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Theory of Colossal Magnetoresistance in Doped Manganites

Theory of Colossal Magnetoresistance in Doped Manganites
Theory of Colossal Magnetoresistance in Doped Manganites

a r X i v :c o n d -m a t /9812355v 1 [c o n d -m a t .s t r -e l ] 22 D e c 1998Theory of Colossal Magnetoresistance in Doped Manganites

A.S.Alexandrov 1,?and A.M.Bratkovsky 2,?1Department of Physics,Loughborough University,Loughborough LE113TU,UK

2

Hewlett-Packard Laboratories,3500Deer Creek Road,Palo Alto,California 94304-1392

(October 22,1998)The exchange interaction of polaronic carriers with localized spins leads to a ferromag-netic/paramagnetic transition in doped charge-transfer insulators with strong electron-phonon cou-pling.The relative strength of the exchange and electron-phonon interactions determines whether the transition is ?rst or second order.A giant drop in the number of current carriers during the transition,which is a consequence of local bound pair (bipolaron)formation in the paramagnetic phase,is extremely sensitive to an external magnetic ?eld.Below the critical temperature of the transition,T c ,the binding of the polarons into immobile pairs competes with the ferromagnetic exchange between polarons and the localized spins on Mn ions,which tends to align the polaron moments and,therefore,breaks up those pairs.The number of carriers abruptly increases below T c leading to a sudden drop in resistivity.We show that the carrier density collapse describes the colossal magnetoresistance of doped manganites close to the transition.Below T c ,transport occurs by polaronic tunneling,whereas at high temperatures the transport is by hopping processes.The transition is accompanied by a spike in the speci?c heat,as experimentally observed.The gap fea-ture in tunneling spectroscopy is related to the bipolaron binding energy,which depends on the ion mass.This dependence explains the giant isotope e?ect of the magnetization and resistivity upon substitution of 16O by 18O.It is shown also that the localization of polaronic carriers by disorder cannot explain the observed huge sensitivity of the transport properties to the magnetic ?eld in doped manganites.71.30.+h,71.38.+i,72.20.Jv,75.50.Pp,75.70.Pa,71.27.+a I.INTRODUCTION The existence of a metal-insulator transition in lanthanum manganites was established in the early 1950s [1]and has been extensively studied thereafter.The transition is associated with unusual transport properties,including large magnetoresistance in the vicinity of the transition,studied in a family of doped manganites with perovskite structure with the chemical formula Re 1?x D x MnO 3,where Re is the rare earth (Re =La,Pr,Nd),and D is the divalent metal (D =Ca,Sr,Ba).It is worth mentioning the early studies of the transition in La 1?x Pb x MnO 3[2],followed by the studies of Pr 1?x Ca x MnO 3[3],Nd 0.5Pb 0.5MnO 3[4],La 0.67Ba 0.33MnO 3[5],La 0.75Ca 0.25MnO 3[6],La 1?x Ca x MnO 3[7,8](see review [9]).The recent resurgence of interest in these systems is related to the demonstration of a very large negative magnetoresistance in thin ?lms [5,7][sometimes termed colossal magnetoresistance (CMR)],which immediately raised the possibility of technological applications.The colossal magnetoresistance is not limited to doped perovskite manganites,but was also observed in pyrochlore manganites,chromium spinels [9],and some other systems,like europium compounds.The metal-insulator transition in lanthanum manganites [1,7,8]has been traditionally attributed to a ‘double exchange’mechanism,which results in a varying band width of holes doped into the Mn 3+d -shell as a function of the doping concentration and temperature [10].Recently it has been realized [11],however,that the e?ective carrier-spin exchange interaction of the double-exchange model is too weak to lead to a signi?cant reduction of the electron bandwidth and,therefore,cannot account for the observed scattering rate [12](see also Ref.[13])or for localization induced by slowly ?uctuating spin con?gurations [14].In view of this severe shortcoming of the double exchange model,it has been suggested [11]that the essential physics of perovskite manganites lies in the strong

coupling of carriers to the Jahn-Teller lattice distortion.The argument [11]was that in the high-temperature state the electron-phonon coupling constant λis large (so that the carriers are polarons);as temperature decreases the growing ferromagnetic order increases the bandwidth and thus decreases λsu?ciently for metallic behavior to occur below the Curie temperature T c ,in accordance with polaron theory [15].A giant isotope e?ect [16],the sign anomaly of the Hall e?ect,and the Arrhenius behavior of the drift and Hall mobilities [17]over a temperature range from 2T c to 4T c unambiguously con?rmed the polaronic nature of the carriers in manganites.Polaron hopping transport accounts satisfactorily for the resistivity in the paramagnetic phase [17].

