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multiferroic materials , in which ferromagnetic , ferroelectric , and/or ferroelastic orderings coexist , have attracted significant research interest since many years @xcite due to their potential applications in data storage media , spintronics and ferroelectric random - access memories . the co - existence of ferro-orders in multiferroics allows the possibility that the magnetization can be tuned by an applied electric field and vice versa . among the limited choices offered by the multiferroic materials , bifeo@xmath4 ( bfo ) , one of the single - phase multiferroic materials at room temperature , exhibits the co - existence of ferroelectric ordering with curie temperature ( t@xmath8 ) of 1123 k and antiferromagnetic ( afm ) ordering with a nel temperature ( t@xmath9 of 643 k @xcite . in bifeo@xmath4 , magnetic ordering is of antiferromagnetic type , having a spiral modulated spin structure ( smss ) with an incommensurate long - wavelength period of 62 nm @xcite . this spiral spin structure cancels the macroscopic magnetization and inhibits the observation of the linear magnetoelectric effect @xcite . these problems ultimately limit the use of bulk bifeo@xmath4 in functional applications . recent investigations demonstrated that in order to perturb the smss and improve the magnetic properties of bifeo@xmath4 , partial substitution of bi by rare - earth ions @xcite or alkaline - earth ions @xcite and also substitution of fe by transition metal ions @xcite is an effective route . it is also reported that simultaneous minor substitution of bi and fe in bifeo@xmath4 by ions such as la and mn , la and ti , nd and sc etc . , respectively @xcite also enhanced the magnetism and ferroelectricity in bifeo@xmath4 . recently , we have observed that simultaneous substitution of gd and ti in place of bi and fe , respectively in bifeo@xmath4 multiferroics improved their morphological , dielectric and magnetic properties at room temperature @xcite . later on , another group also observed fascinating magnetic , optical and dielectric properties in this gd and ti co - doped bifeo@xmath4 ceramic system at room temperature @xcite . therefore , in this investigation , we were interested to conduct experiments on temperature dependence of magnetic properties of gd and ti co - doped bi@xmath0gd@xmath1fe@xmath2ti@xmath3o@xmath4 ( x = 0.00 - 0.20 ) multiferroic materials . in particular , our interest is to investigate the effect of temperature on remanent magnetization , coercive fields and exchange bias ( eb ) fields of these bulk polycrystalline materials . notably , the eb phenomenon which manifest itself by a shift of a magnetic hysteresis loop in systems containing ferromagnetic / antiferromagnetic bilayers has been studied extensively since many years due to its importance in spintronic applications @xcite . the eb effect usually occurs when the system is cooled down in an external magnetic field through the magnetic ordering temperatures . most of the research in this field is focused on specially prepared systems , however , recent investigations reported the presence of eb effect in perovskite manganites @xcite , cobaltites @xcite , heusler alloys @xcite and multiferroics @xcite . although eb has been observed in various bulk materials , the effect in most cases has been limited to far below room temperature ( @xmath10100 k)@xcite , thus making the systems less attractive for applications .    in our previous investigation , the magnetization vs. magnetic field ( @xmath11 ) hysteresis loops indicated the presence of exchange bias effect in the gd and ti co - doped bi@xmath0gd@xmath1fe@xmath2ti@xmath3o@xmath4 ( x = 0.00 - 0.20 ) ceramics at room temperature although the biasing field was very small @xcite . therefore , in the present investigation , we have explored exchange bias effect in this material system at different temperatures ranging from 20 k to 300 k. we have also investigated the influence of cooling magnetic fields at temperatures 150 k and 250 k to observe a tunable exchange bias in sample composition bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 ( this composition is referred as sample x = 0.10 throughout the manuscript ) . the polycrystalline samples having compositions bi@xmath0gd@xmath1fe@xmath2ti@xmath3o@xmath4 ( x = 0.00 - 0.20 ) were synthesized by using standard solid state reaction technique as was described in details in our previous investigation @xcite . the powder materials and ceramic pellets sintered at 1100 k were used for magnetic characterization . the @xmath11 hysteresis loops of bi@xmath0gd@xmath1fe@xmath2ti@xmath3o@xmath4 ( x = 0.00 - 0.20 ) multiferroic ceramics were carried out at different temperatures using a superconducting quantum interference device ( squid ) magnetometer ( quantum design mpms - xl7 , usa ) . the temperature dependent magnetization measurements were carried out both at zero field cooling ( zfc ) and field cooling ( fc ) processes @xcite . the magnetic hysteresis loops were also carried out at different temperatures by cooling down the sample from 300 k in various cooling fields ( @xmath6 ) @xcite . hysteresis loops of sample x = 0.10 ( composition bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 ) carried out at different temperatures . ( b - h ) an enlarged view of the low - field m - h hysteresis loops of sample x = 0.10 obtained at temperatures : ( b ) 20 k ( c ) 50 k ( d ) 100 k ( e ) 150 k ( f ) 200 k ( g ) 250 k and ( h ) 300 k.,width=302 ] for magnetic characterization , the m - h hysteresis loops of bi@xmath0gd@xmath1fe@xmath2ti@xmath3o@xmath4 ( x = 0.00 - 0.20 ) samples were measured at different temperatures ranging from 20 k to 300 k with an applied magnetic field of up to @xmath1250 koe . as a typical example , the m - h loops of sample x = 0.10 ( composition bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 ) at different temperatures were presented in figure [ fig1 ] ( a ) . figures [ fig1 ] ( b - h ) demonstrate an enlarged view of the low - field m - h hysteresis loops of this sample measured at temperatures : ( b ) 20 k ( c ) 50 k ( d ) 100 k ( e ) 150 k ( f ) 200 k ( g ) 250 k and ( h ) 300 k. the hysteresis loops for the two other compositions were shown in the supplemental figures 1(s1 ) and 2(s2 ) @xcite . it should be noted that the m - h hysteresis loops ( figure [ fig1 ] , supplemental figures 1(s1 ) and 2(s2 ) ) were carried out initially without applying any cooling magnetic field . the coercive fields ( h@xmath13 ) and remanent magnetization ( m@xmath14 ) extracted from the hysteresis loops were quantified as : @xmath15 , where h@xmath16 and h@xmath17 are the left and right coercive fields @xcite and m@xmath18 = @xmath19(m@xmath20-m@xmath21)@xmath19/2 where m@xmath20 and m@xmath21 are the magnetization with positive and negative points of intersection with h = 0 , respectively @xcite . calculated values of h@xmath13 and m@xmath18 are plotted as a function of temperature in figures [ fig2 ] ( a and b ) respectively for bi@xmath0gd@xmath1fe@xmath2ti@xmath3o@xmath4 ( x = 0.00 - 0.20 ) samples . both the coercive fields and remanent magnetizations are higher for sample x = 0.10 than those for x = 0.00 and x = 0.20 . therefore , it is clear that the substitution of 10% ti in place of fe in bi@xmath0gd@xmath1feo@xmath4 compound significantly increased h@xmath13 and m@xmath18 . however , a further increment of ti to 20% in place of fe reduced h@xmath13 and m@xmath18 although their net values are still higher than that of ti undoped bi@xmath0gd@xmath1feo@xmath4 sample . as was reported in our previous investigation @xcite , the larger values of h@xmath13 and m@xmath14 in sample x = 0.10 are related with the microstructure of the composition i.e. with homogeneous small grain size of the material . in the case of la and nb co - substituted bifeo@xmath4 @xcite and pr and zr co - substituted bifeo@xmath4 compounds @xcite , increase in coercive field with the substitution was also attributed to decrease in grain size . the value of h@xmath13 in these materials are much larger than that in pure bifeo@xmath4 @xcite and such a large value of coercivity in gd and ti co - substituted bifeo@xmath4 samples may be related to their magnetic anisotropy @xcite .    ) and ( b ) remanent magnetization ( m@xmath14 ) as a function of temperature in bi@xmath0gd@xmath1fe@xmath2ti@xmath3o@xmath4 ( x = 0.00 - 0.20 ) compounds . both h@xmath13 and m@xmath14 are higher over a wide range of temperatures in sample x = 0.10.,width=340 ]    the remarkable feature observed from figure [ fig2](a ) is that the coercivity of these ceramic samples increases with temperature . figure [ fig7 ] shows , as a typical example for x = 0.10 sample , that while the coercivity increases with increasing temperature , the maximum magnetization ( m@xmath22 ) at 50 koe decreases with increasing temperature @xcite . for all studied samples , the coercivity show a strong temperature dependency and the h@xmath13 values are significantly higher at room temperature than that at 20 k. for example , the h@xmath13 value at room temperature for sample x = 0.10 is three times higher than that at 20 k.    the usual trend in a typical magnetic system is for the coercivity to increase with decreasing temperature @xcite since the anisotropy decreases much more sharply than does the magnetization with increasing temperature @xcite . in similar multiferroic material systems , e.g. la doped bifeo@xmath4 @xcite and lufe@xmath23o@xmath24 @xcite , the h@xmath13 values were found to increase at low temperature