# Low Dimensional Magnetism

## Project details

In quantum spin systems the classical ferro- or antiferro-magnetic ground states are suppressed by strong quantum fluctuations, which become increasingly relevant towards zero temperature. The study of such systems is at the forefront of condensed matter physics. The reason, besides of the significant role of magnetism in materials properties itself, is that magnetism probed by powerful experimental techniques (in particular neutron scattering) became an ideal testing ground for general concepts of many body physics.

Such approach was very fruitful for the understanding of classical phase transitions and their universality classes some decades ago. Current efforts aim to unravel seemingly universal features of quantum phase transitions. Novel collective quantum phenomena were recently observed in magnetic isolators ACuCl

Such approach was very fruitful for the understanding of classical phase transitions and their universality classes some decades ago. Current efforts aim to unravel seemingly universal features of quantum phase transitions. Novel collective quantum phenomena were recently observed in magnetic isolators ACuCl

_{3}, which are based on a crystalline network of dimers formed by two antiferromagnetically coupled Cu^{2+}ions. The dimer ground state is a singlet with total spin S=0, separated by an energy gap from the excited triplet state with total spin S=1. Inelastic neutron scattering experiments performed in TlCuCl_{3}verified that the quantum phase transition could be induced by applied magnetic field [1] and hydrostatic pressure [2] and that this transition is characterized by Bose-Einstein condensation of the bosonic triplet excitations into the ground state. The crystal lattice is often involved in the quantum phase transitions due to the electron-phonon coupling. It was found that in the dimer NH_{4}CuCl_{3}system [3], a spin gap develops by spontaneously breaking the translational symmetry and the lattice becomes effectively dimerized with segregation of the dimers into three subsystems.
New unconventional magnetic properties are expected also for systems composed of more complex magnetic clusters than dimers: trimers, tetramers, etc. Low connectivity of such networks and geometrical frustration of the magnetic coupling within clusters result in weakly interacting coupled quantum systems, a midway between the classical and quantum cases. In the S=1/2 coupled tetrahedra system Cu

_{2}Te_{2}O_{5}X_{2}(X=Cl, Br) an incommensurate anti-ferromagnetic order with the very complex multi-helices spin arrangement [4] and the two mode excitation spectrum has been observed in neutron scattering study. These observations are not consistent with a picture of weakly coupled tetrahedra or with a classical ordered magnetic structure. The reason of such a complex ground state and spin dynamic probably lies in geometrical frustration of the spins due to the intra and inter tetrahedral couplings having similar strengths and strong Dzyaloshinski-Moriya interaction.
The excitation spectrum of a model magnetic system, LiHoF

Since it was established that the 2D quantum (S=1/2) Heisenberg antiferromagnet on a square lattice develop long range order at T=0, albeit with only 60% of the classical moment, it was believed that the excitations of this model should be classical spin waves only weakly renormalized by quantum fluctuations. Through neutron scattering investigations of CFTD [6], an excellent physical realisation of the model system, we have recently discovered i) a moderate deviation from the spin wave prediction for the zone boundary energies and ii) a huge, 50%, deviation in intensity at Q=(pi,0). We interpret this as signature of valence bond type correlations in the quantum fluctuating part of the ground state. Although the valence bond state lacks long range order, which must be introduced through a variational approach, our results suggest that it may actually be a better starting point for approaches to understand spin fluctuations upon hole-doping as in the high temperature superconducting cuprates. Having identified candidate materials with lower energy scale and thereby achievable saturation fields, we plan to pursue theoretical predictions of stronger RVB effects just below the saturation field.

_{4}, has been studied using neutron spectroscopy as the system is tuned to its quantum critical point by an applied magnetic field [5]. The electronic mode softening expected for a quantum phase transition is forestalled by hyperfine coupling to the nuclear spins. We have shown that interactions with the nuclear spin bath control the length scale over which the excitations can be entangled. This generic result limits how far it is possible to approach intrinsic electronic quantum criticality. Further measurements are planned to probe the low-energy composit nuclear-electronic fluctuations around the quantum critical point.Since it was established that the 2D quantum (S=1/2) Heisenberg antiferromagnet on a square lattice develop long range order at T=0, albeit with only 60% of the classical moment, it was believed that the excitations of this model should be classical spin waves only weakly renormalized by quantum fluctuations. Through neutron scattering investigations of CFTD [6], an excellent physical realisation of the model system, we have recently discovered i) a moderate deviation from the spin wave prediction for the zone boundary energies and ii) a huge, 50%, deviation in intensity at Q=(pi,0). We interpret this as signature of valence bond type correlations in the quantum fluctuating part of the ground state. Although the valence bond state lacks long range order, which must be introduced through a variational approach, our results suggest that it may actually be a better starting point for approaches to understand spin fluctuations upon hole-doping as in the high temperature superconducting cuprates. Having identified candidate materials with lower energy scale and thereby achievable saturation fields, we plan to pursue theoretical predictions of stronger RVB effects just below the saturation field.

**Publications**- 1. Ch. Rueegg et al, Nature 423, 62(2003)
- 2. Ch. Rueegg et al, Phys. Rev. Lett. 93, 257201(2004)
- 3. Ch. Ruegg et al., Phys. Rev. Lett. 93, 37207 (2004)
- 4. O. Zaharko et al., Phys. Rev. Lett. 93, 217206 (2004); O. Zaharko et al., Phys. Rev. B 73, 064422 (2006)
- 5. H. M. Ronnow et al., Science 308, 389 (2005)
- 6. N. B. Christensen, H. M. Ronnow et al., submitted