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the investigation of magnetism in the molecule - based solid prussian blue , fe@xmath5[fe(cn)@xmath2@xmath6h@xmath4o , and related analogs has a rich history @xcite , dating back to 1928 @xcite . measurements down to liquid helium temperatures identified the transition to long - range ferromagnetic order @xcite , but an understanding of the magnetic interactions remained elusive until the 1970s , when x - ray @xcite and neutron @xcite diffraction data identified the crystal structure and the spin delocalization from high - spin fe(iii ) to low - spin fe(ii ) . interest in these materials was renewed in the 1990s with the synthesis of several mixed - metal prussian blue analogs with higher magnetic ordering temperatures , along with the 1996 discovery of long - lived photoinduced magnetism in k@xmath7co@xmath8[fe(cn)@xmath2@xmath9h@xmath4o @xcite . a flurry of experimental and theoretical research has elucidated the fundamental nature of the light - induced effects in three - dimensional bulk materials @xcite , and recent efforts have been made to integrate the photoinduced magnetism into films @xcite and nanoparticles , which have technical and biophysical applications . there have been several efforts to synthesize nanoparticles of prussian blue analogs @xcite , but only a few examples of photoinduced magnetism in these particles have been reported ,  including work that isolated k@xmath0co@xmath1[fe(cn)@xmath2@xmath3h@xmath4o particles with typical diameters of @xmath10  nm within a silica xerogel @xcite and other research producing 11  nm @xmath11 70  nm nanorods of mo(cn)@xmath12cu@xmath4 protected by polyvinylpyrrolidone ( pvp ) @xcite . in each case , although photoinduced magnetism was observed , the particles did not exhibit long - range order . the purpose of this paper is to report our ability to synthesize rb@xmath0co@xmath1[fe(cn)@xmath2@xmath3h@xmath4o nanoparticles protected by pvp that exhibit photoinduced magnetism for all sizes and that possess long - range ordering , with coercive fields ranging between 0.25  @xmath13  1.5  kg , in the larger particles . the magnetic properties evolve with size , where at 2  k , the particles with diameters less than approximately 10  nm provide a curie - like magnetic signal . c c c r r c c r r batch & starting & resulting & pvp : co & diameter & @xmath14 & @xmath15 & @xmath16 & @xmath17 + & pvp ( g ) & chemical formula  & ratio & ( nm ) & ( k ) & ( k ) & ( g ) & ( g ) + a & 1.0 & rb@xmath18co@xmath5[fe(cn)@xmath2@xmath19 @xmath20 @xmath21h@xmath4o & 360 & @xmath22 & @xmath23 & @xmath23 & @xmath24 & @xmath24 + b & 0.5 & rb@xmath25co@xmath5[fe(cn)@xmath2@xmath19 @xmath20 @xmath21h@xmath4o & 200 & @xmath26 & 10 & @xmath27 & @xmath28 & @xmath29 + c & 0.2 & rb@xmath30co@xmath5[fe(cn)@xmath2@xmath19 @xmath20 @xmath21h@xmath4o & 60 & @xmath31 & 13 & 17 & 250 & 330 + d & 0.1 & rb@xmath32co@xmath5[fe(cn)@xmath2@xmath33 @xmath20 @xmath34h@xmath4o & 20 & @xmath35 & 19 & 22 & 1000 & 1500 + our rb@xmath0co@xmath1[fe(cn)@xmath2@xmath3h@xmath4o nanoparticles were synthesized by modifying the procedure for prussian blue nanoparticles described by uemura and coworkers @xcite . a 2  ml solution containing both 28  mg k@xmath36fe(cn)@xmath37 ( 0.085  mm ) and 6.8  mg rbno@xmath36 ( 0.046  mm ) was added dropwise to an 8  ml solution containing 30  mg co(no@xmath36)@xmath38h@xmath4o ( 0.103  mm ) and pvp while stirring rapidly . by varying the amount of pvp ( table  1 ) , the protocol produced samples with different particle sizes and size distributions . after 30 minutes of stirring , the solution was allowed to sit for one week . for transmission electron microscopy ( tem ) studies , a 50  @xmath39l aliquot of the suspension was diluted 2000  times , and 8  @xmath39l of the diluted suspension was placed on a holey carbon grid . a representative image is shown in fig .  