMFM b b a a a Distance (A) 。 b a b FIG. 4. (a) Schematic representation of C -type sites along two different directions. The a directionis defined as the one along which there are alternative tetragon and octagon rings, whereas along the b direction the octagon rings are directly connected by sharing one side with each adjacent octagon ring. (b)schematic representation of T -type sites along two different directions. Energy differences between paralleland antiparallel spins as a function of distance and direction for (c) V@ C and (d) Cr@ T . previous section. A. Magnetic coupling
In order to study the long-range magnetic coupling between two adatoms, we model asupercell of a ot -P monolayer with two adatoms at different adsorption sites and along differ-ent directions. One adatom is fixed as the origin, and then the other adatom is placed awayalong two different directions [ Fig. 4 ]. Next, we study the long-range magnetic interactionbetween the origin and the other TM atom (V@ C and Cr@ T as examples) by calculat-ing the energy difference between parallel- ( E ↑↑ ) and antiparallel-spin ( E ↑↓ ) configurations.Anisotropic (isotropic) magnetic interaction is found for adsorption at C ( T ) sites. At the C site, the exchange interaction aligns the spin antiparallel along the a direction, whilealigns the spin parallel along the b direction [ Figs. 4(a) and ]. As for T sites, along10 a) (b) (c)FM pAFM tAFM(d) E ne r g y d i ff e r en c e ( e V ) @ c site V: Δ FM - tAFM V: Δ FM - pAFM Cr: Δ FM - tAFM Cr: Δ FM - pAFM (e) E ne r g y d i ff e r en c e ( e V ) @ t site FM ground state FM ground state
FIG. 5. (a)-(c) The ferromagnetic (FM), parallel antiferromagnetic (pAFM) and total antiferromagnetic(tAFM) order of the TM adatoms in a 4 × C site, corresponding to an adsorptionconcentration of 3 . T -site cases are not shown here). Energy differencebetween FM and pAFM orders, FM and tAFM orders as function of adsorption concentrations for (d)V/Cr@ C and (e) V/Cr@ T systems. both a and b directions the exchange interaction aligns the spin parallel for short distancesand spin antiparallel for long distances as shown in Figs. 4(c) and . There is nomagnetic coupling (∆ E ↑↑ − E ↑↓ = 0) when the separation of two adatoms is larger than 13 ˚A. B. Magnetic order
In order to study the magnetic order under different concentrations, we use a supercellwith 4 adsorption atoms, which are evenly distributed along both horizontal and verticaldirections as shown in
Figs. 5(a)-(c) . Different adsorption concentrations are controlledby adjusting the size of the supercell while keep the number of adatoms in each supercellunchanged. Given two types of adatoms and two different adsorption sites, there are intotal four categories to be considered, V atoms adsorbed at C and T sites, and Cr atomsadsorbed at C and T sites. For adsorption at C sites, four cases corresponding to theadsorption concentration of 3 . . .
5% are considered. On the other11and, as T sites are of lower symmetry than C sites, isotropic systems are only able to beconstructed with three adsorption concentration of 3 . .
25% and 12 . . To determine the magnetic order of the ground state, the energy difference of systemswith different magnetic orders are calculated as shown in
Figs. 5(d) and . In thiswork, we considered two types of antiferromagnetic spin configurations, as shown in
Figs.5(b) and . In particular, the parallel antiferromagnetic configuration has one row ofadatoms with the same sign of spin and the adjacent two rows of adatoms having spin of theopposite sign [
Fig. 5(b) ]. On the other hand, any adatom in the total antiferromagneticconfiguration has opposite sign of spin with its four nearest neighbors[
Fig. 5(c) ]. Totalenergy of FM, pAFM and tAFM configurations is calculated and compared. It is found thatV@ C systems with 5% and 6 . T system with 12 .
5% and Cr@ T system with 6 . C. Curie temperature of ferromagnets As ot -P monolayer is of square lattice geometry, the Curie Temperature of the systemcan be calculated basing on 2D square lattice Ising model. Considering nearest and second-nearest-neighbor interactions without external field, the Hamiltonian of the 2D square Isingmodel is H ( σ ) = − J (cid:88) σ i σ j − K (cid:88) ,
50 100 150 200 250 300 350 V H ea t c apa c i t y ( a . u . ) Temperature (K) @ c (5.0%) V @ c (6.25%) V @ t (12.5%) Cr @ t (6.25%)
3K 38K56K 173K
FIG. 6.
