Room-temperature large edge-magnetism in oxidized few-layer black phosphorus nanomeshes

Transcription

1 Room-temperture lrge edge-mgnetism in oxidized few-lyer blk phosphorus nnomeshes Y. Nknishi 1, D. Sorino 3, C. Oht 1, R. Iwki 1, Y. Ktgiri 1, Y. Fuki 1, K. Nomur 1, T. Nkmur 2, S. Ktsumoto 2, S. Rohe 3,4, J. Hruym 1 1 Fulty of Siene nd Engineering, Aoym Gkuin University, Fuhinobe, Sgmihr, Kngw , Jpn 2 Institute for Solid Stte Physis, The University of Tokyo, Kshiwnoh, Kshiw, Chib , Jpn 3 ICN2-Institut Ctl de Nnoieni i Nnotenologi, Cmpus UAB, Bellterr (Brelon), Spin 4 Instituió Ctln de Reer i Estudis Avnçts (ICREA), Brelon, 08070, Spin The formtion of edge mgnetism in two-dimensionl (2D) mterils hs been only experimentlly observed in hydrogented grphene nnoribbons nd grphene nnomeshes (GNM). The mesured mgnetiztion vlues of these systems re, however, lso fr too smll to llow envisioning prtil pplitions. Herein, we report the experimentl observtion of room-temperture lrge edge ferromgnetism in oxidized few-lyer blk phosphorus nnomeshes (BPNMs). The vlues of the observed robust edge mgnetism per single pore re 100 times lrger thn tht reported for hydrogented GNMs, wheres the mgnetism disppers in hydrogented BPNMs. The ferromgneti oupling of edge P tom with O tom nd the strong spin loliztion of edge vlene bnd n be the origins s well s uniform oxidtion of pore edges nd interlyer edge intertion. Suh finding pves the wy for relizing high-effiieny 2D flexible mgneti nd spintroni devies without the use of rre mgneti elements s tomi lyers repling grphene. The zigzg-type tomi struture of grphene edges leds to spin polriztion nd flt-bnd ferromgnetism (FM) from theoretil viewpoints 1-4. From experimentl respet, flt-bnd FM hs been relized bsed on the fbrition of hydrogen (H)-terminted zigzg-edged GNMs onsisting of honeyomb-like rry of hexgonl nno-pores (similr to Fig. 1E), fbrited using non-lithogrphi method, resulting in low-disordered nd low-ontminted pore edges Beuse GNM orresponds to lrge ensemble of zigzg-edged grphene nnoribbons (GNRs), it is effetive to detet smll mgneti signls rising from the pore edge spins. Nevertheless, the observed mgnetiztion vlues so fr hve been s smll s 10-6 emu/100 m 2, 6,7 exept for some speifi se 8. Mono- or few-lyer blk phosphorus (BP) ppers s high-mobility 2D semiondutor with substntil energy bnd gp 13,14. BP hs pukered honeyomb lttie, esily oxidized under ir tmosphere exposure, with n in-plne nisotropi tomi struture (Fig. 1A) Regrding those mgnetism, only theoretil works hve been reported up to now 17,18,21. In prtiulr, spin polriztion rising from edge dngling bonds hs been predited in pristine zigzg-edged phosphorene NRs (ZPNRs) 17. Oxygen (O)-sturted zigzg PNRs show edge FM due to the spins of unsturted bonds in wek P O bonds long the p z orbitls in the NR plne, wheres H-terminted zigzg PNRs show no edge FM. This behvior highly ontrsts with tht of GNMs 6. Moreover, even stronger nd highly stble edge nti-ferromgnetism (AFM) hs been predited in ZPNRs due to the eletroni instbility indued by the hlf-filled 1D bnds 21. In the present experiments, flkes of few-lyered BPs were mehnilly exfolited from bulk BP (Smrt Element Co.) using the Soth tpe method nd observed vi optil mirosope (Fig. 1C) nd tomi fore mirosope (Fig. 1D). Following pplition of non-lithogrphi method 12 (Supplementry Mteril (SM) 