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theoretical studies@xcite predict that the magnetic geometrically nonfrustrated diamond lattice can host a highly degenerate frustrated state consisting of coplanar spirals , the so - called spiral spin liquid ( ssl ) . this counterintuitive finding is comprehended when taking into account that the diamond lattice is composed of two interpenetrated face - centered cubic ( fcc ) sublattices which on their own are highly frustrated@xcite . the magnetic frustration of the overall diamond lattice is caused by a significant j@xmath0 interaction which couples nearest - neighbor sites within each fcc sublattice . the ssl should evolve@xcite when the ratio @xmath4/@xmath3 exceeds @xmath8 , while for lower @xmath4/@xmath3 a collinear antiferromagnet ( af ) should be the ground state . the labeling of j s reflects the fact that j@xmath9 is the nearest - neighbor coupling of the diamond lattice and j@xmath0 is the next - nearest - neighbor one . the degeneracy of the ssl could be lifted by thermal@xcite or quantum@xcite fluctuations resulting in a magnetic ordering transition via the order - by - disorder mechanism@xcite . within this scenario the ordered state selected by entropy has the highest density of nearby low - energy excitations . this model will be referred to as the @xmath4/@xmath3 or order - by - disorder model . + coal@xmath0o@xmath1 is a good candidate to study ssl , as it adopts the spinel structure ab@xmath0o@xmath1 with magnetic co@xmath2 ions residing on the diamond lattice . however , there is no consensus to which extent the @xmath4/@xmath3 model is relevant for this system . the ratio @xmath4/@xmath3 determined from inelastic neutron scattering@xcite is only 0.109(2 ) , thus , according to the aforementioned model@xcite , this material should have a nondegenerate collinear af ground state . nevertheless , experimental observations by specific heat@xcite , muon spin relaxation@xcite , neutron diffraction@xcite are rather consistent with an unconventional ground state , which might be the ssl . several models have been proposed in the past to explain this behaviour , such as the order - by - disorder @xcite , an order - by - quenched - disorder @xcite or a kinetically inhibited order @xcite models . + in this work we investigate the relevance of an order - by - quenched - disorder model to our system . it is focused on the well - known experimental fact that materials with the spinel structure could have a significant degree of an a / b antisite inversion . that is , b - atoms occupy the a - site and a - atoms - the b - site . in coal@xmath0o@xmath1 samples studied so far@xcite the co / al inversion @xmath10 varies from 2 to 17% . the theory@xcite predicts that impurities would break the degeneracy of the spiral spin liquid and would induce an ordered magnetic ground state , which is different from the one favoured by the order - by - disorder mechanism . finally , the kinetically inhibited order model infers that in coal@xmath0o@xmath1 freezing of magnetic domain walls prevents a true long - range order , @xmath11 the thermal energy is too small to overcome the surface energy of domain walls . thus the size of domains stays arrested at lowest temperatures even in the absence of antisite disorder . + for better understanding of the nonconventional magnetic order in the coal@xmath0o@xmath1 system we focus on neutron single crystal diffraction which probes spin - spin correlations and thus should be able to distinguish the models introduced above . we calculate diffraction patterns for magnetic moment arrangements obtained by the classical monte - carlo ( mc ) simulations varying the @xmath4/@xmath3 ratio , magnetic field and disorder on the a- and b- sites and compare those with experimental patterns . measurements of susceptibility , magnetization and specific heat complement our neutron diffraction results . we conclude that both , the frustration due to the @xmath4/@xmath3 ratio and the presence of the antisite disorder , play a significant role in the observed atypical magnetic ordering . we