Collapse of magnetic moment drives the Mott transition in MnO

Transcription

1 Collpse of mgneti moment drives the Mott trnsition in MnO JAN KUNEŠ, *, ALEXEY V. LUKOYANOV, VLADIMIR I. ANISIMOV, RICHARD T. SCALETTAR 5 AND WARREN E. PICKETT 5 Theoretil Physis III, Center for Eletroni Correltions nd Mgnetism, Institute of Physis, University of Augsurg, Augsurg 865, Germny Institute of Physis, Ademy of Sienes of the Czeh Repuli, Cukrovrniká 0, 6 5 Prh 6, Czeh Repuli Url Stte Tehnil University-UPI, 6000 Yekterinurg, Russi Institute of Metl Physis, Russin Ademy of Sienes-Url Division, 600 Yekterinurg GSP-70, Russi 5 Deprtment of Physis, University of Cliforni Dvis, Dvis, Cliforni 9566, USA *e-mil: jn.kunes@physik.uni-ugsurg.de Pulished online: Ferury 008; doi:0.08/nmt5 The metl insultor trnsition in orrelted eletron systems, where eletron sttes trnsform from itinernt to lolized, hs een one of the entrl themes of ondensed-mtter physis for more thn hlf entury. The persistene of this question hs een onsequene oth of the intriy of the fundmentl issues nd the growing reognition of the omplexities tht rise in rel mterils, when strong repulsive intertions ply the primry role. The initil onept of Mott ws sed on the reltive importne of kineti hopping (mesured y the ndwidth) nd onsite repulsion of eletrons. Rel mterils, however, hve mny further degrees of freedom tht, s is reently ttrting note, give rise to rih vriety of senrios for Mott trnsition. Here, we report results for the lssi orrelted insultor MnO tht reprodue simultneous moment ollpse, volume ollpse nd metlliztion trnsition ner the oserved pressure, nd identify the mehnism s ollpse of the mgneti moment due to n inrese of rystl-field splitting, rther thn to vrition in the ndwidth. We onsider, s one of the simpler exmples of the nonil Mott insultors,, the rok-slt-struture trnsition-metl monoxide (TMMO) mngnese oxide with hlf-filled d shell. MnO is, most ertinly, multi-oritl multi-eletron system with the ompnying omplexities of the tenfold degenery, ut the hlffilled d sttes under mient onditions led to spheril spinonly mgneti moment. Applying pressure to suh system leds to numer of hnges, inluding insultor metl trnsition, oritl repopultion, moment redution nd volume ollpse if firstorder trnsition results. These hnges my our simultneously, or sequentilly over rnge of volumes. Any of these my e ompnied y struturl phse trnsition, tht is, hnge in rystl symmetry, ut n isostruturl volume ollpse my our s well. The d ndwidth of suh Mott insultor is very suseptile to pplied pressure, nd hs een thought to e one of the min ontrolling ftors in the trnsition. Although MnO s hlf-filled shell seems to give it onnetion to well-studied models, this spet lso mkes it typil of trnsitionmetl monoxides, s shown y Sitoh et l. who ompiled effetive prmeters for TMMOs from spetrosopi informtion. An effetive intr-tomi Coulom repulsion energy U eff s defined y them is roughly twie s lrge s for the other d monoxides, nd this hs een used to suggest tht MnO my e the most strongly orrelted TMMO. The omplexity tht should e expeted n e grsped y listing the relevnt energy sles: d ndwidth W, Coulom repulsion U, intr-tomi d d exhnge energy (Hund s rule) J, rystl-field splitting f = ε eg ε tg nd hrge trnsfer energy t ε tg ε p (the differene in Mn d (we use t g ) nd O p site energies). All of these sles evolve s the volume dereses, ltering the vrious mirosopi proesses nd mking the pressure-driven Mott trnsition hllenging phenomenon to desrie. Erly shok dt 5, nd then Rmn nd optil studies 6,7, hd identified trnsformtion in MnO t round GP. Trnsport 8, mgneti 8, struturl nd spetrosopi 9,0, nd refletivity 6 dt ll point to first-order, insultor metl Mott trnsition ner 00 GP with (redued) volume (v = V /V ) ollpse v = nd moment ollpse (from 5 µ B to µ B or less 9,0 ). The struturl dt indite B B8 hnge just efore the Mott trnsition, whih thus ours within