DSpace at VNU: Anomalous magnetic viscosity in alpha-Fe(Co) (Nd,Pr)(2)Fe14B exchange-spring magnet

Journal of Magnetism and Magnetic Materials 323 (2011) 3156–3161 Contents lists available at ScienceDirect Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm Anomalous magnetic viscosity in a-FeðCoÞ=ðNd,PrÞ2 Fe14 B exchange-spring magnet Nguyen Hoang Hai a,Ã, Nguyen Chau a, Duc-The Ngo b, Duong Thi Hong Gam c a Center for Materials Science, Hanoi University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Viet Nam Information Storage Materials Laboratory, Toyota Technological Institute, 2-12-1 Hisakata, Tempaku, Nagoya 468-8511, Japan c The Academy of Cryptography Techniques, 141 Chien Thang, Thanh Tri, Hanoi, Viet Nam b a r t i c l e i n f o a b s t r a c t Article history: Received 14 May 2011 Received in revised form 30 June 2011 Available online July 2011 This article presents an anomalous magnetic viscosity in a-FeðCoÞ=ðNd,PrÞ2 Fe14 B exchange-spring magnet A similar effect has been observed in non-interacting or weakly interacting systems but not in a strong interacting magnetic systems We reported a new procedure to measure magnetic relaxation under various magnetic fields Changing the applied magnetic field by different field protocols during the reversal process, we found that a memory effect of the magnetization appeared if the field change is large enough The mechanism of the phenomenon can be explained in the model of conventional magnetic reversal in strong ferromagnetic systems with an energy barrier distribution The study of such magnetic relaxations can provide some information related to the energy barrier distribution function & 2011 Elsevier B.V All rights reserved Keywords: Magnetic relaxation Exchange spring magnet Hard magnetic material Magnetic viscosity Magnetic reversal Introduction Time dependence in strong magnetic systems provides many interesting information and attracts considerable interest [1] from the experimental and theoretical point of view Recently, study of the dynamics of magnetic nanoscaled systems has been a subject of many articles The magnetic nanoscaled systems are assembly of magnetic nanoparticles Each particle has a singledomain structure with the orientation of the magnetic moment is dependent on magnetic anisotropy, effective applied magnetic field, and temperature Isolated non-interacting magnetic nanoparticles behave as giant spins which theoretically described by superparamagnetism Behaviors of interacting magnetic nanoparticles are complicated due to the competing of different energy types Since a pioneer article on the memory effects of dc magnetization and magnetic relaxation in a weakly interacting magnetic nanoparticle system [2], almost a hundred of related articles have been published to investigate the nature of the effects [2–9] According to Refs [2,9], though the full understanding of the nature of spin glass was unclear but the memory effect of the magnetic relaxation under different applied magnetic field and temperature protocols could be explained by the hierarchical model of spin-glass-like phase of isolated poly-dispersed nanoparticles Other authors claimed that the magnetic Corresponding author Tel.: ỵ 84 3558 2216; fax: ỵ84 3858 9496 E-mail address: nhhai@vnu.edu.vn (N.H Hai) 0304-8853/$ - see front matter & 2011 Elsevier B.V All rights reserved doi:10.1016/j.jmmm.2011.07.002 memory effects could simply be understood by the superparamagnetism with a modification of the distribution of energy barriers [10,11] Magnetic memory effects have been commonly in non-interacting or weakly interacting nanoparticle systems such as ferritin and Fe3N [11], Fe3O4 [12], g-Fe2 O3 [5,13], La0.6Pb0.4MnO3 [14] Until now, there is no report on such type of magnetic relaxation in strongly interacting systems, especially in hard magnetic materials The time dependence of the magnetization during the reversal process of a ferromagnetic system is interpreted by a thermally activated