About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films
The effect of impurity ions on nuclear magnetic relaxation has been considered. It is supposed that an impurity ion introduces an excess electron (or a hole). As a result, magnetic ions with strong spin-orbital interaction appear and magnetization direction distribution becomes inhomogeneous. Therma...
Gespeichert in:
Datum: | 2006 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | English |
Veröffentlicht: |
НТК «Інститут монокристалів» НАН України
2006
|
Schriftenreihe: | Functional Materials |
Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/144373 |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
Zitieren: | About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films / S.N. Polulyakh, N.A. Sergeev // Functional Materials. — 2006. — Т. 13, № 2. — С. 301-304. — Бібліогр.: 7 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraineid |
irk-123456789-144373 |
---|---|
record_format |
dspace |
spelling |
irk-123456789-1443732018-12-21T01:23:20Z About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films Polulyakh, S.N. Sergeev, N.A. The effect of impurity ions on nuclear magnetic relaxation has been considered. It is supposed that an impurity ion introduces an excess electron (or a hole). As a result, magnetic ions with strong spin-orbital interaction appear and magnetization direction distribution becomes inhomogeneous. Thermally activated jumps of the excess electron from one magnetic ion to another generate fluctuations in the magnetization direction. The interaction between the fluctuating magnetization and magnetic nuclei results in the appearance of regions of fast nuclear magnetic relaxation. Spin diffusion contributes to the longitudinal relaxation rate also for nuclei being outside the impurity regions. Taking into account the spin diffusion dependence on nuclear interactions, we have derive the dependence of longitudinal relaxation rate on nuclear interactions, what was observed experimentally in [1]. An assumption about unintentional technological impurities is sufficient to explain the experimental data. Рассматривается влияние примесных ионов на процессы ядерной магнитной релаксации. Предполагается, что примесный ион привносит избыточный электрон (или дырку). В результате появляются магнитные ионы с сильной спин-орбитальной связью и распределение направлений электронной намагниченности становится неоднородным. Термически активированные скачки избыточного электрона с одного магнитного иона на другой порождают флуктуации в направлении намагниченности. Взаимодействие между флуктуирующей намагниченностью и магнитными ядрами приводит к появлению областей с быстрой ядерной магнитной релаксацией. Благодаря спиновой диффузии возрастает скорость продольной релаксации и для ядер, находящихся вне примесных областей. Принимая во внимание зависимость интенсивности спиновой диффузии от ядерно-ядерных взаимодействий, получена зависимость скорости продольной релаксации от межядерных взаимодействий, что наблюдалось экспериментально в работе [1]. Предположение о наличии неконтролируемых технологических примесей является достаточным для объяснения экспериментальных результатов. Розглядається вплив домішок на процеси ядерної магнітної