A New Puzzle about the Magnetization Plateau in NH₄CuCl₃

In some quantum spin systems, the magnetization becomes quantized to a fractional value of the saturation for a finite range of magnetic field. Such magnetization plateaus indicate Mott localization of bosons carrying the magnetization. When the boson density per unit cell is not an integer, a spin superstructure breaking the translational symmetry is generally expected. However, this has been observed so far only in SrCu₂(BO₃)₂, a frustrated 2D dimer spin system [1]. Another candidate is NH₄CuCl₃, a 3D-coupled dimer spin system, which exhibits magnetization plateaus at 1/4 and 3/4 but not at 1/2 of the full saturation [2]. Since all Cu sites are equivalent in the monoclinic crystal structure (P2₁/c, Fig. 1), the plateaus should be associated with symmetry breaking. However, no evidence has been found for magnetic phase transitions in the field range of the plateaus.




Fig. 1. Crystal structure of NH₄CuCl₃ at room temperature (space group P2₁/c) viewed along the a-axis. Zigzag spin chains run along the a-axis. Locations of the inversion center, the b-screw axes, and the c-glide planes are shown.


To explain this puzzle, Matsumoto proposed that three types of inequivalent Cu dimers are formed due to yet unobserved structural transition [3] and they saturate successively with increasing field. The plateaus appear when every dimer is either in singlet state or completely saturated. Although several experiments support this model, microscopic origin of the plateaus is still unknown.


We have performed ¹⁴N nuclear magnetic resonance (NMR) experiments at the field of 7 tesla where the 1/4-plateau appears at low temperatures [4]. Since ¹⁴N nuclei have magnetic diplole and electric quadrupole moments, ¹⁴N NMR is an excellent probe for both the crystal structure and the spin density distribution. From NMR spectra we obtain the quadrupole coupling ƒË_ƒ¿, which is proportional to the electric field gradient along the field direction ƒ¿, and the magnetic hyperfine shift K_ƒ¿ from Cu magnetization.


First we observed a small splitting of ƒË_b below 160 K, indicating a structural transition marginally breaking the b-screw and the c-glide symmetries but preserving the inversion. Another much more prominent line splitting occurs below T_c = 70 K. Figure 2 shows the four-fold splitting of K_c^* and ƒË_c^*. While ƒË_c^* changes rapidly near T_c, substantial variation of K_c^* occurs only at low temperatures. This clearly indicates that what happens at T_c is a structural phase transition, not a magnetic one, most likely associated with orientational order of the NH₄ ions. This would modify the exchange scheme, yielding inequivalent Cu sites with distinct magnetic character. Thus our results support the model by Matsumoto that plateau appears without further symmetry breaking. Figure 2 also indicates a peculiar feature of double transition, which is not understood yet.




Fig. 2. Temperature dependence of (a) K_c^* and (b) ƒË_c^* for the four inequivalent N sites in the low temperature phase at 7 T.


For general field directions both K_c^* and ƒË_c^* show eight-fold splitting. Their angular dependences are approximately symmetric about the ac-plane within two degrees, indicating that c-glide symmetry is still only marginally broken. Meanwhile, Ruegg et al. observed doubling of the unit cell along the b-axis by neutron diffraction [5]. A unit cell of the low temperature phase then contains eight Cu sites, which is the same as the number of NMR lines for the general field directions. Thus, the space group should be P1 and the inversion symmetry must be completely broken.


We now have ample evidence that in the 1/4-plateau 1/4 of Cu spins form fully polarized triplets while the rest remain in singlet. The question then is where the triplets are. All previous studies assume the triplets on the nearest neighbor pairs as shown in Fig. 3(a). This configuration, however, preserves the inversion but completely destroy the c-glide symmetry inconsistent with NMR results. To satisfy the approximate c-glide symmetry, the triplets must be formed over different chains as shown in Fig. 3 (b) and (c). Such configuration would require extremely peculiar exchange coupling scheme. Our NMR results have posed a new puzzle about the spin superstructure in NH₄CuCl₃.




Fig. 2. Possible spin structure for the 1/4-plateau state. The small filled (open) circles indicate the triplet (singlet) Cu sites. Large circles show the N sites. The dashed lines in (b) and (c) indicate the approximate c-glide planes preserved in each spin configurations.





References
[1] K. Kodama et al., Science 298, 395 (2002).
[2] W. Shiramura et al. J. Phys. Soc. Jpn. 67, 1548 (1998).
[3] M. Matsumoto, Phys. Rev. B 68, 180403 (2003).
[4] K. Kodama et al., Prog. Theor. Phys. Suppl. 159, 228 (2005).
[5] Ch. Ruegg et al., Phys. Rev. Lett. 93, 037207 (2004).