process related to the perfectly random crossing of energy barriers E of two-level metastable systems [15–17] The possibility PðtÞ that magnetization reversal occurs between time and t, at temperature T can be written as Ptị ẳ 1expft=tEịg, whereas tðEÞ is the relaxation time—the average crossing time for barrier energy E The Boltzmann–Arrhenius law relating tðEÞ with the intrinsic relaxation time t0 which corresponds to the crossing time of a barrier of zero height is tEị ẳ t0 expfE=kB Tg The variation of magnetization with time is given by [1,18]:    Z 1 Mtị t ẳ DðEÞ dE 2exp À Mð0Þ tðEÞ where DðEÞ is the distribution function of the energy barrier R1 which is normalized by DEị dE ẳ The expression of the magnetic relaxation coefficient, S, is   Z @M t t ẳ 2M0ị Sẳ exp DEị dE ð1Þ @ ln t tðEÞ tðEÞ N.H Hai et al / Journal of Magnetism and Magnetic Materials 323 (2011) 3156–3161 3157 In this expression, the distribution function DðEÞ is weighted by the function ðt=tðEÞÞexpfÀt=tðEÞg which defines the so-called energy window The weighting function is equal to zero everywhere except around tEị ẳ t Due to this window, only a small section of DðEÞ around t contributes to S The position of the window, Ec, at a given time t and a fixed temperature T is Ec ¼ kB T ln ðt=t0 Þ The width of the window is approximately equal to kBT [19] The effects of time and temperature are shifting the energy window towards higher energy values, logarithmically with time and linearly with temperature The effect of the applied magnetic field is mostly changing the distribution function We obtain the expression for the variation of magnetization with time is Z Ec Mtị ẳ 12 DEị dE 2ị M0ị Experimental Exchange-spring magnet a-FeðCoÞ=ðNd,PrÞ2 Fe14 B was fabricated by the conventional melt-spinning technique (Edmund Bueller melt-spinner) in an Ar atmosphere and thermally nanocrystallized in a similar way presented elsewhere [23] The starting materials was adjusted to have the composition of Nd2.25Pr2.25Fe73.8B16.5Co3Ti1Nb1Cu0.2 The tangential speed of the cooper wheel was 30 m s À to form amorphous ribbons The nanocomposite magnet was obtained by annealing amorphous ribbons in Ar at 590 1C in Ar gas followed by quenching in cooled water The magnetic measurements were performed on a DMS 880 vibrating sample magnetometer (VSM) with a maximum magnetic field of 13.5 kOe at room temperature Hysteresis loop was obtained without demagnetizing field correction The structure examination was carried out by using a D5005 Bruker X-ray diffractometer with Cu Ka radiation Results and discussion Fig presents the XRD data of the sample annealed at 590 1C for and 30 under Ar atmosphere The results show a multiphase structure of the soft magnetic phase a-FeðCoÞ and the hard magnetic phases Nd2Fe14B and Pr2Fe14B If the annealing time 150 100 150 50 100 M (emu/g) which is the so-called logarithmic approximation [20] Exchange-spring magnets belong to a type of nanostructured materials of which excellent hard magnetic properties are induced by the combination of two mutually exchange-coupled phases: the hard magnetic phase (e.g Nd2Fe14B, SmFeN) providing large magnetic anisotropy, the soft magnetic phase (e.g bcc-Fe, bcc-FeCo) providing a high saturation magnetization This combination may arise a huge maximum energy product and exchange-spring magnets have been considered as one of the best candidate for high-performance permanent magnets [21,22] We present the study of magnetic viscosity in a-FeðCoÞ= ðNd,PrÞ2 Fe14 B exchange-spring magnet in this article We observed an anomalous behavior in magnetic viscosity which can be explained by the well-known magnetization reversal process [1] Fig X-ray diffraction patterns of sample annealed at 590 1C for and 30 M (emu/g) As magnetization M(t) is a function of E, a scaling law in T lnðt=t0 Þ may be inferred The value of t0 deduced from fitting to experimental data varied from 10 À 12 to  10 À s [19] If DðEÞ is nearly constant in the interval of