the B8 (NiAs) phse rther thn the B (NCl) phse. As the lol environment of the Mn ion remins the sme, this struturl hnge is not expeted to hve muh effet on the Mott trnsition in the disordered phse. Further disussion of experimentl studies of the Mott trnsition in MnO is given in the Supplementry Informtion. Dynmil men field theory (DMFT) s n pproh for studying rel mterils hs een showing impressive suesses. The method tht we hve implemented nd pplied (see the Methods setion) moves the tretment signifintly eyond the methods used erlier for TMMOs, y inluding full thermodynmi verge of lol dynmi proesses resulting from the strong intertion nd ll oritls tht n e relevnt. Cohen et l. lulted the energy nd mgneti moment using only lol-density-pproximtion (LDA)-sed intertions. In LDA, MnO metllizes t (muh too) low pressure; within the metlli phse, they otined moment nd volume ollpse round 50 GP. Fng nd ollortors ddressed this diffiulty y using LDA only for the high-pressure phse, nd modelling 98 nture mterils VOL 7 MARCH 008

2 5 XPS BIS Mgneti moment ( µ B ) Low spin High spin Intensity Experiment Theory Oritl oupny t g e g Figure Amient-pressure X-ry photoemission spetrosopy nd remsstrhlung isohromt spetrosopy dt of vn Elp et l. 9 on oth sides of the energy gp for MnO. XPS: X-ry photoemission spetrosopy; BIS: remsstrhlung isohromt spetrosopy. The upper urve, offset for lrity, is to e ompred with the present DMFT result (ottom urve). Although the seprtion of the min peks is underestimted y 0%, the overll greement in positions of struture is exellent. Figure Evolution of the lol mgneti moment nd Mn d oupnies with volume. The derese in the lol moment orreltes with the oritl ouptions.,, Averge instntneous lol moment M s (lk) nd effetive lol moment M eff (green) (), nd omprison to the Mn d oritl oupnies () resolved into e g (red) nd t g (lk) omponents. The solid lines represent the results otined with the physil vlues U = 6.9 ev, J = 0.86 ev; the dshed lines using the enhned vlue J = ev nd onstnt U/J rtio illustrte how the moment ollpse is suppressed to smller volume if the spin-exhnge oupling is inresed. Closing of the t g nd e g gps is indited y the lk nd red vertil lines respetively, onfirming onnetion etween metlliztion nd moment ollpse. The nlogous losing of the gps for the dotted line se (J = ev) is shifted orrespondingly (not shown here). the low-pressure phse with the orrelted LDA + U method. With two different funtionls, however, it is not possile to otin the trnsition pressure. Four orrelted eletroni struture methods 5, pplied throughout the volume rnge of interest, hve proed the ehviour of MnO under pressure; ll otined high-spin (S = 5/) to low-spin (S = /) moment ollpse ut their preditions differed onsiderly in other respets, demonstrting tht the dynmi tretment of orreltion effets is ruil. The predition of the LDA + U method, whih is regrded s the stti, T = 0 limit of the LDA + DMFT theory used here, is found to e ffeted y mgneti order 6, nd predits zero-temperture moment ollpse in n insultor insultor trnsition round 0 GP (the pressure depends on the vlue of J), with little differene etween the B nd B8 struture results. Thermodynmi flututions hve not een inluded in ny previous study of MnO. MAGNETIC-MOMENT COLLAPSE AND METALLIZATION Following most losely the pproh developed nd implemented y MMhn nd o-workers 5,7,8 for pressure studies of elementl lnthnides, we hve ddressed the pressure-driven ollpse of the orrelted insulting stte, using MnO s the prototype. Figure shows the evolution of the lol mgneti moment nd Mn d oupnies with volume. We use two different mesures of the lol moment: () the men instntneous moment defined s n equl-time orreltion funtion M s = ˆm z nd () effetive lol moment defined through the lol spin suseptiility M eff = Tχ lo. These two moments hve similr T-independent vlues in mterils with Curie Weiss ehviour. Under ompression, the