anticipate that disorder is not random , presumably it happens at @xmath6111@xmath7-twin boundaries restricting the propagation of the collinear af state . [ sec2 ] the monte - carlo calculation was performed minimizing the energy of the classical heisenberg hamiltonian for spins @xmath12 : @xmath13    /@xmath3=0.10 ( left ) , 0.17 ( right ) . middle : the 00l cuts of the h - hl maps with the @xmath4/@xmath3 ratio 0.10 ( red ) , 0.15 ( green ) and 0.17 ( blue ) . note the logarithmic scale for the intensity.,title="fig : " ] /@xmath3=0.10 ( left ) , 0.17 ( right ) . middle : the 00l cuts of the h - hl maps with the @xmath4/@xmath3 ratio 0.10 ( red ) , 0.15 ( green ) and 0.17 ( blue ) . note the logarithmic scale for the intensity.,title="fig : " ] /@xmath3=0.10 ( left ) , 0.17 ( right ) . middle : the 00l cuts of the h - hl maps with the @xmath4/@xmath3 ratio 0.10 ( red ) , 0.15 ( green ) and 0.17 ( blue ) . note the logarithmic scale for the intensity.,title="fig : " ]    here @xmath14 are first- and second - neighbour antiferromagnetic couplings , @xmath15 and @xmath16 are the magnitude and direction of the single - ion anisotropy term , @xmath17 and @xmath18 are the magnitude and direction of a magnetic field . a cluster of 64000 co atoms ( 20x20x20 unit cells ) with periodic boundary conditions was considered . this size is a compromise between two conflicting requirements - the cluster should be sufficiently large to ensure enough resolution in a calculated diffraction pattern , but small enough to spend finite time on a mc calculation . the moments were kept constant in magnitude and equal to 1 @xmath19 ; their direction was changed at random , one at the time . to obtain the ground state only energy - decreasing moves were accepted in the final stage . during a mc cycle 10000 moves of each atom were performed to ensure equilibrium conditions . the results were identical to those obtained by temperature annealing . the fourier transform of the magnetic moment configuration was then calculated for the regions of interest of the reciprocal space . the q - step was chosen to be 0.05 r.l.u . no binning in the direction perpendicular to the cuts was performed . + as the main purpose of the modelling was to understand the magnetic behaviour in the coal@xmath0o@xmath1 system , the exchange couplings and disorder parameter close to ones known for our crystal @xcite were used as the basis , namely @xmath3=9.2 k , @xmath4/@xmath3=0.10 , d / j@xmath9=0.009 and @xmath10=8% @xcite . additionally , to disentangle the influence of the parameters , we varied in reasonable ranges the @xmath4/@xmath3 ratio , amount of random defects and magnetic field strength . we tried two different single - ion anisotropy directions - @xmath20111@xmath21 $ ] and @xmath20100@xmath21 $ ] , however , as the anisotropy in this system is small this did not influence the results .    /@xmath3=0.10 : 0% ( black ) , 4% ( green ) , 8% ( blue ) , 12% ( red ) . note the logarithmic scale for the intensity.,title="fig : " ] /@xmath3=0.10 : 0% ( black ) , 4% ( green ) , 8% ( blue ) , 12% ( red ) . note the logarithmic scale for the intensity.,title="fig : " ]     + representative h@xmath22hl maps for the ideal ( without defects ) model with @xmath4/@xmath3 ratios of 0.10 and 0.17 are presented in fig . two main features are apparent : there are sharp magnetic bragg peaks at the af ( k=0 ) positions ( i.e. 200 , 111 ) and broad diffuse features at the basis of magnetic bragg peaks extending over several reciprocal lattice units ( r.l.u . ) . the broad diffuse features need the log - scale amplification in single crystal calculated patterns , however summing up this sparse signal at the same sin@xmath23 results in a strong diffuse scattering in powder patterns@xcite . as can be seen from the 00l cuts in fig . [ fig1 ] ( middle ) , the broad diffuse features grow with the increase of @xmath4/@xmath3 ( a significant increase happens for @xmath4/@xmath24 0.15 ) , while the bragg intensity decreases and even a hollow forms at the positions of the magnetic bragg peaks for @xmath4/@xmath3= 0.17 . this