energy barriers which the magnetic moments can overcome during the observation time, the magnetization is   MðtÞ t C1À2kB TDðEc Þ ln ð3Þ Mð0Þ t0 -50 50 -50 -100 -100 -150 -150 -10000 -5000 5000 10000 H (Oe) -6000 -3000 3000 6000 9000 12000 H (Oe) Fig Recoil demagnetization curves and hysteresis loop (inset) of the exchangespring magnet was shorter than 20 min, a metastable phase of (Nd,Pr)2Fe23B3 still existed in the sample If the annealing time was longer, this phase was transformed to the (Nd,Pr)2Fe14B and a-Fe The presence of Fe and Co to form FeCo alloy improves the saturation magnetization of this phase The optimal annealing conditions were 590 1C, 30 Hysteresis loop and recoil curves of the a-FeðCoÞ=ðNd,PrÞ2 Fe14 B is given in Fig The sample possesses good hard magnetic properties with the saturation magnetization, Ms of 140 emu/g, the coercive field, Hc of 2.8 kOe, the magnetic squareness, Mr/Ms of 0.8 (Mr is the remanent magnetization), the energy product of 12 MGOe The exchange-spring behavior was presented by studying the isothermal remanent magnetization (mIRM) and the dc demagnetization (mDCD) [24] Interaction in the material is given by the relation: DM ẳ mDCD 12mIRM ị here m¼M/Ms is the reduced magnetization If DM is negative, the particle interaction in the system is essentially governed by the dipole interaction, which is easier to be demagnetized than to be magnetized If the DM is zero, no particle interaction occurs in the system If the DM is positive, the system is dominated by the exchange interaction The field dependence of DM in Fig indicates the presence of the exchange coupling interaction between particles 3158 N.H Hai et al / Journal of Magnetism and Magnetic Materials 323 (2011) 3156–3161 150 IRM (emu/g) DCD (emu/g) 100 0.3 0.2 ΔM M (emu/g) 0.4 50 0.1 0.0 -50 -0.1 -0.2 -100 3000 6000 9000 12000 H (Oe) 3000 6000 9000 12000 H (Oe) Fig The isothermal remanent magnetization (IRM), the dc demagnetization (DCD) and DM plot (inset) of the a-FeðCoÞ=ðNd,PrÞ2 Fe14 B magnet -50 M (emu/g) -50 M (emu/g) -55 -55 -60 -65 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 -60 lnt (s) H = -3000 Oe -65 300 600 900 t (s) nature of the sample However, the two main phases significantly contributed to the distribution function which may result to a variation in the value of this function, that caused the nonlogarithmic dependence of magnetization The relaxation of the soft magnetic material is much faster than that of the hard magnetic one therefore after a short period of time the magnetic relaxation followed the logarithmic law We will conduct other experimental studies in that logarithmic regime Now during the magnetic relaxation process under H1 ¼ À 3000 Oe, we switched the field to a new value, H2 ¼ À 2500 Oe and left the system relax for 350 s before returning to the initial magnetic field as shown in Fig In Fig 5, curve (a) presents a continuous decay of the magnetization under H1 in the similar way as displayed in Fig At t¼255 s, H2 was applied which led to a sudden change in the magnetization from À 66.66 to À 64.24 emu/g When H2 was applied, the magnetization was hardly changed (less than 0.1%) (curve (b)) indicating that the relaxation was halted At t¼ 600 s, the applied magnetic field was switched back to H1 which caused another sudden change in the magnetization from À 64.31 to À 66.94 emu/g, then the relaxation continued as it was before applying H2 (curve (c)) Curve ðc0 Þ obtained by shifting curve (c) to the left by a time period (which equals to the relaxation time under H2) in order to have a continuation of curve (a) (the inset of Fig 5) This behavior is similar to the memory effect in interacting Ni81Fe19 magnetic nanoparticles in which instead of the magnetic field, the temperature was switched [2] The process was repeated three times and the same behavior was observed (Fig 6) in which, three curves under H1 combined as a continuous relaxation We can say that a memory effect is observed in the exchange-spring