Dynamic nuclear polarization and spin-diffusion in non-conducting solids Chandrasekhar Ramanathan∗ Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (Dated: February 2, 2008) Therehasbeenmuchrenewedinterestindynamicnuclearpolarization(DNP),particularlyinthe contextof solid statebiomolecular NMRandmorerecentlydissolution DNPtechniquesforliquids. 8 Thispaperreviewstheroleofspindiffusioninpolarizing nuclearspinsanddiscussestheroleofthe 0 spin diffusion barrier, before going on todiscuss some recent results. 0 2 PACSnumbers: n a Microwave irradiation of a coupled electron-nuclear lar interactions, the electron exchange interaction and J spin system can facilitate a transfer of polarization from theelectron-nuclearhyperfineinteraction(includingboth 4 the electron to the nuclear spin. In dielectric materials the Fermicontactandthe electron-nucleardipolar inter- 1 dynamicnuclearpolarization(DNP)typicallyoccursvia actions). During the DNP process we could add both ] the solideffect,thermal mixing or the crosseffect1,2,3. In microwave and RF fields to irradiate the electronic and r these systems the electron spins are localized and the nuclear spins as needed. The challenge of dealing with e h non-equilibrium polarization of the bulk nuclei is gen- this full Hamiltonian in a systematic quantum mechani- t erated via a two-stage process: a polarization exchange cal formalismunderlies the gaps in our knowledge of the o local to the defect; and spin transport to distribute the fullDNPprocess. Traditionallyresearchershaveadopted . at polarization throughout the sample. Here the DNP pro- acomposite quantum-classicalapproachinwhichaniso- m cess is essentially the inverse of the standard T relax- lated defect spin coupled to one or two nuclear spins is 1 ation mechanism in dielectric solids4. treated quantum-mechanically, and a classical approach - d While much attention is paid to improving the lo- is used to deal with the transport of the polarization ei- n cal polarization transfer efficiency from the electron to ther to or away from the defect. o the neighboring nuclear spins, usually by incorporating c the appropriate electron spins in the sample, the rate- [ limiting step in efficiently polarizing bulk samples is fre- The Bloembergen model 1 quently the spin transport from the defect sites to the v bulk. As we attempt to use DNP to enhance nuclear DNP and spin-lattice relaxation are very similar pro- 0 magnetization in an ever-increasing number of systems, cesses in these systems. Waller7 provided the first theo- 7 1 it is important to understand the many-spin dynamics retical treatment of nuclear magnetic relaxation in ionic 2 that underly the process. As we improve our system crystals, in which the spin-spin interactions between nu- . model for describing DNP dynamics, we will eventually clei were modulated by lattice vibrations. However ob- 1 0 be able toincorporaterecentdevelopmentsinthe theory servedrelaxationtimesweremuchshorterthanthosecal- 8 and practice of optimal control of quantum systems to culated with this model. In 1949 Bloembergen4 postu- 0 further improve our techniques5,6. latedthatNMRrelaxationinthesenon-conductingsolids : Thepurposeofthispaperistoclarifyourunderstand- was mediated by nuclear spin diffusion from the bulk to v i ingofthespindynamicsinlightofrecentexperimentsin the sites of paramagnetic impurities, and that the T1 X our laboratory. The paper begins with a description of were significantly shortened at increased doping densi- r the Bloembergenmodel andexaminesthe different steps tites. a of the transport processes involved in dynamic nuclear Thedynamicsofthenuclearpolarization(p)canthere- polarization, before concluding with a review of recent fore be described by a diffusion equation in the contin- experimental results. uum limit, Inastrongmagneticfield,theHamiltonianofanuclear spin system, doped with electron spins is given by − ∂p =D∇2p+2Wp+ C (p−p ) (2) ∂t r6 0 H =Hn +He +Hn +He +He +H (1) tot Z Z D D E HF