Relaxation in water /spin ice models

Transcription

1 Relaxaton n water /spn ce models Ivan A. Ryzhkn Insttute of Sold State Physcs of Russan Academy of Scences, Chernogolovka, Moscow Dstrct, 1443 Russa

2 Outlne specfcty of approach quaspartcles Jaccard s theory of relaxaton surface and heat effects dfferences between water/spn ces

3 Water/spn ce analogy (ground states) J. D. Bernal, and R. H. Fowler, J. Chem. Phys. 1, 515 (1933) P. W. Anderson, Phys. Rev. 10, 1008 (1956) M. J. Harrs, S. T. Bramwell, et al., Phys. Rev. Lett. 79, 554 (1997)

4 Water/spn ce analogy (Hamltonans) j j j j j j j j nn j nn r r r e r e e e e b J H 3 / 3 j z j z nn j j j j j nn z j z j j r r r z r z z z D J H 3 / ˆ ˆ ˆ ˆ 3 ˆ ˆ 3 3,,, ˆ 3 D r e b J J z e nn nn z B.C. den Hertog, and M.J.P. Gngras, Phys. Rev. Lett. 84, 3430 (000) I. A. Ryzhkn, Sold State Comm. 5, 49 (1984)

5 Ground state s frozen at T=0 water ce structure spn ce structure

6 Fnte energy exctatons at T 0 onc defects: H 3 O +,OH - bond defects: D, L N.Bjerrum, Kongelge Vdens. Selskab Matematsk-fysske Meddelelser 7, 1 (1951) H. Grancher, Zetscrft fur Krstallographc 110, 43 (1958)

7 Fnte energy exctatons n spn ce magnetc monopoles no analogs of bond defects Is t possble to create an extended spn ce model whch ncludes analogs of bond defects?? I.A. Ryzhkn, JETP 101, 481 (005) C. Castelnovo, R. Moessner, and S. Sondh, Nature 451, 4 (008)

8 Concentratons (non-nteractng quaspartcles) T k E T k E T k E N N N N B B B exp 3 exp exp kt E kt E kt E N N exp 1 1 exp exp

9 Concentratons (nteractng quaspartcles) Coulomb nteracton between quaspartcles sometmes could leads to I order phase transtons.

10 Phase dagram of spn ce Lne s a temperature of I-order phase transton versus E. Sold (dashed) parts of the lne Corresponds to satsfacton (volaton) of Debye approxmaton. Bold pont corresponds to a crtcal pont of phase transton. Concentraton of monopoles Increases stepwse across the lne. I.A. Ryzhkn, Sold State Commun. 56, 57 (1985) I.A. Ryzhkn, A.V. Klyuev et al, JETP Letters 95, 30 (01)

11 Strngs and polarzaton of vacuum by movng quaspartcles quaspartcle movement polarzes or depolarzes ground state (or vacuum) what gves the mechansm of relaxaton (specfc and useful property of quaspartcles) the same property means that quaspartcles are not pont lke exctatons, they are sooner strngs how to deal wth strng exctatons?

12 Macroscopc effect of strngs can be descrbed by vector feld C. Jaccard, Physk der Kondenserten Matere 3, 99 (1964) M. Hubmann, Zetschrft fur Physk B3, 17 (1979) t dt j j j j t r , V V e V a t r / lm, 0 I.A. Ryzhkn, R.W. Whtworth, J.Phys.: Cond. Matter 9, 395 (1997)

13 Confguraton vector and entropy S c T S 0 c I.A. Ryzhkn, R.W. Whtworth, J. Phys.: Cond. Matter 9, 395 (1997) 8 3 T ak B Ths formula leads an addtonal source (or snk) of heat, and gves rse to generalzed thermodynamc forces. TS TS TS 4 1 n TS c je e E j X j 4 1 X j 4 e j 1, 1, 1, 1 e 1 E

14 Jaccard s theory of relaxaton (water ce) t dt j n D e E e j 0 dvj t n n n e E dv

15 Jaccard s theory of relaxaton (spn ce) t dt j dvj t n n D H q q j n n q H dv

16 Susceptblty tensor of spn ce (equal conductvtes of monopoles) q H M k t t t 1, 4 1, q D k q H M k l l l / q q T k D B q m a

17 Effect of surface on proton orderng: Fletcher s model of surface layer Surface nevtably brngs some dsturbances and generally dctates a dfferent type of orderng than bulk of crystal. That leads to formaton of near surface transton layer wth ncreased concentratons of quaspartcles (lqud lke layer of water ce). N.H. Fletcher, Phlosophcal Magaznes 18, 187 (1968)

18 Does a specfc layer exst n spn ce? Surface orderng mechansm (spn ce): Ice rules ensure an ordered structure N 1 up = N up = N up = Loss of entropy, ncrease of Helmholtz free energy Formaton of thn near surface layer wth ncreased concentraton of monopoles decreases free energy.