1 , and selected area electron diffraction was compared to powder x - ray diffraction patterns to confirm the structure @xcite . in addition , infrared spectra displayed a c@xmath13n stretch of 2124  @xmath40 , consistent with a co(iii)@xmath13fe(ii ) low - spin pair . using image j imaging software @xcite , the tem images were analyzed to obtain the particle size distributions shown in fig . these data were fit to a log - normal function that yielded the characteristic diameters shown in fig .  2 and table  1 . to isolate the particles , three volumes of acetone were added to the synthesis solution , which was centrifuged , and then further washed with acetone and dried under vacuum . chemical analysis was obtained from a combination of chn combustion analysis and inductively coupled plasma mass spectrometry ( icp - ms ) , and the resulting formulae are listed in table  1 , along with the ratio of the pvp repeat unit per cobalt . the extent of h@xmath4o coordination to the co was estimated by considering the fe vacancies implicit with the measured co : fe ratio . co@xmath5[fe(cn)@xmath2@xmath41(h@xmath4o)@xmath42 nanoparticles from batch  d , see table  1 . [ fig1],width=288 ]    , height=432 ] the temperature dependences of the dc magnetic susceptibilities , @xmath43 , of the four batches of particles are shown in fig . 3 . a standard commercial squid magnetometer was employed , and the samples were mounted to commercial transparent tape and could be irradiated with light from a room - temperature , halogen source by using a homemade probe equipped with a bundle of optical fibers @xcite . small diamagnetic background contributions from the holder and tape ( representing @xmath44% of the total signal ) were independently measured and have been subtracted from the data . the magnetic signals are expressed per mole of sample using the chemical formula listed in table  1 . the dark state zfc data were obtained after cooling in zero applied field from 300  k , while the dark state fc data were taken after cooling in 100  g from 300  k. the light state was established after field cooling the samples from 300  k to 5  k in 100  g and subsequently irradiating with light for 5  hours , which saturated the photoinduced response . in order to avoid spin glass - like relaxation , the light state fc data were obtained after cycling the sample to 30  k in 100  g.    ) , field - cooled ( fc ) dark ( @xmath45 ) , and fc light ( @xmath46 ) states of each batch produced . the insets display the differences between the fc light and dark states , as described in the text . finite values for this difference can only arise from photoinduced magnetism . [ fig3],width=288 ] it is noteworthy to recall that the photoinduced magnetism of the prussian blue analogs depends upon a charge transfer induced spin crossover event ( ctist effect ) , requiring the presence of vacancies to allow crystalline flexibility @xcite . more specifically for rb@xmath0co@xmath1[fe(cn)@xmath2@xmath3h@xmath4o , the spins of an co@xmath13fe pair can exist in either of two arrangements . the low - spin state consists of co(iii ) ( @xmath47 ) and fe(ii ) ( @xmath47 ) , while the high - spin state possesses co(ii ) ( @xmath48 ) and fe(iii ) ( @xmath49 ) . the presence of the ctist effect depends on the local chemical environment defined by the values of @xmath50 , @xmath51 , @xmath52 and @xmath53 in the chemical formula . for limiting ratios , co and fe spins can be locked into either their high - spin or low - spin states for all accessible temperatures . alternatively , with the proper tuning of the chemical ratios , the co and fe ions can exist in high - spin states at room temperature and then experience a crossover to their low - spin states at approximately 150  k. the spin crossover phenomenon generates the pairs involved in the photoinduced magnetism . however , since the ctist effect may not be 100% efficient , some regions remain locked in their high - spin states , and we refer to them as _ primordial _ spins @xcite . for example , these primordial spins are responsible for the magnetic signals observed for the dark state of the largest particles . when irradiated , the low - spin regions , near the primordial high - spin clusters , are photoinduced to the high - spin magnetic state , resulting in a growth of the magnetic domain . this scenario is supported by our description of the anisotropic photoinduced magnetism observed in thin films @xcite and by the local probe investigations of others @xcite . all samples show a photoinduced increase in their magnetic signals , and the strength of the change is correlated with the size of the particles . the differences between the fc susceptibilities of the light and dark states , @xmath54 are plotted in the insets of fig . 