1-5), few-lyer BPNMs were fbrited (Fig.1E). Interpore regions orrespond to BPNRs, but only two edges of eh hexgonl pore n be simultneously perfet zigzg shped beuse of the topologil reson tht the inner ngle of the pukered honeyomb lttie (Fig. 1B) nnot be ligned to the inner ngle of the hexgonl pore of 120. This is different from the se of GNM. The smples were nneled t ritil temperture (T ) of 300 C in high vuum ( 10 6 torr) (SM 6) 26. Absene of substntil bkground mgneti impurities nd mgneti ontmintion hs been lso onfirmed by Eletron Energy Loss Spetrosopynd Miro-Auger Eletron Spetrosopy in four smples. Subsequently, eh smple ws pled in n ir tmosphere t 300 K for 2 h, resulting in O-termintion of pore edges 23. Immeditely following this nneling proess, mgnetiztion ws mesured using superonduting quntum interferene devies (Quntum Design Co.). Figure 2A shows mesurement results of the mgnetiztion of the O-terminted BPNM. Ferromgneti (FMC)-hysteresis loops re observed with M s 10-4 emu/100 m 2. Importntly, the hysteresis loop t T = 2 K pproximtely remins s it is 1

2 even t T = 300 K. On the other hnd, the few-lyer bulk BP flkes with ll the sme fbrition proess s those for Fig. 2A-smple but forming no pore (Fig. 2B) nd just with Ar gs ething proess without using porous lumin templte msk (but with the sme ondition s tht for pore forming) (inset of Fig. 2B) showed no mgnetiztion. This importnt result indiretly reonfirms tht the FM observed in Fig. 2A origintes solely from the formtion of oxidized nno-pores. This no mgnetism hs been onfirmed t lest in three smples. Indeed, observtion of this FMC-BPNM by mgneti fore mirosope shows presene of polrized spins round pore edges (inset of Fig. 2A). Sine the oxidtion of pore edges is esily obtined by exposing BPNM into ir tmosphere, one n ssume tht ll pores in BPNM re O-terminted nd n beome mgneti. With suh n ssumption, the mgneti moment per single pore re ( pore ) is estimted to be ( )/ ( B = ) B, where B is the Bohr mgneton 29. Following ref. 6, pore of prtilly ( 10%) H-terminted FMC-GNM nneled under H 2 tmosphere ws estimted to be B. Therefore, pore of the O-terminted BPNM is pproximtely 100-times lrger thn tht in the H-terminted GNM 6,7. Aordingly, BP hs signifint dvntge in whih O-terminte edge generte room-temperture mgnetism, in ontrst with the muh smller mgnetism obtined by prtilly H-terminted edges in GNM. Figure 2C revels tht the non-nneled BPNM demonstrtes FMC hysteresis loop with M s vlue 4 times less thn those of the T -nneled smples (i.e., Fig. 2A). This result implies tht nneling t the T is importnt for introduing lrge FM. Indeed, reproduibility of mgnetism in non-nneled BPNMs is poor nd some smples even show M s vlues smller thn emu/100 m 2 (inset of Fig. 2C). In the FMC-GNMs, the zigzg-type edge tomi struture is the most stble struture from both therml nd hemil perspetives 6,10-12, hene nneling t the T resulted in the formtion of zigzg pore edges nd the subsequent pperne of FM fter H-termintion. The ourrene of similr pore-edge tomi reonstrution to zigzg is lso expeted for the pores of the present BPNMs (Fig. 1B) following nneling t the T, thus lso leding to FM fter O-termintion (Fig. 2A). This n be onfirmed by Rmn spetrosopy in lter prt. Figure 2D shows the mgnetiztion urve for the BPNM obtined fter nneling under n H 2 tmosphere t 300 C for 2 h immeditely fter formtion of the