apparent diamagnetism in quasi-two-dimensional heisenberg antiferromagnets

Current Applied Physics 9 (2009) 1330–1333

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Current Applied Physics

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Apparent diamagnetism in quasi-two-dimensional Heisenberg antiferromagnets

Kyu Won Lee, Cheol Eui Lee *

Department of Physics, Korea University, Seoul 136-701, Republic of Korea

a r t i c l e i n f o

Article history:Received 9 October 2008Received in revised form 24 October 2008Accepted 13 November 2008Available online 28 February 2009

PACS:75.10.Hk75.30.Kz75.40.Mg

Keywords:Apparent diamagnetismQuasi-two-dimensional Heisenberg cantedantiferromagnetsThermal quenching

1567-1739/$ - see front matter � 2009 Elsevier B.V. Adoi:10.1016/j.cap.2008.11.009

* Corresponding author. Tel.: +82 2 3290 3098; faxE-mail address: rscel@korea.ac.kr (C.E. Lee).

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We observed an apparent diamagnetism in representative quasi-two-dimensional Heisenberg cantedantiferromagnets, (CnH2n+1NH3)2MnCl4, indicating that the quasi-one-dimensionality is not essentialfor the apparent diamagnetism. The apparent diamagnetic response seems to be promoted by a thermalquenching and is characterized by a linear response to the applied magnetic field with a constant internalfield.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction elements) [4–8]. The RVO systems with V3+ magnetic ions under-

Apparent diamagnetism, which exhibits a negative magnetiza-tion against the applied magnetic field but originates from electronspins in contrast to the conventional diamagnetism originatingfrom circuit currents, has been found in various cases. A represen-tative case is a ferrimagnetic system, where a negative magnetiza-tion against applied magnetic field was attributed to acompensation effect of two-sublattice magnetization [1]. Anothertype of apparent diamagnetism was observed in inhomogeneousferromagnetic systems, and attributed to a discrepancy betweenthe bulk and surface critical temperatures [2]. A novel type of neg-ative magnetization, distinct from the above cases, was reported inan electrochemically deposited chromium cyanide thin film [3]. Inthat case, the magnetization of the film, cooled in a small negativefield, remained negative even after the application of a sizable po-sitive field, which was attributed to the presence of the rotationalbarrier of magnetization. Except for the case of the ferrimagneticsystems, the apparent diamagnetism or the negative magnetiza-tion reported thus far include impurities or defects as a physicalorigin [2,3].

Recently, another type of apparent diamagnetism was reportedin a canted antiferromagnetic phase of RVO3 (R = rare earth

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go several magnetic and orbital ordering (Jahn–Teller ordering)transitions, where the orbital long range orders are strongly cou-pled to the magnetic orders [9,10]. Upon weak-field cooling, poly-crystalline LaVO3 exhibits a magnetization opposite to the appliedmagnetic field [4]. It has been suggested that the diamagnetic re-sponse is due to a reversal of a canted-spin moment on coolingthrough the first-order Jahn–Teller phase transition slightly belowthe Neel temperature and that the enhanced angular momentumon cooling through the transition temperature can reverse the Dzy-aloshinsky–Moriya (DM) vector or V3+-ion atomic momentthrough a spin–orbit coupling [5]. While polycrystalline LaVO3

shows apparent diamagnetism upon weak-field cooling or quench-ing, polycrystalline CeVO3 shows it upon zero-field cooling orquenching [6]. Furthermore, polycrystalline YVO3 and RuVO3 donot show apparent diamagnetism, which has been attributed tothe chemical pressure effect [6]. On the other hand, a YVO3 singlecrystal clearly showed temperature-induced magnetization rever-sals whether the crystal was field-cooled or zero-field-cooled,and the apparent diamagnetism was not accompanied by anystructural change [7,8]. The competition of the single-ion magneticanisotropy and the DM antisymmetric exchange interaction wassuggested to be the origin. The reason why the anisotropy-inducedspin canting opposes the spin canting arising from the DM interac-tion was proposed to be the opposite signs of spin–orbit couplingparameters to which the single-ion anisotropy and the DM interac-tion are proportional [11].