lol moment nd Mn d oritl oupnies retin their mient-pressure high-spin vlues (S = 5/) down to out v = Further ompression rpidly degrdes the moment, whih is ompnied y redistriution of eletrons e g t g within the Mn d shell. The lol moments nd oritl oupnies strt to level off to the low-spin vlues round v = The redution of M eff elow M s in the low-spin stte indites tht the lol moment sreening (hrge flututions) is enhned in omprison with the high-spin stte. Next we ddress the spetrl properties, where the shortomings of the LDA spetrum hve een ler for dedes. Figure shows omprison of the lulted totl Mn d spetrl funtion t mient pressure with the photoemission dt of vn Elp et l. 9. Exellent greement is otined for the gp nd for the pek positions. (We note tht using the enhned vlue of J = ev gives signifintly poorer greement.) Hving otined orret mient-pressure spetrum, we proeed in the study of the Mott trnsition y following the evolution with deresing volume of the symmetry-resolved (t g,e g ) spetrl densities, shown in Fig.. The onset of the moment ollpse round v = 0.68 is signlled y, nd ssoited with, losing of the gp in the t g hnnel, wheres the e g gp is still visile t v = 0.6. This oritl seletivity 0, in metlliztion nnot e n ext property euse oth e g nd t g nds hyridize with the sme O p nds throughout the Brillouin zone; however, the smllness of t g p mixing llows the oritl seletivity to e remrkly pronouned. As the t g gp loses, qusiprtile pek ppers t the hemil potentil (E = 0) s hs een seen in simple models. One in the lowspin stte, the spetrl funtions er strong resemlne to the prent LDA nds. In prtiulr, the LDA (U = J = 0) t g spetrum ontins shrp pek just t/elow the hemil potentil, so it is not ertin how muh of the pek rising t the trnsition is due to the mny-ody nture of the system. nture mterils VOL 7 MARCH

3 Spetrl density v = 0.5 v = 0.57 v = 0.6 v = 0.68 v = Δ t Δ f t pd σ Experiment 0.7 Theory Pressure (GP) Figure View of the evolution of the Mn d spetrl densities under pressure. (Pressure inresing from ottom to top.),, The single-prtile spetrl funtions re resolved into e g () nd t g () irreduile representtions for vrying reltive volume. Note the spetrl weight shift under pressure: de-ouption of e g ours s the inrese in ouption of t g proeeds (ouption integrted weight over negtive energies). For the lowest volume, we show the unorrelted (LDA) spetr for omprison (dshed lines). Apprently the min spetrl fetures t high pressure originte from the unorrelted nd struture with some mny-ody renormliztion. At even higher pressures, the spetr remin qulittively unhnged with some redution of the weight of the high-energy shoulders. Figure 5 Two representtions of the eqution of stte tht quntifies the volume ollpse trnsition.,, The internl energy versus volume (dshed line represents spline interpoltion) () nd the resulting volume versus pressure urve (shding indites estimted unertinty) (), otined s derivtive of the spline interpoltion of E(V ). The red r on the V(P ) urve lying t the theoretil trnsition pressure P th = 0±5 GP determines the volume ollpse v = The dotted urve represents V(P ) for the enhned vlue of exhnge J = ev, showing the shift of the Mott trnsition to higher pressure with lrger J. The width of the shded red r indites the unertinty of P th due to the stohsti nture of the QMC method. The inset in shows the evolution of seleted tight-inding prmeters (units of eletronvolts); note the ftor of three inrese in f. High spin e g Low spin Figure Shemti energy digrms of the spin sttes t oth mient pressure nd t high pressure in the ollpsed phse. Ouptions of the Mn d levels re shown for oth high spin (left) nd low spin (right). In the high-spin stte, two spin-up eletrons oupy e g oritls t the ost of f in energy, ut the spin-exhnge energy gin is 0J (5 / = 0 pirs of prllel spin eletrons). In the low-spin stte, the rystl-field energy ost hs eome too gret, nd