magnet For further studies, we argue that the change in magnetic field, in this case, DH ¼ H2 ÀH1 ¼ 500 Oe is large Let examine an extreme case where DH is very small, smaller than the precision of the magnetic device (the VSM), that is no field changing It is clear that the magnetic relaxation will be a continuous process with no such magnetic memory effect therefore there will be a value of DH smaller 500 Oe at which the memory effect starts to occur, as presented in Fig Fig presents the relaxation of the magnetization with DH ¼ 30 Oe, i.e., H2 ¼ 2970 Oe Obviously the memory effect is Fig Relaxation of magnetization under a negative applied magnetic field of À 3000 Oe as a function of time in the exchange-spring magnet -55 Δt = 22 (s) ΔM = 0.22 (emu/g) -60 H1 = -3000 Oe M (emu/g) -55 M (emu/g) The relaxation of magnetization under a negative applied magnetic field, H, of À 3000 Oe as a function of time in the exchange-spring magnet is illustrated in Fig The time dependence of magnetization does not simply follow the logarithmic law as described by Eq (3) in the whole range of measuring time When the measuring time is small, a deviation from a linear function was observed But with the measuring time larger than about 90 s, the logarithmic dependence is obeyed The logarithmic dependence was deduced from Eq (2) by supposing that the value of the distribution function DðEÞ is constant in the interval of energy barriers The violation of logarithmic law have been commonly observed in magnetic systems in which a large distribution of the energy barrier are presented Such systems normally follow the T lnðt=t0 Þ scaling law [19] The large distribution can be resulted from a large distribution of particle size (EpKV, where K is the anisotropy field, V is the volume of the particle) or a multi-phase character of the magnetic system In our sample, there are at least two main phases of the soft magnetic material a-FeðCoÞ and hard magnetic material (Nd,Pr)2Fe14B In addition, the presence of Ti and Nb supporting the formation of the amorphous state, the presence of Cu helping the phase separation after heat treatments, created a multi-phase -60 (a) -65 -70 3.5 (c’) 4.0 4.5 H2 = -2500 Oe -65 5.0 5.5 6.0 6.5 lnt (s) (b) (a) H1 = -3000 Oe (c) (c’) -70 300 600 900 t (s) Fig Relaxation of the magnetization under negative applied magnetic fields H1 ¼ À 3000 Oe and H2 ¼ À 2500 Oe When H changed from H1 to H2 then returned back to the initial value, the magnetization seems to continuously decay as it was before changing the field The inset presents the logarithmic dependence as time varied, which shows that the magnetization does not change with time under H2 N.H Hai et al / Journal of Magnetism and Magnetic Materials 323 (2011) 3156–3161 3159 -45 -45 H2 = -2500 Oe -50 M (emu/g) M (emu/g) -50 H1 = -3000 Oe H2 = -2500 Oe H2 = -2500 Oe -55 H2 = -2970 Oe -55 H1 H1 = -3000 Oe H1 H2 H1 -60 H1 = -3000 Oe H1 = -3000 Oe -60 H2 300 600 900 H (Oe) 200 400 600 800 t (s) Fig Relaxation of the magnetization under negative applied magnetic fields H1 ¼ À 3000 Oe and H2 ¼ À 2500 Oe as a function of time The field protocol was repeated three times Fig Relaxation of the magnetization under negative applied magnetic fields H1 ¼ À 3000 Oe and H2 ¼ À 2970 Oe as a function of time The field protocol was repeated three times -45 -45 Δt = 100 (s) ΔM = 1.15 (emu/g) -60 -60 (c’) H1 = -3000 Oe -55 -65 3.5 -60 4.0 4.5 5.0 5.5 6.0 6.5 lnt (s) (a) H2 = -2970 Oe ΔM (a) (a) -55 M (emu/g) M (emu/g) -50 M (emu/g) H1 = -3000 -50 -80 (b) H1 = -3000 Oe (c) Δt (c’) H2 = -3500 -100 H1 = -3000 (c’) (b) -65 300 600 900 t (s) 200 400 600 800 t (s) Fig Relaxation of the magnetization under negative applied magnetic fields H1 ¼ À 3000 Oe and H2 ¼ À 2970 Oe as a function of time The magnetization under H2 reduces almost linearly with time Fig Relaxation of the magnetization under negative applied magnetic fields H1 ¼ À 3000 Oe and H2 ¼ À 3500 Oe as a function of time not present There is