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The competition of the single-ion anisotropy and the DMinteraction as an origin of the apparent diamagnetic responsewas questioned because the single-ion anisotropy determines onlyan easy-axis but not an easy-direction, and a ferrimagnetic modelwas suggested by Kimishima et al. [12]. In practice, neutron dif-fraction studies reveal that the magnitudes of DM interactionand the single-ion anisotropy are largely different from those ex-pected in the model based on the competing single-ion anisotropyand DM interaction and also no ferrimagnetic moment exists [13].Recently, Tung et al. argued that the apparent diamagnetism ob-served in RVO3 can be attributed to inhomogeneities caused by asmall amount of defects in the orbital sector in the quasi-one-dimensional orbital system [14]. Their argument was based on aPaduan-Filho et al.’s work on the quasi-one-dimensional antiferro-magnet with nonmagnetic impurities, where an apparent diamag-netism was also observed [15]. Paduan-Filho et al. attributed themagnetization reversal to a discrepancy between the bulk and sur-face critical temperatures, though the origin of distinct criticaltemperature is not clear. Paduan-Filho et al.’s argument is similarwith that for the apparent diamagnetism observed in inhomoge-neous ferromagnetic system, where the thin surface layer containsmore magnetic moments than those in the bulk [2]. In Paduan-Fil-ho et al. ’s argument, the quasi-one-dimensionality and nonmag-netic impurities give rise to a net ferromagnetic moment but notto the apparent diamagnetic response. The origin of apparent dia-magnetism seems to be unclear up to now and seems to return tothe mechanism based on a very small amount of defect orimpurity.

In this work, we will report an observation of apparent diamag-netism in the well known quasi-two-dimensional Heisenbergcanted antiferromagnets, (CnH2n+1NH3)2MnCl4 (CnMn), indicatingthat the quasi-one-dimensionality is not essential for the apparentdiamagnetism. The CnMn compounds have been regarded as rep-resentative quasi-two-dimensional Heisenebrg canted antiferro-magnets [16–22], consisting of alternating magnetic andnonmagnetic layers. The nonmagnetic layers are constituted of or-ganic chains, whose length can be easily controlled. Thus, the inter-layer separation and the interlayer magnetic interaction betweenthe magnetic layers can be systematically controlled. Accordingto the studies for short-chain compounds, the magnetic momentsin the antiferromagnetic phase are aligned along the layer-normaldirection with neighboring spins in the same layer pointing inopposite directions [18,19]. Structurally, the MnCl6 octahedra areslightly tilted from the inorganic layer as a consequence of thehydrogen bonding. Because the tilt angle is staggered the single-ion anisotropy axis is also staggered, which may lead to a spincanting in the layer-parallel direction [19,23]. The CnMn systemswith Mn2+ 3d magnetic ions with spin S = 5/2 undergo a cantedantiferromagnetic transition around 40 K [22]. The intralayer ex-change energy is J � 6–7 K and the interlayer one is �10�5 J [22].The single-ion anisotropy and the DM interaction energies have asimilar order of magnitude of 10�3 J [16,22,20] and the comparablestrengths may give rise to a competition between them. Due to thevery small values of the single ion anisotropy and the DM interac-tion, the spin–orbit coupling would be fairly small, and the crystalfield effect will also be very small for the Mn2+ ions and no Jahn–Teller distortion takes place in CnMn [23]. Except for the staggeredsingle-ion anisotropy which may compete with the DM interaction,the magnetic environments in CnMn with Mn2+ magnetic ions arevery different from those in RVO3 with V3+ magnetic ions.

