%0 Book Section %1 statphys23_0263 %A Maleyev, S.V. %A Grigoriev, S.V. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K field helimagnets magnetic phase quantum spin statphys23 topic-8 transitions waves %T Cubic helimagnets with Dzyaloshinskii-Moriya interaction: spin-waves and magnetic field behavior %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=263 %X During decades cubic helimagnets (MnSi etc.) with Dzyaloshinskii-Moriya interaction (DMI) attracted a lot of attention due to their unusual magnetic properties and sets of phase transitions in magnetic field and applied pressure (1 and references therein). The DMI is responsible for the helical structure of these compounds. Violating the total spin conservation law it must play crucial role for the spin dynamics as well. In our work we use the well known Bak-Jensen model and consider the hierarchy of interactions:the ferromagnetic exchange, the DMI, the anisotropic exchange and the cubic anisotropy accompanied by the Zeeman energy. Below we list our principal theoretical results and their experimental confirmation 2. 1) The classical energy depends on the field component along the helix wave-vector $k$. Critical field for transition to ferromagnetic state is given by: $H_C2=A k^2$, where $A$ is the spin-wave stiffness for $qk$ in agreement with experiment. 2) The DMI leads to umklapp interaction connecting spin-waves with momentums $q$ and $qk$ and gives rise to the spin-wave anisotropy: excitations with $qk$ and $qk$ have energies $A k q$ and $3A q^2/8$ respectively. 3) The field perpendicular to $k$ gives quantum contribution to the ground-state energy mixing spin-waves with $q=0$ and $ \pmk$. Their amplitudes become classical variables (Bose condensation) and the ground-state energy is given by $$E_G=-H_\parallel^2/(2H_C2)-(H^2_\perp\Delta^2)/4H_C2(\Delta^2-H^2_\perp/2)+$$ $$L(k/k),$$ where $\Delta$ is the spin-wave gap and $L$ is a cubic invariant responsible for $k$ orientation with respect to the cubic axes. If $H_\perp>\Delta\sqrt2$ the system is unstable and $k$ rotates toward the field in agreement with neutron scattering data in MnSi which demonstrated also that $\Delta0.1TH_C2/6$. 4)There are two contributions to $\Delta^2$: spin-wave interaction and cubic anisotropy. At $H=0$ the former survives only but with the field increases two contributions compete. For MnSi at $H1,1,1$ we have $\Delta^2<0$ at $H>H_C10.5 H_C2$ and spin-wave spectrum becomes unstable. In this case a partly disordered chiral state appears instead of the long-range helical structure. The system becomes ferromagnetic at $H>H_C2$. In summary, we present microscopic low-$T$ theory of non-center-symmetric cubic helimagnets which is confirmed by the experiment.\\ 1) C. Pfleiderer et al., Nature(London) 427, 227 (2004); D. Belitz, T.R. Kirkpatrick, Phys. Rev. B 73, 054431 (2006).\\ 2) S. Grigoriev, S. Maleyev et al., Phys. Rev. B 72, 134420 (2005); S. Maleyev, Phys. Rev. B 73, 174402 (2006); S. Grigoriev, S. Maleyev et al., Phys. Rev. B 74, 214414 (2006); S. Maleyev, S. Grigoriev, to be published.

@incollection{statphys23_0263, abstract = {During decades cubic helimagnets (MnSi etc.) with Dzyaloshinskii-Moriya interaction (DMI) attracted a lot of attention due to their unusual magnetic properties and sets of phase transitions in magnetic field and applied pressure ([1] and references therein). The DMI is responsible for the helical structure of these compounds. Violating the total spin conservation law it must play crucial role for the spin dynamics as well. In our work we use the well known Bak-Jensen model and consider the hierarchy of interactions:the ferromagnetic exchange, the DMI, the anisotropic exchange and the cubic anisotropy accompanied by the Zeeman energy. Below we list our principal theoretical results and their experimental confirmation [2]. 1) The classical energy depends on the field component along the helix wave-vector $\mathbf k$. Critical field for transition to ferromagnetic state is given by: $H_{C2}=A k^2$, where $A$ is the spin-wave stiffness for $q\gg k$ in agreement with experiment. 2) The DMI leads to umklapp interaction connecting spin-waves with momentums $\mathbf q$ and $\mathbf{q\pm k}$ and gives rise to the spin-wave anisotropy: excitations with $\mathbf{q\parallel k}$ and $\mathbf{q\perp k}$ have energies $A k q$ and $3A q^2/8$ respectively. 3) The field perpendicular to $\mathbf k$ gives quantum contribution to the ground-state energy mixing spin-waves with $\mathbf q=0$ and $ \pm\mathbf k$. Their amplitudes become classical variables (Bose condensation) and the ground-state energy is given by $$E_G=-H_\parallel^2/(2H_{C2})-(H^2_\perp\Delta^2)/[4H_{C2}(\Delta^2-H^2_\perp/2)]+$$ $$L(\mathbf k/k),$$ where $\Delta$ is the spin-wave gap and $L$ is a cubic invariant responsible for $\mathbf k$ orientation with respect to the cubic axes. If $H_\perp>\Delta\sqrt2$ the system is unstable and $\mathbf k$ rotates toward the field in agreement with neutron scattering data in MnSi which demonstrated also that $\Delta\approx 0.1T\approx H_{C2}/6$. 4)There are two contributions to $\Delta^2$: spin-wave interaction and cubic anisotropy. At $\mathbf H=0$ the former survives only but with the field increases two contributions compete. For MnSi at $\mathbf H\parallel [1,1,1]$ we have $\Delta^2<0$ at $H>H_{C1}\approx 0.5 H_{C2}$ and spin-wave spectrum becomes unstable. In this case a partly disordered chiral state appears instead of the long-range helical structure. The system becomes ferromagnetic at $H>H_{C2}$. In summary, we present microscopic low-$T$ theory of non-center-symmetric cubic helimagnets which is confirmed by the experiment.\\ 1) C. Pfleiderer et al., Nature(London) {\bf 427}, 227 (2004); D. Belitz, T.R. Kirkpatrick, Phys. Rev. B {\bf 73}, 054431 (2006).\\ 2) S. Grigoriev, S. Maleyev et al., Phys. Rev. B {\bf 72}, 134420 (2005); S. Maleyev, Phys. Rev. B {\bf 73}, 174402 (2006); S. Grigoriev, S. Maleyev et al., Phys. Rev. B {\bf 74}, 214414 (2006); S. Maleyev, S. Grigoriev, to be published.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Maleyev, S.V. and Grigoriev, S.V.}, biburl = {https://www.bibsonomy.org/bibtex/254c871b17ba9a04c638609c4d4bdd230/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {e6d6e14fc5377862fd44855830f0768a}, intrahash = {54c871b17ba9a04c638609c4d4bdd230}, keywords = {field helimagnets magnetic phase quantum spin statphys23 topic-8 transitions waves}, month = {9-13 July}, timestamp = {2007-06-20T10:16:15.000+0200}, title = {Cubic helimagnets with Dzyaloshinskii-Moriya interaction: spin-waves and magnetic field behavior}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=263}, year = 2007 }