However,the known relation between magnetization and transport below T c and the unusual magnetic ion dynamics have prompted the conclusion that polaronic hopping is also the prevalent conduction mechanism below T c [18].Low-

1

temperature optical[19–21],electron-energy-loss(EELS)[22]and photoemission spectroscopies[23]showed that the idea[11,14]of a‘metalization’of manganites below T c is not tenable.A broad incoherent spectral feature[19–21,23] and a pseudogap in the excitation spectrum[23–25]were observed while the coherent Drude weight appeared to be two orders of magnitude smaller[20]than is expected for a metal,or even zero in the case of layered manganites [23].EELS[22]con?rmed that manganites are charge-transfer doped insulators having p-holes as the current carriers rather than d(Mn3+)electrons.The photoemission and O1s x-ray absorption spectroscopy of La1?x Sr x MnO3showed that the itinerant holes doped into LaMnO3are indeed of oxygen p character,and their coupling with the d4local moments on Mn3+ions aligns the moments ferromagnetically[26].Moreover,measurements of the mobility[9,27] do not show any?eld dependence and there are signi?cant deviations from Arrhenius behavior close to T c[28,17]. The resistivity calculated from the modi?ed double-exchange theory is in poor agreement with the data and the characteristic theoretical?eld(~15T)for CMR is too high compared with the experimental one(~4T)[11].As a result,self-trapping above T c and the idea of metalization below T c do not explain CMR either.Carriers retain their polaronic character well below T c,as manifested also in the measurements of resistivity and thermoelectric power under pressure[29].

Therefore,the experimental evidence overwhelmingly suggests that the low-temperature phase of the doped man-ganites is not a metal,but a doped polaronic semiconductor.The double exchange and the presence of polaronic carriers are insu?cient to explain the physics of colossal magnetoresistance.One can also add that there are known classes of CMR materials where it is guaranteed that double exchange is non-existent,like in pyrochlore manganites, chromium spinels[9],and other compounds.

In the present paper,we propose a new theory of the ferromagnetic/paramagnetic phase transition accompanied by a current carrier density collapse(CCDC)and CMR.Taking into account the tendency of polarons to form local bound pairs(bipolarons)as well as the exchange interaction of p polaronic holes with d electrons,we?nd a novel ferromagnetic transition driven by non-degenerate polarons in doped charge-transfer magnetic insulators.The crux of the matter is that in the paramagnetic state above the critical temperature a large fraction of polarons is bound into immobile pairs(bipolarons).As the temperature decreases in the paramagnetic phase(T>T c),so does the density of mobile polarons,and the resistivity quickly increases with the decline of the number of carriers.With the onset of ferromagnetic order at T c,the situation changes dramatically.As a result of the exchange interaction with the localized Mn spins,the energy of one of the polaron spin sub-bands sinks abruptly below the energy of the bound pairs.The pairs break up,the density of carriers(mobile polarons)jumps up,and the resistivity suddenly declines,as observed experimentally.The occurrence of the deep minimum in the carrier density close to the transition point,which we suggest calling a current carrier density collapse,allows us to explain the magnetization and temperature/?eld dependence of the resistivity of La1?x Ca x MnO3close to T c as well as the giant isotope e?ect,the unusual tunneling gap,and the speci?c heat anomaly.

II.FERROMAGNETIC TRANSITION IN DOPED MANGANITES

The Hamiltonian containing the physics compatible with the experimental observations mentioned above is

H= k,s E k h?k s h k s?J pd

The essential results are readily obtained within the Hartree-Fock approach for the exchange interaction[32]and the Lang-Firsov polaron transformation[33]which removes terms of?rst order in the electron-phonon interaction in Eq.(1),?H=e U He?U,where

U= j q s h?js h js u j q(b??q+b q),(2) h js=N?1/2 k h k s exp(?k·R j),u j q=(2N)?1/2γq exp(?q·R j),and R j is the lattice vector.

With the use of this transformation one?nds spin-polarized p bands

?k↑(↓)=?k?(+)1

N i,j t ij e?k·(R i?R j)e?g2ij≈E k e?g2(4) where

g2ij=1

2k B T (5)

where g2~γ2is the characteristic value of g2ij andωq is the phonon frequency.Equation(5)describes the polaronic band narrowing[33]and the isotope e?ect[16].The bare hopping integrals t ij de?ne the unrenormalized LDA(local density approximation)band dispersion in the initial Hamiltonian(1)E k=1

2N qˉhωq|γq|2.(6)

The ions Mn3+are subject to a molecular?eld J pd m/(2g MnμB),according to(1),and their magnetizationσ≡ S z n /S is given by

σ=B S J pd m+2g MnμB H

N k m k = d?N(p)(?)[f p(?k↑)?f p(?k↓)].(8)

Here B S(x)=[1+1/(2S)]coth[(S+1/2)x]?[1/(2S)]coth(x/2)is the Brillouin function,g Mn the Lande g-factor for Mn3+in a manganite,N(p)(?)the density of states in the narrow polaron band,and f p(?k s)=[y?1exp(?k s/k B T)+1]?1 the Fermi-Dirac distribution function with y=exp(μ/k B T)determined by the chemical potentialμ.Note that for J pd<0(antiferromagnetic coupling)the main system of equations(16)-(18)remains the same after a substitution J pd→|J pd|.