than that at room temperature . the unexpected decreasing trend of h@xmath13 at low temperature as compared with the room temperature values for all compositions investigated here may be explained by the presence of magnetoelectric coupling in these multiferroic materials @xcite . the presence of the magnetoelectric coupling produces additional contribution to the anisotropy that actually acts to decrease the effective magnetic anisotropy @xcite . if @xmath25 is the uniaxial anisotropy constant in the absence of coupling effects and @xmath26 is the uniaxial anisotropy constant in the presence of magnetoelectric coupling , then    @xmath27 +   + here @xmath28 is the homogeneous magnetoelectric co - efficient that is related to the dzyaloshinsky moriya magnetic field , @xmath29 is the magnetic susceptibility in the direction perpendicular to the antiferromagnetic vector , @xmath30 is the spontaneous electric polarization @xcite . thus the temperature variation in h@xmath13 is determined by the competition between the magnetic anisotropy and the magnetoelectric coupling @xcite . ( the maximum magnetization at 50 koe ) and h@xmath13 as a function of temperature in sample x = 0.10 ( bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4).,width=340 ]    the higher values of h@xmath13 and m@xmath14 in sample x = 0.10 than those of x = 0.00 and 0.20 compositions motivated us to investigate further its magnetic properties in details . therefore , we have carried out the temperature dependence of the magnetization ( @xmath31 ) of bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 bulk sample . the @xmath31 curves measured in zfc and fc modes in the presence of 500 oe applied magnetic field is shown in figure [ fig3 ] . in zfc process , the sample is initially cooled from 300 k to the lowest achievable temperature and data were collected while heating in the presence of the applied field . on the other hand , in the fc mode , data values are collected while cooling in the presence of the magnetic field which is commonly known as ` cooling magnetic field ' @xcite . here the temperature dependence magnetization measurements demonstrate clearly that both zfc and fc curves of bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 ceramic coincide with each other without showing any bifurcation which indicates the absence of any spin flipping effect @xcite . in similar multiferroic materials both the zfc and fc curves were also found to coincide with each other @xcite . curves ) of bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 sample measured in zfc and fc processes in the presence of 500 oe applied magnetic fields . both zfc and fc curves coincide with each other without showing any bifurcation.,width=340 ]     + as shown in figures 1(a - h ) , the room temperature @xmath11 hysteresis loop as well as the loops taken at other temperatures exhibit an asymmetric shift towards the magnetic field axes @xcite . this is a signature of the presence of an exchange bias effect in multiferroic bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 material @xcite . in the present investigation , the hysteresis loops of gd and ti co - doped bifeo@xmath4 ceramic system is unsaturated even with an applied magnetic field of up to @xmath1250 koe . which confirm the basic antiferromagnetic nature of the compounds . notably , undoped bifeo@xmath4 possesses a very narrow hysteresis loop with a very small but non - zero remanent magnetization ( 0.0009 emu / g ) and a coercive field of @xmath32110 oe at room temperature @xcite . compared to pure bifeo@xmath4 , the center of m - h loops of bi@xmath0gd@xmath1fe@xmath2ti@xmath3o@xmath4 ( x = 0.00 - 0.20 ) compounds are wider ( as shown typically in the enlarged view of sample x = 0.10 , figures [ fig1 ] ( b - h ) ) which suggests a weak ferromagnetic nature @xcite of this co - doped ceramic system . the weak ferromagnetic nature of this material system is also revealed from temperature dependent magnetization curves @xcite . in this way we anticipate the co - existence of strong - anisotropic ferri / ferromagnetic ( fm ) and antiferromagnetic domains in this multiferroic material system . as a consequence of the exchange coupling at interfaces between these multiple magnetic domains , it is expected that the system acts as a natural system for generating eb effect in bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 multiferroics @xcite .    ) as a function of temperature in bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 . the h@xmath33 values were calculated from the asymmetric shift of the @xmath34-@xmath35 hysteresis loops of figures [ fig1](b - h ) . the hysteresis loops were taken without applying a cooling magnetic field.,width=9 ]    the exchange bias field ( h@xmath33 ) from the loop asymmetry along the field axis can be quantified as @xmath36 where @xmath37 and @xmath38 are the left and right coercive fields , respectively @xcite . the variation of h@xmath33 as a function of temperature in bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 calculated from the asymmetric shift of the @xmath34-@xmath35 hysteresis loops of figures [ fig1](b - h ) is shown in figure [ fig4 ] . the temperature dependence of h@xmath33 for two other compositions were presented in the supplementary information ( supplementary table 1 ) @xcite .    as was mentioned earlier , the eb effect usually occurs when the system is cooled down in an external magnetic field through the nel temperature ( t@xmath39 ) . it is worth mentioning that in bifeo@xmath4 ceramic system the exchange bias effect was observed without any magnetic - field - annealing process through t@xmath39 @xcite which is the conventional method of inducing unidirectional anisotropy @xcite . it has also been observed without using any alloy layers @xcite , however , then the biasing strength of bifeo@xmath4 is observed to be very weak with @xmath7 = 36 oe @xcite at room temperature . the exchange bias fields indicate the strength of the exchange coupling of an exchange bias system . as shown in figure [ fig4 ] , values of @xmath7 of bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 at 150 k and 250 k are higher than that at any other temperatures . the @xmath7 values shown in figure [ fig4 ] is observed without applying any cooling magnetic field and therefore the biasing strength is weak and random . in the case of a fm / afm bilayer system , it is well known that cooling magnetic field plays an important role in establishing a strong unidirectional anisotropy due to the exchange coupling @xcite . hence , in the following experiments , the magnetic hysteresis loops of bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 material were carried out at temperatures 150 k and 250 k by cooling down the sample from 300 k in various cooling magnetic fields ( @xmath6 ) ranging from 20 koe to 60 koe . in each experiment related to cooling magnetic fields , the measuring magnetic fields were from -30 koe to 30 koe . the details of the loop asymmetry at different cooling fields and temperatures can be found in the supplementary figures 3(s3 ) and 4(s4 ) @xcite .    ) at 150 k and 250 k for bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 ceramic . the graph also demonstrates the dependency of @xmath7 on temperature . , width=340 ]    the influence of cooling magnetic fields on exchange bias effect at temperatures 150 k and 250 k in bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 multiferroic material is illustrated in figure [ fig5 ] . the @xmath7 values increased significantly upon the application of cooling magnetic fields . for example , at temperature 250 k and cooling magnetic field 60 koe , the biasing field increased more than twelve times than that for a cooling magnetic field of 20 koe . during the field cooling experiments , the @xmath7 values reduced with increasing temperature , figure [ fig5 ] , which is similar to results reported in previous investigations @xcite . the @xmath7 values are higher than those in related material systems @xcite specifically at high temperatures . in the present investigation , the temperature dependent zfc and fc measurements ( figure [ fig3 ] ) demonstrate the absence of any bifurcation from 300 k down to 5 k and therefore , we had conducted the field cooling experiments by cooling the sample from 300 k down to 150 k and 250 k. by using the squid magnetometer ( quantum design mpms - xl7 , usa ) , it was not possible to heat the sample above 300 k ; therefore , the field cooling experiments were not possible to conduct by cooling down this sample through t@xmath39 which is around 520@xmath40 k for bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 ceramic measured from temperature dependent dielectric measurements ( data not shown here ) . as was mentioned earlier , the eb has been observed in various bulk materials , however , the effect in most cases has been limited to low temperatures @xcite . the observation of eb up to room temperature is of interest from the perspective of practical applications . therefore , in future we intend to conduct field cooling experiments at room temperature by cooling bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 material through t@xmath39 which is above the room temperature . the influence of @xmath6 on coercive fields were also measured at temperatures 150 k and 250 k and the results are displayed in table 1 . notably , in figures [ fig2 ] and [ fig7 ] , we have shown the effect of temperature on @xmath5 without applying any cooling magnetic field . here in table 1 , we have inserted the