Peculiar Ferrimagnetism Associated with Charge Order in Layered Perovskite GdBaMn2O5
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J un Peculiar Ferrimagnetism Associated with Charge Order in Layered PerovskiteGdBaMn O . A. A. Taskin and Yoichi Ando
Central Research Institute of Electric Power Industry, Komae, Tokyo 201-8511, Japan
The magnetic properties of GdBaMn O . , which exhibits charge ordering, are studied from 2 to400 K using single crystals. In a small magnetic field applied along the easy axis, the magnetization M shows a temperature-induced reversal which is sometimes found in ferrimagnets. In a largemagnetic field, on the other hand, a sharp change in the slope of M ( T ) coming from an unusualturnabout of the magnetization of the Mn sublattices is observed. Those observations are essentiallyexplained by a molecular field theory which highlights the role of delicate magnetic interactionsbetween Gd ions and the antiferromagnetically coupled Mn /Mn sublattices. PACS numbers: 75.30.Cr, 75.47.Lx, 75.50.Gg, 75.30.Et
Ferrimagnetism is a complex but intriguing type ofmagnetic ordering. It occurs when antiferromagneticallyaligned spins have different local moments, resulting intheir incomplete cancellation. The characteristics of thistype of ordering stems from the fact that it combines fea-tures of both ferromagnetic (FM) and antiferromagnetic(AF) systems. Moreover, if more than two spin sublat-tices are involved, a new level of complexity, and hencenew physics, can emerge [1]. So far, only a few families offerrimagnetics with three magnetic sublattices — spinelferrites and rare-earth garnets being the most famous ex-amples [2] — have been discovered. These materials areproved to be not only fundamentally interesting, but alsotechnologically important [3], inspiring the search for newpromising magnetic compounds.Recently, half-doped A -site ordered manganite per-ovskites R BaMn O x (where R is a rare-earth element)have been synthesized in an effort to clarify the role ofthe random potential effect in the colossal magnetoresis-tance (CMR) phenomena [4, 5, 6, 7, 8]. It has been foundthat in addition to the interesting electronic properties,these compounds possess another potentially useful qual-ity, a variability of the oxygen content [4, 5, 6, 9]. Byvarying the oxygen concentration from x =0 to x =1, onecan readily change the valence state of Mn ions from2+ through 3+ to 4+, generating a variety of possi-ble magnetic states. In particular, Mn ions adopt twovalence states, Mn and Mn , and develop a chargeorder in the reduced composition R BaMn O . ( x =0)[4, 5]. Since most rare-earth ions ( R ) are also mag-netic, R BaMn O . can be a three-sublattice magneticsystem with potentially ferrimagnetic type of ordering;among the rare-earths, Gd with the largest spin andzero orbital angular momentum would make a bench-mark compound of this family. It is worth noting thatthe layered crystal structure of these compounds natu-rally implies an anisotropy in its magnetic properties and,therefore, single crystals would have a great advantagefor studying their magnetic behavior; however, previousstudies on R BaMn O . [4, 5, 6] only used polycrystalline samples.In this Letter, we present the first study of the mag-netic properties of GdBaMn O . single crystals, whichshow unusual behavior: At T N =144 K, a long-range or-der of Mn and Mn magnetic moments is established.Upon decreasing temperature in a small magnetic fieldalong the c axis, a magnetization reversal occurs at thecompensation point T comp , below which the net magneticmoment is opposite to the magnetic-field direction. Onthe other hand, in a large magnetic field the magnetiza-tion M is positive at all temperature, and shows a sharpkink in the M ( T ) curve at T comp . We show that theobserved magnetic behavior is essentially understood ifGd spins, which remain paramagnetic through