релаксації. Робиться припущення, що іон домішки надає надлишковий електрон (або дірку). Внаслідок цього з’являються магнітні іони із сильним спін-орбітальним зв’язком і розподіл напрямку електронної намагніченості стає неоднорідним. Термічно активовані стрибки надлишкового електрона з одного магнітного іона на іншій породжують флуктуації у напрямку намагніченості. Взаємодія між флуктуаціями намагніченості та магнітними ядрами призводить до появи регіонів зі швидкою ядерною магнітною релаксацією. Завдяки спіновій дифузії зростає швидкість подовжньої релаксації і для ядер, що знаходяться поза регіонами домішок. Приймаючи до уваги залежність інтенсивності спінової дифузії від ядерно-ядерних взаємодій, отримано залежність швидкості поздовжньої релаксації від взаємодій між ядрами, що спостерігалося експериментально у роботі [1]. Припущення про наявність неконтрольованих технологічних домішок є достатнім для пояснення експериментальних результатів. 2006 Article About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films / S.N. Polulyakh, N.A. Sergeev // Functional Materials. — 2006. — Т. 13, № 2. — С. 301-304. — Бібліогр.: 7 назв. — англ. 1027-5495 http://dspace.nbuv.gov.ua/handle/123456789/144373 en Functional Materials НТК «Інститут монокристалів» НАН України |
institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
collection |
DSpace DC |
language |
English |
description |
The effect of impurity ions on nuclear magnetic relaxation has been considered. It is supposed that an impurity ion introduces an excess electron (or a hole). As a result, magnetic ions with strong spin-orbital interaction appear and magnetization direction distribution becomes inhomogeneous. Thermally activated jumps of the excess electron from one magnetic ion to another generate fluctuations in the magnetization direction. The interaction between the fluctuating magnetization and magnetic nuclei results in the appearance of regions of fast nuclear magnetic relaxation. Spin diffusion contributes to the longitudinal relaxation rate also for nuclei being outside the impurity regions. Taking into account the spin diffusion dependence on nuclear interactions, we have derive the dependence of longitudinal relaxation rate on nuclear interactions, what was observed experimentally in [1]. An assumption about unintentional technological impurities is sufficient to explain the experimental data. |
format |
Article |
author |
Polulyakh, S.N. Sergeev, N.A. |
spellingShingle |
Polulyakh, S.N. Sergeev, N.A. About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films Functional Materials |
author_facet |
Polulyakh, S.N. Sergeev, N.A. |
author_sort |
Polulyakh, S.N. |
title |
About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films |
title_short |
About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films |
title_full |
About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films |
title_fullStr |
About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films |
title_full_unstemmed |
About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films |
title_sort |
about the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷fe nuclei in yig films |
publisher |
НТК «Інститут монокристалів» НАН України |
publishDate |
2006 |
url |