nnopores. In ontrst to the O-terminted BPNM, it n be seen tht the H-terminted BPNM brely exhibit FMC-hysteresis loop. Moreover, the M s of n O-terminted smple subsequently nneled under n H 2 tmosphere t T 300 C for 5 h (Fig. 2E) is 3 times less thn tht of the originl O-terminted smple (Fig.2A). The dispperne of FM in the H-terminted BPNM is onsistent with the theoretil predition of the dispperne of FM in PNRs with H-terminted zigzg edges 26. In prtiulr, the result in Fig. 2E suggests tht O-termintion of the zigzg pore edges is highly stble nd nnot be entirely repled by H-termintion. Temperture-dependene of M s nd mgnetiztion lose to residul mgnetiztion (M r ) re shown in Fig. 2F (SM 8). Both M vlues monotonilly inrese with deresing temperture (e.g., from emu/100 m 2 (300K) to emu/100 m 2 (2K) for H = 10 Oe nd 0.7 (300K) to 1.2 (2K) for H = 200 Oe). Hene, the differene of M s nd M r vlues between 2K nd 300K is evident. This result definitely supports the presene of the FMC hysteresis loops t 2K nd 300K in our O-terminted BPNMs. Figure 3 shows the residul mgnetiztion (M r ) of FMC-BPNMs (O-terminted BPNMs) s funtion of the interpore distne (W), whih is identil to the width of PNR, nd M s s funtion of the thikness (d) nd smple re (S). The M r vlue seems to be not very sensitive to W (Fig. 3A). This is ontroversil when ompred to flt bnd FM in GNMs, there the Coulomb exhnge intertion between opposite edges strongly dereses with W, leding to loss of the stbility of the FMC spin ordering nd hene lower M r 15. This is, however, onsistent with previous theories of ZPNRs 17,21 nd with our theoretil predition desribed below. On the other hnd, the M s vlues re linerly enhned s d nd S inreses (Figs. 3B nd 3C). In prtiulr, the dependene on d suggests tht M s vlue of mono-lyer BPNM beomes negligible. This is ssoited with strong interlyer intertions in AB stking of BP (Fig. 1A), whih fvors the FMC spin onfigurtion nd nlogous to grphene 19. Our theoretil lultions for zigzg-pnr tully support this result nd lso indite even muh stronger interlyer intertion s explined in lter prt (Fig. 5E, 5F). This interlyer spin intertion mkes long-rnge spin ordering stble even t 300 K (Fig. 2A). The liner dependene on S (Fig. 3C) rises beuse the re of the O-terminted zigzg pore edges linerly inreses with inresing S. This mens tht the fully O-terminted pores uniformly exist through ll lyers in individul smples. This implies tht the O-termintion of the pore edges of BPNMs n be esily relized only by exposing smples to ir tmosphere nd signifintly ontributes to the observed lrge-mgnitude edge mgnetism. As disussed bove, nneling t T my use the reonstrution of the pore-edge tomi struture, resulting in formtion of zigzg pore edges nd subsequent ourrene of FM fter O-termintion 26. Evlution of typil Rmn spetr of BPNMs tht did nd did not exhibit FM evidently supports this rgument (Fig. 4A). From Fig. 4A, it is onfirmed tht the heights of the bnd peks due to the phonons resulting from interlyer intertions (I Ag1 ) re nerly the sme in the 2