lthough the spin-exhnge energy is less ( J from / (up) + (down) = pirs) there is net energy gin. The LDA energy differene is lso ftor. MECHANISM OF THE MOTT TRANSITION IN MnO We now ddress fundmentl point of this work, nmely the onnetion etween moment ollpse nd metl insultor trnsition, y oservtion of the impt of pressure on the effetive hmiltonin. As U nd J do not hnge, the pressure enters the lultion only through the qudrti (one-eletron) prt of the effetive hmiltonin. Reduing the role of pressure down to fundmentls, we end up with two effets: () rodening of the d nds nd () inrese of the rystl-field splitting f, whih is shown shemtilly in Fig. long with the stte ouptions. t g (We define f in terms of the site energies of the e g nd t g Wnnier funtions; the e g t g nd splitting is sustntilly lrger owing to lignd field effets.) The evolution of the leding nd struture quntities, whih re the nerest-neighour hopping mplitude t pdσ, f nd t, re shown in the inset of Fig. 5. As the d ndwidth rises minly through Mn d O p hyridiztion (W t / pd t), the inrese of t pd hopping with pressure is to some extent ompensted y the overll lowering of the p nds (inrese in t ). So fr we hve demonstrted onnetion etween the moment ollpse nd metl insultor trnsition, yet the hiken-nd-egg question whih property drives? whih property follows? is not yet nswered. To this end, we hve rried out further lultion t v = 0.8 (well within the insulting high-spin stte) without ny intr-tomi exhnge (J = 0). In spite of the lrge U nd sme U/W rtio, low-spin solution is otined, whih is metlli lthough strongly renormlized. This result lerly shows tht the metl insultor trnsition is driven y the ollpse of the moment, whih nnot withstnd the inrese of f. The trnsition is hrterized s evolving from five hlf-filled nds t g + e g (high spin) to three t g nds with one hole per site (low spin), s shown in Fig.. The intertion energy ost of moving n eletron from site to site is determined y U eff = d n+ + d n d n. Using the tomi onfigurtions orresponding to high-spin nd low-spin sttes, we rrive t n effetive repulsion U HS eff = U +J = 0. ev nd U LS eff = U J = 5.9 ev respetively, inditing muh stronger inhiition of the eletron propgtion in the high-spin stte. Moreover, the Mn d(e g ) O p hyridiztion provides further sreening hnnel for the effetive t g t g intertion in the low-spin stte. Indeed, lultion rried out in the low-spin stte with O p sttes integrted out (keeping the d ndwidth unhnged) efore solving the interting prolem leds to more pronouned 00 nture mterils VOL 7 MARCH 008

4 high-energy shoulders s ompred with the solution with O p sttes fully inluded. These results estlish tht the trnsition is ontrolled y ompetition etween the rystl-field spitting f (fvouring the low-spin stte) nd the intr-tomi exhnge oupling J (fvouring the high-spin stte). Although oth energy sles re importnt for the outome of the lultions, only the former ( f ) is sensitive to n pplied pressure. The importne of the vlue of J ws lso found in LDA + U studies of the Mott trnsition 6. Reently, Werner nd Millis studied two-nd model with ompeting intr-tomi exhnge nd rystl-field splitting. In the prmeter rnge relevnt for the present study, they found three different phses relized in the following order with inresing rystl-field splitting: () spin-polrized Mott insultor, () metl with lrge oritl nd spin flututions nd () oritlly polrized insultor. Moreover, they found n oritlly seletive losing of the gp on doping in the viinity to the () () phse oundry. The orrespondene etween their spin-polrized insultor phse () nd the high-spin stte of MnO is evident. The trnsition regions in MnO nd phse () re oth hrterized y metlliztion nd strong oritl flututions s well s the oritlly seletive gp ehviour. In ddition, the low-spin stte of MnO nd phse () of the model exhiit similrity, the oritl polriztion. The insulting hrter of their phse () is ditted