where D is the diffusion coeffient, W ≈ γ2B2T is the 1 2 corresponding to the nuclear and electron Zeeman inter- rate at which the applied RF drives nuclear spin transi- actions, the nuclear-nuclear and electron-electron dipo- tions, and C/r6 describes the rate at which the nuclear spinsatadistancerfromtheimpurityarerelaxed. Here, a single defect spin is surrounded by a large number of nuclei, in the presence of an applied RF field. The equa- ∗Electronicaddress: [email protected] tion can be summed over all the defect spins to describe 2 bulk nuclear spin polarizations following DNP. Leifson andJeffries14 andKhutsishvili15modifiedBloembergen’s (cid:78)(cid:85)(cid:67)(cid:76)(cid:69)(cid:65)(cid:82)฀(cid:83)(cid:80)(cid:73)(cid:78)(cid:83)฀(cid:73)(cid:78)฀(cid:66)(cid:85)(cid:76)(cid:75) equation to incorporate the effect of driving the elec- tron spin transitions. In the presence of both RF and (cid:69)(cid:76)(cid:69)(cid:67)(cid:84)(cid:82)(cid:79)(cid:78)฀(cid:83)(cid:80)(cid:73)(cid:78) microwave irradiation of the nuclear and electron spins respectively Khutsishvili16 obtained the following differ- ential equation for the bulk nuclear spin magnetization (M) (cid:83)(cid:80)(cid:73)(cid:78)฀(cid:68)(cid:73)(cid:70)(cid:70)(cid:85)(cid:83)(cid:73)(cid:79)(cid:78)฀(cid:66)(cid:65)(cid:82)(cid:82)(cid:73)(cid:69)(cid:82) ∂M M −M (M −M ) = 0 +D∇2M −C 0 ∂t T |r−r |6 d Xm m M ∓ηM 0 FIG. 1: Schematic illustration of the spin diffusion barrier −2WM −Γ± (4) |r−r |6 around the electron spin. Nuclear spin diffusion within the Xm m barrier is suppressed due to the large difference in Zeeman energies between the spins. (from Ref.(8)) where η = γe/γn is the DNP enhancement factor, Td is the nuclear relaxation rate due to extraneous impuri- ties that do not contribute to DNP, and Γ± is the DNP the dynamics of the entire sample. driving rate and the signindicates whichESR transition The spin diffusion process is mediated by energy- was being irradiated. This result does not take into ac- conserving flip-flop transitions that take place during countelectron-electroncouplings andis thus validin the evolution under the dipolar Hamiltonian. In a strong limit of a low concentration of paramagnetic impurities. external magnetic field, the secular dipolar Hamiltonian The boundary conditions for this macroscopic transport can be written as equationaredetermined by the physics in the vicinity of the electron spin, and it is useful to explore this region 1 HD =Xi,j dij(cid:18)2IziIzj − 2(cid:16)I+i I−j +I−i I+j(cid:17)(cid:19) (3) in more detail. where dij = γ2¯h2(1−3cos2θij)/2ri3j, rij is the distance The spin diffusion barrier between spins i and j, and θ is the angle between the ij internuclearvectorandtheexternalmagneticfield. How- Khutsishvili provided a first formal theory of the spin ever, the nuclear spins in an inner core around the im- diffusion barrier17. He defined the barrier to be the dis- purity experience a large local field gradient due to the tance d from the paramagnetic impurity at which the impurity spin, and as a consequence have significantly difference of the hyperfine-shifted Zeeman frequencies of different effective Zeeman energies (Figure 1). This en- two neighboring nuclei is equal to the nuclear resonance ergydifferencesuppressestheflip-floptermsintheabove linewidth (dipolar broadened). Blumberg18 defined the equation, creating a “spin-diffusion barrier” around the barriertobethedistanceatwhichthefieldduetotheion impurity, within which the polarization is “frozen”, and equals the local dipolar field which results in a slightly the diffusion coeffient is zero. largerdistanceforthebarrier. Thedescriptionswerefor- Thusinthismodel,thenuclearspinsinsidethebarrier malizedfurther byRorschach19 andKhutsishvili20 yield- were relaxed directly by the impurity electron spin, and ing were isolated from the nuclear spins in the bulk. At the edge of the barrier, spins are in contact with both the impurity spin as well as the neighboring