T N and T comp , are weakly coupled ferromagnetically (antiferro-magnetically) with Mn (Mn ) neighbors and gradu-ally align their spins parallel (antiparallel) to the Mn (Mn ) sublattice with decreasing T in low fields. Whatis special here is that in high magnetic fields, due to theweak Gd-Mn coupling, the Gd spins are aligned alongthe external magnetic field, which eliminates the magne-tization reversal; intriguingly, in this situation an abruptturnabout of the magnetization of the Mn sublattices oc-curs at T comp , which, to our knowledge, has never beenobserved in any ferrimagnets. Hence, the peculiar ferri-magnetism in GdBaMn O . is quite distinct from othertransition-metal oxides showing magnetization reversals[1, 2, 10, 11].The high-quality single crystals of GdBaMn O x usedfor this study were grown by the floating-zone technique.The as-grown crystals were annealed in flowing argon-hydrogen mixture at 600 ◦ C for several days to obtainthe stoichiometry of x = 0, which is confirmed by thethermogravimetric analysis. Parallelepiped samples werecut and polished with all faces adjusted to the crystal-lographic planes to within 1 ◦ . Magnetization measure-ments were carried out using a SQUID magnetometer atfields up to 70 kOe applied parallel or perpendicular tothe c axis.Figure 1 shows the temperature dependences of the H = 100 Oe
H || the c axis, cooling H || the c axis, heating H the c axis T comp T N M ( m B / f . u . ) T (K)
FIG. 1: (Color online) Temperature dependences of M underdifferent conditions. Upon cooling in H = 100 Oe appliedalong the c axis (circles), M ( T ) becomes negative at T comp and eventually returns to positive at lower temperature; uponheating, nearly a “mirror image” is observed after applying ahigh magnetic field ( H = 3 kOe at T = 35 K for the curveshown by triangles). The squares show M ( T ) measured in H = 100 Oe applied along the ab plane for both cooling andheating. magnetization of GdBaMn O . in a magnetic field of100 Oe applied parallel or perpendicular to the spin easyaxis. Upon cooling in a magnetic field along the c axis, M ( T ) (shown by circles) rapidly increases below the N´eeltemperature, T N =144 K, indicating the onset of a mag-netic ordering. About 10 K below T N , M ( T ) reaches amaximum, then starts to decrease and eventually goes tozero at T comp =95 K. This temperature, which is calledthe compensation point, marks the state where mag-netic contributions of all sublattices cancel each other.Below T comp , M ( T ) becomes negative, indicating thatthe net magnetic moment is opposite to the externalmagnetic-field direction. This phenomenon is called the temperature-induced magnetization reversal [1, 2, 10, 11].Upon further decrease in temperature and concomi-tant development of sublattice magnetizations, the netmagnetic moment grows too large to remain in thismetastable state. Eventually a magnetic field (even assmall as 100 Oe) can overcome the coercive force, lead-ing to a rotation of the net magnetization. As a conse-quence, another sign change of M ( T ) occurs at around20–30 K. The effect of this rotation of the net magneticmoment can be illustrated even more clearly in the fol-lowing experiment: First, the direction of the sublatticemagnetizations in the sample cooled down to an inter-mediate temperature in 100 Oe are switched by applyinga large magnetic field (for example, H = 3 kOe at T =35 K as shown in Fig. 1). Then, the magnetic field isreduced down to 100 Oe again and M ( T ) is measuredupon heating. As can be seen in Fig. 1, M ( T ) showsalmost a “mirror image” of the magnetization recorded upon cooling, indicating that the 180 ◦ -spin-rotated stateis kept intact up to T N once it is formed.A comparison of M ( T ) measured along different crys-tallographic axes reveals another important feature of themagnetic behavior in GdBaMn O : The magnetizationis strongly anisotropic