3 spetr of the two smples, while the intensity of the bnd ttributed to the phonon from the Si substrte (I Si ) is signifintly lrger in the non-fmc smple, leding to low I Ag1 /I Si vlue. We find tht this tendeny grees with tht onfirmed for the bulk regions nd edges of few-lyer BP flkes (i.e., without nno-pores) of different d tht were not nneled t T (Fig. 4B). Fig. 4B implies tht the I Ag1 /I Si rtios observed t the edges is lower thn those of the orresponding bulk regions in nerly ll of the smples (Inset), nd n pproximtely liner orreltion between the I Ag1 /I Si rtio nd d ws obtined 16. The lower I Ag1 /I Si vlues t the edges n be obtined from the sme reltionship s tht in Fig. 4A (i.e., the higher pek vlue of I Si ). Indeed, the I Ag1 /I Si vlues for the FMC ( ) nd non-fmc ( ) BPNMs, inluding those shown in Fig. 4A, follow the pek trends for the bulk regions nd edges plotted in Fig. 4B, respetively. The lower I Ag1 /I Si vlues t the edges of BP flkes n be ttributed to presene of the rmhir-rih edges, while the I Ag1 /I Si vlues 1 in the bulk region suggests presene of zigzg-rih edges, from the following two resons. First, beuse the BP flkes without nno-pores were just mehnilly exfolited from bulk BP without ny intentionl lignment of rystl xis nd not by nneling t the T, the edge tomi strutures should be rough edges but rm hir rih. This is beuse zigzg edge ppers only when rystl xis is perfetly ligned long Y xis in Fig. 1A, while in ny other ses the bukling rmhir edge ppers. Seond, the intensity of the phonons from the Si substrte t the rmhir edges is higher thn tht of phonons t the zigzg edges, beuse the bukling rmhir strutures re formed long z-xis (Fig. 1A) nd the surfe of the Si substrte n esily osillte under them (e.g., beneth gry P toms) 20. However, these effets re suppressed in bulk region in few lyer BPs nd, hene, the I Ag1 /I Si vlues re not high. On the other hnd, ll phonons re indued more effetively in smple edges thn t bulk regions, beuse the smple hs free end. This induement is more signifint for phonon rising from Si substrte under the rm hir struture from the bovementioned resons. Hene the low I Ag1/I Si rtios rising from the high I Si vlues deteted t the edges (Fig. 2B) is ttributed to the bukling rmhir edge. This behvior should be nlogous to the behvior observed in the non-fmc nd FMC BPNMs (Figs. 4A nd 4B), beuse BPNM is lrge ensemble of BPNRs with edges (Fig. 1E). Hene, the low I Ag1 /I Si rtios in Fig. 4A suggest the rmhir-rih pore edges in the non-fmc BPNM. In ontrst, it n be onluded tht the pore edge of the FMC BPNMs is zigzg rih, whih re formed by edge reonstrution during nneling t the T. This lso suggests emergene of prtil zigzg edges in other four pore edges in ddition to the two zigzg pore edges (inset of Fig. 2A) (SM 7) 27. To theoretilly reonfirm the present edge-mgnetism in O-terminted ZPNRs, we hve rried out first priniples lultions (SM 9). Figure 5A shows the bnd struture of the relxed O-terminted 10-ZPNRs (Fig. 5B) onsidered in our lultions. The left nd right pnels orrespond to the spin-unpolrized nd -polrized ses, respetively. Similrly to previous lultions, pir of midgp sttes (red rrow in Fig.5A) spn ross the bnd gp nd ross the Fermi level t round /2 of the Brillouin zone (BZ) induing metlli stte. The midgp sttes t nd X (right pnel of Fig. 5A) re ompletely lolized long the edges s seen in Figs.5Bnd 5C. This is relted to the smll bnd splitting observed t the -point for O-terminted PNRs, whih is muh smller thn [25], nd implies strong redution of inter-edge oupling in presene of O 28. This is in greement with Fig.3A. The mgneti moments emerging t the O toms ouple ferromgnetilly with the ones t the neighboring P edge toms giving