nuclear spins 2Sγ α e d≈ a (5) while the bulk nuclear spins do not experience the field (cid:18) γ (cid:19) n of the impurity spin directly. if τ >Tn or S¯hγ B /kT >1, and 2 e 0 Relaxation and DNP γ S¯hγ B α e e 0 d≈ 2S B a (6) (cid:20) γ (cid:18) kT (cid:19)(cid:21) n The process of microwave irradiation of an electron spincoupledtoanuclearspinhasbeenwelldescribed1,9, ifτ <TnorS¯hγ B /kT <1,whereaistheinter-nuclear 2 e 0 and detailed quantum-mechanical treatments of the iso- distance,S istheelectronspin,B(·)istheBrillouinfunc- latedtwo spin systemare alsoavailable10,11,12,13. As the tion and α = 1/4 for Khutsishvili’s original definition of focus of this paper is on the transport processes, we will the barrier and α = 1/3 for the Blumberg definition. not discuss this aspect of DNP further. Hereτ isthecorrelationtimeoftheS componentofthe z It was recognized early on that the relaxation process electronspin. FordilutespinsitcorrespondstoTe,while 1 described above was essentially the same physical model for dipolar- or exchange-coupled electron spins it corre- that was needed to describe the development of large sponds to Te. If the electron spin is fluctuating rapidly 2 3 on the timescale of the nuclear T , it is only the mean fluoride they observedthat only the first shell of nuclear 2 thermalpolarizationthatneedstobetakenintoaccount. spins was isolated from the bulk30. The smaller barrier at lower electron polarization makes it easier to achieve higher DNP enhancments. However, if the goal is to achieve large nuclear spin polarizations Transport through the spin diffusion barrier it is necessary to start with a highly polarized electron spin system which results in a large spin diffusion bar- The discrepancy arises from the assumption that spin rier. It should be noted however that these classically diffusion is completely quenched within the barrier. Po- defined models are defined in the continuum limit and larizationtransportwithinthebarrierwouldre-introduce assume no anisotropyof the spindiffusion barrier. If the a measure of thermal contact between these nuclei and barrierisdefinedbyelectron-nucleardipolarinteractions, the bulk. However, as noted by Bloembergen, transport the angular dependence will have the same (1−3cos2θ) throughthe spin diffusionbarrierdoes notconserveZee- dependence with respect to the external field. man energy. Thus it is necessary for this additional en- Khutsishvili21 and de Gennes22 introduced the pseu- ergy to be provided by another energy reservoir. dopotential radius b, also called the scattering parame- Horvitz31 suggested that the fluctuating fields of the ter. Thisdistancecharacterizesthecompetitionbetween electronspin itself could facilitate transportthrough the direct relaxation due to the paramagnetic impurity and barrier. The electron spin-phonon coupling gives rise to spindiffusion. Ifthedistancebetweenimpuritiesislarger a fluctuating electron spin, which has components at all than b the T relaxation (and DNP) is diffusion-limited, frequencies,includingatthemismatchofthenuclearZee- 1 whileifthe distancebetweenimpurites issmallerthanb, manenergies. AslongastheT1oftheelectronsisnottoo spin diffusion is relatively unimportant in T and DNP. long, this can facilitate transportthrough the spin diffu- 1 If d < b then the relaxation is limited by the diffusion sionbarrier. Wolfe experimentallyobservedthiseffectin of the magnetization to the sites of the impurities, while both Yb-doped YES and CaF228,29,30. Wolfe29 also ob- if d > b polarization diffuses to the site of the impurity servedthattheelectronspindipolarcouplingscanfacili- fasterthantheparamagneticimpuritycantransmititto tatetransportthroughthebarrier. Inhisexperimentshe the lattice. showedthatthe effective spindiffusionbarrierdecreased Using the definition given by Blumberg (α = 1/3), as the concentration of impurities increased. Goldman23 estimated the radius of the spin diffusion Goldman23 suggested that the nuclear dipolar reser- barrier in