with an easy direction along the c axis (see Fig 1), simplifying significantly a possible ar-rangement of Mn , Mn , Gd spins.In order to obtain further insight into the observedphenomena, the field dependence of the magnetizationhas been measured at 2 K where the magnetizations ofall sublattices are expected to be fully developed. Asshown in Fig. 2(a), a magnetic field of about 1 kOe ap-plied along the c axis is enough to reach the saturation.A much higher magnetic field (about 50 kOe) must beapplied perpendicular to the easy axis to reach the samesaturation level. The equality of the saturation mag-netization M sat ≈ µ B /f.u. achieved along differentcrystallographic axes suggests that the obtained value re-flects the net saturated moment, which should be simplycomposed of the sublattice magnetizations.Obviously, there is a unique combination of spin-only moments of the three spin sublattices — Mn ( S Mn =2), Mn ( S Mn =5/2), and Gd ( S Gd =7/2)— that can be consistent with the experimentally ob-served value of the saturated magnetization: gµ B ( S Mn − S Mn + S Gd ) = 6 µ B , (1)where g =2 is the Land´e g -factor and µ B is the Bohr mag-neton. This equation suggests an AF coupling betweenMn and Mn and a FM (AF) interaction of Gd ions -60 -40 -20 0 20 40 60-6-4-20246 -60 -40 -20 0 20 40 60 T = 2 K (a) M ( m B / f . u . ) H || the c axis H the c axis Gd (PM) H (kOe) (b)
FIG. 2: (Color online) (a) M ( H ) curves of GdBaMn O . with H along the c axis (circles) and the ab plane (squares).The calculated paramagnetic response from the Gd sublat-tice is shown by the dashed line. (b) A sketch of the crys-tal and magnetic structure of GdBaMn O . , showing threemagnetic sublattices composed of Mn , Mn , and Gd .Nonmagnetic Ba and O are omitted for the sake of clarity. with the Mn (Mn ) sublattice. Note that the param-agnetic (PM) contribution of Gd alone [shown by thedashed line in Fig 2(a)] would give a larger saturatedmagnetization than observed. The spin-only magneticmoments of Mn , Mn , and Gd ions are expectedto be a good approximation in GdBaMn O . , becausethe high-spin (HS) Gd (4 f ) and Mn (3 d ) have zeroorbital angular momentum. For HS-Mn (3 d ), a stateof the e g symmetry is unoccupied, also implying a lackof the orbital contribution to the total magnetic momentof Mn .Thus, both M ( T ) and M ( H ) data point to a ferrimag-netic type of ordering among the three magnetic sub-lattices of GdBaMn O . . Neutron powder diffractionstudies [4, 5] as well as density-functional calculationsof electronic structure [12, 13] have reported a rock-saltarrangement of Mn and Mn with a G-type AF order-ing in YBaMn O . and LaBaMn O . , compounds withrare-earth ions from opposite ends of the lanthanide se-ries. It would be natural to assume that the same typesof charge and magnetic ordering among Mn ions are real-ized in GdBaMn O . . Magnetic Gd ions with a half-filled 4 f shell are expected to interact ferromagneticallywith Mn and antiferromagnetically with Mn sublat-tices according to the Goodenough-Kanamori rules [14],although this interaction should be rather weak.The magnetic structure most likely realized inGdBaMn O . is shown in Fig. 2(b). Below T N , Mn ( S =5/2) and Mn ( S =2) ions develop a long-range fer-rimagnetic order with the spin directions along the c axis.Because of the weak magnetic interaction between Gd and Mn /Mn , the alignment of Gd spins ( S =7/2)grows rather slowly with the development of the magne-tization of the Mn sublattices below T N , but eventuallyalmost all Gd spins are aligned along the Mn spins atlow enough T and add to the large M sat . As can be seenin Fig 2(a), the magnetization vectors of the ordered sub-lattices can be 90 ◦ rotated by applying a magnetic fieldof ∼