19 Model based on surface states of monopoles Unform dstrbuton of postve monopoles leads to the loss of both electrostatc and entropy contrbutons nto Helmholtz free energy. That leads to creaton of surface layer wth ncreased concentratons of postve monopoles.

20 Surface layer as a precursor of bulk phase transton Fletcher model gves nsuffcently hgh concentratons of quaspartcles nto surface layer. It s necessary to amplfy Fletcher s ncrease. A bulk phase transton nto state wth hgh concentratons of quaspartcles could be drvng force for a surface layer wth extremely hgh concentraton of quaspartcles just below the crtcal temperature. I.A. Ryzhkn, and V.F. Petrenko, Phys. Rev. B65, 105 (001) I.A. Ryzhkn, and V.F. Petrenko, JETP Letters 108, 68 (009)

21 Lqud lke layer n water (spn) ce based on the I order phase transton nto the bulk bulk and surface phase transton space dependence of concentraton (log scale)

22 Magnetocalorc (electrocalorc) effects Let us come back to the formula for the tme dervatve of entropy that we descrbe n the form: TS n TS TS c 1 q q H It s seen from ths equaton that the second term plays a role of source of heat (postve for orderng and negatve for dsorderng processes). Besdes of Joule heatng we have addtonal non-joule mechansm. Ths s an electrocalorc effect n water ce (magnetocalorc for spn ce). I.A. Ryzhkn, JETP 108, 60 (009) I.A. Ryzhkn, V.F. Petrenko, J.Phys.Chem. A 115, 60 (011)

23 Estmatons Addtonal heatng of spn ce (profound effect) T m 3k B H Tc p 1K, for T K, H and t ncreases as temperature decreases 0,5T Addtonal heatng of water ce (neglgble effect) T 3e1 E K, for T 53K, E 10 V 16k TC B p / m

24 Expermental appearance MCE n spn ce Effect can be measured drectly (demagnetzaton coolng). M. Orendac et al, Phys. Rev. B 75, (007). Avalanches durng magnetzaton at low temperature could be explaned by magnetocalorc effect (local orderng releases heat, ncreases local temperature, strongly decreases relaxaton tme, and accelerates orderng (relaxaton). Avalanches must takes the place for all orderng processes at very low temperature (slow relaxaton, low heat capacty).

25 Dfferences between water/spn ce model Let us come back to the formula t r, t j j j j dt For water ce an electrc current s possble wthout polarzaton of vacuum state. That s not possble n standard model of spn ce. Can one put forward an extended spn ce model totally emulatng water ce? (analogs of D and L)

26 Standard model of spn ce The standard spn ce model does not nclude bond defects.

27 Extended model of spn ce Model wth four states of bonds

28 Creaton of quas-partcles n extended model

29 . Is a quaspartcles nteracton essental? For water ce even at the hghest temperature we have: q n T 1/3 E1 kt, q 0.6e, nt N exp, E1 3 kt 1eV For spn ce we can neglect by nteracton at temperatures: q 3 T 0.K f 4.10 J, E1 5K a At hgher temperatures mean dstance between monopoles becomes small and nteracton becomes essental.

30 Summary analogy between water and spn ce mght be very useful for understandng of many spn ce propertes Jaccard s theory of relaxaton s very convenent way of theoretcal descrpton of relaxaton nto spn ce and n other frustrated systems there are quanttatve and qualtatve dfferences between water and spn ce models magnetc monopoles pctures an economcal way of theoretcal descrpton of spn ce materals

31 Extra goal of the presentaton To attract an attenton of spn ce socety to water ce. Water ce s very nterestng substance, ts propertes unusual and mportant for many applcatons. The next Internatonal Symposum on Physcs and Chemstry of Ice wll be held n Hanover, New Hampshre, Dartmouth College, 014, organzers: Ian Baker and Vctor Petrenko

32 Thank you for attenton!

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34 Susceptbltes n coordnate presentaton: r t q t r t exp, 3/ exp, Dt Dt r t q q t r l How are these results related wth equlbrum correlaton functons (wth dpole correlatons)?

35 Hamltonan of extended model H J 1 j J j looks lke one n water ce model, but physcs s dfferent. Man dfference: postve monopole and postve bond defect modfy vacuum dentcally. That lead to the concluson: t s not possble to create DC- magnetc current j

36 quantum phase transton n water ce (phase transton nto a state wth symmetrcal hydrogen bonds)

37 Polarzaton and coarse granng procedure (a) and (b) are dentcal after averagng over small volumes (coarse granng procedure)

38 Creaton of space charge near blockng electrodes Formaton of space charge near contacts leads to addtonal relaxaton tmes or characterstc frequences. For water ths problem was studed n

39 Schematcally the results for water ce can be pctured as a followng

40 Water ce wth onc defects only

41 General soluton (n SI system of unts)