paradibromobenzene to be 17 ˚A. His mea- voir could make up the energy mismatch. In a slightly surements suggested a steep decrease of the diffusion differentcontextRedfieldandYu32 consideredspindiffu- coefficient at the spin diffusion barrier. Schmugge and sioninamacroscopicallyinhomogeneousfield,andnoted Jeffries24 estimated the size of the barrier in Nd-doped that this results in a transfer of energy between the nu- Lanthanum Magnesium Nitrate (LaMN) to be 16 ˚A, clear spin Zeeman and dipolar reservoirs. Genack and based on the same model. Redfield33 observed the coupling of nuclear spin Zee- man and dipolar energy reservoirs in superconducting However, experiments by a number of other authors vanadium. They derived a set of coupled differential suggested that the effective barrier was infact much smaller than this. Ramakrishna and Robinson25 were equations34 to describe the macroscopic transfer of en- ergy between the Zeeman and dipolar reservoirs. Ne- able to study the dynamics of the protons close to the glecting relaxation, they obtained defect site, by first irradiating one forbidden transition for a long time, and then switching the irradiation fre- ∂β D (∇B) quency to the other forbidden transition. Their results ∂td =DD∇2βd+ ZB2 ·(∇(BβZ)−βD∇B) (7) suggesteda spin diffusion barrier of 5-7 ˚A, which is even loc smaller than that obtained using the Khutsishvili defini- and tion (α=1/4) which gives 9 ˚A. Ramakrishna26 was also ∂β D abletoobserveasmallanisotropyofthebarrier. Tseand Z = Z∇[∇(Bβ )−β ∇B] (8) Z d Lowe also found the experimentally observed spin diffu- ∂t B sion barrier in calcium fluoride was about a factor or 2 whereβ andβ aretheinversespintemperaturesofthe d Z smallerthanthatpredictedbytheKhutsishvilitheory27. dipolar and Zeeman reservoirs,D and D are the spin D Z Using high sensitivity NMR techniques to directly de- diffusion rates of dipolar and Zeeman order, B is the loc tect the near-nuclei around the paramagnetic impurity, strength of the local dipolar field and ∇B is the gradi- Wolfe and collaborators were able to directly probe the ent of the magnetic field around the impurity. In many thermal contact between these hyperfine-shifted nuclei samples it is this coupling of the Zeeman and dipolar and the bulk nuclear spins. In Yb/Nd doped yttrium reservoirs at the impurity or defect sites that permits ethyl sulphate (YES) they observed that very few spins the transport of polarization through the barrier. This were not in thermal contact with the bulk, and that the process has recently been re-examined by Furman and diffusionbarrieronlycontained1-2shellsofnuclearspins Goren35. It has also been suggested that if spin diffu- aroundthe impurity, indicating a barrier on the orderof sion is rapid within the field gradients of the paramag- 3 ˚A28,29. In a similar experiment on Eu-doped calcium neticimpurity,thentheheatcapacityofthenuclearspin 4 dipolar reservoir is significantly enhanced, as the hyper- TABLE I: Summary of the experimental results of the spin fine shifted nuclear spins in the barrier are more tightly diffusion rate of spin-spin energy, DD, and Zeeman energy, coupled to the nucleardipolar reservoirthan the nuclear Zeeman reservoir36. DZ for single crystal calcium fluoride. (from Ref.(62)) Furman and Goren37 have suggested that it should Ref.62 [001] [111] D001/D111 D|| (×10−12cm2/s) 29 ± 3 33 ± 4 0.88 ± 0.14 be possible to short-circuit the spin diffusion barrier, by D performinga standardHartmann-Hahn38 crosspolariza- DZ|| (×10−12cm2/s) 6.4 ± 0.9 4.4 ± 0.5 1.45 ± 0.26 tionexperimentbetweenthespinswithinthebarrierand Ref.61 [001] [111] D001/D111 thoseinthebulk. Thiswouldalsopermittheindirectde- DZ|| (×10−12cm2/s) 7.1 ± 0.5 5.3 ± 0.3 1.34 ± 0.12 tection of the spins within the barrier. It is also possible Theoretical studies of DZ|| [001] [111] D001/D111 thatthesizeofthespindiffusionbarriercanchangedur- Ref.53 (×10−12cm2/s) 6.98 4.98 1.4 ing microwave irradiation of the electron spins24. Under Ref.54 (×10−12cm2/s) 8.22 6.71 1.22 strongmicrowaveirradiation,theelectronscaneffectively Ref.58 (×10−12cm2/s) 7.43 – – be decoupled from the distant nuclear spins, thus reduc- Theoretical studies of DD|| [001] [111] D001/D111 ing the size of the barrier significantly. Ref.55 (×10−12cm2/s) 8.53 8.73 0.98 The presence of the nuclear spin diffusion barrier has Ref.58 (×10−12cm2/s) 13.3 – – alsobeenobservedinavarietyofESRexperiments. The Ratio of DD to DZ [001] [111] Ref.62 4.5±0.8 7.5±1.3 – dipolar coupling between the electronspin and the more Ref.55 1.22 1.75 – distant nuclear spins gives rise to weak satellite lines in Ref.58 1.79 – – theESRspectrum39. Theseso-called“spin-flip”(s)tran- sitionssaturatemoreslowlyundermicrowaveirradiation comparedtothemainESRline40. Mims41hasalsonoted thatthepresenceofafrozen-coreofnuclearspinsaround havealsobeenanumberofattemptstocalculatetherate the electron spin can extend its coherence time. This of spin diffusion in single crystals, for both the Zeeman frozen core has also been observed Pr3+-doped LaF in energy and the dipolar energy of the spin system using 3 optically-detected ESR experiments42,43, and in ruby44. theoreticalmodels4,21,22,32,51,52,53,54,55,56,57,andclassical Combined microwave and optical techniques have been simulation58,59. used to analyze the barrier in fluorene-h10 doped with Spin diffusion provides a well-posed problem in the fluorene-d1045. studyofmulti-bodydynamics,astheHamiltonianofthe Coherent neutron scattering experiments have also system is well known, and the nuclear spins are well iso- been used to probe polarized nuclei close to paramag- lated from other degrees of freedom in the crystal. The netic impurities46,47, yielding an estimate of about 1nm study ofthe diffusion ofthe Zeemananddipolar ordered for the spin-diffusion barrier. Neutron scattering could states is essentially the study of the evolution of differ- beanimportanttoolinexploringthephysicsofthenear- ent initial states under the secular dipolar Hamiltonian. nuclei, giventhe largedifference in the protonscattering In particular the Zeeman ordered state consists of sin- cross-section of spin polarized neutrons, depending on glespinpopulationtermsonly,whilethe dipolarordered whether the two spins are aligned or anti-aligned1. state consistsofcorrelatedtwospinstates60. In astrong magnetic field these quantities are independently con- served,andhavedifferentdiffusionratesandspin-lattice Bulk spin diffusion of Zeeman and dipolar energy relaxation times. During the spin diffusion process, the spins are in dy- The signal observed in an NMR experiment is usually namicalequilibriumundertheactionoftheseculardipo- not from the spins closest to the electron spin. In addi- lar Hamiltonian, and the constants of the motion are tion to being much smaller in number, the spins in and only defined for the total spin system. If the identity around the diffusion barrier are both frequency-shifted of individual spins can be distinguished, the spins are andbroadenedcomparedtothenuclearspinsinthebulk. clearly seen to evolve in time as in the case where we The nuclear spins in the bulk only experience the pres- write a position dependent phase on the spins. This is ence of the electronsindirectly — mediatedby bulk spin the essence of reciprocal space diffusion measurements. diffusion as discussed above. ZhangandCoryusedreciprocalspacetechniquesto per- Since Bloembergen’s original description of spin diffu- form the first direct experimental measurement of spin sionanditsroleintheroleinmediatingspin-latticerelax- diffusion in a crystal of CaF261. We recently extended ation in ionic solids, the process has been studied exten- this technique to directly measure the spindiffusion rate sively in a variety of materials. It was soon understood of dipolar energy62. While theoretical studies have sug- thatZeemananddipolarenergycanbetransportedinde- gestedthatthespindiffusionratesofZeemananddipolar pendentlyinthehighfieldlimit. Historically,attemptsto