reproduces well the spiral surfaces of the free energy calculated by bergman _ [ ] . +    /@xmath3= 0.10 model with magnetic fields applied along @xmath20110@xmath21 $ ] ( left ) and @xmath20100@xmath21 $ ] ( middle ) and for the model with 8% defects for 4 t with field along @xmath20100@xmath21 $ ] ( red ) and @xmath20110@xmath21 $ ] ( green ) ( right).,title="fig : " ] /@xmath3= 0.10 model with magnetic fields applied along @xmath20110@xmath21 $ ] ( left ) and @xmath20100@xmath21 $ ] ( middle ) and for the model with 8% defects for 4 t with field along @xmath20100@xmath21 $ ] ( red ) and @xmath20110@xmath21 $ ] ( green ) ( right).,title="fig : " ] /@xmath3= 0.10 model with magnetic fields applied along @xmath20110@xmath21 $ ] ( left ) and @xmath20100@xmath21 $ ] ( middle ) and for the model with 8% defects for 4 t with field along @xmath20100@xmath21 $ ] ( red ) and @xmath20110@xmath21 $ ] ( green ) ( right).,title="fig : " ]    to understand the effect of the co / al antisite disorder we considered random defects on the two sites a ( co)- and b ( al ) separately . we considered models with random a - defects and b - defects . first , up to 12% of magnetic atoms were removed from the a - sites . this significantly changed the intensity distribution , as is presented in fig . [ fig2 ] left for the ratio @xmath4/@xmath3=0.10 . there appeared sharp ferromagnetic peaks ( _ i.e. _ 000 , 220 ) , the af bragg peaks became wider and the broad diffuse scattering increased . these tendencies grow with the number of the a - defects . inspection of atoms in the vicinity of the defects shows that the antiferromagnetic coupling between them is broken and their magnetic moments are aligned along the single - ion anisotropy axis @xmath16 . this results in the emergence of long - range ferromagnetic correlations at the cost of the antiferromagnetic ones . + next we inserted up to 12% of magnetic atoms on the b - sites ( see fig . [ fig2 ] right ) . this model , introduced first by savary_et  al . _ [ ] , argues that the coupling between the magnetic b - atom and its six nearest - neighbor a - atoms should be very strong . we adopted this model to the coal@xmath0o@xmath1 case considering the ratio @xmath4/@xmath3=0.10 and we varied the concentration of impurities in the 2 - 12% range . the results imply that b - defects suppress the af long - range order much stronger than the a - defects . for concentrations above 4% antiferromagnetic bragg peaks vanish . also at these concentrations ferromagnetic short - range correlations emerge ; they were not detected either for the ideal or a - defect models . /@xmath3=0.10 with a magnetic field applied along @xmath20100@xmath21$].,title="fig : " ] /@xmath3=0.10 with a magnetic field applied along @xmath20100@xmath21$].,title="fig : " ]     + further , we wanted to know how a perturbation , such as a magnetic field , would affect diffraction patterns of the ideal and defect models . for that we calculated diffraction patterns for the @xmath4/@xmath3=0.10 ratio without defects and with a - defects . application of magnetic fields along the principal directions lead to significant changes in magnetic correlations for the ideal model ( fig . [ fig3 ] left and middle ) . the common features are : increase of ferromagnetic bragg peaks , decrease of antiferromagnetic peaks ( they vanish at the magnetic field of 5 tesla ) and enhancement of broad diffuse af features . still , there are differences . when magnetic field is applied along @xmath20110@xmath21 $ ] ( fig . [ fig3 ] left ) , diffuse scattering is concentrated around the bragg peaks , the peaks themselves stay sharp . for h@xmath25100@xmath21 $ ] ( fig . [ fig3 ] middle ) the af peaks become wider . in addition to diffuse scattering located near the af bragg peaks ( as presented in fig . [ fig4 ] left for the 0kl plane with h@xmath25100@xmath21 $ ] ) , short - range correlations form diffuse streaks along @xmath6111@xmath7 . they are more pronounced in the @xmath6hk - k@xmath7 plane for h@xmath25100@xmath21 $ ] ( fig . [ fig4 ] right ) compared to the @xmath6h - hl@xmath7 plane