http://dspace.nbuv.gov.ua/handle/123456789/144373 |
citation_txt |
About the influence of nuclear interactions on longitudinal magnetic relaxation of ⁵⁷Fe nuclei in YIG films / S.N. Polulyakh, N.A. Sergeev // Functional Materials. — 2006. — Т. 13, № 2. — С. 301-304. — Бібліогр.: 7 назв. — англ. |
series |
Functional Materials |
work_keys_str_mv |
AT polulyakhsn abouttheinfluenceofnuclearinteractionsonlongitudinalmagneticrelaxationof57fenucleiinyigfilms AT sergeevna abouttheinfluenceofnuclearinteractionsonlongitudinalmagneticrelaxationof57fenucleiinyigfilms |
first_indexed |
2025-07-10T19:16:41Z |
last_indexed |
2025-07-10T19:16:41Z |
_version_ |
1837288664193826816 |
fulltext |
$ERXW�WKH�LQIOXHQFH�RI�QXFOHDU�LQWHUDFWLRQV�RQ�ORQJLWXGLQDO�PDJQHWLF�UHOD[DWLRQ�RI���)H QXFOHL�LQ�<,*�ILOPV
6�1�3ROXO\DNK��1�$�6HUJHHY
�����������7DXULGD�1DWLRQDO�8QLYHUVLW\��������6LPIHURSRO��8NUDLQH�
,QVWLWXWH�RI�3K\VLFV��8QLYHUVLW\�RI�6]F]HFLQ���������6]F]HFLQ��3RODQG��
�7KH�HIIHFW�RI�LPSXULW\�LRQV�RQ�QXFOHDU�PDJQHWLF�UHOD[DWLRQ�KDV�EHHQ�FRQVLGHUHG��,W�LV
VXSSRVHG� WKDW� DQ� LPSXULW\� LRQ� LQWURGXFHV� DQ� H[FHVV� HOHFWURQ� �RU� D� KROH��� $V� D� UHVXOW�
PDJQHWLF� LRQV� ZLWK� VWURQJ� VSLQ�RUELWDO� LQWHUDFWLRQ� DSSHDU� DQG� PDJQHWL]DWLRQ� GLUHFWLRQ
GLVWULEXWLRQ� EHFRPHV� LQKRPRJHQHRXV�� 7KHUPDOO\� DFWLYDWHG� MXPSV� RI� WKH� H[FHVV� HOHFWURQ
IURP� RQH�PDJQHWLF� LRQ� WR� DQRWKHU� JHQHUDWH� IOXFWXDWLRQV� LQ� WKH�PDJQHWL]DWLRQ� GLUHFWLRQ�
7KH�LQWHUDFWLRQ�EHWZHHQ�WKH�IOXFWXDWLQJ�PDJQHWL]DWLRQ�DQG�PDJQHWLF�QXFOHL�UHVXOWV�LQ�WKH
DSSHDUDQFH� RI� UHJLRQV� RI� IDVW� QXFOHDU�PDJQHWLF� UHOD[DWLRQ�� 6SLQ� GLIIXVLRQ� FRQWULEXWHV� WR
WKH�ORQJLWXGLQDO�UHOD[DWLRQ�UDWH�DOVR�IRU�QXFOHL�EHLQJ�RXWVLGH�WKH�LPSXULW\�UHJLRQV��7DNLQJ
LQWR� DFFRXQW� WKH� VSLQ� GLIIXVLRQ� GHSHQGHQFH� RQ� QXFOHDU� LQWHUDFWLRQV�� ZH� KDYH� GHULYH� WKH
GHSHQGHQFH� RI� ORQJLWXGLQDO� UHOD[DWLRQ� UDWH� RQ� QXFOHDU� LQWHUDFWLRQV�� ZKDW� ZDV� REVHUYHG
H[SHULPHQWDOO\�LQ�>�@��$Q�DVVXPSWLRQ�DERXW�XQLQWHQWLRQDO�WHFKQRORJLFDO�LPSXULWLHV�LV�VXI�
ILFLHQW�WR�H[SODLQ�WKH�H[SHULPHQWDO�GDWD��
cȰ°äÈ�¯ÒmÈË�°«�mãÒ«ÓÒË�¹¯Òä˰ө²�ÒºÓºm�ÓÈ�¹¯º�˰°©�«�˯Ӻ®�äÈ�ÓÒ�Óº®�¯HãÈ}�
°È�ÒÒ�� �¯Ë�¹ºãÈ�ÈË�°«�� ��º� ¹¯Òä˰ө®� ÒºÓ� ¹¯ÒmÓº°Ò�� ÒÏ©�º�Ó©®� ªãË}�¯ºÓ� �ÒãÒ
�©¯}����{�¯ËÏ�ã �È�Ë�¹º«mã«
�°«�äÈ�ÓÒ�Ó©Ë�ÒºÓ©�°�°Òã Óº®�°¹ÒÓ�º¯Ò�Èã Óº®�°m«Ï
Ò�¯È°¹¯Ë�ËãËÓÒË�Óȹ¯ÈmãËÓÒ®�ªãË}�¯ºÓÓº®�ÓÈäÈ�ÓÒ�ËÓÓº°�Ò�°�ÈÓºmÒ�°«�Ó˺�Óº¯º�Ó©ä�
�˯äÒ�˰}Ò�È}�ÒmÒ¯ºmÈÓÓ©Ë�°}È�}Ò�ÒÏ©�º�Óº�º�ªãË}�¯ºÓÈ�°�º�Óº�º�äÈ�ÓÒ�Óº�º�ÒºÓÈ
ÓÈ� �¯��º®� ¹º¯ºÎ�È
�� Áã�}��È�ÒÒ� m� Óȹ¯ÈmãËÓÒÒ� ÓÈäÈ�ÓÒ�ËÓÓº°�Ò�� {ÏÈÒäº�Ë®°�mÒË
äËÎ���Áã�}��Ò¯�
�Ë®�ÓÈäÈ�ÓÒ�ËÓÓº°�
� Ò�äÈ�ÓÒ�Ó©äÒ�«�¯ÈäÒ�¹¯Òmº�Ò��}� ¹º«mãË�
ÓÒ
� ºãȰ�Ë®�°�©°�¯º®�«�˯Ӻ®�äÈ�ÓÒ�Óº®�¯ËãÈ}°È�ÒË®��rãÈ�º�ȯ«�°¹ÒÓºmº®��ÒÁÁ��
ÏÒÒ�mºÏ¯È°�ÈË��°}º¯º°� �¹¯º�ºã Óº®�¯ËãÈ}°È�ÒÒ�Ò��ã«�«�˯��ÓȲº�«�Ò²°«�mÓË�¹¯Òä˰�
Ó©²�ºãȰ�Ë®���¯ÒÓÒäÈ«�mº�mÓÒäÈÓÒË�ÏÈmÒ°Ò亰� �ÒÓ�ËÓ°ÒmÓº°�Ò�°¹ÒÓºmº®��ÒÁÁ�ÏÒÒ
º��«�˯Ӻ�«�˯ө²�mÏÈÒäº�Ë®°�mÒ®��¹ºã��ËÓÈ�ÏÈmÒ°Ò亰� �°}º¯º°�Ò�¹¯º�ºã Óº®�¯ËãÈ}�
°È�ÒÒ�º��äËΫ�˯ө²�mÏÈÒäº�Ë®°�mÒ®����º�ÓÈã
�È㺰 �ª}°¹Ë¯ÒäËÓ�Èã Óº�m�¯Èº�Ë�>�@�
�¯Ë�¹ºãºÎËÓÒË�º�ÓÈãÒ�ÒÒ�ÓË}ºÓ�¯ºãÒ¯�Ë䩲��˲Ӻãº�Ò�˰}Ò²�¹¯Òä˰ˮ�«mã«Ë�°«��º�
°�È�º�Ó©ä��ã«�º�«°ÓËÓÒ«�ª}°¹Ë¯ÒäËÓ�Èã Ó©²�¯ËÏ�ã �È�ºm��
7KH�1XFOHDU�0DJQHWLF�5HVRQDQFH� �105�
LV�D�SRZHUIXO�PHWKRG�WR�VWXG\�PDJQHWLF�PD�
WHULDOV� GXH� WR� LWV� PLFURVFRSLF� QDWXUH�� $V� D
UXOH�� LW� LV� MXVW� WKH�105�VSHFWUD��ZKLFK�UH�
IOHFW� WKH� K\SHUILQH� ILHOG� GLVWULEXWLRQ�� WKDW
DUH�WKH�VXEMHFW�RI�105�LQYHVWLJDWLRQV��7KH
RSSRVLWH� FDVH� WDNHV� SODFH� LQ� WKH� DQDO\VLV� RI
QXFOHDU� PDJQHWLF� UHOD[DWLRQ� GDWD�� 7KH
VWURQJ� VHQVLWLYLW\� RI� UHOD[DWLRQ� SDUDPHWHUV
WR� LPSXULWLHV�� HYHQ� WR� WKH� XQLQWHQWLRQDO
WHFKQRORJLFDO� RQHV�� LV� DPRQJ� SRVVLEOH� GLIIL�
FXOWLHV�LQ�WKDW�ZD\�
7KH�QXFOHDU�PDJQHWLF�UHOD[DWLRQ�LV�VXEGL�
YLGHG�LQWR�WUDQVYHUVH�DQG�ORQJLWXGLQDO�FRP�
SRQHQWV�� ,W� LV� ZHOO� NQRZQ� >�@� WKDW� WKH� QX�
FOHDU� LQWHUDFWLRQ� LQIOXHQFHV� WKH� WUDQVYHUVH
UHOD[DWLRQ�RQO\��LI�WKH�ULJLG�ODWWLFH�PRGHO�LV
FRQVLGHUHG�� 2Q� WKH� RWKHU� KDQG�� WKH� LQIOX�
HQFH� RI� DEXQGDQW� PDJQHWLF� QXFOHL� RQ� WKH
ORQJLWXGLQDO� UHOD[DWLRQ� KDV� EHHQ� REVHUYHG
H[SHULPHQWDOO\�LQ�\WWULXP�LURQ�JDUQHW��<,*�
ILOPV� DW� ��� .�� 'LVFXVVLRQ� RI� WKH� PHFKD�
QLVPV� UHVSRQVLEOH� IRU� WKLV� SKHQRPHQRQ� LV
WKH�PDWWHU�RI�WKLV�ZRUN�
)XQFWLRQDO�0DWHULDOV�����1R��������� ��������,QVWLWXWH�IRU�6LQJOH�&U\VWDOV
)XQFWLRQDO�PDWHULDOV������������� ���
:H�KDYH�GHYHORSHG�D�FRQFHSW�SURSRVHG�LQ
>��@�� 7KH�PDLQ� LGHD� LV� WKH� DVVXPSWLRQ� RQ
WKH�LQIOXHQFH�RI�XQLQWHQWLRQDO�WHFKQRORJLFDO
QRQ�PDJQHWLF� LPSXULWLHV� ZKLFK� FDXVH� D� UH�
GLVWULEXWLRQ�RI�LRQ�FKDUJHV��$V�D�UHVXOW��WKH
LRQV� RI� DOWHUQDWLYH� FKDUJH� DSSHDU� LQ� PDJ�
QHWLF�ODWWLFH�RI�WKH�VDPSOH��7KH�PRVW�GLIILFXOW
SRLQW� RI� WKH� DSSURDFK� SUHVHQWHG� LQ� >��@� LV
WKH� DVVXPSWLRQ� RQ� HQHUJ\� OHYHOV� RI� VXFK
PDJQHWLF� LRQV�� LW� LV� VXSSRVHG�� WKH� LRQ� KDV
PDJQHWLF� OHYHOV� DW� D� GLVWDQFH� FRQVLVWHQW
ZLWK� WKH� 105� IUHTXHQF\� �RI� RUGHU� RI� WHQV
0+]�IRU��G� LRQV��� ,Q�FRQWUDVW��ZH�KDYH�GH�
YHORSHG�WKH�FRQFHSW�RI�IOXFWXDWLRQV�LQ�PDJ�
QHWL]DWLRQ� RULHQWDWLRQ�� SURSRVHG� EHIRUH� IRU
WKH�DQDO\VLV�RI�UHOD[DWLRQ�GDWD�>�@��:H�KDYH
VKRZQ�KHUH�� WKDW� WKH�UHDVRQ�IRU� WKHVH� IOXF�
WXDWLRQV� LV� WKH� WKHUPDOO\� DFWLYDWHG� PLJUD�
WLRQ� RI� H[FHVV� �RU� PLVVLQJ�� FKDUJH� LQWUR�
GXFHG� E\� WKH� LPSXULW\� LRQ�� 7KH� LPSXULW\
UHJLRQV�IRU�WKH�LPSXULW\�LRQV�DUH�UHJLRQV�RI
VKRUW�ORQJLWXGLQDO�UHOD[DWLRQ�UDWH��VR�WKDW�WKH
DVVXPSWLRQ� RQ� XQLQWHQWLRQDO� WHFKQRORJLFDO
LPSXULWLHV�DQG�VSLQ�GLIIXVLRQ�LV�VXIILFLHQW�WR
H[SODLQ�WKH�H[SHULPHQWV�GHVFULEHG�LQ�>�@�
7KH�<,*�IUHH�RI�LPSXULWLHV�FRQWDLQV�PDJ�
QHWLF�LRQV�RI�RQH�W\SH�RQO\��WKHVH�DUH�)H��
LRQV�� 7KH� LPSXULW\� LRQV��ZKLFK� FRQWULEXWH
DQ� H[FHVV� HOHFWURQ� �RU� D� KROH�� VWLPXODWH
WKH� DSSHDUDQFH� RI� )H��� RU� )H��� LRQV�� 7KH
GLIIHUHQWO\� FKDUJHG� PDJQHWLF� LRQV� GLIIHU
DOVR� LQ�PDJQHWLF�PRPHQW�� H[FKDQJH� LQWHU�
DFWLRQV�DQG�PRUH�VWURQJ�VSLQ�RUELWDO�LQWHU�
DFWLRQ��7R�DQDO\]H�WKH�LQIOXHQFH�RI�GLIIHU�
HQWO\�FKDUJHG� LRQV�RQ�PDJQHWLF�SURSHUWLHV
RI� <,*�� ZH� KDYH� EXLOW� D� VLPSOH� FRPSXWHU
VLPXODWLRQ� PRGHO�� 7KH� PRGHO� GHDOV� ZLWK
PDJQHWLF�LRQV�RQO\��7KH�FODVVLFDO�PDJQHWLF
PRPHQWV� PP� KDYH� EHHQ� SODFHG� LQWR� RFWDKH�
GUDO� DQG� WHWUDKHGUDO� SRVLWLRQV� RI� WKH� JDU�
QHW�ODWWLFH��7KH�QHJDWLYH�H[FKDQJH�LQWHUDF�
WLRQV� RI� +HLVHQEHUJ� W\SH� EHWZHHQ� QHDUHVW
LRQV� KDYH� EHHQ� WDNHQ� LQWR� DFFRXQW�� 7KH
]HUR� SRLQW� KDV� EHHQ� FKRVHQ� DW� DQ� RFWDKH�
GUDO�SRVLWLRQ�DQG�PDJQHWLF�PRPHQW�DW�WKLV
SRLQW� KDV� EHHQ� VHW� WR� EH� ��������PP�� 7KH
LRQ� DW� ]HUR� SRLQW� VLPXODWHV� RSSRVLWHO\
FKDUJHG� PDJQHWLF� LRQ�� 7R� VLPXODWH� WKH� LQ�
LWLDO� VWDWH�� ZH� KDYH� GLUHFWHG�PDJQHWLF� PR�
PHQWV� RI� DOO� LRQV� FROOLQHDUO\� WR� WKH� ����!