order should approximately be the same, we found that measure the spin diffusion rate of Zeeman48,49 and dipo- dipolardiffusionwassignificantlyfasterthanZeemandif- larenergy50 reliedonthe theoreticalmodels thatrelated fusion (see Table 1). the diffusion rate to observed relaxation times. There Anexaminationofthephysicalprocessesleadingtothe 5 (a) 2 (b) 3 4 1.4 1.4 1.2 1.2 K) K) e ( 1 e ( 1 ur ur at0.8 at0.8 er er p p em0.6 em0.6 1 1 2 z pin t0.4 pin t0.4 s s (c) 2 (d) 3 4 0.2 DD = DZ 0.2 DD = 4 DZ 0 0 0 20 40 60 0 20 40 60 distance (nm) distance (nm) FIG.3: (Coloronline)Zeeman(blackdash-dotline)anddipo- lar(bluedashedline)spintemperaturesfollowing1secondof 1 1 2 spindiffusion,obtainedfromsimulationswhere(a)DD =DZ FIG. 2: (a) For the diffusion of Zeeman order along the z and (b) DD =4DZ. The inital spin temperatures at the left directionspins1and2needtoundergoaflip-flop. (b)Forthe edgeare10µKand20mKforthedipolarandZeemanreser- diffusion of dipolar orderalong thez direction, there are two voirs respectively. The solid red line indicates the final spin possibilities,bothspins1and3,andspins2and4canflip,or temperature following adiabatic transfer. (from Ref.(8)) spins1and 2, andspins3and 4can flip. Thereare thustwo differentpathstothesamefinalstateandinterferenceeffects maybeobserved. (c)Ifspins1and2areinitiallyinthesame couplings are of the dipolar form. Patel and Bowers66 state (both ↑ or both ↓), no evolution takes place. (d) Even usedmultiple-quantumNMRtechniquestoshowthecre- if states 3 and 4 are initially ↑ and ↓, two different evolution ation of dipolar order in both gallium arsenide and in- pathsarepresent. Spins1and2canflipandspins3and4can dium phosphide, following optical pumping. flip orspins1 and4 and spins2and 3can flip. Thusdipolar diffusion dynamicsare less easily quenched. (from Ref.(62)) In a microwave-inducedDNP experiment on a 40 mM frozen solution of 4-amino TEMPO (in a 40:60 wa- ter/glycerolmixture),werecentlyobservedthatthebulk diffusionshows thatthe dynamicscanbe quite different. proton dipolar reservoir is cooled to a spin tempera- Figure 2 shows a simple illustrative model that suggests ture that is significantly lower than the Zeeman spin that the diffusion of dipolar order should be faster (and temperature8. In addition we were able to enhance the morecomplicated)thanthatofZeemanorder,duetothe NMR signal by 50 % by equilibrating the the tempera- increaseinthenumberofpossiblepathsforthepropoga- tures of the nuclear Zeeman and dipolar reservoirs. We tion of the dipolar ordered state. The rapid diffusion of believethataGenackandRedfieldmechanismisrespon- dipolar order is very likely a consequence of a construc- sible for producing the low dipolar spin temperature in tive interference effect in the many-spin dynamics the vicinity of the electron spins. Moreover, as we ob- Recently a direct real space measurement of spin served in our earlier spin diffusion measurements, dipo- diffusion was made using a magnetic resonance force larspin diffusionis significantlyfaster thanZeemanspin microscope63. They extracted a Zeeman diffusion co- diffusion61,62, and the bulk dipolar reservoir cools faster effient ofD =(6.2±0.7)×10−12 cm2/s, andestimated thanthebulkZeemanreservoir. Inprinciple,thisprocess Z the dipolar diffusion rate to be D = (11±11)×10−12 canbe exploitedtorapidlypolarizethe nuclearspins,by D cm2/sfromtheirmeasurement,inagreementwithearlier repeatedly cooling the dipolar system and transferring results. the polarization to the Zeeman reservoir. The ability to increase the Zeeman magnetization via contactwiththedipolarreservoirisexciting,asitshould Recent experiments be possible to polarize a sample more rapidly by repeat- edly cooling the dipolar reservoir and transferring this A number of recent experiments have re-emphasized polarizationtotheZeemanreservoir(seeFigure3). Note the importanceofthe roleofboththe spindiffusion bar- that this transfer of order occurs in the bulk crystal,not rier and bulk spin