y ndfilling nd does not invlidte the ove nlogy. Like lmost ll previous studies using LDA + DMFT, we hve inluded only the density density terms of the Coulom repulsion. Although they re not expeted to influene first-order volume ollpse (see the next setion) espeilly ove,000 K, it is grtifying to otin some onfirmtion. Werner nd Millis used the full Coulom intertion in their study, nd the similrity of the ehviour of their model to wht is found here for MnO provides some verifition of the unimportne of the negleted terms. EQUATION OF STATE AND THE CRITICAL PRESSURE To ompre to high-pressure experiments, knowledge of phse stility is needed, whih n e otined from free energy versus volume (eqution of stte). The theoretil justifition for pplying DMFT using the underlying LDA desription relies on well-defined thermodynmi grnd nonil potentil funtionl, for whih speifi reliztions hve een suggested 5,7,. As it is diffiult to extrt the entropi term 8 in the free energy, we restrit ourselves to evlution of the internl energy; in ny se the vrition of the entropy term is very smll on the energy sle of severl eletronvolts involved in the hnges of totl energy, nd the hnge in spin entropy will e prtilly ompensted y hnge in oritl entropy. We use the internl energy sheme of MMhn nd o-workers 5,7,8 tht is similr to tht of Svrsov nd Kotlir orresponding to the expression E(V,T) = E LDA (V ) + [E DMFT (V,T) E MF (V )], where E LDA is the ll-eletron (unpolrized) LDA energy, E DMFT is the internl energy orresponding to the self-onsistent (dynmi) DMFT solution for the effetive hmiltonin nd E MF is the stti men-field internl energy. The eqution-of-stte urve is shown in Fig. 5, oth s E(V ) nd onverted to V (P). The min feture is the devition from onvexity in the trnsition region, whih leds to lulted volume ollpse v th = t P th = 0 GP. The metlliztion nd moment ollpse otined here re not fr from the high-pressure dt 8 0, with the trnsition volume (pressure) eing smller (lrger) thn the experimentl vlues = 00 GP. The stte just ove the ollpse gp out to lose. The ollpsed stte is low spin, the e g gp hving just losed mking it metlli in oth sushells. v exp = , P exp is high-spin insultor, with the t g OUTLOOK These results demonstrte tht the underlying LDA nd struture, uttressed y onsite intertions (U, J) treted within the dynmil DMFT nstz, provides relisti desription of the Mott trnsition in MnO without input from experiment. This study finlly enles determintion of the mehnism of the trnsition, whih ould not e unovered y experiment lone: the mgneti moment ollpse, volume ollpse nd metl insultor trnsitions our simultneously, ut it is the inresing rystl-field splitting (enrohment of the O ion on the internl struture of the Mn ion) nd not the inresing ndwidth tht tips the lne. The urrent results illustrte suess of the LDA + DMFT pproh in desriing pressure-driven Mott trnsition in strongly orrelted insultor, joining the growing numer of suesses of this pproh in other strongly orrelted rel mterils. The Kondo volume ollpse trnsition in Ce (refs 5,8) nd other elementl lnthnides 7 nd the relisti modelling of prts of the omplex phse digrm 6 nd multiplet effets 5 in Pu reflet the progress in orrelted metls, with low-temperture properties (hevy fermion hrteristis) remining n imposing hllenge. Impressive progress hs lso een demonstrted in the desription of struturlly driven 7,6 nd doping-driven 7 metl insultor trnsitions in trnsition-metl oxides. Exittion spetr, of the hrge-trnsfer ompound NiO t mient pressure, where O p sttes re entngled with the d sttes, hve shown exellent greement with experiment. These results on MnO ring further lss of mterils into the list of strongly orrelted systems whose ehviour is eoming understood owing to reent theoretil developments. METHODS SINGLE-PARTICLE HAMILTONIAN AND INTERACTION TERM The LDA + DMFT omputtionl sheme 9 in its present implementtion, pplied previously