Magnon pairing in quantum spin nematic

Transcription

1 Magnon parng n quantum spn nematc (Grenoble) n collaboraton wth Hro Tsunetsugu (Tokyo)

2 Introducton Outlne Introducton Bound magnon states: from 1D chan to frustrated square lattce Condensate of bound magnon pars: spn nematc state

3 Introducton Spn Lquds Tradtonal quantum magnetsm: ordered magnetc states, spn chans, ladders, Mordern theores: possblty of spn lquds n arbtrary dmenson short-range RVB, long-range RVB, Z 2, U(1), topologcal, Recent experments: trangular organcs, (hyper)kagome, 3 He monolayers, anythng else exotc?

4 Introducton states of Matter Matter Magnetc Matter Defnng property gas paramagnet dlute lqud spn-lqud sotropc sold ordered magnets ansotropc lqud crystal spn-nematc* partal symmetry breakng *(a.k.a. multpolar states) descrbed by tensor order parameters, searched for the past 40 years, were rarely observed so far

5 Introducton Spn nematcs n lterature and n nature magnets wth S 1 and bquadratc exchange on ste tensor S S K( S S Blume & Hsech (1969) j 2 ) preformed CEF multpoles: J, m ( l) n such that ( l) ( l) k J ( l) ( l) n 0, whle J J 0 k n NpO 2, Ce x La 1-x B 6 spn-nematc order from strong correlatons n a system of magnetc dpoles

6 Introducton Multpoles: symmetry classfcaton zero magnetc feld, rreps of SO(3), classfcaton n L fnte magnetc felds, rreps of SO(2), classf. n L z, spn nematc L z = ± 2

7 Introducton Magnon BEC n appled feld Bosons U(1) gauge nvarance condensate wavefuncton (r) chemcal potental µ Spns SO(2) rotaton symmetry staggered magnetzaton M j S magnetc feld H x j S y j

8 Introducton Magnon BEC: quest for new physcs change bosons: add flavor, valley ndex, trplet polarzaton, change knetc energy: localzed magnons n flat bands Schulenburg et al (2002) change potental energy: add attracton, competng ferro- and antferromagnetc bonds

9 Introducton Par superfludty n attractve Bose gases par condensaton versus densty collapse Valatn (1958), Nozéres (1982) constraned Bose-Hubbard model, n 2 Bonnes & Wessel (2011)

10 Introducton Frustrated ferromagnets chan materals LCuVO 4, L 2 CuO 2, L 2 ZrCuO 4 layered square-lattce afms 90 o Cu-O-Cu bonds yeld FM n.n. exchange J 1 <0 wth AF n.n.n. J 2 >0 by A. Tsrln

11 Bound pars Magnon parng n strong felds fully polarzed state ] sngle spn-flps (magnons) unstable at H s1 par of spn flps unstable at H s2 = H s1 + ½E B 0 cf. Worts (1963) 0 1 f S ( 0 ) 2 1 J J H k k 0 2 j j S S f p k q k q k q p q p k q k q k p f J J J J q f ) ( ) ( ) ( ) ( 2 / / / 2 / 2 2

12 Bound pars Magnon pars n 1D frustrated spn chan Chubukov (1991), Kuzan et al (2007), Ueda et al (2009) bound magnon pars wth k = π and E B J /( J J ) numercal studes Honecker et al (2006), Hkhara et al (2008), Sudan et al (2009) Nshmoto et al (2011)

13 Bound pars Magnon pars n LCuVO 4 weakly coupled chans J 1 = -1.6meV, J 2 = 3.6meV, J 5 ~ -0.4meV Enderle et al (2004) par condensaton H s2 = 47.1T and H s1 = 46.5T Tsunetsugu & MZ (2010)

14 Bound pars Magnon pars n 2D: J 1 -J 2 SAFM bound pars wth k=(0,0) f k ( q) (cos qx cos qy) E B 2 je j cf. Shanon et (2006)

15 Bound pars Magnon pars n 2D antferromanetc chans coupled by frustratng ferromagnetc bond frustraton s essental as t suppresses the knetc energy of sngle spn flps

16 Par Condensate Condensate of magnon pars Bogolyubov theory va the coherent boson states Tsunetsugu & MZ (2010) a0 a 0 e 0 0 ( a 0 ) sngle-magnon condensate = canted AF state exp( S Q ) 0 S e Qr dpolar symmetry coherent par condensate z C exp f S S 0 j j nematc symmetry z C

17 Par Condensate Spn correlatons absence of the sub-lattce magnetzaton S 0 exponental decay n transverse and longtudnal channels S 2 S * j fl l f lj z z ` 2 S S j fj 2 quadrupolar (nematc) order parameter Q j 2 1 S S j S S j Q xx j Q xy j 1 S S j 2 2 f j

18 Par Condensate Self-consstent BCS-type theory bosonzaton va Holsten-Prmakoff tranformaton mean-feld averages j a a j n r a a r quaspartcle exctatons: unpared magnons 2 2 q Aq B / 2 q J( r) 2 A 1 n n sn qr sn 1 kr k r 2 r H J( r) 1 n n cos qr cos 1 kr q 2 r 2 B q J( r) r cos qr

19 Par Condensate Self-consstentctheory: results energy-feld dagram magnon exctatons for LCuVO 4 : H s2 = 47T and H c = 44T Tsunetsugu & MZ, EPL 92, (2010)

20 Par Condensate New ultra-hgh-feld phase n LCuVO 4 pulsed feld experments Banks et al (2006) ultra-hgh feld phase Svstov et al (2011) the ultra hgh-feld phase s a transverse spn-nematc state

21 Par Condensate New hgh-feld phases n LCuVO 4 not so hgh-feld phase: longtudnal SDW n sotropc AFM? Banks et al (2006) Buetgen et al (2008,10) relaton to the transverse spn-nematc at hgher felds?

22 Par Condensate Longtudnal SDW n LCuVO 4 neutron dffracton Masuda et al (2011) long-range SDW order? Q 1 z (1 2m 2 )

23 Par Condensate 2D spn-nematc? spn-nematc phase n frustrated SAFM BaCdVO(PO 4 ) 2? Tsrln et al (2008) the hgh-feld regon s easly achevable n a Lab: H s =4.2 T; varous expermental technques may be appled

24 The End Summary magnon par condensate = spn nematc (quadrupole) state smokng gun for spn-nematc: hdden-order transtons,.e. wthout evdent order parameters dynamcal propertes: collectve quadrupole mode n longtudnal channel? nstabltes n the spn nematc phase: longtudnal IC state n LCuVO 4 nematc LRO n BaCdVO(PO 4 ) 2 and other frustrated 2D FMs

25 Magnon parng ar a root to spn-nematc Thank you!