rise to huge enhnement of the edge mgnetism (the green rrows in Fig. 5C; SM 9). The vlues of the lol mgneti moment M L t the P edge nd O toms for the O-terminted 10-ZPNR re M P = 0.55 B nd M O = 0.4 B, respetively (very similr to the O-terminted 6-ZPNR). The lulted totl M L is round 1 B per P=O dimer, lmost seven times bigger thn those in [21]. We lso revel tht t the X-point the spin densities from the vlene bnds re only lolized long the edges of the NR whih strongly ontributes to the edge-anti-fmc stte (SM 9). Although the M L vlue is only few times lrger thn tht of the FMC-GNMs (M L 0.2 or 0.3 B ), the uniform oxidtion of pore edges through ll lyers in BPNM llows this lrge mgnetism. Sine the H-termintion elimintes the bovementioned unsturted bond, mgnetism disppers. Behvior of interlyer edge-spin oupling in the O-terminted ZPNRs is shown in Fig. 5D (SM 9). Mislignment of interlyer djent O=P edge toms in AB stking llows FMC spin onfigurtion in bilyer ZPNRs s well s the se of few-lyer GNRs. However, the strong interlyer intertion due to the O tom (SM 9) indues this FMC spin lignment nd mkes spin ordering more stble. Indeed, the liner sling of the bsolute mgnetiztion, defined s the sum of the bsolute vlues of the M L (m i ) on eh tom, M = i m i, is onfirmed with the number of lyers (N) s shown in Fig.5D. This is qulittively onsistent with Fig. 3B. The uthors thnk J. Akimitsu, K. Horigne, T. Murnk, T. Enoki, M. Ymmoto, S. Truh, T. Ando, A. H. Mdonld, P. Seneor, R. Wiesendnger, nd M. S. Dresselhus for their tehnil ontribution, fruitful disussions, nd enourgement. This work t Aoym Gkuin ws prtly supported by Grnt-in-id for Sientifi Reserh (Bsi 3

4 reserh A: ) nd grnt for privte University in MEXT nd AOARD grnt (135049) in U.S. Air Fore Offie of Sientifi Reserh. The Tokyo University s work ws lso supported by the Speil Coordintion Funds for Promoting Siene nd Tehnology. D. S. nd S.R. knowledge the Spnish Ministry of Eonomy nd Competitiveness for funding (MAT ), the Seretri de Universiddes e Investigión del Deprtmento de Eonomi y Conoimiento de l Generlitt de Ctluny nd the Severo Oho Progrm (MINECO SEV ). 4

5 Referenes nd notes 1. Nkd, K., Fujit, M., Dresselhus, G., nd Dresselhus, M. S., Phys. Rev. B 54, (1996). 2. Sorino, D. et l., Phys. Rev. Lett. 107, (2011). 3. Lee, H. et l., Chem. Phys. Lett. 398, 207 (2004). 4. Kuskbe, K. nd Mruym, M., Phys. Rev. B 67, (2003). 5. Shimizu, T., Hruym, J. et l., Nture Nnoteh. 6, 45 (2011). 6. Td, K., Hruym, J., Chshiev, M. et l, Phys. Sttus Solidi B 249, 2491 (2012). In GNM, H-terminted zigzg edges yielded flt-bnd FM, while O-terminted edges exhibited dimgnetism. 7. Kto, T., Nkmur, T., Hruym, J. et l., Appl. Phys. Lett. 104, (2014). 8. Hshimoto, T., Hruym, J., Sorino, D., Rohe, S. et l., Appl. Phys. Lett. 105, (2014). 9. Hshimoto, T., Hruym, J. et l., Mt. Sienes nd Appl. 5(1), 1 (2014). 10. Ji, X., Dresselhus, M. S. et l., Siene 323, 1701 (2009). 11. Girit, C. O. et l., Siene 323, 1705 (2009). 12. You, Y., Ni, Z., Yu, T. nd Shen, Z. Appl. Phys. Lett. 93, (2008). 13. Li, L. et l., Nture Nnoteh. 9, 372 (2014). 14. Herrero, P.-J. et l., Nture Nnoteh. 9, 330 (2014). 15. Koenig, S. P. et l., Appl. Phys. Lett. 104, (2014). 16. Gomez, A. C. et l., 2D Mterils 1, (2014). 