diffusion in the DNP process. Michal just locally to the defect sites. When the weak spin- and Tycko64 observed the creation of optically pumped locking field is applied the cross polarization between dipolar order in the 115In spins of indium phosphide. the Zeemananddipolarsystemsoccursonamuchfaster They suggested that the low dipolar spin temperature timescale,sinceitdoesnotrequiremacroscopictransport they observed could be the produced indirectly by po- of the polarization. The transport is not limited by the larization transport through the field gradients of the small heat capacity of the dipolar reservoir. trapped electrons at the optical pumping sites as pro- Tycko has suggestedthat since semiconductor materi- posed by Genack and Redfield33,34 or directly by optical alslikeindium phosphidecanbe hyperpolarizedbyopti- pumping. Tycko65 noted that nuclear-spin dipolar order cal pumping techniques, it might be possible to polarize can directly result fromoptical pumping if the hyperfine organic or biological systems that are deposited on such 6 substrates by polarization transfer processes65. In ad- Challenges dition to spin diffusion from the optical pumping sites to the bulk, this process requires spin diffusion across In the above discussion, we have ignored the details the semiconductor/organic interface during the cross- of the electron spin relaxation process, though the in- polarization process. Goehring and Michal recently ob- fluence of the phonon bottleneck at low temperatures is served that it was possible to transfer approximately 20 well known1. As can be seen from the above discussion, %ofthetotalnuclearspinpolarizationfrommicronsized the polarization of bulk nuclei following DNP irradia- InP particles to an organic layer on the surface67 using tionis a complex,multi-step process. Many DNP exper- Hartmann-Hahn techniques38. iments are characterized by trial and error, rather than Polarization transport by spin diffusion across such a first principles design. Efforts to develop optimal con- a heterogeneous interface following DNP has also been trol techniques for DNP are likely to be focused on a observed. Griffin and co-workers have demonstrated single step, until we can deal with the complexity of the that the DNP-enhanced nuclear spin polarization of the many-bodydynamicsinvolved. The models dealingwith protons of an aqueous solvent (containing the birad- the spin-diffusion barrier are very approximate, as they ical TOTAPOL), could be transferred to the protons ignore the discrete nature of the lattice and depend on of nanocrystals of the peptide GNNQQNY, via spin a continuum transport model. Bulk spin diffusion also diffusion68. Thoughtheirnanocrystalswereonthe order remains an open problem in many-body spin dynamics. of 100-200 nm, their model suggests that the nanocrys- The physics of these systems is rich and complex, and tals upto 1 µm in diameter could be efficiently polar- care should be taken when dealing with simple models. ized using this technique. In a related experiment, we The field, temperature, concentration of electron spins, found that microwave irradiation of the electrons (dan- andthenatureofthenuclearspinsystemallstronglyin- gling bonds) of the amorphous surface layer of silicon fluencetheDNPprocessandtheparticularexperimental microparticles(range 1-5 µm) produceda large dynamic conditions can strongly determine the outcome. nuclearpolarization,whichwaseventuallytransferredto the crystalline core by spin diffusion69. X-ray diffraction revealedthatthis samplewasapproximately80%amor- Acknowledgements phous and 20 % crystalline. Though the surface nuclei had a relatively short T (on the order of minutes), the C.R. thanks Gregory Boutis, HyungJoon Cho, David 1 nuclear spins in the crystalline core had very long T s Cory, Anatoly Dementyev, Daniel Greenbaum and 1 (ontheorderofafewhours),astheT ofthecoreisme- Jonathan Hodges for stimulating discussions. 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