effect of cooling magnetic field on @xmath5 and the measurements were carried out at two different temperatures close to room temperature . the exchange bias fields are strongly affected by cooling magnetic field as shown in figure [ fig5 ] , however , the @xmath5 values ( table 1 ) are influenced merely by a small extent . this is not unusual , in the case of nife / co bilayers , similar effect was previously observed , i.e. the exchange bias field is strongly affected by cooling magnetic field whereas the @xmath5 is weakly influenced @xcite . .the table shows the effect of cooling magnetic fields on @xmath5 of bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 sample at temperatures 150 k and 250 k. notably , the effect of temperatures on @xmath5 of bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 sample without applying cooling magnetic fields was inserted in figure [ fig2 ] . [ tab1 ] [ cols= " < , < , < , < , < " , ]     in our previous investigation @xcite , we have synthesized nanoparticles of the same composition i.e. of bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 with a mean size of 40 - 100 nm directly from their bulk powder by using the sonication technique described in ref . @xcite . in this specially prepared nanoparticle system , we have observed exchange bias effect and the magnitude of the exchange bias fields were also found to increase with cooling magnetic fields @xcite . obviously , the cooling field dependence of @xmath7 values of bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 bulk system were weaker than those of specially prepared bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 nanoparticles . for example , in both bulk and nanoparticle system the highest @xmath7 values were observed at temperature 150 k by applying 60 koe cooling magnetic field . at this temperature and cooling magnetic field , the @xmath7 value of the bulk system is 20 % less than that of nanoparticles having sizes 40 - 100 nm . this is worth noting as the preparation of bulk materials is comparatively easy and straightforward considering the multistep processing for the preparation of nanoparticles . we have observed a strong influence of temperature on coercive fields and exchange bias fields of gd and ti co - doped bifeo@xmath4 multiferroics . the coercive fields of this multiferroic system were enhanced anomalously with increasing temperature . the anomalous enhancement of the coercivity with increasing temperature and particularly the observation of the high values of @xmath5 near / at room temperature may be of future use in potential applications where a coercivity stability at high temperature is crucially effective . we have also observed the presence of exchange bias effect due to the interface exchange coupling between fm and afm domains of gd and ti co - doped bifeo@xmath4 material system . the magnitude of the exchange bias fields in bulk bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 were also found to increase with cooling magnetic field . this magnetically tunable exchange bias obtained in bulk multiferroic bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 material up to temperatures 250 k is promising , as most of the bulk materials show eb only far below room temperature . we anticipate that the presence of both exchange and magnetoelectric coupling in bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 multiferroic material might be worthwhile for potential applications in novel multifunctional devices . this work was supported by the world academy of sciences ( twas ) , ref.:14 - 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we have investigated the effect of temperature on magnetic properties of bi@xmath0gd@xmath1fe@xmath2ti@xmath3o@xmath4 ( x = 0.00 - 0.20 ) multiferroic system . 
 unexpectedly , the coercive fields ( @xmath5 ) of this multiferroic system increased with increasing temperature . the coercive fields and remanent magnetization were higher over a wide range of temperatures in sample x = 0.10 i.e. in sample having composition bi@xmath0gd@xmath1fe@xmath0ti@xmath1o@xmath4 than those of x = 0.00 and 0.20 compositions . 
 therefore , we have carried out temperature dependent magnetization experiments extensively for sample x = 0.10 . 
 the magnetic hysteresis loops at different temperatures exhibit an asymmetric shift towards the magnetic field axes which indicate the presence of exchange bias effect in this material system . 
 the hysteresis loops were also carried out at temperatures 150 k and 250 k by cooling down the sample from 300 k in various cooling magnetic fields ( @xmath6 ) . the exchange bias field ( @xmath7 ) 
 values increased with @xmath6 and decreased with temperature . 
 the @xmath7 values were tunable by field cooling at temperatures up to 250 k.