Along with the band narrowing e?ect,the strong electron-phonon interaction binds two polarons into a local pair (bipolaron),as described in detail in Ref.[15].These bipolarons are practically immobile in manganites because of the strong electron-phonon interaction,in contrast with cuprates,where bipolarons are mobile and responsible for in-plane transport[34],owing to their geometry[35]and their moderate coupling with phonons[36].

If these bound pairs are extremely local objects,i.e.two holes on the same oxygen,then they will form a singlet. If,however,these holes are localized on di?erent oxygens,then they may well have parallel spins and form a triplet state.The latter is separated from the singlet state by some exchange energy J st,with some interesting consequences discussed below.Because of their zero spin,the only role of the singlet bipolarons in manganites is to determine the chemical potentialμ,which can be found with the use of the total doping density per cell x[34].

3

The interplay between the localization of p-holes into bipolaron pairs and the exchange interaction with the Mn d4 local moments is responsible for CMR.The density of these pairs has a sharp peak at the ferromagnetic transition when the system is cooled down through the critical temperature T c.As the system is cooled,but is still in a paramagnetic state above T c,an increasing fraction of the polarons forms immobile pairs(bipolarons),and the resistivity of the system increases.Below T c,the binding of polarons into immobile pairs competes with the ferromagnetic exchange, which tends to align the polaron moments and,therefore,breaks those pairs apart.The number of carriers abruptly increases below T c leading to a sudden drop in resistivity.These competing interactions lead to the unusual behavior of CMR materials and the extreme sensitivity of their transport to external?elds.

To prove the point,we shall?nd the thermodynamic potential and solve for its extremal value to?nd the equation of state for the polarons.The thermodynamic potential?

?=?p+?bp+?S+

1

2k B T

,(11)

whereν(=3)is the degeneracy of the polaron p band.

Polarons,bound in bipolarons with a binding energy?,give a contribution

?bp=?k B T ln 1+ν2y2De?/k B T ,(12)

where D accounts for the presence of triplet bipolarons(see below Sec.VI).We shall consider here a simple case when the separation of the triplets from the singlets,J st,is much larger than the critical temperature.In this case D=1. Finally,for the localized spin contribution we will have

?S=?k B T ln sinh(S+1

sinh1

2J pd m+g MnμB H)/k B T.

The density of polarons n=?(??p/?μ)T is found from the condition that the total number of carriers is given by the doping concentration x[34]:

x=?(??/?μ)T,(14) whereas one can?nd equations for the magnetization and the normalized spinσfrom the following conditions:

(??/?σ)T=(??/?m)T=0.(15) Thus,we obtain the following main system of mean?eld equations,assuming for a moment that the contribution from triplet bipolarons is small(D=1):

n=2νy cosh[(σ+h)/t],(16)

m=n tanh[(σ+h)/t],(17)

σ=B2[(m+4h)/(2t)],(18) and

4

c E T

T>T FIG.1.Schematic of free polaron (P)and polaron bound pair (BP)densities of states at temperatures below and above T c for up (↑)and down (↓)spin moments.The pairs (BP)break below T c if the exchange J pd S between p -hole polarons and Mn d 4local spins exceeds the pair binding energy ?,as in the case shown.The exchange interaction of polarons with the localized spins sets in below T c ,the spin-up polaron sub-band sinks abruptly below the bipolaron band,causing the break-up of the immobile bipolarons (left panel).A sudden drop (collapse)of the density of the current carriers (polarons)in the vicinity of the ferromagnetic transition is the cause of a large peak in resistivity and colossal magnetoresistance.

y 2=x ?n

0.10.20.30.4

t 02468

10

x /n

h=0

h=0.005

h=0.01

0.00000.0075

h

0.16

0.20

t

c

FERRO PARA

FIG.2.Inverse polaron density x/n in a doped charge-transfer insulator for di?erent magnetic ?elds h ≡gμB H/J pd S ,?/J pd S =0.5,doping x =0.25.?is the pair binding energy,J pd S is the exchange energy of the O p hole polarons with Mn d localized spins.For other notations see text.Note that the transition is a strong ?rst order,and then becomes continuous when the external magnetic ?eld exceeds some critical value.Inset:temperature of the phase transition as a function of external magnetic ?eld.

n 1/2c

ln 2(x ?n c )

0501000

50

100x /n

200250300

050

100ρ(m ?-c m )FIG.3.Resistivity of La 0.75Ca 0.25MnO 3calculated within the present theory for ?=900K,J pd S =2250K for a temperature independent mobility (a).The experimental results [8]are shown on panel (b).Note the extreme sensitivity of the theoretical resistivity to the external magnetic ?eld (a),also observed experimentally for the doped manganite (b)(thin solid line is a guide to the eye).Panel (c):Resistivity calculated with a temperature dependent mobility according to Eq.(26)with ω0=50meV and E a =300meV and temperature dependent polaron density from panel (a)compared with the experimental results.Note the crossover of the transport mechanism from low-temperature tunneling to high-temperature hopping at about the transition temperature.For notations see caption to Fig.2.

hopping events since the polaron narrowing factor g 2grows linearly with T ,making tunneling in a narrow polaron band virtually impossible at k B T >ˉh ω0/2,where ω0is the characteristic phonon frequency [33].A simple estimate for the so-called adiabatic hopping conductivity together with the Einstein relation between di?usion constant and mobility immediately yields

μ(hop)p ~μ0k B T exp(?E a /k B T ),(22)

where μ0=ea 2/ˉh is the characteristic mobility (one can estimate a as the O-O distance in manganites),and E a is the activation energy for the hopping.Tunneling mobility is given by

μ(tun)p =μ0ˉt

2e ?2g 2

[15].We have ?tted the observed resistivity to the above expression [Fig.3(c)]using for ω0a value of 50meV,which is close to the phonon cuto?in LCMO (50-70meV [41]).