to NiO (refs,), proeeds in two steps: () onstrution of n effetive multi-nd Hurd hmiltonin H vi Wnnier trnsformtion from onverged (unpolrized, metlli) LDA solution orreted for doule ounting of the onsite intertion, nd () self-onsistent solution of the DMFT equtions,0 using the quntum Monte Crlo (QMC) impurity solver 8. H = k,σ,α,β + k,σ,α,γ + i,σ,σ,α,β h dd k,αβ d kασ d kβσ + k,σ,γ,δ h dp k,αγ d kασ p kγσ + U σσ αβ nd iασ nd iβσ, k,σ,γ,α h pp k,γδ p kγσ p kδσ h pd k,γα p kγσ d kασ where d kασ (p kγσ ) is the Fourier trnsform of the opertor d iασ (p iγσ ), whih nnihiltes the d (p) eletron with oritl nd spin indies ασ (γσ) in the ith unit ell, nd n d iασ is the orresponding d ouption numer opertor. The single-prtile prt of the hmiltonin ws otined y Wnnier funtion projetion method 9, whih mounts to unitry trnsformtion in the Hilert spe ontining Mn d, O p nds nd the next-lowest empty (polriztion) ondution nd. The site energy of the Mn d oritls ws orreted for doule ounting of the d d intertion y sutrting from the LDA site energy ε d Hrtree-like term giving ε d = ε d (N )Ūn LDA, where N = 0 is the totl numer of oritls per Mn site, Ū is the verge Coulom repulsion nd n LDA is the verge oupny per d oritl. As the p d nd seprtion t in MnO, whih is to some extent influened y the hoie of the doule-ounting term, is lrge in the trnsition region, smll vrition of t will not hnge the results. THE COULOMB INTERACTION MATRIX The onsite Coulom intertion Uαβ σσ (U,J) within the Mn d shell, restrited to only density density terms, ws expressed s usul 0 in terms of the diret nture mterils VOL 7 MARCH

5 (U) nd exhnge (J) intertion strengths relted to the Slter integrls F 0, F, F. The numeril vlues of U = 6.9 ev nd J = 0.86 ev were otined y the onstrined LDA method. As they exhiit only smll pressure dependene, these vlues were used for ll volumes. We used L = 00 imginry time points in the Monte Crlo simultion, in whih the stndrd single-field-flip moves were ugmented y speil glol moves tht plyed ruil role in ensuring ergodi smpling in the trnsition region. To otin n indition of the roustness of our results we rry out, in prllel with these initio intertion strengths, lultions with n enhned (y 5%) vlue of J = ev (nd fixed U/J rtio). All of the presented results were otined t the temperture T =,60 K, in the rok-slt struture. MONTE CARLO PROCEDURE; INTRODUCTION OF GLOBAL MOVES The DMFT equtions were solved numerilly on Mtsur ontour (using symptoti expnsions for frequenies ω n > 500 ev), nd the k-spe integrls were rried out y summtion over,75 k-points in the first Brillouin zone. The hemil potentil ws djusted in eh DMFT itertion to gurntee the totl eletron ount of ± 0 6. The impurity prolem ws solved using the Hirsh Fye QMC lgorithm 8 modified for multiple oritls. The onsite intertion ws deoupled using single inry Hurd Strtonovih uxiliry field S αβ (l) for eh pir of oritls αβ nd eh of L imginry time slies (5 uxiliry fields for eh time slie). The key innovtion in this pplition to MnO in the trnsition regime ws introdution of glol Monte Crlo moves in ddition to the usul single flips of the uxiliry fields. These moves llow for flututions etween high-spinnd low-spin-like onfigurtions, whih re otherwise prtilly unrehle with the stndrd single-uxiliry-field-flip moves. The purpose of glol moves is to mimi trnsferring eletrons etween oritls. In generl there is no strightforwrd reltionship etween given onfigurtion of uxiliry fields, desried y inry L-vetor S αβ nd the oupny of oritls. However, in the se of two tomi oritls, the proility distriution is peked round uxiliry field onfigurtions orresponding to prtiulr oritl oupny, nd flipping ll fields orresponds to swpping oupnies of the two oritls. This n e generlized to multiple oritls s follows. To swp oupnies of oritls α nd β, we hve to: () flip fields in S αβ, () for ll remining fields in oritls γ oupled to oritls α or β swp the onfigurtions