still an abrupt change from the curve (a) to the curve (b) but less spectacularly Under the field H2 ¼2970 Oe, the magnetization reduces almost linearly with time from À59.32 to À 60.24 emu/g When the magnetic field returns to H1, the highest value of the magnetization of curve (c) is much lower than the magnetization in curve (a) We construct curve ðc0 Þ by shifting curve (c) to the left in order to have a continuation in magnetic relaxation It is not like Fig where curve ðc0 Þ is an immediate continuation of curve (a), In Fig (the inset), there is a gap between the two curves, which is characterized by DM ¼ 1:15 emu=g and Dt ¼ 100 s Precisely, there is a small gap in Fig with DM ¼ 0:22 emu=g and Dt ¼ 22 s, which is much smaller than the gap appeared in Fig The behavior was observed when three such field protocols were repeated (Fig 8) The decay rate of curves reduced from (b), (d), and (f) We conducted the same measurement procedures with H2 ¼2950, 2980, 2990 Oe and observed very similar results (data not shown) When the magnetic system relaxed, instead of increasing the applied magnetic field, we reduced it to H2 ¼ À 3500 Oe and the results are presented in Fig There is a huge reduction of magnetization from À 62.08 to À101.32 emu/g after the field change Then the system under H2 magnetically relax in a similar way of curve (a) Curve (c) was obtained after a sudden but less spectacular jump from À 104.10 to À 100.45 emu/g and the magnetization almost did not change with time To explain the results, we come back to Eq (1) The value of the magnetic viscosity is determined by the energy window and the distribution function The strong magnetic anisotropy in the sample came from the uniaxial anisotropy of the hard magnetic phase (Nd,Pr)2Fe14B which in turn is due to the strong spin–orbit coupling of the rare-earth elements [25] When the applied magnetic field is parallel to the easy axis, the energy barrier is determined by E ẳ KV1H=Ha ị2 [25,8], where K is the magnetocrystalline anisotropy constant, V is the volume of the particle, Ha is the anisotropy magnetic field The anisotropy field of (Nd,Pr)2Fe14B can reach 70 kOe [25], so that the magnetic field applied on the sample is much lower than Ha As the result, ignoring the second order factor, we obtain EpH The reduce of the magnetization with measuring time in Fig can be explained by shifting to energy window towards higher energy values logarithmically with time N.H Hai et al / Journal of Magnetism and Magnetic Materials 323 (2011) 3156–3161 If the field H changes, the energy barrier E changes accordingly by an amount proportional to the change of the magnetic field, DEpDH which means that the energy barrier distribution function DðEÞ in Eq (2) is shifted to higher energy values If DðEÞ is shifted to much relative to the weighted function ðt=tðEÞÞexpfÀt=tðEÞg, the overlap between these two functions is small, as the result, the integration in Eq (1) is zero which is corresponding to the case of no magnetic relaxation Applying to the results presented in Fig 5, as the applied field changed from À3000 to À 2500 Oe, corresponding to DH ¼ 500 Oe, the energy barrier increased significantly which caused a halt in magnetic relaxation The magnetic moments in the sample could not overcome the high energy barrier so that no magnetic moment reversed When the field came back to the initial value, the relaxation process continued as if there was no change in the field, which is denoted by curve (a) and ðc0 Þ in Fig The small discontinuation characterized by DM ¼ 0:22 emu=g, Dt ¼ 22 s can be ascribed to a lag time when the VSM changed the applied field If the field change is small as indicated in Fig (DH ¼ 30 Oe), the energy barrier was lifted by a small value In the sample, the distribution function is broad due to the presence of many magnetic phases and also the distribution in size of particles Therefore, there is still some moments with higher energy than others can overcome the energy