The ?t indicates that the activation energy is close to E a =300meV.A crossover from tunneling to hopping occurs around the critical temperature T c ,which is not very di?erent from ˉh ω0/2k B [42].Agreement with the experiment (Fig.3(c))supports the idea that the temperature dependence of the resistivity is due primarily to CCDC.The temperature dependence of the small polaron mobility then allows the resistivity far away from the transition both above and below T c to be explained.

V.ANOMALOUS SPECIFIC HEAT

The carrier density collapse is also evident through anomalies in thermodynamic quantities.Indeed,we have shown above that the ferromagnetic transition is ?rst order,or second order close to ?rst order,as observed.The thermodynamic potential changes rather abruptly in the vicinity of the phase transition and this results in a sharp peak in the speci?c heat C ,Fig.4,which has been observed [43].Note that this is not a result of critical ?uctuations as suggested earlier [43],since they are absent or severely suppressed when the phase transition is ?rst order,or close to it.We see that our theory is in quantitative agreement with the experiment for this anomalous thermodynamic quantity.

200220240260280

T(K)0.000.050.100.15

0.20

C /T (J /m o l e K 2)FIG.4.Calculated anomalous part of the speci?c heat for di?erent values of the magnetic ?eld H .Inset:experimental results for La 0.67Ca 0.33MnO 3[42](thin solid line is a guide to the eye).

VI.TRIPLET BIPOLARONS

Let us now discuss the modi?cation which arises if we include exchange between O-holes bound into bipolarons.This exchange generally induces a splitting J st between singlet and triplet states of the bipolaron.This changes somewhat the thermodynamic potential of the bipolarons,since the triplet is subject to a Zeeman splitting.The factor D is then

D =1+e ?J st /k B T sinh(3ξ/2)/sinh(ξ/2)(26)

as it accounts for thermal excitations of singlet bipolarons into the triplet state,separated from the singlet by the energy J st .The parameter

ξ=(?J

pd Sσ+V bp m +gμB H )/k B T,(27)

8

0.10.20.3

t 010

20

30x /n

FIG.5.Inverse polaron density x/n for di?erent magnetic ?elds for a system with triplet and singlet bipolarons versus temperature t ≡2k B T /J pd S .(?/J pd S =0.5,doping x =0.25,and we assume J st ??).The jump in carrier density is much larger in a system with triplet bipolarons,but the critical temperature and sensitivity of the critical temperature

to

the

magnetic ?eld is lower in comparison with singlet bipolarons.For notations see caption to Fig.2.

depends on exchange interaction of the bipolarons with Mn 3+spins given by the exchange constant ?J

pd ,and delocalized polarons,given by the exchange constant V bp .Note that D =4at J st /k B T ?1,whereas D =1for J st /k B T ?1,which re?ects the higher statistical weight of triplet states compared to singlets.

It is assumed,as is usually the case,that the triplet states lie higher in energy than the singlet state,J st >0.If the singlet-triplet splitting becomes smaller than the gap,J st <~?,then,because of a higher number of the triplet states,their thermal population leads to a deeper minimum in the density of polarons and,therefore,to a larger jump in resistivity (Fig.5).The dependence of the population of the triplet states on external ?eld makes the system somewhat less sensitive to the ?eld.We make an essential assumption that J st >0and that the exchange between spins on Mn and triplet bipolarons,?J

pd ,is suppressed to values ?J pd because the bipolarons are strongly localized [we also expect that the exchange constant V bp is the smallest one in (27)].Otherwise,the triplet bound pairs,if they were formed in the paramagnetic phase,can survive in the ferromagnetic phase thus reducing or eliminating the carrier density collapse.

The equation (19)is changed to read

y 2=x ?n

Dn 2c [1?(x ?n c )/2]=23/2δ,(29)

which is similar to the case of singlet polarons and also indicates a crossover from ?rst-to second-order phase transition.We compare the carrier density collapse in a system with triplet bipolarons to that with singlet bipolarons alone in Fig.5.The jump in the carrier density at the transition is a few times larger in this case as compared to singlet bipolarons.At the same time the critical temperature shifts to lower values,and the sensitivity to external magnetic ?eld slightly reduces.