ODWWLFH� GLUHFWLRQ� �HDV\�PDJQHWL]DWLRQ� GLUHF�
WLRQ� LQ� <,*��� 7KH� PRGHO� GHDOV� ZLWK� LRQV
EHLQJ� DW� GLVWDQFHV� IURP� WKH� FHQWHU� QRW� H[�
FHHGLQJ��D��D��<,*�ODWWLFH�FRQVWDQW��WRWDO
������LRQV��
7KH�HIIHFWLYH�PDJQHWLF�ILHOG�RI�H[FKDQJH
LQWHUDFWLRQV�DSSOLHG�WR�WKH�LRQ�KDV�EHHQ�FDO�
FXODWHG� DV�%H[� �-¦�PPM�� +HUH�� -� LV� WKH� H[�
FKDQJH�LQWHUDFWLRQ�FRQVWDQW��WKH�VXPPDWLRQ
LV�DVVXPHG�RYHU�WKH�QHDUHVW�QHLJKERUV�RQO\�
)RU� WKH� ERXQGDU\� LRQV�� WKH� H[LVWHQFH� RI
�LPDJLQH�� LRQV� ZDV� VXSSRVHG� DQG� GLUHFWLRQ
RI� PDJQHWLF� PRPHQWV� IRU� WKHVH� LRQV� ZDV
VWURQJO\�DVVRFLDWHG�ZLWK�����!�GLUHFWLRQ��7R
VLPXODWH� WKH� VSLQ�RUELW� LQWHUDFWLRQV�� ZH
KDYH� LQWURGXFHG� DQ� DGGLWLRQDO� HIIHFWLYH
PDJQHWLF�ILHOG�%6/�GLUHFWHG�DORQJ���
BB��!��GL�
UHFWLRQ� DQG� DSSOLHG� WR� WKH� RSSRVLWHO\
FKDUJHG� LRQ� RQO\�� 7R� EXLOG� WKH� HTXLOLEULXP
VWDWH��ZH�VHTXHQWLDOO\�VHOHFW�LRQV�DQG�GLUHFW
WKH� PDJQHWLF� PRPHQW� RI� LRQ� VWULFWO\� DORQJ
WKH� HIIHFWLYH� PDJQHWLF� ILHOG�� 7KH� HQHUJ\� RI
LQWHUDFWLRQ�EHWZHHQ�PDJQHWLF�PRPHQW�DQG�HI�
IHFWLYH�ILHOG�KDV�EHHQ�XVHG�DV�D�FULWHULRQ�IRU
WKH� LWHUDWLRQV�� 7KH� FDOFXODWHG� GHYLDWLRQV� LQ
GLUHFWLRQV�RI�PDJQHWLF�PRPHQWV�IURP�WKH�LQ�
LWLDO�����!�RQH�DV�D�IXQFWLRQ�RI�LRQ�GLVWDQFH
LV� JLYHQ� LQ� )LJ�� IRU� WKH� FDVH�%/6� ����-P�:H� KDYH� DVVXPHG� WKH� VSLQ�RUELW� LQWHUDF�
WLRQV� WR� UHVXOW� LQ� GHYLDWLRQV� RI� PDJQHWLF
PRPHQW� RULHQWDWLRQ� RI� RSSRVLWHO\� FKDUJHG
LRQ�IURP�HTXLOLEULXP�GLUHFWLRQ�IRU�WKH�FU\V�
WDO�� 'XH� WR� WKH� H[FKDQJH� LQWHUDFWLRQV�� WKLV
GHYLDWLRQ� LV� WUDQVIHUUHG� WR� RWKHU� PDJQHWLF
LRQV��VR�WKDW�WKH�ZHDN�VSLQ�RUELW�LQWHUDFWLRQ
�WKUHH� GHFLPDO� RUGHUV� ZHDNHU� WKDQ� WKH� H[�
FKDQJH� LQWHUDFWLRQ�� FDQ� SURYLGH� GHYLDWLRQ
DERXW���� LQ� WKH� VL]H� UDQJH�RI�DERXW� VHYHUDO
XQLW� FHOOV�� 'HYLDWLRQV� RI� VXFK� RUGHU� KDYH
EHHQ�XVHG�WR�H[SODLQ�WKH�H[SHULPHQWV�LQ�>�@�
6SHFLDO� H[SHULPHQWV� SHUIRUPHG� RQ� <,*
ILOPV� GRSHG� ZLWK� 6L� KDYH� VKRZQ� WKDW� WKH