for h@xmath25110@xmath21 $ ] ( not shown ) . this suggests that magnetic field along @xmath20100@xmath21 $ ] lowers the energy of low - lying states more efficiently than magnetic field along @xmath20110@xmath21 $ ] . in clear contrast , when 8% a - defects are present ( fig . [ fig3 ] right ) , the magnetic field enhances all magnetic correlations - not only the ferromagnetic long - range bragg contributions and af diffuse scattering , but also the af bragg contributions grow . + our mc calculations show that magnetic field is a sensitive parameter to identify the relevance of the @xmath4/@xmath3 model and to distinguish the presence or absence of random a- and b - defects . following these conjectures we decided to perform a neutron single crystal diffraction experiment in the applied magnetic field . [ sec3 ]      prior to neutron diffraction we characterized our single crystal by bulk measurements to compare our results with other numerous studies of the coal@xmath0o@xmath1@xcite . the growth of the coal@xmath0o@xmath1 crystal by the floating zone method was reported by maljuk _ . _ @xcite ; parts of this crystal were used in the previous neutron scattering experiments @xcite . susceptibility , magnetization and specific heat measurements presented here were performed on a part of this crystal with the mass of 12.5 mg using a quantum design squid vibrating sample magnetometer ( svsm ) and a quantum design ppms , respectively . +     measured with a dc field @xmath26=0.005 t. solid symbols represent field cooled and open symbols - zero field cooled data . green - magnetic field applied along the @xmath20111@xmath21 $ ] direction , blue - @xmath20110@xmath21 $ ] , red - @xmath20100@xmath21 $ ] . inset : inverse susceptibility for three principal directions . middle : temperature variation of ac magnetic susceptibility @xmath27 for different frequencies with a dc field @xmath26= 0.1 t along @xmath20111@xmath21 $ ] . right : magnetization at 2 k ( open symbols ) and 30 k ( solid symbols ) . insets : a ) change of @xmath28 with h@xmath29111@xmath21 $ ] . b ) variation of @xmath28 with temperature at different strength of magnetic field along @xmath20111@xmath21$].,title="fig : " ]   measured with a dc field @xmath26=0.005 t. solid symbols represent field cooled and open symbols - zero field cooled data . green - magnetic field applied along the @xmath20111@xmath21 $ ] direction , blue - @xmath20110@xmath21 $ ] , red - @xmath20100@xmath21 $ ] . inset : inverse susceptibility for three principal directions . middle : temperature variation of ac magnetic susceptibility @xmath27 for different frequencies with a dc field @xmath26= 0.1 t along @xmath20111@xmath21 $ ] . right : magnetization at 2 k ( open symbols ) and 30 k ( solid symbols ) . insets : a ) change of @xmath28 with h@xmath29111@xmath21 $ ] . b ) variation of @xmath28 with temperature at different strength of magnetic field along @xmath20111@xmath21$].,title="fig : " ]   measured with a dc field @xmath26=0.005 t. solid symbols represent field cooled and open symbols - zero field cooled data . green - magnetic field applied along the @xmath20111@xmath21 $ ] direction , blue - @xmath20110@xmath21 $ ] , red - @xmath20100@xmath21 $ ] . inset : inverse susceptibility for three principal directions . middle : temperature variation of ac magnetic susceptibility @xmath27 for different frequencies with a dc field @xmath26= 0.1 t along @xmath20111@xmath21 $ ] . right : magnetization at 2 k ( open symbols ) and 30 k ( solid symbols ) . insets : a ) change of @xmath28 with h@xmath29111@xmath21 $ ] . b ) variation of @xmath28 with temperature at different strength of magnetic field along @xmath20111@xmath21$].,title="fig : " ]    the low temperature zero field cooled ( zfc ) and field cooled ( fc ) susceptibility measured with a dc magnetic field @xmath26= 0.005 t applied along three principal directions is shown in fig . [ fig5 ] left . the high - temperature part , above 100 k , follows a curie - weiss law with a weiss temperature @xmath30= -85.2 k. the determined effective magnetic moment 4.60 @xmath19/f.u . and g - factor 2.37 are in good agreement with other studies @xcite . a broad hump at @xmath3111 k indicates building up of short range antiferromagnetic correlations . below t@xmath328 k a small splitting between the zfc and fc susceptibilities without a pronounced cusp is observed . remarkably , there is no frequency dependence of this anomaly in the ac susceptibility ( fig . [ fig5 ] middle ) . these observations are in excellent agreement with the systematic study of antisite disorder in the co@xmath33al@xmath34(al@xmath33co@xmath35)@xmath0o@xmath1 system by hanashima _ et  al._@xcite , which attributes such behaviour to a spin liquid state ( samples of suzuki _ et  al._@xcite and roy _ et  al._@xcite belong to this regime as well ) . et  al._@xcite report a crossover between spin liquid ( sl ) and spin glass ( sg ) regimes with a threshold at the 8% inversion level . samples belonging to the sg regime have a cusp in the dc susceptibility at the zfc and fc splitting point and the real part of the ac susceptibility is frequency dependent ( samples of tristan _ et  al . _ @xcite belong to this range ) . presumably in the sl regime defects only perturb the degenerate ground state , while in the sg regime they start to dominate magnetic behaviour . as both , the zfc and fc splitting in the susceptibility and the broad magnetic peaks in neutron diffraction in our crystal @xcite , appear at t@xmath368 k , we identify this anomaly as the emergence of an unconventional ordered magnetic state . + isothermal magnetization curves for our crystal with the field along three principal axes for 2 k and 30 k are presented in fig . [ fig5 ] right . at 30 k magnetization is linear with the field as expected for a paramagnet , while at 2 k the behavior is nonlinear ( as emphasized in the inset ( a ) for @xmath20111@xmath21 $ ] direction ) . such nonlinearity would be expected for reorientation of magnetic domains , however @xmath28 is identical regardless of the field direction thus suggesting that magnetic anisotropy in this system is very weak . +     measured in zero and 6 t magnetic field applied along three principal directions : red @xmath20100@xmath21 $ ] , blue @xmath20110@xmath21 $ ] , green @xmath20111@xmath21 $ ] . heat capacity of znal@xmath37o@xmath38 ( non - magnetic analog ) taken from ref . [ ] is also plotted . inset : difference of c@xmath39 measured in 6 t and without field . right : magnetic entropy @xmath40 calculated from these data . the dashed horizontal line indicates the high temperature limit of @xmath40= 11.56 j / mol k for s=3/2 . inset : magnetic contribution to the heat capacity c@xmath41 fitted to a power law with @xmath42=2.1.,title="fig : " ]   measured in zero and 6 t magnetic field applied along three principal directions : red @xmath20100@xmath21 $ ] , blue @xmath20110@xmath21 $ ] , green @xmath20111@xmath21 $ ] . heat capacity of znal@xmath37o@xmath38 ( non - magnetic analog ) taken from ref . [ ] is also plotted . inset : difference of c@xmath39 measured in 6 t and without field . right : magnetic entropy @xmath40 calculated from these data . the dashed horizontal line indicates the high temperature limit of @xmath40= 11.56 j / mol k for s=3/2 . inset : magnetic contribution to the heat capacity c@xmath41 fitted to a power law with @xmath42=2.1.,title="fig : " ]    the temperature dependence of the heat capacity measured in zero field and in the applied magnetic field of 6 t along the three principal directions are very much alike ( fig . [ fig6 ] left ) . for all measurements the crystal was cooled in zero field and then a magnetic field was applied . a broad peak located at @xmath319.8 k in zero field slightly shifts to lower temperature when magnetic field is applied ( inset of fig . [ fig6 ] left ) . the change though tiny and independent of the field direction , suggests that only few degrees of freedom are involved and their response to the magnetic field averages throughout the sample . to obtain the magnetic contribution @xmath43 we subtracted the heat capacity of the crystal lattice modelled by the debye approximation @xcite . as shown in the inset of fig . [ fig6 ] right , @xmath43 follows the power law t@xmath44 with @xmath42=2.1 ( red solid line ) within the temperature range @xmath45 k. in other samples reported in literature the power laws vary from @xmath42=2.5 , @xmath42=2.23 for the sl regime samples @xcite to @xmath42=2 for the gs sample @xcite . these @xmath42-values should be compared to the power law expected for a classical antiferromagnetic order ( @xmath46 t@xmath47 ) , for the spiral surface ( @xmath4/@xmath3 ) model ( @xmath46 t@xmath48)@xcite and a linear behavior typical for spin glass systems ( @xmath46 t ) . the agreement is in favor of the @xmath4/@xmath3 model and the presence of defects seems to affect the entropy very little . notably , the saturation of the magnetic entropy @xmath40 evaluated by integrating @xmath49 over t ( fig . [ fig6 ] right ) is significantly lower than the expected high - temperature limit for @xmath50 systems ( 11.56 j / molk ) . presumably a significant part of entropy remains in the system up to higher temperatures . neutron single crystal experiments were performed on a 0.2755 g crystal cut from the coal@xmath0o@xmath1 ingot at the base temperature of 1.8 k on the single crystal diffractometer trics at sinq , villigen . magnetic field was applied vertically along the principal directions @xmath20010@xmath21 $ ] , @xmath20110@xmath21 $ ] and @xmath20111@xmath21 $ ] by reorienting the crystal in a ma06 cryomagnet . the neutron wavelength of 1.18   and a 80 collimator in front of a @xmath51he detector were used . in zero - field , the magnetic peaks of the @xmath600@xmath52 family are significantly ( _ c.a . _ 3 times ) broaden ( fig . [ fig7 ] ) compared to the instrumental resolution . this resembles broad peaks of the mc model with a - defects and not the features of the ideal mc model ( sharp peaks and broad diffuse scattering extending over several r.l.u . ) . however , contrary to the predictions of the models with random defects , no magnetic intensity is present at the ferromagnetic ( nuclear ) positions in zero field . + in a magnetic field , the intensity and shape of magnetic peaks change and these changes strongly depend on the field direction . the magnetic field applied along the @xmath20110@xmath21 $ ] direction ( fig . [ fig7 ] left ) reduces the width of the ( 002 ) magnetic reflection and significantly ( 15% ) increases the peak intensity at the maximum . however , the total intensity remains almost the same . this observation suggests that long - range correlations grow at the cost of short - range correlations perpendicular to ( 002 ) being in accord with the increase of the af long - range correlations in the mc model with a - defects . + for h@xmath29010@xmath21 $ ] ( fig . [ fig7 ] right ) the intensity on the ( 200 ) magnetic peak maximum decreases by 37% and the total intensity decreases by 21% . this contradicts the mc model with a - defects , which predicts an enhancement of the af long - range correlations . the field applied along the @xmath20111@xmath21 $ ] direction ( fig . [ fig7 ] middle ) changes the peak maximum and the total intensity of the magnetic peaks ( 200 ) , ( 00 - 2 ) and ( 020 ) very little . this also contradicts the mc model with a - defects . + it should be noted that our experimental findings can not be explained within the conventional model of a multidomain af structure either . that model postulates the presence of magnetic domains , each of them having the same magnetic structure with a fixed magnetic moment direction along one of complementary preferred easy axes ( for example , octet of the @xmath6111@xmath7 axes ) . when a magnetic field is applied , domains with magnetic moments orthogonal to the field direction grow at the cost of domains with unfavourable moment axes . in our case , however , it seems that magnetic moments rotate orthogonal to the applied magnetic field but not necessarily into domains of the complementary easy axis . such soft magnetic behaviour can explain the increase of the ( 002 ) intensity maximum for h@xmath25110@xmath21 $ ] and its