9

0.150.250.35

t c 0.100.30

0.50

δ

FIG.6.Relation between the gap δ≡?/J pd S and the critical temperature t c ≡2k B T c /J pd S calculated from the present theory.Inset:tunneling gap in the density of states for samples with di?erent temperatures of the transition:La 0.8Ca 0.2MnO 3,T tr =196K;(NdLa)0

.73

Pb

0.27MnO 3(T tr =275K);La 0.7Pb 0.3MnO 3(T tr =338K)[24].For notations see caption to Fig.2.

VII.TUNNELING GAP AND GIANT ISOTOPE EFFECT

Recent tunneling measurements have shown that in the vicinity of T c a gap in the quasiparticle spectrum opens up

[24,25].Again,it is di?cult to reconcile this gap with the notion of a (half-)metallic ferromagnetic state below T c [44].In half-metallic ferromagnets,like CrO 2or Fe 3O 4,there is a band gap for electron states of only one spin direction.The opposite spin electrons have no gap at the Fermi level,similar to a standard metal situation.These states will contribute to tunnel current as in conventional metals,so that there would be no such temperature dependent gap feature in the tunnel spectroscopy [44]like the one observed for the doped manganites [24].

We note that within the framework of our theory there should be a temperature dependent gap ?related to the breakdown of a bipolaron into two polaronic carriers.The density of bipolarons peaks at T c ,whereas the polaron density dips there (Figs.1,2)and,therefore,the gap feature in the tunneling I ?V curves will be most pronounced in this region,as observed [24].Spin-polarized polarons will provide a gapless background for tunneling current,which is least important in the vicinity of the transition temperature.We note that STM should also be sensitive to the presence of the one-particle charge-transfer gap between ?lled Mn d and empty O p states.In addition to the temperature dependence,we can predict how the gap feature will depend on the critical temperature of the transition (Fig.6).Namely,as already follows from our discussion,with the increase of ?the critical temperature T c goes down

[38].Very similar behavior has indeed been observed experimentally on samples with di?erent critical temperatures (Fig.6,inset)[24].

The giant isotope e?ect in La 0.8Ca 0.2MnO 3,where a shift of -21K in T c was observed as a result of 16O to 18O substitution [16],is quantitatively explained within our https://www.sodocs.net/doc/7a2466534.html,ly,the gap is given by [45]

?=2E p ?V C ?1

18/16?1),(31)

10

0.0

0.51.0M /M 0

T/T c 02

4

x /n

FIG.7.Isotope e?ect on magnetization (a)and inverse carrier density (b)of La 0.8Ca 0.2MnO 3+y calculated in the present theory.Inset:experimental results [16].Substitution 16O →18O leads to increased resistivity (b).

where indices mark the quantities for the corresponding isotopes of oxygen.According to (31)?18is always larger than ?16.This automatically leads to a lowering of T c as a result of the isotope substitution,as observed [16],in Fig.7.The resistivity,on the other hand,is larger in 18O substituted samples,and this correlation seems to be supported by recent experiments [46].Note that the single parameter de?ning the isotope e?ect on the magnetic transition and the resistivity jump is W g 216,since neither E p nor V C depend on the ion mass.

VIII.LOCALIZATION OF POLARONS BY DISORDER

We have also studied the localization of p -holes due to a random ?eld with a gap ?/2between localized impurity levels and the conduction band.The energy of polarons on impurity centers is given by

E i ↑(↓)=??

2V ip m ?(+)μB H,(32)

where V ip is the exchange interaction between localized and delocalized polarons.The band diagram for this case is the same as in Fig.1with the replacement of the bipolarons by localized polarons.

Assuming that the Hubbard repulsion prevents a double occupancy of the impurity centers,one can easily obtain the thermodynamic potential for impurities

?i =?k B T ln 1+2νye ?/2k B T cosh 1

k B T

(33)The chemical potential is found to be

y =

x ?n 2V ip m +μB H )/k B T ,if we assume that the total number of impurity states is x (≡doping).

We have found similar features of the phase transition in zero ?eld in the impurity case,as compared with the previous case with bipolarons.Thus,we obtain,by linearizing the system of equations of state (16)-(18)with (34),the following equation for the polaron density at the transition in zero ?eld:

n 1/2c ln x ?n c

Apparently,it has solutions only forδ<δc(x).Therefore,the transition is?rst order forδ≡?/J pd S>δc(x)and

second order forδ<δc(x),withδc(x)slightly larger than in the case of the bipolaron localization.This follows from the same consideration as in our previous discussion of Eq.(21).

The?eld sensitivity in the case of disorder localized polarons is much lower than for the bipolarons.This stems from the di?erent functional dependence of the chemical potential.The present approximations are valid in the limit

y?1,meaning that the polaron carriers are non-degenerate.In contrast to the case of the bound polaron pair formation,in the impurity case the expression(34)for y is singular,y∝1/n,in the limit of small polaron density.