3 , and finite values can only arise from the photoinduced magnetism . it is important to stress that photoinduced magnetism is observed even in small particles possessing only curie - like behavior .    ) and fc ( @xmath45 ) states show a signal associated with long - range order for the two batches displaying a mix of magnetic behavior after subtracting the curie - like contribution . the susceptibility of batch  a only exhibits a curie - like contribution , while the magnetic signal for batch  d is dominated by spins that are ordered , see text for details . for each sample , a curie - like contribution was obtained by fitting the dark state data above 30  k , and this magnetic signal was subtracted from the fc and zfc dark state data shown in fig .  3 . [ fig4],width=288 ]    two main features are seen when considering the evolution of material properties due to the increasing average size of the separate batches , namely the onset of long - range magnetic order and an increasing net magnetization . this scaling of magnetization is linked to an increased diamagnetic - surface to magnetically - active - volume ratio at smaller particle sizes . at low temperatures , the high - spin co and fe ions interact antiferromagnetically , giving rise to a ferrimagnetic transition at @xmath55 , which is about 24  k for bulk powder specimens with a similar chemical formula @xcite . for the magnetic data shown in fig .  3 , the onset of this transition can be estimated , and these macroscopic temperatures are listed in table  1 . we contend that particles larger than a critical size will allow domains large enough to approach bulk - like magnetic properties . conversely , smaller particles may put limits on allowed domain size , suppressing the ordering temperature . microscopically , if the size of the magnetic domains is less than or of the order of the magnetic coherence length , then a spectrum of @xmath55 values can be expected , and evidence of this trend is observed in batches c and d , see the insets of fig . 3 . in other words , the size distributions may include particles both above and below the critical size that leads to bulk - like properties . as a result , the magnetic response of each batch may include contributions from curie - like and bulk - like fractions . the percentage of each can be estimated by subtracting a curie - like signal from each @xmath56 plot , and the results for batches b and c are shown in fig . in contrast , batch  a follows curie - like behavior , whereas the active sites in batch  d are almost entirely ferrimagnetically ordered . this analysis of the data suggests the curie - like contribution for each of the four batches of nanoparticles ( smallest to largest ) is 100% , 90% , 50% , and 10% . consequently , at least down to 2  k , nanoparticles with sizes below @xmath57  nm do not exhibit long - range order . these interpretations are consistent with our @xmath58 versus @xmath59 measurements performed at 2  k , where coercive fields , @xmath60 , and remnant magnetization values are observed for the largest sets of particles but not for the smallest set of particles , fig .  5 and table  1 . furthermore , the differences between the fc and zfc data for the dark states in batches b , c , and d are consistent with spin glass or cluster glass behavior @xcite , and our ac susceptibility data are presented in the appendix . k magnetization versus magnetic field sweeps for the two largest sizes of nanoparticles , batches c and d , are shown for the light ( @xmath61 and @xmath46 ) and dark ( @xmath62 and @xmath45 ) states . the coercive fields , @xmath60 for the light and dark states for each batch are listed in table  1 , and the lines are guides for the eyes . [ fig5],width=480 ] in conclusion , we have synthesized four different sizes of rb@xmath0co@xmath1[fe(cn)@xmath2@xmath63h@xmath4o nanoparticles protected by pvp . each batch of particles exhibits photoinduced magnetism , but the strength of this effect , as well as other global properties , e.g.  @xmath55 and @xmath60 , are correlated with the intrinsic particle size distributions of each batch . the combination of photoinduced magnetism and nanosized prussian blue analog particles with finite coercive fields is unique and establishes a length scale limit of @xmath57  nm for these properties . the next advances in the field will undoubtedly employ prussian blue analogs with higher transition temperatures @xcite that may have a variety of technical applications , including , for example , the exploitation of optically controlled magnetocaloric properties @xcite . ) and imaginary ( @xmath64 ) ac susceptibilities of the zfc dark states , i.e.  primordial states , are shown for all four batches of nanoparticles . all batches were measured with no applied static field and an alternating field of 4  g , except for batch  d , which was measured in 1  g. the frequency dependence was studied at 1  hz ( ) , 10  hz ( ) , 100  hz ( @xmath65 ) , and 1  khz ( ) for all batches , except for batch  d , which has an additional measurement at 333  hz  ( @xmath66 ) . arrows are guides for the eyes and pass through the peaks.,width=480 ]    the temperature dependences of the real ( @xmath67 ) and imaginary ( @xmath64 ) ac susceptibilities of the zfc dark states , i.e.  primordial states , of all four batches are shown in fig . the phenomenological parameter , @xmath68 , given by @xcite @xmath69 where @xmath70 is the freezing temperature given by the cusp in @xmath71 and @xmath72 is the angular frequency , is @xmath73 for batches c and d , and this observation is consistent with spin glass or cluster glass behavior @xcite . 10 dunbar k r and heintz r a 1997 in _ progress in inorganic chemistry _ karlin k d ed ( new york ny : wiley and sons ) vol 45 p 283 verdaguer m and girolami g 2004 in _ magnetism : molecules to materials v _ miller j s and drillon m eds ( weinheim : wiley - vch ) p 284 davidson d and welo l a 1928 1191 holden a n , matthias b t , anderson p w and lewis h w 1956 1463 bozorth r m , williams h j and walsh d e 1956 572 ito a , suenaga m and no k 1968 _ j. chem . phys . _ * 48 * 3597 buser h j , schwarzenbach d , petter w and ludi a 1977 _ inorg . chem . _ * 16 * 2704 day p , herren f , ludi a , gudel h u , hulliger f and givord d 1980 _ hel . . acta _ * 63 * 148 sato o , iyoda t , fujishima a and hashimoto k 1996 _ science _ * 272 * 704 ohkoshi s and hashimoto k 2001 _ j. photochem . c : photochem . * 2 * 71 varret f , nogues m and goujon a 2002 in _ magnetism : molecules to materials i _ miller j s and drillon m eds ( weinheim : wiley - vch ) p 257 yamamoto t , umemura y , sato o and einaga y 2004 _ chem . * 33 * 500 park j - h , cimr e , meisel m w , huh y d , frye f , lane s and talham d r 2004 _ appl . lett . _ * 85 * 3797 yamamoto t , umemura y , sato o and einaga y 2004 _ chem . mater . _ * 16 * 1195 park j - h , frye f , lane s , cimr e , huh y d , talham d r and meisel m w 2004 _ polyhedron _ * 24 * 2355 yamamoto t , umemura y , sato o and einaga y 2005 _ j. am . chem . soc . _ * 127 * 16065 park j - h 2006 _ ph.d . 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nanoparticles of rubidium cobalt hexacyanoferrate ( rb@xmath0co@xmath1[fe(cn)@xmath2@xmath3h@xmath4o ) were synthesized using different concentrations of polyvinylpyrrolidone ( pvp ) to produce four different batches of particles with characteristic diameters ranging from 3 to 13  nm . upon illumination with white light at 5  k , the magnetization of these particles increases . 
 the long - range ferrimagnetic ordering temperatures and the coercive fields evolve with nanoparticle size . at 2  k , particles with diameters less than approximately 10 
 nm provide a curie - like magnetic signal .