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Fig. 1. Molar susceptibility measured at 0.3 T following zero-field cooling, whichshows broad maxima around 73 K attributable to the antiferromagnetic short rangeorder and a sharp peak around 40 K due to a weak ferromagnetism (cantedantiferromagnetism).

2. Experiment

Powder samples of CnMn were synthesized following the stan-dard method [22], and the magnetic susceptibilities were mea-

sured employing a superconducting quantum interference device(SQUID) magnetometer. Concentration of some nonmagneticimpurities such as Zn and Cd were estimated to be lower than50 ppm. The samples were cooled either rapidly (quenching)(�5 K/s) or slowly (cooling) (�0.02 K/s) from room temperatureto 5 K with no applied magnetic field, followed by susceptibilitymeasurements, in various magnetic fields as warming the samples.The trapped field in the SQUID magnetometer was estimated andcorrected within ±0.1 mT using a palladium standard sample.

3. Results and discussion

Fig. 1 shows the molar magnetic susceptibility of C12Mn mea-sured at 0.3 T after zero-field cooling, which clearly shows a cantedantiferromagnetic (weak ferromagnetic) behavior. The antiferro-magnetic ordering temperature of C12Mn is TN = 43 ± 1 K and theintralayer exchange energy is about 6 K [22]. The humps around160 and 230 K seem to be due to structural changes [24]. All themeasurements described in this work were carried out for C12Mn.

The magnetic susceptibilities, with a measuring field of 2 mT,for zero-field quenching (j) and for zero-field cooling (h), areshown in Fig. 2, where the susceptibility shows apparent diamag-netic responses in the zero-field quenched case. On the other hand,in the zero-field cooling and in the field-cooling (�) cases, a well-known canted antiferromagnetic behavior is shown to be recov-ered. But the zero-field cooling and field-cooling measurement stillgives a quite distinct magnetization, which can be usually observedin spin glasses, superparamagnets as well as in systems with largemagnetic anisotropy. An apparent diamagnetic response was alsoobserved even with a measuring field of 10 mT (> ), followingthe zero-field quenching. The magnitude of the negative magneti-zation was very sensitive to the quenching rate, which may not becontrolled accurately. The temperature from which quenching orslow cooling starts also affected the resultant magnetization.

A very small trapped field smaller than 0.1 mT in the SQUID

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Fig. 2. Molar susceptibilities measured at 2 mT following zero-field quenching (j)and zero-field cooling (h), at 10 mT following zero-field quenching (> ), and at 2 mTafter field-cooling in the same field (�). Apparent diamagnetism is manifest in thezero-field quenched cases.

1332 K.W. Lee, C.E. Lee / Current Applied Physics 9 (2009) 1330–1333

remanent field in the magnetometer. The negative magnetizationis reversed to the direction of measuring field slightly below TN.The magnetization reversal temperature To seems to hardly dependon the measuring field.

In view of the competing interaction model for apparent dia-magnetism [8], the magnetization reversal temperature To can bederived by using a mean-field approximation, TN � To = (2A/D)c,where A, D, and c are the single-ion anisotropy energy, DM interac-tion energy, and the canting angle due to the single-ion anisotropy,respectively. In the case of YVO3, the single-ion anisotropy energyis about two orders of magnitude larger than the DM interactionenergy, resulting in To far below TN [8]. In the case of CnMn, the sin-gle-ion anisotropy energy is similar to the DM interaction energyin magnitude, which would give a To quite close to TN, indeed as ob-served in Fig. 2.