This means that in the vicinity of the current carrier density collapse the value of y sharply increases in the case of polarons localized on impurities.As a result,the collapse becomes less pronounced,and transport becomes far less

sensitive to an external?eld.We note also that Eq.(34)contains a factor depending on the external magnetic?eld in the denominator.This is in contrast with the case of bipolarons(28),where the?eld dependence is suppressed

by a small factor exp(?J st/k B T c).This?eld dependence,however,is small since alwaysμB H/k B T c?1,and it quickly vanishes in the low-temperature phase when the exchange interaction sets in(m=0),as one can see from

the expression for the parameterζabove.The singular behavior of y as a function of the density for n→0,and the Zeeman splitting of the impurity states makes the transition far less sensitive to the magnetic?eld.As a result,no

quantitative description of the experimental CMR data has been found with the localization of polarons due to disorder.

IX.CONCLUSION

In conclusion,we have developed a theory of the ferromagnetic-paramagnetic phase transition in doped magnetic

charge-transfer insulators with a strong electron-phonon coupling.We have found that a few non-degenerate polarons in the p band polarize localized d electrons because of the huge density of states in the narrow polaronic band.For a su?ciently large p?d exchange J pd S>?,we have obtained a current carrier density collapse at the transition owing to the formation of immobile local pairs in the paramagnetic phase with the binding energy?about twice that of the polaron level shift[15].Depending on the ratio?/(J pd S),the transition is?rst or second order[38].

We have explained the resistivity peak and the colossal magnetoresistance of doped perovskite manganites,Fig.3,

as the result of the current carrier density collapse due to the binding of polarons into local pairs(bipolarons).The density of these immobile pairs has a sharp peak at the ferromagnetic transition when the system is cooled down through the critical temperature T c.Below T c the binding of polarons into pairs competes with the ferromagnetic exchange of p-holes with the Mn d4local moments,which tends to align the polaron moments and,therefore,breaks those pairs apart.The spin-polarized polaron band falls below the bipolaron band upon decrease in temperature,so that all carriers are unpaired at T=0if J pd S≥?.Above T c,the bipolaron density decreases because of thermal activation across the polaron binding energy.These competing interactions lead to the unusual behavior of CMR materials,the huge sensitivity of their transport to external?eld,and the very large negative magnetoresistance. There is a crossover around the transition temperature from polaron tunneling at low temperatures to polaron hopping,where the latter dominates at high temperatures.This explains the temperature behavior of the resistivity in a wide temperature range around the transition.The ferromagnetic to paramagnetic transition is also accompanied by a sharp anomaly in the speci?c heat.

The present theory provides a natural explanation for the temperature dependent gap feature in tunneling spectra [24]and the giant isotope e?ect on the temperature of the ferromagnetic transition[16].One of our main conclusions is that the highly polarized ferromagnetic phase of manganites is a polaronic doped semiconductor rather than a metal.

We expect that the present theory is general enough to also account for the giant magnetoresistance observed

in pyrochlore manganites[47]and other systems[9].It is worth mentioning in this regard that the present theory requires the presence of strong electron-phonon coupling of any origin,but it does not require the presence of Jahn-Teller distortions and/or the double exchange mechanism.Note that the Jahn-Teller distortions and the double exchange mechanism are certainly absent in,for instance,pyrochlore manganites,chromium spinels[9],and other CMR systems,so that the ideas based on the double exchange cannot be applied there at all.It is believed that at least in perovskite manganites the local Jahn-Teller distortion may be involved in de?ning the crystal structure of the

parent insulating phases[48],although tilting distortions of MnO6octahedra are just a result of steric conditions[49,9].

Apparently,the ratio of the sum of Mn and O ionic radii,r Mn+r O,and(r La+r O)/

are less distorted[50].This argument,which may have supported the relevance of the double exchange mechanism for at least perovskite manganites,contradicts the site-sensitive spectroscopic probes[22,26],which show unambiguously

that holes reside on O sites.It also neglects two important facts,that(i)the doping is heavy(>~1021e/cm3)and there is a substantial size di?erence between the impurity and host atoms and(ii)the O p-holes are hybridized

with the d states on Mn3+,depending on the value of the charge-transfer gap.Both e?ects,together with screened Coulomb hole-hole repulsion,can apparently explain the observed changes in the lattice distortion upon doping without invoking the Jahn-Teller mechanism.These short-range interactions may well be responsible for the charge-ordered phases observed at some doping levels in manganites[9].It would be interesting,in this regard,to perform quantum-chemical calculations of MnO6clusters with holes doped onto O site(s).

Changes and the amount of disorder in the bond lengths are very important for characterizing the properties

of polaronic systems.The reduction in bond length distribution width as a result of cooling through T c in doped manganites has been attributed to(at least partial)delocalization of doped carriers in low-temperature‘metallic’phase.Since the data shows that the carriers retain their polaronic character below T c,and the residual width of the Mn-O bond length distribution remains larger than that of CaMnO3[50],where the Jahn-Teller Mn3+ions are absent,the reduction of the width should be mainly related to instability of bipolarons in this temperature region. Breaking of polaron bound pairs below T c may result in a reduction of bond length distribution width,and we shall address this question elsewhere.It is worth repeating that whether or not the Jahn-Teller distortions play any role in doped perovskite manganites and the exact location of the carriers is of no importance for the present scenario of the CMR.