S γα S γβ. As the deoupling is ntisymmetri with respet to the ordering of oritls, uxiliry fields must e flipped in step () whenever the order of oritls hnges etween S γα nd S γβ. Testing severl types of the ove moves, we found tht only simultneous moves of two eletrons etween t g nd e g oritls of opposite spin (tht is, moves intuitively expeted in low-spin high-spin flututions) hve ppreile eptne. The eptne rte of the glol moves ws found to e lrge only in the trnsition regime, whih hd een hrterized y unusully slow onvergene of the DMFT yle. We heked for the possiility of multiple solutions, ut found none t the temperture of these simultions. The numeril vlue of the totl energy, limited y the stohsti error of the E DMFT term, ws onverged to the ury of 0.06 ev in the trnsition regime nd 0.0 ev nywhere else. The spetrl densities were lulted y the mximum entropy nlyti ontinution tehnique pplied to the imginry-time Green funtions from QMC-simultion sweeps olleted into,000 0,000 ins. Reeived 7 July 007; epted 7 Jnury 008; pulished Ferury 008. Referenes. Mott, N. F. The Bsis of the eletron theory of metls, with speil referene to the trnsition metls. Pro. Phys. So. Lond. A 6, 6 (99).. Mott, N. F. Metl insultor trnsition. Rev. Mod. Phys. 0, (968).. Imd, M., Fujimori, A. & Tokur, Y. Metl insultor trnsitions. Rev. Mod. Phys. 70, 09 6 (998).. Sitoh, T., Bouquet, A. E., Mizokw, T. & Fujimori, A. Systemti vrition of the eletroni struture of d trnsition-metl ompounds. Phys. Rev. B 5, (995). 5. Noguhi, Y., Kus, K., Fukuok, K. & Syono, Y. Shok-indued phse trnsition of MnO round 90GP. Geophys. Res. Lett., 69 7 (996). 6. Mit, Y. et l. Optil study of MnO under pressure. Phys. Sttus Solidi B, 7 5 (00). 7. Mit, Y., Izki, D., Koyshi, M. & Endo, S. Pressure-indued metlliztion of MnO. Phys. Rev. B 7, 000 (005). 8. Ptterson, J. R. et l. Pressure-indued metlliztion of the Mott insultor MnO. Phys. Rev. B 69, 00 (00). 9. Yoo, C. S. et l. First-order isostruturl Mott trnsition in highly ompressed MnO. Phys. Rev. Lett. 9, 550 (005). 0. Rueff, J.-P., Mttil, A., Bdro, J., Vnkò, G. & Shukl, A. Eletroni properties of trnsition-metl oxides under high pressure reveled y X-ry emission spetrosopy. J. Phys. Condens. Mtter 7, S77 S76 (005).. Metzner, W. & Vollhrdt, D. Correlted lttie fermions in d = dimensions. Phys. Rev. Lett. 6, 7 (989).. Georges, A., Kotlir, G., Kruth, W. & Rozenerg, M. J. Dynmil men-field theory of strongly orrelted fermion systems nd the limit of infinite dimensions. Rev. Mod. Phys. 68, 5 (996).. Kotlir, G. & Vollhrdt, D. Strongly orrelted mterils: Insights from dynmil men-field theory. Phys. Tody 57, 5 59 (00).. Lihtenstein, A. I. & Ktsnelson, M. I. A initio lultions of qusiprtile nd struture in orrelted systems: LDA++ pproh. Phys. Rev. B 57, (998). 5. Held, K., MMhn, A. K. & Slettr, R. T. Cerium volume ollpse: Results from the merger of dynmil men-field theory nd lol density pproximtion. Phys. Rev. Lett. 87, 760 (00). 6. Svrsov, S., Kotlir, G. & Arhms, E. Eletroni orreltions in metlli plutonium within dynmil men-field piture. Nture 0, (00). 7. Held, K., Keller, G., Eyert, V., Vollhrdt, D. & Anisimov, V. I. Mott-Hurd metl insultor trnsition in prmgneti V O : An LDA+DMFT(QMC) study. Phys. Rev. Lett. 86, (00). 8. Georges, A. Strongly orrelted eletron mterils: Dynmil men field theory nd eletroni struture. AIP Conf. Pro. 75, 7 (00). 9. Held, K. et l. Relisti investigtions of orrelted eletron systems with LDA+DMFT. Phys. Sttus Solidi B, (006). 0. Kotlir, G. et l. Eletroni struture lultions with dynmil men field theory. Rev. Mod. Phys. 78, (006).. Kuneš, J., Anisimov, V. I., Lukoynov, A. V. & Vollhrdt, D. Lol orreltions nd hole doping in NiO: A dynmil men field study. Phys. Rev. B 75, 655 (007).. Kuneš, J., Anisimov, V. I., Skornykov, S. L., Lukoynov, A. V. & Vollhrdt, D. NiO: Correlted nd struture of hrge-trnsfer insultor. Phys. Rev. Lett. 99, 560 (997).. Cohen, R. E., Mzin, I. I. & Isk, D. G. Mgneti ollpse in trnsition metl oxides t high pressure: Implitions for the Erth. Siene 75, (997).. Fng, Z., Solovyev, I. V., Swd, H. & Terkur, K. First priniples study on eletroni strutures nd phse stility of MnO nd FeO under high pressure. Phys. Rev. B 59, (999). 