barrier so that the magnetic reversal occurred even the possibility for that is much lower Mathematically, the shifting of the distribution function relative to the weighted function in Eq (1) reduces the overlap of these functions, which causes a smaller value of the magnetic viscosity This can explain the fact that the linear decay of the magnetization (Fig 5, curve (b)) is slower than the logarithmic decay of curves (a) and (c) The magnetic relaxation in this region may be comparable to the logarithmic relaxation after a very long time The width of the distribution function can determine the range of DH at which the memory effect starts to occur The gap between curves (a) and ðc0 Þ in Fig characterized by DM ¼ 1:15 emu=g, Dt ¼ 100 s cannot only be ascribed to relaxation during the time for changing applied field of the VSM It is also due to the relaxation of the magnetization as time under H2 In this case, the magnetization change under H2 of 0.92 emu/g is smaller than DM ¼ 1:15 emu=g by an amount of 0.23 emu/g which is comparable to the magnetization gap of 0.22 emu/g appeared in Fig We can proclaim that the change in magnetization between curves (a) and (c) in Fig originates from the magnetic relaxation under H2 and the time lag of the machine Imagine that if we have a system containing perfectly homogeneous particles with exactly the same energy barrier, any increase in the applied magnetic field above À 3000 Oe will halt the relaxation Therefore, the relaxation presented under H2 is due to the large distribution in energy barrier of the sample If the distribution function is broad, DH should be high and vice versa in order to observe the magnetic memory effect Put it in another way, measuring the field change at which the magnetic memory effect starts to occur we can have an idea about the value of the width of the energy barrier The above arguments can be applied to explain the memory effect presented in literature [2–8] To check the validity of the theory of magnetic reversal, we performed another field protocol in which H2 ¼ þ3000 Oe (Fig 10) No memory effect is observed Each curve presents as a normal relaxation in both negative and positive applied magnetic fields The relaxation process depends strongly on the magnetic history of the system In all curves (a) of the previous experiments and curve (a) of Fig 10, the relaxation occurred after being saturated at a high magnetic field of 13.5 kOe If the magnetic field is high enough to obtain the major hysteresis loop that field can wipe out the previous magnetic states From the hysteresis loop in the inset of Fig 2, the magnetic field at which previous magnetic states can be erased of 8.5 kOe was determined from the reversible part at high magnetic fields Curves (c), (e), and (g) of Fig 10 are relaxation H2 = 3000 Oe 110 (b) 105 M (emu/g) 3160 (d) -45 (f) (a) -50 (c) (e) -55 H1 = -3000 Oe (g) -60 300 600 900 t (s) Fig 10 Multi-relaxation of the magnetization under negative applied magnetic elds H1 ẳ 3000 Oe and H2 ẳ ỵ3000 Oe as a function of time processes after applying the magnetic field of kOe which is smaller than the value of 8.5 kOe Therefore those relaxations are different after each time of changing the applied magnetic fields The values of magnetization at which the magnetic decay started reduced from curves (a) to (g) This, in fact, is the magnetization determined from the minor hysteresis loops, in which the previous magnetic states were partly wiped out Curves (b), (d), and (f) can be explained in a similar way Conclusion Anomalous magnetic viscosity have been observed in a-FeðCoÞ=ðNd,PrÞ2 Fe14 B exchange-spring magnet under different field protocols, which can be explained in the model of conventional magnetic reversal in strong ferromagnetic systems Our study supports the theory of energy distribution which presented to explain the relaxation in non-interacting and weakly interacting nanoparticles It also can 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