We acknowledge useful discussions with A.R.Bishop,D.M.Edwards,J.P.Franck,K.M.Krishnan,P.B.Littlewood, S.von Molnar,V.G.Orlov,W.E.Pickett,D.J.Singh,S.A.Trugman,and R.S.Williams.We especially grateful to G.Aeppli,D.S.Dessau,M.F.Hundley,H.-T.Kim,A.P.Ramirez,and G.-m.Zhao for useful discussions and communicating their data.

[22]H.L.Ju,H.C.Sohn,and K.M.Krishnan,Phys.Rev.Lett.79,3230(1997).

[23]D.S.Dessau,T.Saitoh,C.H.Park,Z.X.Shen,P.Villella,N.Hamada,Y.Moritomo,and Y.Tokura,Phys.Rev.Lett.81,

192(1998).

[24]A.Biswas,S.Elizabeth,A.K.Raychaudhuri,and H.L.Bhat,cond-mat/9806084.

[25]J.Y.T.Wei,N.-C.Yeh,and R.P.Vasquez,Phys.Rev.Lett.79,5150(1997).

[26]T.Saitoh,A.E.Bocquet,T.Mizokawa,H.Namatame,A.Fujimori,M.Abbate,Y.Takeda,M.Takano,Phys.Rev.B51,

13942(1995).

[27]H.-T.Kim,Y.-J.Kim,and K.-Y.Kang,preprint(1998).

[28]P.White,M.Jaime,M.B.Salamon,and M.Rubinstein,Bull.Am.Phys.Soc.41,116(1996).

[29]J.-S.Zhou,J.B.Goodenough,A.Asamitsu,and Y.Tokura,Phys.Rev.Lett.79,3234(1997).

[30]W.E.Pickett and D.J.Singh,Phys.Rev.B53,1146(1996).

[31]H.Fehske,H.R¨o der,G.Wellein,and A.Mistriotis,Phys.Rev.B51,16582(1995).

[32]See,e.g.:K.Yosida,Theory of Magnetism(Springer-Verlag,Berlin,1996),p.201.

[33]https://www.sodocs.net/doc/7a2466534.html,ng and Yu.A.Firsov,Zh.Eksp.Teor.Fiz.43,1843(1962)[JETP16,1301(1963)].

[34]A.S.Alexandrov,A.M.Bratkovsky,and N.F.Mott,Phys.Rev.Lett.72,1734(1994).

[35]A.S.Alexandrov,Phys.Rev.B53,2863(1996).

[36]All objections,recently raised by V.K.Chakraverty et al.[Phys.Rev.Lett.81,433(1998)]with respect to a bipolaron

model of cuprates,are completely erroneous(see A.S.Alexandrov,cond-mat/9807185).

[37]Otherwise,there will be a prefactor1

皮下脂肪瘤介绍及治疗方法

【精编】皮下脂肪瘤介绍及治疗方法(含民间偏方) 1 皮下脂肪瘤皮下脂肪瘤在中医称为痰核。“肉瘤”之名出《干金要方》。多因郁滞伤脾,痰气凝结所致。以皮下肉中生肿块,大如桃、拳,按之稍软,无痛为主要表现的瘤病类疾病。最常见的好发部位为颈,肩,背,臀和乳房是起源于脂肪组织的良性肿瘤,由成熟的脂肪组织所构成。 1 疾病简介皮下脂肪瘤(lipoma)是脂肪组织的良性肿瘤。由成熟的脂肪组织所构成,凡体内有脂肪存在的部位均可发生。脂肪瘤有一层薄的纤维内膜,内有很多纤维索,纵横形成很多间隔,最常见于颈、肩、背、臀和乳房及肢体的皮下组织,面部、头皮、阴囊和阴唇,其次为腹膜后及胃肠壁等处;极少数可出现于原来无脂肪组织的部位。如果肿瘤中纤维组织所占比例较多,则称纤维脂肪瘤。 2 疾病分类根据脂肪瘤的可数目可分为有孤立性脂肪瘤及多发性脂肪瘤二类。此类肿瘤好发于肩、背、臀部、四肢、腰、腹部皮下及大腿内侧,头部发病也常见。位于皮下组织内的脂肪瘤大小不一,大多呈扁圆形或分叶,分界清楚;边界分不清者要提防恶性脂肪瘤的可能。单个称为孤立行型脂肪瘤。两个或两个以上的称为多发性脂肪瘤。