The temperature-dependent heat capacity ( C ) of all the previously found ferromagnetic sys-tems. The peak of the heat capacity ( C ) to temperature T curve corresponding to the ferromagnetic-to-paramagnetic phase transition temperature, i.e. the Curie temperature. Among all the systems, ot -P+V@C2system with adsorption concentration of 5% is found to exhibit the highest Curie temperature of 173K. E pAF M = E nm + 8 K. (5)By adding and subtracting equation 3, 4 and 5, we can obtain the expression for J and K as: J = E tAF M − E F M , (6) K = − E tAF M + E F M − E pAF M . (7)The Curie Temperature is the temperature at which the ferromagnetic-paramagnetic transi-tion happens. It is expected that the peak of the temperature-dependent heat capacity ( C )of the system will be observed at phase transition temperature, i.e. the Curie Temperature.Here, the heat capacity ( C ) of the system can be calculated using the expression: C = lim ∆ T → ∆ E T ∆ T , (8)where ∆ E T is the change of the total energy of the system caused by redistribution of spinswhen the temperature is increased by ∆ T .In this work, we used 100 ×
100 lattice points containing 10 local magnetic moments tosample our systems. For each system at each temperature the simulation of spin distribu-tion is looped for 2 × times. By observing the peak of the temperature-dependent heat13apacity of all the systems, we found that V@ C system with adsorption concentration of5% have the highest Curie temperature of 173 K as shown in Fig. 6 . Such low adsorptionconcentration makes it possible in the experiment . Even though the 173 K Curie tem-perature is still lower than the room temperature, it is larger than most traditional DMS,such as 5% Mn doped GaAs ( T c ∼
120 K) , 5% C doped ZnO ( T c = 80 K) . Due tothe quantum confinement effect, the Curie temperature of zigzag phosphorene nanoribbonsis estimated to be above room temperature using the Monte Carlo method . Thus, the ot -P nanoribbons may have higher T c than 173 K and above room temperature. Noticethat the mean-field approximation usually overestimates the Curie temperature . Forexample, the Curie temperature of the same ot -P with 5% V@ C is around 600 K if we usethe mean-field approximation.Using the first-principles calculations, we find that ot -P+TM systems have high struc-tural stabilities and able to exhibit collective magnetic moments for adatoms from Sc toCo. The adatoms with localized magnetism on ot -P monolayers provide magnetic activesites, which can be used in sensors for detecting magnetic gas molecules. In particular,V@ C system with 5% concentration is found to have the most stable ferromagnetic groundstate. Its Curie temperature can achieve up to 173 K, which makes it a good candidate forspintronics applications. V. ACKNOWLEDGEMENTS
The Authors thank Yuan Ping Feng, Chun Zhang, Jiajun Linhu for their helpful discus-sions and comments. The first-principles calculations were carried out on the GRC-NUShigh-performance computing facilities. L.S. would like to acknowledge support from theACRF Tier 1 Research Project (Project No. R-144-000-361-112). L.S. is member of theSingapore Spintronics Consortium (SG-SPIN).
APPENDIX: BAND STRUCTURE AND PHONON DISPERSION E ne r g y ( e V ) G M X G G M X G F r equen cy ( H z ) PBEHSE
FIG. 7. (a) The calculated band structure of ot -phosphorus. The band gap is 1.96 eV using PBE and 2.77eV using HSE. (b) The phonon dispersion of ot -phosphorus. It shows that the structure of ot -phosphorus isstable since there is no non-trivial imaginary frequency. ∗ [email protected] S. Z. Butler, S. M. Hollen, L. Cao, Y. Cui, J. A. Gupta, H. R. Guti´errez, T. F. Heinz, S. S.Hong, J. Huang, A. F. Ismach, et al. , Acs Nano , 2898 (2013). Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, Nat. Nanotechnol. , 699 (2012). A. Lopez-Bezanilla, J. Huang, H. Terrones, and B. G. Sumpter, Nano. Lett. , 3267 (2011). E. S. Reich, Nature , 19 (2014). L. Li, Y. Yu, G. J. Ye, Q. Ge, X. Ou, H. Wu, D. Feng, X. H. Chen, and Y. Zhang, Nat.Nanotechnol. , 372 (2014). H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tom´anek, and P. D. Ye, Acs Nano (2014). S. P. Koenig, R. A. Doganov, H. Schmidt, A. C. Neto, and B. Oezyilmaz, Appl. Phys. Lett. , 103106 (2014). A. S. Rodin, A. Carvalho, and A. H. Castro Neto, Phys. Rev. Lett. , 176801 (2014). X. Peng, Q. Wei, and A. Copple, Phys. Rev. B , 085402 (2014). Z. Zhu and D. Tom´anek, Phys. Rev. Lett. , 176802 (2014). Z. Zhu, J. Guan, and D. Tom´anek, Phys. Rev. B , 161404 (2015). J. Guan, Z. Jin, Z. Zhu, C. Chuang, B.-Y. Jin, and D. Tom´anek, Phys. Rev. B , 245403(2014). J. Guan, W. Song, L. Yang, and D. Tom´anek, Phys. Rev. B , 045414 (2016). R. Fei and L. Yang, Nano. Lett. , 2884 (2014). R. Fei, V. Tran, and L. Yang, Phys. Rev. B , 195319 (2015). V. Tran, R. Soklaski, Y. Liang, and L. Yang, Phys. Rev. B , 235319 (2014). V. Tran and L. Yang, Phys. Rev. B , 245407 (2014). B. Ghosh, B. Singh, R. Prasad, and A. Agarwal, Phys. Rev. B , 205426 (2016). Q. Wu, L. Shen, M. Yang, Y. Cai, Z. Huang, and Y. P. Feng, Phys. Rev. B , 035436 (2015). L. C. Gomes and A. Carvalho, Phys. Rev. B , 085406 (2015). A. Ziletti, A. Carvalho, P. E. Trevisanutto, D. K. Campbell, D. F. Coker, and A. H. Castro Neto,Phys. Rev. B , 085407 (2015). M. Elahi, K. Khaliji, S. M. Tabatabaei, M. Pourfath, and R. Asgari, Phys. Rev. B , 115412(2015). D. C¸ ak ır, C. Sevik, and F. M. Peeters, Phys. Rev. B , 165406 (2015). A. Maity, A. Singh, P. Sen, A. Kibey, A. Kshirsagar, and D. G. Kanhere, Phys. Rev. B ,075422 (2016). R. Ma, H. Geng, W. Y. Deng, M. N. Chen, L. Sheng, and D. Y. Xing, Phys. Rev. B , 125410(2016). P. Rivero, C. M. Horvath, Z. Zhu, J. Guan, D. Tom´anek, and S. Barraza-Lopez, Phys. Rev. B , 115413 (2015). G. Yang, S. Xu, W. Zhang, T. Ma, and C. Wu, Phys. Rev. B , 075106 (2016). L. Seixas, A. Carvalho, and A. H. Castro Neto, Phys. Rev. B , 155138 (2015). P. Z. Hanakata, A. Carvalho, D. K. Campbell, and H. S. Park, Phys. Rev. B , 035304 (2016). H.-H. Fu, D.-D. Wu, L. Gu, M. Wu, and R. Wu, Phys. Rev. B , 045418 (2015). M. Tahir, P. Vasilopoulos, and F. M. Peeters, Phys. Rev. B , 045420 (2015). Y. Jiang, R. Rold´an, F. Guinea, and T. Low, Phys. Rev. B , 085408 (2015). J. M. Pereira and M. I. Katsnelson, Phys. Rev. B , 075437 (2015). B. Ostahie and A. Aldea, Phys. Rev. B , 075408 (2016). X. Zhou, W.-K. Lou, F. Zhai, and K. Chang, Phys. Rev. B , 165405 (2015). A. Ziletti, A. Carvalho, D. K. Campbell, D. F. Coker, and A. H. Castro Neto, Phys. Rev. Lett. , 046801 (2015). J. Guan, Z. Zhu, and D. Tom´anek, Phys. Rev. Lett. , 226801 (2014). J. Guan, Z. Zhu, and D. Tom´anek, Phys. Rev. Lett. , 046804 (2014). S. E. Boulfelfel, G. Seifert, Y. Grin, and S. Leoni, Phys. Rev. B , 014110 (2012). Y. Zhang, J. Lee, W.-L. Wang, and D.-X. Yao, Comp. Mater. Sci. , 109 (2015). T. Zhao, G. Wang, and Y. Liao, Chem Phys Lett , 1 (2016). K. Sato, L. Bergqvist, J. Kudrnovsk`y, P. H. Dederichs, O. Eriksson, I. Turek, B. Sanyal,G. Bouzerar, H. Katayama-Yoshida, V. Dinh, et al. , Rev Mod Phys , 1633 (2010). W. Zhou, X. Zou, S. Najmaei, Z. Liu, Y. Shi, J. Kong, J. Lou, P. M. Ajayan, B. I. Yakobson,and J.-C. Idrobo, Nano. Lett. , 2615 (2013). P. Hohenberg and W. Kohn, Phys. Rev. , B864 (1964). W. Kohn and L. J. Sham, Phys. Rev. , A1133 (1965). G. Kresse and J. Furthm¨uller, Phys. Rev. B , 11169 (1996). G. Kresse and D. Joubert, Phys. Rev. B , 1758 (1999). G. Kresse and J. Furthm¨uller, Comput. Mater. Sci. , 15 (1996). P. E. Bl¨ochl, Phys. Rev. B , 17953 (1994). T. Dietl, Nat. Mater. , 965 (2010). H. Pan, J. B. Yi, L. Shen, R. Q. Wu, J. H. Yang, J. Y. Lin, Y. P. Feng, J. Ding, L. H. Van,and J. H. Yin, Phys. Rev. Lett. , 127201 (2007). K. Sato, P. Dederics, and H. Katayama-Yoshida, EPL (Europhysics Letters) , 403 (2003)., 403 (2003).