The magnetic field dependence of magnetization following azero-field quenching to 5 K is shown in Fig. 3. The magnetization

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Fig. 3. The magnetization as a function of field (hysteresis) after zero-fieldquenching to 5 K. The right-down inset is the rescaled graph between the magneticfields of �0.1 T and 0.1 T. The left-up inset is the result obtained in the low fieldregion, in which the magnetic field was applied in the sequence 0 T ?�10 mT ? +15 mT ? 0 T. No hysteresis is observed and the field dependenceshows a paramagnetic response in this low-field region.

is at a glance linear to the field up to 2 T and the slope change atabout 2.5 T can be attributed to the spin-flop transition[16,18,20]. The right-down inset is a magnification of the samedata between the magnetic fields of �0.1 T and 0.1 T, showing aweak ferromagnetic hysteresis. On the other hand, the left-up insetshows a measurement in the low field region between �10 mT and15 mT. While no magnetic hysteresis was observed and a paramag-netic response is evident, there appears to exist an internal mag-netic field of about �7 mT. The magnitude of the apparentinternal field was also dependent on the quenching rate and mayexceed 10 mT. In ferromagnets, internal fields arise from magneticordering and give nonlinear magnetic responses and magnetic hys-teresis. In C12Mn, the apparent internal field behaves like a con-stant external field in the direction opposite to the applied field,giving rise to the apparent diamagnetic response in small appliedfields.

Fig. 4 shows a series of successive measurements of the magne-tization. Firstly, the sample was zero-field quenched from 300 K to5 K, and the magnetization was measured (1) as increasing thetemperature up to 55 K in 2 mT (j) and (2) as decreasing temper-ature down to 5 K in the same field (field cooling) (+). Then, at 5 K,the magnetic field was reversed to �2 mT, and the magnetizationwas measured (3) with increasing temperature up to 55 K in thesame field (h) and (4) with decreasing temperature in the samefield (�). Steps 1 and 2 reproduce the results in Fig. 2. After field-cooling to 5 K (step 2), the magnetization was positive, corre-sponding to a positive magnetic field, and interestingly enough,the positive magnetization was not changed by a sudden reversalof magnetic field to �2 mT. Step 3 shows that the positive magne-tization, corresponding to a diamagnetic response, in the negativemagnetic field is maintained up to the magnetization reversal tem-perature To. Step 4 with decreasing temperature from above TN in�2 mT shows that a weak ferromagnetism is recovered. As shownin the left-up inset of Fig. 3 the applied field lower than the con-stant internal field cannot reverse the magnetization.

Similar results were repeatedly reproduced with a large enoughquenching rate, confirming that the phenomena are intrinsic to thesystems and thermal quenching promotes the apparent diamag-netic response. The apparent diamagnetic response was also foundin other CnMn systems with different hydrocarbon lengths, such as

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Fig. 4. Successive measurements of the magnetization. After zero-field quenchingto 5 K, magnetization was measured (1) as increasing the temperature up to 55 K in2 mT (j) and (2) as decreasing the temperature down to 5 K in the same field (+). At5 K, the magnetic field was reversed to �2 mT. And then, the magnetization wasmeasured (3) as increasing the temperature up to 55 K in the same field (h) and (4)as decreasing the temperature in the same field (�).

K.W. Lee, C.E. Lee / Current Applied Physics 9 (2009) 1330–1333 1333

C4Mn and C8Mn. Thus, the apparent diamagnetic response takesplace regardless of the hydrocarbon chain length, which governsthe separation between the inorganic MnCl6 layers. A very smallamount of impurity or defect may give rise to a rotational barrierof magnetization, which may be intensified by the low-dimension-ality and may be responsible for the apparent diamagnetism inCnMn.

In summary, we have observed an apparent diamagneticresponse in thermally quenched quasi-two-dimensional cantedantiferromagnets, (CnH2n+1NH3)2MnCl4. While the magnetic envi-ronments are different between the CnMn and RVO3 systems,apparent diamagnetic response is observed in the canted antiferro-magnetic (weak ferromagnetic) state in both systems.

Acknowledgement

This work was supported by the Korea Ministry of Education,Science and Technology (NRL Program R0A-2008-000-20066-0,User Program of Proton Engineering Frontier Project, KRF-2006-005-J03601). The measurements at the Korean Basic Science Insti-tute (KBSI) are acknowledged.

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