按部位不同可分为皮下脂肪瘤和血管平滑肌脂肪瘤(又称错钩瘤)。根据脂肪瘤发生的部位皮下脂肪瘤为扁平或分叶状、质软,边界清楚的皮下限局性肿物。质软,可推动,表面皮肤正常,发展慢,数目多达数百个,常在皮下。血管平滑肌脂肪瘤错钩瘤多发生于各个器官(肾脏,肝脏较为多见)的毛细血管的平滑肌组织之间的脂肪瘤(又称肾错构瘤,肝错钩瘤)。 3 发病原因皮下脂肪瘤指“脂肪瘤致瘤因子”在患者体细胞内也存在一种致瘤因子,在正常情况下,这种致瘤因子处于一种失活状态(无活性状态),皮下脂肪瘤正常情况下是不会发病,但在各种内外环境的诱因影响作用下,这种脂肪瘤致瘤因子的活性处于活跃状态具有一定的活性,在机体抵抗力下降时,机体内的淋巴细胞、单核吞噬细胞等免疫细胞对致瘤因子的监控能力下降,再加上体内的内环境改变,慢性炎症的刺激、全身脂肪代谢异常的诱因条件下,脂肪瘤致瘤因子活性进一步增强与机体的正常细胞中某些基因片断结合,形成基因异常突变,使正常的脂肪细胞与周围的组织细胞发生一种异常增生现象,导致脂肪组织沉积有关,并向体表或各个内脏器官突出的肿块,称之脂肪瘤。[1] 4 发病机制皮下脂肪瘤是相当常见的皮肤病灶,由正常脂肪细胞集积而成,占软组织良性肿瘤的 80%左右,无明显特殊病因,常发于皮

完整版皮下脂肪瘤介绍及治疗方法含民间偏方

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眼角长了个小疙瘩怎么办

如对您有帮助,可购买打赏,谢谢 眼角长了个小疙瘩怎么办 导语:眼睛长了个小疙瘩是很常见的现象,在这样的情况之下,就好好的进行观察,自己的小疙瘩是什么样的,然后及时的去医院做检查,及时的检查,及 眼睛长了个小疙瘩是很常见的现象,在这样的情况之下,就好好的进行观察,自己的小疙瘩是什么样的,然后及时的去医院做检查,及时的检查,及时的治疗,这是非常不错的,这样就会更好的让自己的身体恢复健康,这样是非常的不错的,那就好好的进行治疗就好了。 应该是麦粒肿的症状,别担心,初起有眼睑痒、痛、胀等不适感觉,之后以疼痛为主,少数病例能自行消退,大多数患者逐渐加重。检查见患处皮肤红肿,触摸有绿豆至黄豆大小结节,并有压痛。如果病变发生在近外眼角处,肿胀和疼痛更加明显,并伴有附近球结膜水肿。部分患者在炎症高峰时伴有恶寒发热、头痛等症状。外麦粒肿3~5日后在皮肤面,内麦粒肿2~3日后在结膜面破溃流脓,炎症随即消退。也有部分麦粒肿既不消散,也不化脓破溃,硬结节长期遗留者。它是一种没有明显疼痛的表面皮肤隆起,主要是眼睑腺体阻塞造成的伴有炎症的话才会自觉的疼痛的症状。小的霰粒肿可以热敷或者理疗按摩疗法,促进消散吸收,较大大的或长时间不能吸收的可以择期手术治疗. 这是脂肪粒,等长时间长了,熟了自己挤就行。先说说脂肪粒的产生(从其他地方转来D,自己还没那么厉害,呵呵 1、体内原因:眼部、面部出现油脂粒大多是由于近期身体内分泌有些失调,致使面部油脂分泌过剩,再加上皮肤没有得到彻底清洁干净,导致毛孔阻塞,很快形成脂肪粒。2、外在因素:眼睛周围是全身最薄的皮肤,约0.07毫米,又没有皮下腺,加上人眼一天频繁眨动,特别容易缺水、干燥、 预防疾病常识分享,对您有帮助可购买打赏

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酸,或含果酸、乳酸等成分的产品保养皮肤,改善皮肤的角化程度。可去药店咨询医生购买水杨酸类软膏。 ★缺乏维生素A加重小红疙瘩 皮肤下面有小红疙瘩除了与天生体质有关以外,缺乏维生素A引起全身性的皮肤干燥也是加重症状的原因之一。 ★对策 1、洗澡不要用太热的水。过热的水会让皮肤上的皮脂过分流失,这样会加重皮肤干燥。 2、洗澡后抹身体乳。保证皮肤水分充足能有效减轻腿上小红疙瘩,所以可以在每次洗澡后涂上身体乳液。

★可能是闭头粉刺 如果是额头、下巴等部位皮肤下有疙瘩,刚开始是黄白色,不痛不痒,天气炎热脸上油脂分泌旺盛时会有发红,多是闭头粉刺。 ★对策 1、及时清洁皮肤,注意补水,不要使用刺激性护肤品,不要用过于油腻滋润的面霜。 2、多运动促进皮肤排汗,使毛孔中的油脂脏污随着汗水排出,防止油脂堵塞毛孔发炎。 3、多喝水、多吃蔬果,饮食清淡。

4、必要时看医生。 ★可能是脂肪粒 如果皮下的疙瘩是乳白色的,不痛不痒,不受天气、温度等影响,用手不容易挤出,且多分布在眼角周围,考虑是脂肪粒。 ★对策 1、脂肪粒多是皮肤营养过剩引起的,建议不要使用太油腻的护肤品。 2、可取美容院用针挑破,挤出脂肪粒。(别用手挤,小心皮肤感染发炎)

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