H[FHVV� HOHFWURQ� �RU� D� KROH�� PLJUDWHV� IURP
RQH� LURQ� LRQ� WR� DQRWKHU� >�@�� 7KH� IUHTXHQF\
RI� WKRVH� PLJUDWLRQV� H[FHHGV� WKH� 105� IUH�
TXHQF\� >�@�� 7DNLQJ� LQWR� DFFRXQW� GLIIHUHQW
ORFDO�D[HV�IRU�GLIIHUHQW�ODWWLFH�SRVLWLRQV��ZH
)LJ��&DOFXODWHG� GHSHQGHQFH� RI� GHYLDWLRQ� LQ
PDJQHWL]DWLRQ�GLUHFWLRQ�RQ�WKH�GLVWDQFH�IURP
LPSXULW\�LRQ�
6�1�3ROXO\DNK��1�$�6HUJHHY���$ERXW�WKH�LQIOXHQFH�RI����
��� )XQFWLRQDO�PDWHULDOV�������������
FRQFOXGH� WKDW� WKH�PLJUDWLRQ� RI� H[FHVV� HOHF�
WURQ� �RU� D� KROH�� JHQHUDWHV� IOXFWXDWLRQV� LQ
WKH�PDJQHWL]DWLRQ�GLUHFWLRQ��
:KHQ�DQDO\]LQJ�QXFOHDU�PDJQHWLF�UHOD[D�
WLRQ�� OHW� XV� IROORZ� WKH� DSSURDFK� RI� >��@�
:H�VXSSRVH�WKH�IROORZLQJ�UHOD[DWLRQ�PHFKD�
QLVPV�� �L�� 'LUHFW� IOXFWXDWLRQV� RI� ORFDO�PDJ�
QHWLF� ILHOGV� FDXVHG� E\� IOXFWXDWLRQV� LQ�PDJ�
QHWL]DWLRQ� GLUHFWLRQ� DQG� K\SHUILQH� ILHOG
IOXFWXDWLRQV� FDXVHG� E\� FKDQJH� LQ� LRQ
FKDUJHV�� �LL�� ,QWHUDFWLRQ� LQYROYLQJ� YLUWXDO
PDJQRQV� EHWZHHQ� PDJQHWLF� QXFOHL� �6XKO�
1DNDPXUD� LQWHUDFWLRQV� >�@�� DQG� EHWZHHQ
PDJQHWLF� QXFOHL� DQG� IOXFWXDWHG� PDJQHWL]D�
WLRQ��7KH�ODVW�PHFKDQLVP�LV�LPSRUWDQW�LI�WKH
PDJQHWL]DWLRQ� IOXFWXDWLRQV� KDYH� QRQ�]HUR
VSHFWUDO�GHQVLW\�DW�105�IUHTXHQF\�
$V�D�UHVXOW��ZH�FDQ�VXEGLYLGH�DOO�WKH�QX�
FOHL� LQWR� WZR� W\SHV�� ZKLFK� DUH� GLIIHUHQW� LQ
UHOD[DWLRQ�UDWH��7KH��XFOHL�RI�IDVW�PDJQHWLF
UHOD[DWLRQ� DUH� ORFDOL]HG� ZLWKLQ� WKH� VL]H
UDQJH�RI�561�QHDU�LPSXUH�LRQ��+HUH��561�LVWKH�GLVWDQFH�RI�6XKO�1DNDPXUD�LQWHUDFWLRQV�
7KH� IDVW� PDJQHWLF� UHOD[DWLRQ� IRU� WKH� ILUVW�
W\SH�QXFOHL�LV�FDXVHG�E\�PDJQHWL]DWLRQ�IOXF�
WXDWLRQV��ZKLFK� WDNH�SODFH�IRU�WKH�PDJQHWL�
]DWLRQ� YDOXH� DV� ZHOO� DV� IRU� PDJQHWL]DWLRQ
GLUHFWLRQ� DQG� DUH� FDXVHG� E\� WKHUPDOO\
VWLPXODWHG� PLJUDWLRQV� RI� H[FHVV� FKDUJH� LQ�
WURGXFHG� E\� LPSXULWLHV��$OO� RWKHU� QXFOHL� LQ
WKH� VDPSOH� DUH� QXFOHL� RI� VORZ�PDJQHWLF� UH�
OD[DWLRQ�
,I�WKH�PDJQHWLF�UHOD[DWLRQ�LQ�D�VDPSOH�LV