reduction for the h@xmath25010@xmath21 $ ] magnetic field direction . +    200@xmath7 reflections of coal@xmath37o@xmath38 crystal measured at 1.8k without ( 0 t , black ) and with ( 5 t , red ) magnetic field applied along @xmath20110@xmath21 $ ] ( left ) , @xmath20111@xmath21 $ ] ( middle ) and @xmath20010@xmath21 $ ] ( right).,title="fig : " ] 200@xmath7 reflections of coal@xmath37o@xmath38 crystal measured at 1.8k without ( 0 t , black ) and with ( 5 t , red ) magnetic field applied along @xmath20110@xmath21 $ ] ( left ) , @xmath20111@xmath21 $ ] ( middle ) and @xmath20010@xmath21 $ ] ( right).,title="fig : " ] 200@xmath7 reflections of coal@xmath37o@xmath38 crystal measured at 1.8k without ( 0 t , black ) and with ( 5 t , red ) magnetic field applied along @xmath20110@xmath21 $ ] ( left ) , @xmath20111@xmath21 $ ] ( middle ) and @xmath20010@xmath21 $ ] ( right).,title="fig : " ] [ sec4 ] in sec . [ sec2 ] we calculated the single - crystal neutron diffraction patterns based on the ideal order - by - disorder model and extended the simulation to the order - by - quenched - disorder models with random a- and b- defects . in sec . [ sec3 ] our experimental data on our coal@xmath0o@xmath1 single crystal are presented . our macroscopic ( susceptibility , magnetization and specific heat ) and microscopic ( single crystal neutron diffraction in zero and in the applied magnetic field ) experimental findings confirm that the magnetic order in the frustrated diamond lattice antiferromagnet coal@xmath0o@xmath1 is unconventional . comparison of bulk properties of our crystal with those of other studied samples identifies our crystal as located in the spin liquid regime@xcite and its magnetic properties are isotropic on the macroscopic scale . this is definitely not the case on the microscopic level as testified by neutron diffraction . single crystal patterns reveal that changes of magnetic correlations with the applied field are anisotropic . the patterns are similar to those calculated from the monte - carlo models , but none of the considered models explains the data completely . in zero field , the measured peaks are broadened , as the model with a - defects predicts , however , the anticipated ferromagnetic contribution is missing . in addition , while the experimentally observed increase of long - range af correlations for h@xmath25110@xmath21 $ ] is in accord with this model , its decrease for h@xmath25100@xmath21 $ ] contradicts the predictions . furthermore , the presence of random b - defects should induce broad ferromagnetic features , but they are not observed in the experiment . + thus , the magnetic behaviour in the studied material is not captured by simplistic models supposing random disorder on the a- and b - sites considered so far . one of the possible reasons of the failure could be different electronic states of the defect atoms as the assumed ones . for example , the co@xmath53 ions inserted into the octahedral b - sites are assumed to be in the same spin state as in the a - site . however dft calculations @xcite suggest the low spin configuration for the co@xmath53 ions in the octahedral coordination for the inversion levels up to @xmath10=50% . another possible reason of disagreement could be a complex morphology of defects which we assumed to be random . spinels are known to form complicated twin structures @xcite , which lead to stacking faults of the @xmath6111@xmath7 planes . such faults have been observed in mgal@xmath0o@xmath1 by transmission electron microscopy ( tem ) @xcite . starting from the ideal spinel structure shown in fig . [ fig8 ] ( a ) a stacking fault develop at the ( 111 ) plane indicated by the black solid line . at such twin boundary the cation composition can be either preserved ( fig . [ fig8 ] b ) , or it can become b(al)-rich ( fig . [ fig8 ] c ) or a(co)-rich ( fig .  [ fig8 ] d ) . if the distribution of stacking faults is similar in all eight directions within the @xmath6111@xmath7 family , macroscopic magnetic properties of a crystal would remain also isotropic . + clearly , the frustration due to the @xmath4/@xmath3 ratio is the basic ingredient of the magnetic behaviour of coal@xmath0o@xmath1 . this is the case even when the @xmath4/@xmath3 ratio is below @xmath8 . the @xmath4/@xmath3 model correctly predicts the temperature evolution of specific heat , the wave vector of magnetic ordering and the presence of low - lying excited states with @xmath54= @xmath6111@xmath7 . however , not all experimental observations emerge from the @xmath4/@xmath3 physics . both , the difference in zfc / fc susceptibility and the broadening of the af peaks in neutron diffraction result from the antisite disorder . comparison of neutron patterns from the mc modelling and the experiment prompts that these models are too simplistic . tem would be the key method for a systematic study of the microstructure and its influence on magnetic correlations in this material reconciling contradicting isotropic macroscopic and anisotropic microscopic observations . +    1 - 10@xmath21 $ ] projection of the ab@xmath0o@xmath1 spinel structure with a ) ideal arrangement of co@xmath53 a - tetrahedra ( violete ) and al@xmath55 b - octahedra ( green ) and @xmath6111@xmath7-twin boundaries preserving the cation composition ( b ) or resulting in the b - rich ( c ) , a - rich ( d ) regions . ] 99 d. bergman , j. alicea , e. gull , _ et al . _ , nature physics * 3 * , 487 ( 2007 ) . m. v. gvozdikova , m. e. zhitomirsky , jetp lett . * 81 * , 236 ( 2005 ) . bernier , m. j. lawler , y. b. kim , phys . * 101 * , 047201 ( 2008 ) . j. villian , r. bidaux , j .- carton , r. conte , j. phys . * 41 * , 1263 ( 1980 ) . c. l. henley , phys . rev . lett . * 62 * , 2056 ( 1989 ) . n. tristan , j. hemberger , a. krimmel , h .- a . krug von nidda , v. tsurkan , and a. loidl , phys . b * 72 * , 174404 ( 2005 ) . n. tristan , v. zestrea , g. behr , _ et al . b * 77 * , 094412 ( 2008 ) . t. suzuki , n. nagai , m. nohara , h. takagi , j. phys . : condens . matter * 19 * , 145265 ( 2007 ) . o. zaharko , a. cervellino , v. tsurkan , n. b. christensen , a. loidl , phys . b * 81 * , 064416 ( 2010 ) . o. zaharko , n. b. christensen , a. cervellino , v. tsurkan , a. maljuk , u. stuhr , c. niedermayer , f. yokaichiya , d. n. argyriou , m. boehm , a. loidl , phys . b * 84 * , 094403 ( 2011 ) . g. j. macdougall , d. gout , j. l. zarestky , g. ehlers , a. podlesnyak , m. a. guire , d. mandrus , s. e. nagler , pnas * 108 * , 15693 ( 2011 ) . l. savary , e. gull , s. trebst , j. alicea , d. bergman , l. balents , phys . b * 84 * , 064438 ( 2011 ) . k. hanashima , y. kodama , d. akahoshi , _ et al . _ , j. phys . . jpn . * 82 * , 024702 ( 2013 ) . preparing this manuscript we revisited the x - ray diffraction refinements and found that the degree of inversion in our crystal is actually lower , 5% . a. maljuk , v. tsurkan , v. zestrea , o. zaharko , a. cervellino , a. loidl , d. n. argyriou , j. crystal growth * 311 * , 3997 ( 2009 ) . b. roy , abhishek pandey , q. zhang , t. w. heitmann , d. vaknin , d. c. johnston , and y. furukawa , phys . b * 88 * , 174415 ( 2013 ) . p. debye , ann . 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coal@xmath0o@xmath1 spinel with magnetic co@xmath2 ions on the diamond a - lattice is known to be magnetically frustrated . 
 we compare neutron single crystal diffraction patterns measured in zero and applied magnetic fields with the ones obtained from classical monte - carlo models . in simulations we test the influence of various parameters on diffraction patterns : the ratio of nearest- , @xmath3 , and next - nearest , @xmath4 , neighbor interactions , magnetic field applied along the principal crystallographic directions , and random disorder on the a(co@xmath2)- and b(al@xmath5)- sites . 
 we conclude that the models considered so far explain the broadening of magnetic bragg peaks in zero magnetic field and their anisotropic response to applied magnetic field only partly . as bulk properties of our single crystal 
 are isotropic , we suggest that its microstructure , specifically @xmath6111@xmath7-twin boundaries , could be a reason of the nonconventional magnetic order in coal@xmath0o@xmath1 .