50 kOe perpendicular to the easy axis.Another piece of information about the magnetic be-havior of GdBaMn O . comes from the susceptibilitymeasurements in the paramagnetic phase above T N . Fig-ure 3 shows the inverse molar susceptibility, measured in H = 100 Oe parallel (circles) and perpendicular (squares)to the c axis. Both curves coincide at high temperature,demonstrating the isotropic nature of the paramagneticphase. In the molecular field theory [1], the tempera-ture dependence of the inverse susceptibility of a three-sublattice ferrimagnetic material above T N is given by1 χ = 1 χ + TC − σ ( T ) T − T N , (2)with C the effective Curie constant, T N the N´eel temper-ature, and σ ( T ) = ( σ T + m ) / ( T + θ ); χ , σ , m , and θ areall constants. The slope of the high-temperature inversesusceptibility shown by the straight dash-dotted line in T comp H || the c axis H the c axis T N / c m ( m o l / e m u ) T (K)
FIG. 3: (Color online) Inverse molar susceptibility 1 /χ m ,measured in H = 100 Oe parallel (circles) and perpendicular(squares) to the c axis, is in agreement with a ferrimagnetictype of ordering. The dashed line is a calculation within themolecular field theory (see text). The dash-dotted line is aguide to the eye. Fig. 3 is solely given by the effective Curie constant C ,which is the sum of the Curie constants of the three mag-netic sublattices. The obtained value of 15.1 emu K/moleis only 1% less than what is expected for Mn ( S =2),Mn ( S =5/2), and Gd ( S =7/2) [15], giving furthersupport to the proposed magnetic structure.When one assumes that only Mn sublattices develop along-range magnetic order at T N , the exchange couplingconstant J can be estimated, to first approximation, fromthe following equation [16]: T N = q (2 + α + β ) C Mn C Mn C Mn + C Mn , (3)where C Mn and C Mn are the Curie constants forMn and Mn . Here, q = ( zJ ) / ( N a g µ B ) is themolecular field constant related to the Mn -Mn ex-change interaction, where z = 6 is the number of nearestMn neighbors of Mn (and vice-versa), N a is Avo-gadro number, and the coefficients α and β give thestrengths of the nearest-neighbor exchange interactionsin each sublattice of Mn and Mn , respectively. Notethat all constants in Eq. (2) are determined entirely bythese exchange interaction parameters and the Curie con-stants. The fitting curve shown by the dashed line inFig. 3 is calculated with J/k B = 30.5 K, α = − .
63, and β = − .
69, and it obviously reproduces the data verywell, supporting the assumption that Gd spins remainessentially paramagnetic across T N .With the obtained exchange interaction parameters,the molecular field theory [1, 16] can be applied to theanalysis of the temperature dependence of M in the or-dered state below T N . The temperature-induced mag-netization reversal observed at low magnetic fields canbe reproduced [as shown by the solid line in Fig. 4(a)]
50 100 150-0.4-0.3-0.2-0.10.00.1 T N T comp (a) M ( m B / f . u . ) T (K) 0 100 200 300 4000123456 T comp T N (b) M ( m B / f . u . ) T (K) Mn Mn Gd M ( m B / f . u . ) T (K)50 100 150-4-2024 Mn Mn Gd M ( m B / f . u . ) T (K)
FIG. 4: (Color online) Temperature dependence of the easy-axis magnetization in (a) H = 10 Oe and (b) H = 70 kOe.Solid lines are calculations within the molecular field theorywith the same parameters as for Fig. 3 (see text). Insetsshow the contributions of individual sublattices to the overallmagnetization. only if there is a weak FM (AF) coupling between Gd ions and the Mn (Mn ) sublattice. Furthermore, thevalue of the compensation temperature is very sensitiveto the strength of this interaction. For T comp = 95 K,the molecular field constant related to the Gd -Mn FM exchange is found to be about 0.01 q , i.e., two ordersof magnitude smaller than the AF exchange interactionbetween Mn and Mn . This value corresponds to aneffective magnetic field of approximately 35 kOe, whilefor the ferrimagnetic spin order in the Mn /Mn sub-lattices it is ∼ -Mn and Gd-Mn is crucial for theunderstanding of the observed magnetic