17. Zhu, Z. et l., Appl. Phys. Lett. 105, (2014). Non-fully relxed struture ws ssumed in order to void Peierls trnsition. This predited lol edge mgneti moments M L of 0.27 B for the O tom, 0.39 B for the edge P tom, nd 0.13 B for its nerest neighbor, respetively. 18. Peng, X. et l., J. Appl. Phys. 116, (2014). 19. Crvlho, A., Rodin, A. S., nd Neto, A. H. C., Euro. Phys. Lett. 108, (2014). 20. Ong, Z. Y., Ci, Y., Zhng, G., Zhng, Y. W., rxiv: The phonon dispersion long the zigzg diretion ws shown to be shrper thn tht long the rmhir diretion using first-priniples lultions for BP. 21. Du, Y. et l., Si. Rep. 5, 8921 (2015). The hlf-filled 1D bnds rossed the Fermi level t round /2 for ZPNRs, showing emergene of no Peierls trnsition. This with edge-afmc ordering reported B for the edge P. 22. Zhu, W. et l., Nno Lett. 15, 1883 (2015). 23. Ziletti, A., Neto, A. H. C. et l., Phys. Rev. B 91, (2015). Oxidtion resulted in O-termintion of the pore edges, beuse oxidized top lyers serve s protetion lyers of underneth BP lyers preventing their bulk oxidtion 24. Di, J. nd Zeng, X. C., J. Phys. Chem. Lett. 5, 1289 (2014). 25. Luo, X., Lu, X., et l., Nno Letters 15, 3931 (2015). 26. Beuse the BPNM tends to dispper when nneling t T > 350 C, the nneling temperture of 300 C is pproximtely the T, t whih the reonstrution of pore-edge tomi strutures ours in the BPNMs. This T is muh lower thn 800 C for the FMC-GNMs. 27. Only two out of ten BPNMs did not result in zigzg-rih pore edges fter nneling t the T, thus did not exhibit FM due to this rmhir-rih edge (SM 7). It lso suggests tht the bukling rmhir edge requires higher energy for stbility fter the T nneling nd is hrd to be relized. The reonstrution by the T nneling my introdue relxed struture to interpore BPNRs, whih onventionlly results in Peierls trnsition nd dispperne of mgnetism 18, 21. However, the present BPNM struture, in whih six BPNRs with typil width 20nm form one hexgonl unit ell leving nno pore t the enter, my prevent ourrene of Peierls trnsition. 28. We hve lso heked inter-edge mgneti oupling for both prllel nd ntiprllel ouplings of edge-fmc nd edge-anti-fmc (AFMC) onfigurtions in the doubly relxed unit ells. We found tht the totl energies were very similr ( E < 1 mev), whih highlights the smll spin intertion between edges. The edge-fmc onfigurtion with ntiprllel inter-edge oupling (similr to zigzg GNRs) lwys led to non -mgneti or bd onverged solutions. In ontrst, the edge-afmc onfigurtion lwys onverged very fst while keeping the initil AFMC guess long the edge. Interestingly, the O toms were not initilly polrized nd beme mgneti during the self-onsisteny lultion. 29. (1) The totl re of typil few-lyer bulk BP flkes used for the nnomesh formtion is 10 3 m 2. (2) The re of one hexgonl unit ell with pore is S = 6(3-1/2 /2)(/2) nm 2, where = [80 nm (pore dimeter) + 20 nm (pore sping)]. (3) Thus, the totl number of holes is ( 10 3 m 2 10 lyers)/ (4300 nm 2 ) [i.e., (1)/(2)]. (4) The sturtion mgnetiztion per single pore re is thus estimted to be (emu) 10-3 / = (J/T). 5

6 B B 30 m b C d e d e Fig. 1 50nm 900 m 2 Bulk (no pores) flke with sme proess s () exept for pore formtion T=2K S 900 m 2 T nneling +O termintion B b S 1000 m 2 No T nneling +O termintion T=2K d H-termintion e f Fig. 2 6

7 b Fig. 3 b Fig. 4 7

8 P O 10 b X N = 1 N = 2 b 0 d ; N Fig. 5 8