5. Ksinthn, D. et l. Mott trnsition of MnO under pressure: omprison of orrelted nd theories. Phys. Rev. B 7, 950 (006). 6. Ksinthn, D., Koepernik, K. & Pikett, W. E. Pressure-driven mgneti moment ollpse in the ground stte of MnO. New J. Phys. 9, 5 6 (007). 7. MMhn, A. K., Held, K. & Slettr, R. T. Thermodynmi nd spetrl properties of ompressed Ce lulted using omined lol-density pproximtion nd dynmil men field theory. Phys. Rev. B 67, (00). 8. MMhn, A. K. Comined lol-density nd dynmil men field theory lultions for the ompressed lnthnides Ce, Pr, nd Nd. Phys. Rev. B 7, 55 (005). 9. vn Elp, J., Potze, R. H., Eskes, H., Berger, R. & Swtzky, G. A. Eletroni struture of MnO. Phys. Rev. B, (99). 0. Liesh, A. Mott trnsitions in multioritl systems. Phys. Rev. Lett. 9, 60 (00).. Kog, A., Kwkmi, N., Rie, T. M. & Sigrist, M. Oritl-seletive Mott trnsitions in the degenerte Hurd model. Phys. Rev. Lett. 9, 60 (00).. Anisimov, V. I., Znen, J. & Andersen, O. K. Bnd theory nd Mott insultors: Hurd U insted of Stoner I. Phys. Rev. B, 9 95 (99).. Werner, P. & Millis, A. J. High-spin to low-spin nd oritl polriztion trnsitions in multioritl Mott systems. Phys. Rev. Lett. 99, 605 (007).. Svrsov, S. Y. & Kotlir, G. Spetrl density funtionls for eletroni struture lultions. Phys. Rev. B 69, 50 (00). 5. Shik, A., Hvel, L., Koloren, J. & Drhl, V. Multiplet effets in the eletroni struture of δ-pu, Am nd their ompounds. Europhys. Lett. 77, 700 (007). 6. Pvrini, E. et l. Mott trnsition nd suppression of oritl flututions in orthorhomi d perovskites. Phys. Rev. Lett. 9, 760 (00). 7. Cro, L., Ld, M. S., Leoni, S. & Muller-Hrtmnn, E. Insultor metl trnsition in the doped d trnsition metl oxide LTiO. Phys. Rev. B 70, 956 (00). 8. Hirsh, J. E. & Fye, R. M. Monte Crlo method for mgneti impurities in metls. Phys. Rev. Lett. 56, 5 5 (986). 9. Anisimov, V. I. et l. Full oritl lultion sheme for mterils with strongly orrelted eletrons. Phys. Rev. B 7, 59 (005). 0. Shik, A. B, Liehtenstein, A. I. & Pikett, W. E. Implementtion of the LDA+U method using the full potentil linerized ugmented plne wve sis. Phys. Rev. B 60, (999).. Anisimov, V. I. & Gunnrsson, O. Density funtionl lultion of effetive Coulom intertions in metls. Phys. Rev. B, (99).. Slettr, R. T., Nok, R. M. & Singh, R. R. P. Ergodiity t lrge ouplings with the determinnt Monte Crlo lgorithm. Phys. Rev. B, (99).. Jrrell, M. & Guerntis, J. E. Byesin inferene nd the nlyti ontinution of imginry-time quntum Monte Crlo dt. Phys. Rep. 69, 95 (996). Aknowledgements J.K. grtefully knowledges the Reserh Fellowship of the Alexnder von Humoldt Foundtion. We knowledge numerous disussions with D. Vollhrdt nd A. K. MMhn, nd useful intertion with K.-W. Lee during the ltter stges of this work. This work ws supported y SFB 8 of the Deutshe Forshungsgemeinshft (J.K.), y the Russin Foundtion for Bsi Reserh under the grnts RFFI , RFFI (V.I.A. nd A.V.L.) nd the Dynsty Foundtion (A.V.L.), y DOE grnt No. DE-FG0-0ER6 nd y DOE Strtegi Siene Ademi Alline grnt No. DE-FG0-06NA60. This reserh ws lso enourged nd supported y the US Deprtment of Energy s Computtionl Mterils Siene Network (J.K., R.T.S. nd W.E.P.). Correspondene nd requests for mterils should e ddressed to J.K. Supplementry Informtion ompnies this pper on Author ontriutions J.K. wrote the ode nd performed the DMFT (QMC) lultions. J.K., R.T.S., W.E.P. nd V.I.A. formulted the pproh nd hose the pplition to MnO. A.V.L. nd V.I.A. lulted the LDA quntities nd rried out the Wnnier trnsformtion to the lol representtion. J.K. nd W.E.P. wrote the pper. Reprints nd permission informtion is ville online t 0 nture mterils VOL 7 MARCH 008