behavior inGdBaMn O . . Just below T N , Mn spins, being an-tiferromagnetically coupled to the Mn sublattice, areopposite to the applied magnetic field, and at low fieldsGd spins tend to align in the same direction as the Mn sublattice [see inset of Fig. 4(a)], though their alignmentis weak; below T comp , the sum of the magnetic momentsof Gd and Mn overgrows the magnetic moment ofMn , giving rise to a negative magnetization. Intrigu-ingly, the situation changes completely in a high magneticfield which is strong enough to compete with the Gd-Mnexchange interaction: In this case, Gd spins tend to alignalong the external magnetic-field direction, causing a pos-itive magnetization at all temperature as shown in Fig.4(b), and the magnetization reversal is eliminated. It isnoteworthy that the Mn spins also behave differently andshows a novel turnabout; namely, just below T N their ori-entation is the same as in the low magnetic field case, butwith decreasing temperature this state becomes energet-ically unfavorable as the influence of Gd spins grows. Asa result, near the compensation point, an abrupt turn-about of the magnetization of the Mn sublattices takes place [see inset of Fig. 4(b)], which is manifested in thesharp change of the slope of M ( T ). Note that in thepresent case the strong Ising anisotropy probably plays akey role in the abrupt turnabout.To conclude, the present study shows that un-usual magnetic behavior of a new three-sublattice fer-rimagnetic manganite GdBaMn O . — a temperature-induced magnetization reversal at low magnetic fieldsand a novel turnabout of Mn sublattice magnetizationsat high magnetic fields — are governed by an elabo-rate interplay between its magnetic sublattices that areformed by the A -site ordering as well as the charge or-dering of Mn into Mn and Mn . In the present case,the weak coupling of Gd spins with magnetically or-dered Mn /Mn sublattices is the source of novel fer-rimagnetism not found elsewhere before. This result notonly enriches our knowledge about ferrimagnetics, butalso points to the potential of charge-order-susceptibletransition-metal oxides for discovering physically inter-esting and technologically useful properties.We thank I. Tsukada for helpful discussions. [1] L. N´eel, Ann. Phys. (Paris) , 137 (1948); Science ,985 (1971).[2] K. P. Belov, Phys. Usp. , 623 (1996); ibid. , 711(1999); ibid. , 407 (2000).[3] M. Pardavi-Horvath, JMMM , 171 (2000).[4] F. Millange, E. Suard, V. Caignaert, and B. RaveauMater. Res. Bull. , 1 (1999).[5] F. Millange, V. Caignaert, B. Domeng`es, B. Raveau, andE. Suard, Chem. Mater. , 1974 (1998).[6] S. V. Trukhanov, I. O. Troyanchuk, M. Hervieu, H. Szym-czak, and K. B¨arner, Phys. Rev. B , 184424 (2002).[7] D. Akahoshi, M. Uchida, Y. Tomioka, T. Arima, Y. Mat-sui, and Y. Tokura, Phys. Rev. Lett. , 177203 (2003).[8] Y. Kawasaki, T. Minami, Y. Kishimoto, T. Ohno, K.Zenmyo, H. Kubo, T. Nakajima, and Y. Ueda, Phys.Rev. Lett. , 037202 (2006).[9] A. A. Taskin, A. N. Lavrov, and Y. Ando, Appl. Phys.Lett. , 091910 (2005).[10] Y. Ren, T. T. M. Palstra, D. I. Khomskii, E. Pellegrin,A. A. Nugroho, A. A. Menovsky, and G. A. Sawatzky,Nature , 441 (1998).[11] J. Hemberger, S. Lobina, H.-A. Krug von Nidda, N. Tris-tan, V. Yu. Ivanov, A. A. Mukhin, A. M. Balbashov, andA. Loidl Phys. Rev. B , 024414 (2004).[12] R. Vidya, P. Ravindran, A. Kjekshus, and H. Fjellv˚ag,Phys. Rev. B , 144422 (2002).[13] R. Vidya, P. Ravindran, P. Vajeeston, A. Kjekshus, andH. Fjellv˚ag, Phys. Rev. B , 092405 (2004).[14] H. Weihe and H. U. G¨udel, Inorg. Chem , 3632 (1997).[15] The Curie constant C i of an individual sublattice is C i = N a ( gµ B ) S i ( S i + 1) / k B , where S i is the spin ofthe magnetic ion i .[16] See, for example, R. Kubo, H. Ichimura, T. Usui, N.Hashitsume, Statistical Mechanics: An Advanced Coursewith Problems and Solutions (North-Holland, Amster-(North-Holland, Amster-