The Origin and Coupling Mechanism of the Magnetoelectric Effect in TM Cl 2-4 SC ( NH 2 ) 2 ( TM = Ni and Co )

1 National High Magnetic Field Laboratory (NHMFL), MPA-CMMS Group, Los Alamos National Laboratory (LANL), Los Alamos, NM 87545, USA 2Department of Physics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 3Department of Chemistry and Biochemistry, Eastern Washington University, Cheney, WA 99004, USA 4Materials Synthesis & Integrated Devices, LANL, Los Alamos, NM 87545, USA 5Material Science and Technology Division, LANL, Los Alamos, NM 87545, USA


Introduction
In magnetoelectric multiferroics, magnetic and electric order coexist and are coupled to each other.For example, if a magnetic field can modify ferroelectricity or an electric field can modify magnetic order, new functionalities can be envisioned with applications to electric devices and sensors [1][2][3].A great effort has been dedicated to finding new classes of multiferroic materials and understanding magnetoelectric coupling mechanisms [4].Molecule-based magnets are a promising class of materials in which to couple magnetic and electric order.Here, magnetism can derive from magnetic metal ions and ferroelectricity from electrically polar organic molecule fragments [5][6][7].
NiCl 2 -4SC(NH 2 ) 2 , dichloro-tetrakis-thiourea-nickel (DTN) [8][9][10][11], has been extensively studied for its quantum magnetism.It possesses a field-induced quantum phase transition that has been analyzed in terms of Bose-Einstein condensation of the spin degrees of freedom [12].Recently it was also found to show magnetostriction consistent with exchange striction in the antiferromagnetic state [7].DTN is a molecule-based magnet in which NiCl 2 -4SC(NH 2  the c-axis components are added to create a net electric polarization along c, which could be responsible for the magnetic field-modified ferroelectricity in this material.The Ni 2+ S = 1 spins are gapped at zero field due to single ion anisotropy, with an   = 0 ground state and an   = ±1 excited state [9].Application of a magnetic field along the c-axis lowers the   = 1 state until it becomes degenerate with the   = 0 ground state.The two levels are degenerate between 2 and 12 T since the levels are broadened (dispersed) by antiferromagnetic coupling.At 2 T, where the ground state and   = 0 state first become degenerate, antiferromagnetic order results with the spins in the ab-plane, perpendicular to the applied field.Above 2 T the spins increasingly "cant" as the magnetic field is increased, until they saturate at 12 T.For magnetic fields in the ab-plane, the different   levels mix together, the spin gap never closes, and no magnetic ordering occurs for any field.For H ‖ c it has been observed that the electric polarization also shows a strong magnetic-field dependence between 2 and 12 T [7] similar to the magnetization.We have suggested [7] that the thiourea molecules could be responsible for the electric polarization, and their angles with respect to the crystalline axes are changed when magnetostriction acts on the Ni spins and distorts the shape of the unit cell.Thus, we proposed that an indirect magnetostrictive mechanism is responsible for magnetoelectric coupling in DTN.Here we present new results on CoCl 2 -4SC(NH 2 ) 2 (DTC), which shows magnetism but no electric polarization, confirming our assumption.

Results and Discussion
The literature shows that single crystals of DTN can be grown at room temperature from an aqueous solution [13], whereas single-phase samples of DTC require an ethanol solution [14][15][16].In this work, CoCl 2 and SC(NH 2 ) 2 were dissolved in warm ethanol in separate glass beakers.After slowly mixing the solutions, the solvent was evaporated for a two-week period, and sub-mm dark blue plate-like crystals with clear facets were obtained, with the c-axis perpendicular to the plate surface.X-ray diffraction measurements at room temperature found a tetragonal structure with 4 2 / and lattice parameters  = 13.4571Å,  = 9.0356 Å [14][15][16].The crystal structures of DTN and DTC are shown in Figure 1.
In DTC, the Co ions pack in a face-centered arrangement, in contrast to DTN which is body centered.Each Co is surrounded by four thiourea molecules in the ab-plane, and two Cl's along the c-axis.The Co-Cl axes are tilted 4 deg with respect to the c-axis, and the plane of the four Co-S bonds is tilted 8 deg from the ab-plane with the tilt angle alternating from one nearest-neighbor Co to the next along , , and  (see Figure 1).The temperature and magnetic-field dependence of the magnetization, (, ), of DTC was measured in a Quantum Design (QD) Physical Property Measurement System (PPMS) with a vibrating sample magnetometer (VSM) option up to  0  = 13T and down to  = 2K.In addition, () measurements were extended up to  0  = 60 T and down to  = 0.5 K in pulsed magnetic fields (10 ms rise and 40 ms decay time) with an extraction magnetometer [17] at the National High Magnetic Field Laboratory (NHMFL) in Los Alamos National Laboratory.Specific heat,   (), was measured by the relaxation technique down to  = 50 mK in a QD PPMS with a dilution refrigerator option.The electric polarization change, Δ(), as a function of magnetic field was measured in pulsed magnetic fields for both ΔP and H parallel and perpendicular to c-axis [6,7].Platinum contacts were sputtered onto the samples to measure the induced magnetoelectric currents.The induced magnetoelectric currents onto the electrode generated by the sample Δ are recorded by using a Stanford Research 570 current-to-voltage amplifier.
The inverse magnetic susceptibility, /, as a function of temperature is linear above 120 K and no anisotropy between the ab-plane and the c-axis is observed as shown in Figure 2. A fit to the Curie-Weiss law above 120 K results in a paramagnetic Curie temperature   ∼ −35 K and the effective moment  eff ∼ 5.5   , which is somewhat bigger than the expected free Co 2+ ion value with spin S = 3/2.The inset to Figure 2 shows the specific heat versus temperature at various magnetic fields.At zero field it shows a peak consistent with long-range magnetic ordering below   = 0.94 K, as shown in the inset of Figure 2, in agreement with the earlier results [14,15].We found that applying a magnetic field of ∼3 T is sufficient to suppress   below the lowest measured temperature of 50 mK.Thus DTC does not require a magnetic field to close a spin gap and induce magnetic order, in contrast to DTN.
The magnetization isotherms, (), for DTC were measured at  = 0.5 K up to 60 T (see Figure 3(a)).As the magnetic field increases, () rises rapidly until ∼2 T. The 0 ≤  ≤ 2 T region also corresponds to the suppression of long-range order in the specific heat.For  0  > 2 T, () curves for both ab-plane and c-axis increase monotonically, reaching the value of ≈3.2   /f.u. at  0  = 60 T. The effective moment and the saturated magnetization value are close to the expected Co 2+ S = 3/2 value, while no magnetic anisotropy can be resolved for DTC.The lack of anisotropy in an  = 3/2 ion implies that the three unpaired electrons in

Figure 2 :
Figure 2: Inverse magnetic susceptibility, /(), of CoCl 2 -4SC(NH 2 ) 2 as a function of temperature for magnetic fields H of 1 kOe applied ‖ ab and ‖ c.Solid lines represent a Curie-Weiss fit.Inset shows specific heat data at selected magnetic fields for H ‖ c.