LQKRPRJHQHRXV�� WKH� VSLQ� GLIIXVLRQ� WDNHV
SODFH�� )ROORZLQJ� WR� >�@�� ZH� FDQ� ZULWH� WKH
QXFOHDU�GLIIXVLRQ�HTXDWLRQ�DV�
wP]
wW � �''P]���
P]���P�
7�I �
+HUH�P�LV�QXFOHDU�PDJQHWL]DWLRQ�GHSHQG�
HQW� ERWK� RQ� WLPH� DQG� SRVLWLRQ�� � 7�I�� WKHORQJLWXGLQDO�UHOD[DWLRQ�WLPH�IRU�WKH�IDVW�UH�
OD[LQJ� QXFOHL�� �'� �561� ��7��� WKH� GLIIXVLRQ
SDUDPHWHU�� DQG� 7��� WKH� WUDQVYHUVH� UHOD[D�WLRQ�WLPH�FDXVHG�E\�LQWHUDFWLRQ�EHWZHHQ�QX�
FOHL�� $VVXPLQJ� DYHUDJH� GLVWDQFH�5� EHWZHHQ
WKH� IDVW� PDJQHWLF� UHOD[DWLRQ� FHQWHUV� �GLV�
WDQFH� EHWZHHQ� LPSXULWLHV�� LV� ODUJH� DV� FRP�
SDUHG� WR� 561�� ZH� REWDLQ� IRU� ORQJLWXGLQDOUHOD[DWLRQ�WLPH�RXWVLGH�WKH�LPSXULW\�FHQWHUV
7���� �7���
561�
5� ��
�7KH�UHODWLRQVKLS�EHWZHHQ�WUDQVYHUVH�DQG
ORQJLWXGLQDO� UHOD[DWLRQ� LV� NQRZQ� IURP� H[�
SHULPHQW� IRU� WKH� VDPSOH� HQULFKHG� LQ� PDJ�
QHWLF� QXFOHL��7��� �7��|����� >�@��7KH� GLV�WDQFH�RI�6XKO�1DNDPXUD�LQWHUDFWLRQV�FDQ�EH
HVWLPDWHG�DV�561�a�����������D��ZKHUH�D� LVWKH�ODWWLFH�FRQVWDQW�>�@��$V�D�UHVXOW��ZH�FDQ
HVWLPDWH�WKH�DYHUDJH�GLVWDQFH�EHWZHHQ�LPSX�
ULW\�FHQWHUV�DV�5|��������y�����D��
7KXV�� WKH� DYHUDJH� GLVWDQFH� EHWZHHQ� LP�
SXULW\� FHQWHUV�� DV� GHULYHG� IURP� H[SHULPHQ�
WDO�YDOXHV� IRU� UHOD[DWLRQ� WLPHV�� HYLGHQFHV�D
YHU\� ORZ� LPSXULW\� FRQFHQWUDWLRQ�� 7KH� GH�
SHQGHQFH�RI�ORQJLWXGLQDO�UHOD[DWLRQ�WLPH�RQ
QXFOHDU� DEXQGDQFH� LV� FDXVHG� E\� VSLQ� GLIIX�
VLRQ�DQG�IDVW�QXFOHDU�UHOD[DWLRQ�QHDU�LPSX�
ULWLHV�� ,Q�FRQWUDVW� WR� >��@��ZH�GR�QRW�QHHG
WR� KDYH� IRU� HQHUJ\� OHYHOV� RI� LPSXULW\� LRQV
WKH� GLVWDQFHV� RI� WKH�105�IUHTXHQF\�RUGHU�
7KH�PDJQHWL]DWLRQ�IOXFWXDWLRQV�DW�105�IUH�
TXHQF\�DSSHDU�DV�D�UHVXOW�RI�WKHUPDO�PLJUD�
WLRQV�RI�H[FHVV�HOHFWURQ��RU�KROH���ZKLFK�DS�
SHDUV�LQ�ODWWLFH�GXH�WR�WKH�LPSXULW\�LRQ��
5HIHUHQFHV
� ���9�1�%HU]KDQVNLM�� 6�1�3ROXO\DNK�� 6RY��3K\V�
6ROLG�6WDWH������������������
� ���0�,�.XUNLQ��(�$�7XURY��105�LQ�0DJQHWLFDOO\
2UGHUHG� 0DWHULDOV� DQG� LWV� $SSOLFDWLRQV�
1DXND��0RVNRZ��������>LQ�5XVVLDQ@�
� ���$�9�=DOHVVN\��9�*�.ULYHQNR��9�6�/XWRYLQRY�HW
DO���=K��(NVS��7HRU��)L]�������������������
� ���6�9�,YDQRY��0�,�.XUNLQ��-��0DJQ��0DJQ��0DWHU��
�����������������
� ���/�/�%XLVKYLOL�� 6�9�,YDQRY�� $�9�.XQHYLWFK�
0�,�.XUNLQ�� )L]��0HWDO��L�0HWDOORYHG��� ���� ��
��������
� ���*�1�$EHO\DVKHY��6�1�3ROXO\DNK��9�1�%HU]KDQ�
VNLM��1�$�6HUJHHY��-��0DJQ��0DJQ��0DWHU�������
�����������
� ���9�1�%HU]KDQVN\�� $�,�*RUERYDQRY�� 6�1�3ROX�
O\DNK�� 1�$�3URQLQD�� 3K\V��6RO��6WDWH��� ���
������������
6�1�3ROXO\DNK��1�$�6HUJHHY���$ERXW�WKH�LQIOXHQFH�RI����
)XQFWLRQDO�PDWHULDOV������������� ���
�¯º�m¹ãÒm�«�˯ÓÒ²�mÏȼäº�L®�ÓÈ�¹ºÏ�ºmÎÓ
�äÈ�ÓL�Ó��¯ËãÈ}°È�L
���)H���¹ãLm}Ȳ�ÏÈãLϺ�L�¯L¼mº�º��¯ÈÓÈ��
v�s��ºã�㫲��s�k�v˯�¼¼m
cºÏ�ã«�ȼ� °«� m¹ãÒm� �ºäL�º}� ÓÈ� ¹¯º�˰Ò� «�˯Ӻ�� äÈ�ÓL�Óº�� ¯ËãÈ}°È�L��� cºÒ� °«
¹¯Ò¹��ËÓÓ«�� �º� LºÓ� �ºäL�}Ò� ÓÈ�ȼ� ÓÈ�ãÒ�}ºmÒ®� ËãË}�¯ºÓ� �Ⱥ� �L¯}���� {ÓȰãL�º}
� º�º� Ï�«mã«
� °«�äÈ�ÓL�ÓL� LºÓÒ� LÏ� °Òã ÓÒä� °¹�Ó�º¯L�Èã ÓÒä� Ïm�«Ï}ºä� L� ¯ºÏ¹º�Lã� ÓÈ�
¹¯«ä}�� ËãË}�¯ºÓÓº�� ÓÈäÈ�ÓL�ËÓº°�L� °�ȼ� Ó˺�Óº¯L�ÓÒä�� �˯äL�Óº� È}�ÒmºmÈÓL� °�¯Ò}Ò
ÓÈ�ãÒ�}ºmº�º� ËãË}�¯ºÓÈ� Ï�º�Óº�º�äÈ�ÓL�Óº�º� LºÓÈ�ÓÈ� LÓ�L®�¹º¯º�Î�
� �Áã�}��È�L�� �
Óȹ¯«ä}��ÓÈäÈ�ÓL�ËÓº°�L��{Ïȼäº�L«�äLÎ�Áã�}��È�L«äÒ�ÓÈäÈ�ÓL�ËÓº°�L��È�äÈ�ÓL�ÓÒäÒ
«�¯ÈäÒ� ¹¯ÒÏmº�Ò� � �º� ¹º«mÒ� ¯Ë�LºÓLm� ÏL� �mÒ�}º
� «�˯Ӻ
� äÈ�ÓL�Óº
� ¯ËãÈ}°È�L¼
�
~Èm�«}Ò� °¹LÓºmL®� �ÒÁ�ÏL�� ϯº°�ȼ� �mÒ�}L°� � ¹º�ºmÎÓ º�� ¯ËãÈ}°È�L�� L� �ã«� «�˯�� �º
ÏÓȲº�«� °«� ¹ºÏÈ� ¯Ë�LºÓÈäÒ� �ºäL�º}�� �¯Ò®äÈ
�Ò� �º� �mÈ�Ò� ÏÈãËÎÓL°� � LÓ�ËÓ°ÒmÓº°�L
°¹LÓºmº�� �ÒÁ�ÏL�� mL�� «�˯Ӻ�«�˯ÓÒ²� mÏȼäº�L®�� º�¯ÒäÈÓº� ÏÈãËÎÓL°� � �mÒ�}º°�L� ¹º�
Ï�ºmÎÓ º��¯ËãÈ}°È�L��mL��mÏȼäº�L®�äLÎ�«�¯ÈäÒ���º�°¹º°�˯L�È㺰«�Ë}°¹Ë¯ÒäËÓ�Èã Óº��
¯ºº�L� >�@�� �¯Ò¹��ËÓÓ«� ¹¯º� ÓÈ«mÓL°� � ÓË}ºÓ�¯ºã ºmÈÓÒ²� �˲Ӻãº�L�ÓÒ²� �ºäL�º}� ¼
�º°�È�ÓLä��ã«�¹º«°ÓËÓÓ«�Ë}°¹Ë¯ÒäËÓ�Èã ÓÒ²�¯ËÏ�ã �È�Lm�
6�1�3ROXO\DNK��1�$�6HUJHHY���$ERXW�WKH�LQIOXHQFH�RI����
��� )XQFWLRQDO�PDWHULDOV�������������
|