9 Figure ptions Fig. 1 () Shemti ross-setionl nd top views of pukered honeyomb lttie of two-lyer blk phosphorens with AB stking. Gry nd red symbol s P toms lote within different height. Zigzg edge is within mono lyer long y xis, while bukling rm hir edge is formed to z-xis diretion long x xis. (b) Shemti top view of BPNM, in whih two pore edges re perfetly ligned to zigzg struture. In tul struture, pore size nd interpore sping re muh lrger nd lrger number of P toms exists t the interpore BPNR regions. () Optil mirosope imge of flke of few-lyer BP mehnilly exfolited from bulk BP. (d) Cross-setionl imge of () obtined using tomi-fore mirosope. (e) Atomi-fore mirosope top-view imge of BPNM with lrge number ( ) of pores, whih ws fbrited vi. non-lithogrphi method (SM1-5) in n extremely reful wy (e.g., using plsti tweezers) to void inorporting mgneti impurities, mgneti defets, nd mgneti ontmintion. Inset: Higher mgnifition imge. Fig. 2 (, -e), Mgnetiztion urves for BPNMs with () T nneling nd O-termintion, () no T nneling nd O-termintion, (d) H-termintion, (e) H-termintion of the smple in (). Inset of (), Observtion of ()-smple by mgneti fore mirosope under H = 10 Oe t T = 300K. Drker prts men higher density of polrized spins. Inset of (), Sturtion mgnetiztion (M s ) of T - nd no T -nneled BPNMs (eh five smples) BPNMs t 2K. (b) Mgnetiztion urve for few-lyer bulk BP flke (i.e., without nno pores) through ll the sme fbrition proess s those for ()-smple exept for the pore formtion. Inset of (b); Mgnetiztion for bulk thik BP (with no pores) with Ar gs ething proess without using porous lumin templte msk (but with the sme ondition s tht for pore forming). For ll smples, no bkground mgnetism ws subtrted exept for (), in whih dimgneti bkground line ws subtrted. S is the smple re inluding the totl pore re. Results of Fig. 2(b) re independent of S. (f) Temperture dependene of mgnetiztion vlues of mgneti BPNM (i.e., with T nneling nd O-termintion) mesured with deresing tempertures. Fig. 3 () Residul mgnetiztion (M r) of FM BPNMs s funtion of the interpore distne (W) (i.e., width of the interpore PNR regions), nd M s s funtion of the (b) thikness (d) nd () smple re (S). Fig. 4 () Typil miro Rmn spetr for two BPNMs tht do nd do not exhibit ferromgnetism. (b) Correltion of the d nd I Ag1 /I Si vlues in the Rmn spetr mesured in the bulk nd t the edges of three few-lyer BP flkes (i.e., without nnopores) without T nneling. The liner dotted lines indite trends for the individul orreltions. The I Ag1 /I Si vlues for the FM ( ) nd non FM ( ) BPNMs, inluding the result of Fig. 4(), re lso noted. Inset: Exmple of Rmn mpping for smple BP4 in min pnel. Red, ornge, nd yellow symbols men the mesured points with results of I Ag1 /I Si > 0.5, 0.5 > I Ag1 /I Si > 0.3, 0.3 > I Ag1 /I Si, respetively. Fig. 5 () Bnd strutures for O-terminted 10-ZPNR. Left nd right pnels orrespond to spin-unpolrized nd -polrized ses (SM9). (b) Chrge density ontribution (shown in green) of one of the midgp sttes (red rrow in ()) t nd X. The struture orresponds to O-terminted interpore ZPNR region of BPNM. Distnes re very similr to those reported for mono-lyer PNR. The distne between P nd O toms t the edges is 1.5 Å, whih orresponds to P=0 double bond. () Illustrtion of the edge nti-fm emerging t the zigzg edges of (b). Green rrows orrespond to the spin mgneti moment omputed on eh tom. (d) Sling of the bsolute mgnetiztion per unit ell with number of lyers (N). Relxed interlyer-distne (d z nm) is round 0.1 nm shorter thn previously report. 9